adapting lapack wrappers

10 files changed, 6073 insertions, 7 deletions

diff --git a/HSSL.cabal b/HSSL.cabal
index 739ad8b..28fe130 100644
--- a/HSSL.cabal
+++ b/HSSL.cabal
@@ -20,9 +20,12 @@ ghc-options:        -O
 hs-source-dirs:     lib
 Exposed-modules:    Data.Packed.Internal.Vector,
                     Data.Packed.Internal.Matrix,
-                    Data.Packed.Internal.Tensor
+                    Data.Packed.Internal.Tensor,
+                    LAPACK.Internal,
+                    LAPACK
 Other-modules:
-C-sources:          lib/Data/Packed/Internal/aux.c
-extra-libraries:    gsl cblas
+C-sources:          lib/Data/Packed/Internal/aux.c,
+                    lib/LAPACK/lapack-aux.c
+extra-libraries:    gsl cblas lapack
 cc-options:         -O4
 ghc-prof-options:   -auto-all
diff --git a/examples/pru.hs b/examples/pru.hs
index a935d93..8b25780 100644
--- a/examples/pru.hs
+++ b/examples/pru.hs
@@ -4,6 +4,7 @@
 import Data.Packed.Internal.Vector
 import Data.Packed.Internal.Matrix
 import Data.Packed.Internal.Tensor
+import LAPACK
 
 import Complex
 import Numeric(showGFloat)
diff --git a/lib/Data/Packed/Internal/Matrix.hs b/lib/Data/Packed/Internal/Matrix.hs
index ec6657a..db53cd1 100644
--- a/lib/Data/Packed/Internal/Matrix.hs
+++ b/lib/Data/Packed/Internal/Matrix.hs
@@ -160,6 +160,10 @@ toRows m = toRows' 0 where
     toRows' k | k == r*c  = []
               | otherwise = subVector k c v : toRows' (k+c)
 
+-----------------------------------------------------------------
+
+liftMatrix f m = m { dat = f dat, tdat = f tdat } -- check sizes
+
 ------------------------------------------------------------------
 
 dotL a b = sum (zipWith (*) a b)
@@ -208,6 +212,16 @@ multiplyD order a b
 
 ----------------------------------------------------------------------
 
+outer u v = dat (multiply RowMajor r c)
+    where r = matrixFromVector RowMajor 1 u
+          c = matrixFromVector RowMajor (dim v) v
+
+dot u v = dat (multiply RowMajor r c) `at` 0
+    where r = matrixFromVector RowMajor (dim u) u
+          c = matrixFromVector RowMajor 1 v
+
+----------------------------------------------------------------------
+
 -- | extraction of a submatrix of a real matrix
 subMatrixR :: (Int,Int) -- ^ (r0,c0) starting position 
            -> (Int,Int) -- ^ (rt,ct) dimensions of submatrix
diff --git a/lib/Data/Packed/Internal/Tensor.hs b/lib/Data/Packed/Internal/Tensor.hs
index b66d6b8..67dcb09 100644
--- a/lib/Data/Packed/Internal/Tensor.hs
+++ b/lib/Data/Packed/Internal/Tensor.hs
@@ -27,10 +27,6 @@ data Tensor t = T { dims   :: [(Int,(IdxTp,String))]
 
 rank = length . dims
 
-outer u v = dat (multiply RowMajor r c)
-    where r = matrixFromVector RowMajor 1 u
-          c = matrixFromVector RowMajor (dim v) v
-
 instance (Show a,Storable a) => Show (Tensor a) where
     show T {dims = [], ten = t} = "scalar "++show (t `at` 0)
     show T {dims = ds, ten = t} = "("++shdims ds ++") "++ show (toList t)
diff --git a/lib/LAPACK.hs b/lib/LAPACK.hs
new file mode 100644
index 0000000..cab437c
--- /dev/null
+++ b/lib/LAPACK.hs
@@ -0,0 +1,21 @@
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  LAPACK
+-- Copyright   :  (c) Alberto Ruiz 2006-7
+-- License     :  GPL-style
+-- 
+-- Maintainer  :  Alberto Ruiz (aruiz at um dot es)
+-- Stability   :  provisional
+-- Portability :  portable (uses FFI)
+--
+-- Wrappers for a few LAPACK functions (<http://www.netlib.org/lapack>).
+--
+-----------------------------------------------------------------------------
+
+module LAPACK (
+    --module LAPACK.Internal
+    eigC,
+    linearSolveLSR
+) where
+
+import LAPACK.Internal
diff --git a/lib/LAPACK/Internal.hs b/lib/LAPACK/Internal.hs
new file mode 100644
index 0000000..4c755bc
--- /dev/null
+++ b/lib/LAPACK/Internal.hs
@@ -0,0 +1,112 @@
+{-# OPTIONS_GHC -fglasgow-exts #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  LAPACK.Internal
+-- Copyright   :  (c) Alberto Ruiz 2006-7
+-- License     :  GPL-style
+-- 
+-- Maintainer  :  Alberto Ruiz (aruiz at um dot es)
+-- Stability   :  provisional
+-- Portability :  portable (uses FFI)
+--
+-- Wrappers for a few LAPACK functions (<http://www.netlib.org/lapack>).
+--
+-----------------------------------------------------------------------------
+
+module LAPACK.Internal where
+
+import Data.Packed.Internal.Vector
+import Data.Packed.Internal.Matrix
+import Complex
+import Foreign
+import Foreign.C.Types
+import Foreign.C.String
+
+-----------------------------------------------------------------------------
+-- dgesvd
+foreign import ccall "lapack-aux.h svd_l_R"
+    dgesvd :: Double ::> Double ::> (Double :> Double ::> IO Int)
+
+-----------------------------------------------------------------------------
+-- dgesdd
+foreign import ccall "lapack-aux.h svd_l_Rdd"
+    dgesdd :: Double ::> Double ::> (Double :> Double ::> IO Int)
+
+-----------------------------------------------------------------------------
+-- zgesvd
+foreign import ccall "lapack-aux.h svd_l_C"
+    zgesvd :: (Complex Double) ::> (Complex Double) ::> (Double :> (Complex Double) ::> IO Int)
+
+-----------------------------------------------------------------------------
+-- zgeev
+foreign import ccall "lapack-aux.h eig_l_C"
+    zgeev :: (Complex Double) ::> (Complex Double) ::> ((Complex Double) :> (Complex Double) ::> IO Int)
+
+-- | Wrapper for LAPACK's /zgeev/, which computes the eigenvalues and right eigenvectors of a general complex matrix:
+--
+-- if @(l,v)=eigC m@ then @m \<\> v = v \<\> diag l@.
+--
+-- The eigenvectors are the columns of v.
+-- The eigenvalues are not sorted.
+eigC :: Matrix (Complex Double) -> (Vector (Complex Double), Matrix (Complex Double))
+eigC (m@M {rows = r}) = unsafePerformIO $ do
+    l <- createVector r
+    v <- createMatrix ColumnMajor r r
+    dummy <- createMatrix ColumnMajor 1 1
+    zgeev // mat fdat m // mat dat dummy // vec l // mat dat v // check "eigC" [fdat m]
+    return (l,v)
+
+-----------------------------------------------------------------------------
+-- dgeev
+foreign import ccall "lapack-aux.h eig_l_R"
+    dgeev :: Double ::> Double ::> ((Complex Double) :> Double ::> IO Int)
+
+-----------------------------------------------------------------------------
+
+-- dsyev
+foreign import ccall "lapack-aux.h eig_l_S"
+    dsyev :: Double ::> (Double :> Double ::> IO Int)
+
+-----------------------------------------------------------------------------
+-- zheev
+foreign import ccall "lapack-aux.h eig_l_H"
+    zheev :: (Complex Double) ::> (Double :> (Complex Double) ::> IO Int)
+
+-----------------------------------------------------------------------------
+-- dgesv
+foreign import ccall "lapack-aux.h linearSolveR_l"
+    dgesv :: Double ::> Double ::> Double ::> IO Int
+
+-----------------------------------------------------------------------------
+-- zgesv
+foreign import ccall "lapack-aux.h linearSolveC_l"
+    zgesv :: (Complex Double) ::> (Complex Double) ::> (Complex Double) ::> IO Int
+
+-----------------------------------------------------------------------------------
+-- dgels
+foreign import ccall "lapack-aux.h linearSolveLSR_l"
+    dgels :: Double ::> Double ::> Double ::> IO Int
+
+-- | Wrapper for LAPACK's /dgels/, which obtains the least squared error solution of an overconstrained real linear system or the minimum norm solution of an underdetermined system, for several right-hand sides. For rank deficient systems use 'linearSolveSVDR'.
+linearSolveLSR :: Matrix Double -> Matrix Double -> Matrix Double
+linearSolveLSR a b = subMatrix (0,0) (cols a, cols b) $ linearSolveLSR_l a b
+
+linearSolveLSR_l a@(M {rows = m, cols = n}) b@(M {cols = nrhs}) = unsafePerformIO $ do
+    r <- createMatrix ColumnMajor (max m n) nrhs
+    dgels // mat fdat a // mat fdat b // mat dat r // check "linearSolveLSR" [fdat a, fdat b]
+    return r
+
+-----------------------------------------------------------------------------------
+-- zgels
+foreign import ccall "lapack-aux.h linearSolveLSC_l"
+    zgels :: (Complex Double) ::> (Complex Double) ::> (Complex Double) ::> IO Int
+
+-----------------------------------------------------------------------------------
+-- dgelss
+foreign import ccall "lapack-aux.h linearSolveSVDR_l"
+    dgelss :: Double -> Double ::> Double ::> Double ::> IO Int
+
+-----------------------------------------------------------------------------------
+-- zgelss
+foreign import ccall "lapack-aux.h linearSolveSVDC_l"
+    zgelss :: Double -> (Complex Double) ::> (Complex Double) ::> (Complex Double) ::> IO Int
diff --git a/lib/LAPACK/clapack.h b/lib/LAPACK/clapack.h
new file mode 100644
index 0000000..cad9a4c
--- /dev/null
+++ b/lib/LAPACK/clapack.h
@@ -0,0 +1,5079 @@
+#ifndef __CLAPACK_H
+#define __CLAPACK_H
+ 
+/* Subroutine */ int cbdsqr_(char *uplo, integer *n, integer *ncvt, integer *
+        nru, integer *ncc, real *d__, real *e, complex *vt, integer *ldvt, 
+        complex *u, integer *ldu, complex *c__, integer *ldc, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int cgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
+         integer *kl, integer *ku, complex *ab, integer *ldab, real *d__, 
+        real *e, complex *q, integer *ldq, complex *pt, integer *ldpt, 
+        complex *c__, integer *ldc, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgbcon_(char *norm, integer *n, integer *kl, integer *ku,
+         complex *ab, integer *ldab, integer *ipiv, real *anorm, real *rcond, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgbequ_(integer *m, integer *n, integer *kl, integer *ku,
+         complex *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real 
+        *colcnd, real *amax, integer *info);
+ 
+/* Subroutine */ int cgbrfs_(char *trans, integer *n, integer *kl, integer *
+        ku, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer *
+        ldafb, integer *ipiv, complex *b, integer *ldb, complex *x, integer *
+        ldx, real *ferr, real *berr, complex *work, real *rwork, integer *
+        info);
+ 
+/* Subroutine */ int cgbsv_(integer *n, integer *kl, integer *ku, integer *
+        nrhs, complex *ab, integer *ldab, integer *ipiv, complex *b, integer *
+        ldb, integer *info);
+ 
+/* Subroutine */ int cgbsvx_(char *fact, char *trans, integer *n, integer *kl,
+         integer *ku, integer *nrhs, complex *ab, integer *ldab, complex *afb,
+         integer *ldafb, integer *ipiv, char *equed, real *r__, real *c__, 
+        complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, real 
+        *ferr, real *berr, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgbtf2_(integer *m, integer *n, integer *kl, integer *ku,
+         complex *ab, integer *ldab, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int cgbtrf_(integer *m, integer *n, integer *kl, integer *ku,
+         complex *ab, integer *ldab, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int cgbtrs_(char *trans, integer *n, integer *kl, integer *
+        ku, integer *nrhs, complex *ab, integer *ldab, integer *ipiv, complex 
+        *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cgebak_(char *job, char *side, integer *n, integer *ilo, 
+        integer *ihi, real *scale, integer *m, complex *v, integer *ldv, 
+        integer *info);
+ 
+/* Subroutine */ int cgebal_(char *job, integer *n, complex *a, integer *lda, 
+        integer *ilo, integer *ihi, real *scale, integer *info);
+ 
+/* Subroutine */ int cgebd2_(integer *m, integer *n, complex *a, integer *lda,
+         real *d__, real *e, complex *tauq, complex *taup, complex *work, 
+        integer *info);
+ 
+/* Subroutine */ int cgebrd_(integer *m, integer *n, complex *a, integer *lda,
+         real *d__, real *e, complex *tauq, complex *taup, complex *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int cgecon_(char *norm, integer *n, complex *a, integer *lda,
+         real *anorm, real *rcond, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgeequ_(integer *m, integer *n, complex *a, integer *lda,
+         real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, 
+        integer *info);
+ 
+/* Subroutine */ int cgees_(char *jobvs, char *sort, L_fp select, integer *n, 
+        complex *a, integer *lda, integer *sdim, complex *w, complex *vs, 
+        integer *ldvs, complex *work, integer *lwork, real *rwork, logical *
+        bwork, integer *info);
+ 
+/* Subroutine */ int cgeesx_(char *jobvs, char *sort, L_fp select, char *
+        sense, integer *n, complex *a, integer *lda, integer *sdim, complex *
+        w, complex *vs, integer *ldvs, real *rconde, real *rcondv, complex *
+        work, integer *lwork, real *rwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int cgeev_(char *jobvl, char *jobvr, integer *n, complex *a, 
+        integer *lda, complex *w, complex *vl, integer *ldvl, complex *vr, 
+        integer *ldvr, complex *work, integer *lwork, real *rwork, integer *
+        info);
+ 
+/* Subroutine */ int cgeevx_(char *balanc, char *jobvl, char *jobvr, char *
+        sense, integer *n, complex *a, integer *lda, complex *w, complex *vl, 
+        integer *ldvl, complex *vr, integer *ldvr, integer *ilo, integer *ihi,
+         real *scale, real *abnrm, real *rconde, real *rcondv, complex *work, 
+        integer *lwork, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgegs_(char *jobvsl, char *jobvsr, integer *n, complex *
+        a, integer *lda, complex *b, integer *ldb, complex *alpha, complex *
+        beta, complex *vsl, integer *ldvsl, complex *vsr, integer *ldvsr, 
+        complex *work, integer *lwork, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgegv_(char *jobvl, char *jobvr, integer *n, complex *a, 
+        integer *lda, complex *b, integer *ldb, complex *alpha, complex *beta,
+         complex *vl, integer *ldvl, complex *vr, integer *ldvr, complex *
+        work, integer *lwork, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgehd2_(integer *n, integer *ilo, integer *ihi, complex *
+        a, integer *lda, complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cgehrd_(integer *n, integer *ilo, integer *ihi, complex *
+        a, integer *lda, complex *tau, complex *work, integer *lwork, integer 
+        *info);
+ 
+/* Subroutine */ int cgelq2_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cgelqf_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cgels_(char *trans, integer *m, integer *n, integer *
+        nrhs, complex *a, integer *lda, complex *b, integer *ldb, complex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cgelsx_(integer *m, integer *n, integer *nrhs, complex *
+        a, integer *lda, complex *b, integer *ldb, integer *jpvt, real *rcond,
+         integer *rank, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgelsy_(integer *m, integer *n, integer *nrhs, complex *
+        a, integer *lda, complex *b, integer *ldb, integer *jpvt, real *rcond,
+         integer *rank, complex *work, integer *lwork, real *rwork, integer *
+        info);
+ 
+/* Subroutine */ int cgeql2_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cgeqlf_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cgeqp3_(integer *m, integer *n, complex *a, integer *lda,
+         integer *jpvt, complex *tau, complex *work, integer *lwork, real *
+        rwork, integer *info);
+ 
+/* Subroutine */ int cgeqpf_(integer *m, integer *n, complex *a, integer *lda,
+         integer *jpvt, complex *tau, complex *work, real *rwork, integer *
+        info);
+ 
+/* Subroutine */ int cgeqr2_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cgeqrf_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cgerfs_(char *trans, integer *n, integer *nrhs, complex *
+        a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex *
+        b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgerq2_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cgerqf_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cgesc2_(integer *n, complex *a, integer *lda, complex *
+        rhs, integer *ipiv, integer *jpiv, real *scale);
+ 
+/* Subroutine */ int cgesv_(integer *n, integer *nrhs, complex *a, integer *
+        lda, integer *ipiv, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cgesvx_(char *fact, char *trans, integer *n, integer *
+        nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer *
+        ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb, 
+        complex *x, integer *ldx, real *rcond, real *ferr, real *berr, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgetc2_(integer *n, complex *a, integer *lda, integer *
+        ipiv, integer *jpiv, integer *info);
+ 
+/* Subroutine */ int cgetf2_(integer *m, integer *n, complex *a, integer *lda,
+         integer *ipiv, integer *info);
+ 
+/* Subroutine */ int cgetrf_(integer *m, integer *n, complex *a, integer *lda,
+         integer *ipiv, integer *info);
+ 
+/* Subroutine */ int cgetri_(integer *n, complex *a, integer *lda, integer *
+        ipiv, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cgetrs_(char *trans, integer *n, integer *nrhs, complex *
+        a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int cggbak_(char *job, char *side, integer *n, integer *ilo, 
+        integer *ihi, real *lscale, real *rscale, integer *m, complex *v, 
+        integer *ldv, integer *info);
+ 
+/* Subroutine */ int cggbal_(char *job, integer *n, complex *a, integer *lda, 
+        complex *b, integer *ldb, integer *ilo, integer *ihi, real *lscale, 
+        real *rscale, real *work, integer *info);
+ 
+/* Subroutine */ int cgges_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+        selctg, integer *n, complex *a, integer *lda, complex *b, integer *
+        ldb, integer *sdim, complex *alpha, complex *beta, complex *vsl, 
+        integer *ldvsl, complex *vsr, integer *ldvsr, complex *work, integer *
+        lwork, real *rwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int cggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+        selctg, char *sense, integer *n, complex *a, integer *lda, complex *b,
+         integer *ldb, integer *sdim, complex *alpha, complex *beta, complex *
+        vsl, integer *ldvsl, complex *vsr, integer *ldvsr, real *rconde, real 
+        *rcondv, complex *work, integer *lwork, real *rwork, integer *iwork, 
+        integer *liwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int cggev_(char *jobvl, char *jobvr, integer *n, complex *a, 
+        integer *lda, complex *b, integer *ldb, complex *alpha, complex *beta,
+         complex *vl, integer *ldvl, complex *vr, integer *ldvr, complex *
+        work, integer *lwork, real *rwork, integer *info);
+ 
+/* Subroutine */ int cggevx_(char *balanc, char *jobvl, char *jobvr, char *
+        sense, integer *n, complex *a, integer *lda, complex *b, integer *ldb,
+         complex *alpha, complex *beta, complex *vl, integer *ldvl, complex *
+        vr, integer *ldvr, integer *ilo, integer *ihi, real *lscale, real *
+        rscale, real *abnrm, real *bbnrm, real *rconde, real *rcondv, complex 
+        *work, integer *lwork, real *rwork, integer *iwork, logical *bwork, 
+        integer *info);
+ 
+/* Subroutine */ int cggglm_(integer *n, integer *m, integer *p, complex *a, 
+        integer *lda, complex *b, integer *ldb, complex *d__, complex *x, 
+        complex *y, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cgghrd_(char *compq, char *compz, integer *n, integer *
+        ilo, integer *ihi, complex *a, integer *lda, complex *b, integer *ldb,
+         complex *q, integer *ldq, complex *z__, integer *ldz, integer *info);
+ 
+/* Subroutine */ int cgglse_(integer *m, integer *n, integer *p, complex *a, 
+        integer *lda, complex *b, integer *ldb, complex *c__, complex *d__, 
+        complex *x, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cggqrf_(integer *n, integer *m, integer *p, complex *a, 
+        integer *lda, complex *taua, complex *b, integer *ldb, complex *taub, 
+        complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cggrqf_(integer *m, integer *p, integer *n, complex *a, 
+        integer *lda, complex *taua, complex *b, integer *ldb, complex *taub, 
+        complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cggsvd_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *n, integer *p, integer *k, integer *l, complex *a, integer *
+        lda, complex *b, integer *ldb, real *alpha, real *beta, complex *u, 
+        integer *ldu, complex *v, integer *ldv, complex *q, integer *ldq, 
+        complex *work, real *rwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int cggsvp_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *p, integer *n, complex *a, integer *lda, complex *b, integer 
+        *ldb, real *tola, real *tolb, integer *k, integer *l, complex *u, 
+        integer *ldu, complex *v, integer *ldv, complex *q, integer *ldq, 
+        integer *iwork, real *rwork, complex *tau, complex *work, integer *
+        info);
+ 
+/* Subroutine */ int cgtcon_(char *norm, integer *n, complex *dl, complex *
+        d__, complex *du, complex *du2, integer *ipiv, real *anorm, real *
+        rcond, complex *work, integer *info);
+ 
+/* Subroutine */ int cgtrfs_(char *trans, integer *n, integer *nrhs, complex *
+        dl, complex *d__, complex *du, complex *dlf, complex *df, complex *
+        duf, complex *du2, integer *ipiv, complex *b, integer *ldb, complex *
+        x, integer *ldx, real *ferr, real *berr, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int cgtsv_(integer *n, integer *nrhs, complex *dl, complex *
+        d__, complex *du, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cgtsvx_(char *fact, char *trans, integer *n, integer *
+        nrhs, complex *dl, complex *d__, complex *du, complex *dlf, complex *
+        df, complex *duf, complex *du2, integer *ipiv, complex *b, integer *
+        ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cgttrf_(integer *n, complex *dl, complex *d__, complex *
+        du, complex *du2, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int cgttrs_(char *trans, integer *n, integer *nrhs, complex *
+        dl, complex *d__, complex *du, complex *du2, integer *ipiv, complex *
+        b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cgtts2_(integer *itrans, integer *n, integer *nrhs, 
+        complex *dl, complex *d__, complex *du, complex *du2, integer *ipiv, 
+        complex *b, integer *ldb);
+ 
+/* Subroutine */ int chbev_(char *jobz, char *uplo, integer *n, integer *kd, 
+        complex *ab, integer *ldab, real *w, complex *z__, integer *ldz, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int chbevd_(char *jobz, char *uplo, integer *n, integer *kd, 
+        complex *ab, integer *ldab, real *w, complex *z__, integer *ldz, 
+        complex *work, integer *lwork, real *rwork, integer *lrwork, integer *
+        iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int chbevx_(char *jobz, char *range, char *uplo, integer *n, 
+        integer *kd, complex *ab, integer *ldab, complex *q, integer *ldq, 
+        real *vl, real *vu, integer *il, integer *iu, real *abstol, integer *
+        m, real *w, complex *z__, integer *ldz, complex *work, real *rwork, 
+        integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int chbgst_(char *vect, char *uplo, integer *n, integer *ka, 
+        integer *kb, complex *ab, integer *ldab, complex *bb, integer *ldbb, 
+        complex *x, integer *ldx, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int chbgv_(char *jobz, char *uplo, integer *n, integer *ka, 
+        integer *kb, complex *ab, integer *ldab, complex *bb, integer *ldbb, 
+        real *w, complex *z__, integer *ldz, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int chbgvx_(char *jobz, char *range, char *uplo, integer *n, 
+        integer *ka, integer *kb, complex *ab, integer *ldab, complex *bb, 
+        integer *ldbb, complex *q, integer *ldq, real *vl, real *vu, integer *
+        il, integer *iu, real *abstol, integer *m, real *w, complex *z__, 
+        integer *ldz, complex *work, real *rwork, integer *iwork, integer *
+        ifail, integer *info);
+ 
+/* Subroutine */ int chbtrd_(char *vect, char *uplo, integer *n, integer *kd, 
+        complex *ab, integer *ldab, real *d__, real *e, complex *q, integer *
+        ldq, complex *work, integer *info);
+ 
+/* Subroutine */ int checon_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *ipiv, real *anorm, real *rcond, complex *work, integer *
+        info);
+ 
+/* Subroutine */ int cheev_(char *jobz, char *uplo, integer *n, complex *a, 
+        integer *lda, real *w, complex *work, integer *lwork, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int cheevd_(char *jobz, char *uplo, integer *n, complex *a, 
+        integer *lda, real *w, complex *work, integer *lwork, real *rwork, 
+        integer *lrwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int cheevr_(char *jobz, char *range, char *uplo, integer *n, 
+        complex *a, integer *lda, real *vl, real *vu, integer *il, integer *
+        iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz, 
+        integer *isuppz, complex *work, integer *lwork, real *rwork, integer *
+        lrwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int cheevx_(char *jobz, char *range, char *uplo, integer *n, 
+        complex *a, integer *lda, real *vl, real *vu, integer *il, integer *
+        iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz, 
+        complex *work, integer *lwork, real *rwork, integer *iwork, integer *
+        ifail, integer *info);
+ 
+/* Subroutine */ int chegs2_(integer *itype, char *uplo, integer *n, complex *
+        a, integer *lda, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int chegst_(integer *itype, char *uplo, integer *n, complex *
+        a, integer *lda, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int chegv_(integer *itype, char *jobz, char *uplo, integer *
+        n, complex *a, integer *lda, complex *b, integer *ldb, real *w, 
+        complex *work, integer *lwork, real *rwork, integer *info);
+ 
+/* Subroutine */ int chegvd_(integer *itype, char *jobz, char *uplo, integer *
+        n, complex *a, integer *lda, complex *b, integer *ldb, real *w, 
+        complex *work, integer *lwork, real *rwork, integer *lrwork, integer *
+        iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int chegvx_(integer *itype, char *jobz, char *range, char *
+        uplo, integer *n, complex *a, integer *lda, complex *b, integer *ldb, 
+        real *vl, real *vu, integer *il, integer *iu, real *abstol, integer *
+        m, real *w, complex *z__, integer *ldz, complex *work, integer *lwork,
+         real *rwork, integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int cherfs_(char *uplo, integer *n, integer *nrhs, complex *
+        a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex *
+        b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int chesv_(char *uplo, integer *n, integer *nrhs, complex *a,
+         integer *lda, integer *ipiv, complex *b, integer *ldb, complex *work,
+         integer *lwork, integer *info);
+ 
+/* Subroutine */ int chesvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer *
+        ipiv, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond,
+         real *ferr, real *berr, complex *work, integer *lwork, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int chetf2_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *ipiv, integer *info);
+ 
+/* Subroutine */ int chetrd_(char *uplo, integer *n, complex *a, integer *lda,
+         real *d__, real *e, complex *tau, complex *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int chetrf_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *ipiv, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int chetri_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *ipiv, complex *work, integer *info);
+ 
+/* Subroutine */ int chetrs_(char *uplo, integer *n, integer *nrhs, complex *
+        a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int chgeqz_(char *job, char *compq, char *compz, integer *n, 
+        integer *ilo, integer *ihi, complex *a, integer *lda, complex *b, 
+        integer *ldb, complex *alpha, complex *beta, complex *q, integer *ldq,
+         complex *z__, integer *ldz, complex *work, integer *lwork, real *
+        rwork, integer *info);
+ 
+/* Subroutine */ int chpcon_(char *uplo, integer *n, complex *ap, integer *
+        ipiv, real *anorm, real *rcond, complex *work, integer *info);
+ 
+/* Subroutine */ int chpev_(char *jobz, char *uplo, integer *n, complex *ap, 
+        real *w, complex *z__, integer *ldz, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int chpevd_(char *jobz, char *uplo, integer *n, complex *ap, 
+        real *w, complex *z__, integer *ldz, complex *work, integer *lwork, 
+        real *rwork, integer *lrwork, integer *iwork, integer *liwork, 
+        integer *info);
+ 
+/* Subroutine */ int chpevx_(char *jobz, char *range, char *uplo, integer *n, 
+        complex *ap, real *vl, real *vu, integer *il, integer *iu, real *
+        abstol, integer *m, real *w, complex *z__, integer *ldz, complex *
+        work, real *rwork, integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int chpgst_(integer *itype, char *uplo, integer *n, complex *
+        ap, complex *bp, integer *info);
+ 
+/* Subroutine */ int chpgv_(integer *itype, char *jobz, char *uplo, integer *
+        n, complex *ap, complex *bp, real *w, complex *z__, integer *ldz, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int chpgvd_(integer *itype, char *jobz, char *uplo, integer *
+        n, complex *ap, complex *bp, real *w, complex *z__, integer *ldz, 
+        complex *work, integer *lwork, real *rwork, integer *lrwork, integer *
+        iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int chpgvx_(integer *itype, char *jobz, char *range, char *
+        uplo, integer *n, complex *ap, complex *bp, real *vl, real *vu, 
+        integer *il, integer *iu, real *abstol, integer *m, real *w, complex *
+        z__, integer *ldz, complex *work, real *rwork, integer *iwork, 
+        integer *ifail, integer *info);
+ 
+/* Subroutine */ int chprfs_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, complex *afp, integer *ipiv, complex *b, integer *ldb, complex *x,
+         integer *ldx, real *ferr, real *berr, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int chpsv_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, integer *ipiv, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int chpsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, complex *ap, complex *afp, integer *ipiv, complex *b, integer *
+        ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int chptrd_(char *uplo, integer *n, complex *ap, real *d__, 
+        real *e, complex *tau, integer *info);
+ 
+/* Subroutine */ int chptrf_(char *uplo, integer *n, complex *ap, integer *
+        ipiv, integer *info);
+ 
+/* Subroutine */ int chptri_(char *uplo, integer *n, complex *ap, integer *
+        ipiv, complex *work, integer *info);
+ 
+/* Subroutine */ int chptrs_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, integer *ipiv, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int chsein_(char *side, char *eigsrc, char *initv, logical *
+        select, integer *n, complex *h__, integer *ldh, complex *w, complex *
+        vl, integer *ldvl, complex *vr, integer *ldvr, integer *mm, integer *
+        m, complex *work, real *rwork, integer *ifaill, integer *ifailr, 
+        integer *info);
+ 
+/* Subroutine */ int chseqr_(char *job, char *compz, integer *n, integer *ilo,
+         integer *ihi, complex *h__, integer *ldh, complex *w, complex *z__, 
+        integer *ldz, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int clabrd_(integer *m, integer *n, integer *nb, complex *a, 
+        integer *lda, real *d__, real *e, complex *tauq, complex *taup, 
+        complex *x, integer *ldx, complex *y, integer *ldy);
+ 
+/* Subroutine */ int clacgv_(integer *n, complex *x, integer *incx);
+ 
+/* Subroutine */ int clacon_(integer *n, complex *v, complex *x, real *est, 
+        integer *kase);
+ 
+/* Subroutine */ int clacp2_(char *uplo, integer *m, integer *n, real *a, 
+        integer *lda, complex *b, integer *ldb);
+ 
+/* Subroutine */ int clacpy_(char *uplo, integer *m, integer *n, complex *a, 
+        integer *lda, complex *b, integer *ldb);
+ 
+/* Subroutine */ int clacrm_(integer *m, integer *n, complex *a, integer *lda,
+         real *b, integer *ldb, complex *c__, integer *ldc, real *rwork);
+ 
+/* Subroutine */ int clacrt_(integer *n, complex *cx, integer *incx, complex *
+        cy, integer *incy, complex *c__, complex *s);
+ 
+/* Subroutine */ int claed0_(integer *qsiz, integer *n, real *d__, real *e, 
+        complex *q, integer *ldq, complex *qstore, integer *ldqs, real *rwork,
+         integer *iwork, integer *info);
+ 
+/* Subroutine */ int claed7_(integer *n, integer *cutpnt, integer *qsiz, 
+        integer *tlvls, integer *curlvl, integer *curpbm, real *d__, complex *
+        q, integer *ldq, real *rho, integer *indxq, real *qstore, integer *
+        qptr, integer *prmptr, integer *perm, integer *givptr, integer *
+        givcol, real *givnum, complex *work, real *rwork, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int claed8_(integer *k, integer *n, integer *qsiz, complex *
+        q, integer *ldq, real *d__, real *rho, integer *cutpnt, real *z__, 
+        real *dlamda, complex *q2, integer *ldq2, real *w, integer *indxp, 
+        integer *indx, integer *indxq, integer *perm, integer *givptr, 
+        integer *givcol, real *givnum, integer *info);
+ 
+/* Subroutine */ int claein_(logical *rightv, logical *noinit, integer *n, 
+        complex *h__, integer *ldh, complex *w, complex *v, complex *b, 
+        integer *ldb, real *rwork, real *eps3, real *smlnum, integer *info);
+ 
+/* Subroutine */ int claesy_(complex *a, complex *b, complex *c__, complex *
+        rt1, complex *rt2, complex *evscal, complex *cs1, complex *sn1);
+ 
+/* Subroutine */ int claev2_(complex *a, complex *b, complex *c__, real *rt1, 
+        real *rt2, real *cs1, complex *sn1);
+ 
+/* Subroutine */ int clags2_(logical *upper, real *a1, complex *a2, real *a3, 
+        real *b1, complex *b2, real *b3, real *csu, complex *snu, real *csv, 
+        complex *snv, real *csq, complex *snq);
+ 
+/* Subroutine */ int clagtm_(char *trans, integer *n, integer *nrhs, real *
+        alpha, complex *dl, complex *d__, complex *du, complex *x, integer *
+        ldx, real *beta, complex *b, integer *ldb);
+ 
+/* Subroutine */ int clahef_(char *uplo, integer *n, integer *nb, integer *kb,
+         complex *a, integer *lda, integer *ipiv, complex *w, integer *ldw, 
+        integer *info);
+ 
+/* Subroutine */ int clahqr_(logical *wantt, logical *wantz, integer *n, 
+        integer *ilo, integer *ihi, complex *h__, integer *ldh, complex *w, 
+        integer *iloz, integer *ihiz, complex *z__, integer *ldz, integer *
+        info);
+ 
+/* Subroutine */ int clahrd_(integer *n, integer *k, integer *nb, complex *a, 
+        integer *lda, complex *tau, complex *t, integer *ldt, complex *y, 
+        integer *ldy);
+ 
+/* Subroutine */ int claic1_(integer *job, integer *j, complex *x, real *sest,
+         complex *w, complex *gamma, real *sestpr, complex *s, complex *c__);
+ 
+/* Subroutine */ int clals0_(integer *icompq, integer *nl, integer *nr, 
+        integer *sqre, integer *nrhs, complex *b, integer *ldb, complex *bx, 
+        integer *ldbx, integer *perm, integer *givptr, integer *givcol, 
+        integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
+        difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
+        rwork, integer *info);
+ 
+/* Subroutine */ int clalsa_(integer *icompq, integer *smlsiz, integer *n, 
+        integer *nrhs, complex *b, integer *ldb, complex *bx, integer *ldbx, 
+        real *u, integer *ldu, real *vt, integer *k, real *difl, real *difr, 
+        real *z__, real *poles, integer *givptr, integer *givcol, integer *
+        ldgcol, integer *perm, real *givnum, real *c__, real *s, real *rwork, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int clapll_(integer *n, complex *x, integer *incx, complex *
+        y, integer *incy, real *ssmin);
+ 
+/* Subroutine */ int clapmt_(logical *forwrd, integer *m, integer *n, complex 
+        *x, integer *ldx, integer *k);
+ 
+/* Subroutine */ int claqgb_(integer *m, integer *n, integer *kl, integer *ku,
+         complex *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real 
+        *colcnd, real *amax, char *equed);
+ 
+/* Subroutine */ int claqge_(integer *m, integer *n, complex *a, integer *lda,
+         real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, char *
+        equed);
+ 
+/* Subroutine */ int claqhb_(char *uplo, integer *n, integer *kd, complex *ab,
+         integer *ldab, real *s, real *scond, real *amax, char *equed);
+ 
+/* Subroutine */ int claqhe_(char *uplo, integer *n, complex *a, integer *lda,
+         real *s, real *scond, real *amax, char *equed);
+ 
+/* Subroutine */ int claqhp_(char *uplo, integer *n, complex *ap, real *s, 
+        real *scond, real *amax, char *equed);
+ 
+/* Subroutine */ int claqp2_(integer *m, integer *n, integer *offset, complex 
+        *a, integer *lda, integer *jpvt, complex *tau, real *vn1, real *vn2, 
+        complex *work);
+ 
+/* Subroutine */ int claqps_(integer *m, integer *n, integer *offset, integer 
+        *nb, integer *kb, complex *a, integer *lda, integer *jpvt, complex *
+        tau, real *vn1, real *vn2, complex *auxv, complex *f, integer *ldf);
+ 
+/* Subroutine */ int claqsb_(char *uplo, integer *n, integer *kd, complex *ab,
+         integer *ldab, real *s, real *scond, real *amax, char *equed);
+ 
+/* Subroutine */ int claqsp_(char *uplo, integer *n, complex *ap, real *s, 
+        real *scond, real *amax, char *equed);
+ 
+/* Subroutine */ int claqsy_(char *uplo, integer *n, complex *a, integer *lda,
+         real *s, real *scond, real *amax, char *equed);
+ 
+/* Subroutine */ int clar1v_(integer *n, integer *b1, integer *bn, real *
+        sigma, real *d__, real *l, real *ld, real *lld, real *gersch, complex 
+        *z__, real *ztz, real *mingma, integer *r__, integer *isuppz, real *
+        work);
+ 
+/* Subroutine */ int clar2v_(integer *n, complex *x, complex *y, complex *z__,
+         integer *incx, real *c__, complex *s, integer *incc);
+ 
+/* Subroutine */ int clarcm_(integer *m, integer *n, real *a, integer *lda, 
+        complex *b, integer *ldb, complex *c__, integer *ldc, real *rwork);
+ 
+/* Subroutine */ int clarf_(char *side, integer *m, integer *n, complex *v, 
+        integer *incv, complex *tau, complex *c__, integer *ldc, complex *
+        work);
+ 
+/* Subroutine */ int clarfb_(char *side, char *trans, char *direct, char *
+        storev, integer *m, integer *n, integer *k, complex *v, integer *ldv, 
+        complex *t, integer *ldt, complex *c__, integer *ldc, complex *work, 
+        integer *ldwork);
+ 
+/* Subroutine */ int clarfg_(integer *n, complex *alpha, complex *x, integer *
+        incx, complex *tau);
+ 
+/* Subroutine */ int clarft_(char *direct, char *storev, integer *n, integer *
+        k, complex *v, integer *ldv, complex *tau, complex *t, integer *ldt);
+ 
+/* Subroutine */ int clarfx_(char *side, integer *m, integer *n, complex *v, 
+        complex *tau, complex *c__, integer *ldc, complex *work);
+ 
+/* Subroutine */ int clargv_(integer *n, complex *x, integer *incx, complex *
+        y, integer *incy, real *c__, integer *incc);
+ 
+/* Subroutine */ int clarnv_(integer *idist, integer *iseed, integer *n, 
+        complex *x);
+ 
+/* Subroutine */ int clarrv_(integer *n, real *d__, real *l, integer *isplit, 
+        integer *m, real *w, integer *iblock, real *gersch, real *tol, 
+        complex *z__, integer *ldz, integer *isuppz, real *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int clartg_(complex *f, complex *g, real *cs, complex *sn, 
+        complex *r__);
+ 
+/* Subroutine */ int clartv_(integer *n, complex *x, integer *incx, complex *
+        y, integer *incy, real *c__, complex *s, integer *incc);
+ 
+/* Subroutine */ int clarz_(char *side, integer *m, integer *n, integer *l, 
+        complex *v, integer *incv, complex *tau, complex *c__, integer *ldc, 
+        complex *work);
+ 
+/* Subroutine */ int clarzb_(char *side, char *trans, char *direct, char *
+        storev, integer *m, integer *n, integer *k, integer *l, complex *v, 
+        integer *ldv, complex *t, integer *ldt, complex *c__, integer *ldc, 
+        complex *work, integer *ldwork);
+ 
+/* Subroutine */ int clarzt_(char *direct, char *storev, integer *n, integer *
+        k, complex *v, integer *ldv, complex *tau, complex *t, integer *ldt);
+ 
+/* Subroutine */ int clascl_(char *type__, integer *kl, integer *ku, real *
+        cfrom, real *cto, integer *m, integer *n, complex *a, integer *lda, 
+        integer *info);
+ 
+/* Subroutine */ int claset_(char *uplo, integer *m, integer *n, complex *
+        alpha, complex *beta, complex *a, integer *lda);
+ 
+/* Subroutine */ int clasr_(char *side, char *pivot, char *direct, integer *m,
+         integer *n, real *c__, real *s, complex *a, integer *lda);
+ 
+/* Subroutine */ int classq_(integer *n, complex *x, integer *incx, real *
+        scale, real *sumsq);
+ 
+/* Subroutine */ int claswp_(integer *n, complex *a, integer *lda, integer *
+        k1, integer *k2, integer *ipiv, integer *incx);
+ 
+/* Subroutine */ int clasyf_(char *uplo, integer *n, integer *nb, integer *kb,
+         complex *a, integer *lda, integer *ipiv, complex *w, integer *ldw, 
+        integer *info);
+ 
+/* Subroutine */ int clatbs_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, integer *kd, complex *ab, integer *ldab, complex *
+        x, real *scale, real *cnorm, integer *info);
+ 
+/* Subroutine */ int clatdf_(integer *ijob, integer *n, complex *z__, integer 
+        *ldz, complex *rhs, real *rdsum, real *rdscal, integer *ipiv, integer 
+        *jpiv);
+ 
+/* Subroutine */ int clatps_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, complex *ap, complex *x, real *scale, real *cnorm,
+         integer *info);
+ 
+/* Subroutine */ int clatrd_(char *uplo, integer *n, integer *nb, complex *a, 
+        integer *lda, real *e, complex *tau, complex *w, integer *ldw);
+ 
+/* Subroutine */ int clatrs_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, complex *a, integer *lda, complex *x, real *scale,
+         real *cnorm, integer *info);
+ 
+/* Subroutine */ int clatrz_(integer *m, integer *n, integer *l, complex *a, 
+        integer *lda, complex *tau, complex *work);
+ 
+/* Subroutine */ int clatzm_(char *side, integer *m, integer *n, complex *v, 
+        integer *incv, complex *tau, complex *c1, complex *c2, integer *ldc, 
+        complex *work);
+ 
+/* Subroutine */ int clauu2_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *info);
+ 
+/* Subroutine */ int clauum_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *info);
+ 
+/* Subroutine */ int cpbcon_(char *uplo, integer *n, integer *kd, complex *ab,
+         integer *ldab, real *anorm, real *rcond, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int cpbequ_(char *uplo, integer *n, integer *kd, complex *ab,
+         integer *ldab, real *s, real *scond, real *amax, integer *info);
+ 
+/* Subroutine */ int cpbrfs_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, complex *ab, integer *ldab, complex *afb, integer *ldafb, 
+        complex *b, integer *ldb, complex *x, integer *ldx, real *ferr, real *
+        berr, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cpbstf_(char *uplo, integer *n, integer *kd, complex *ab,
+         integer *ldab, integer *info);
+ 
+/* Subroutine */ int cpbsv_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, complex *ab, integer *ldab, complex *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int cpbsvx_(char *fact, char *uplo, integer *n, integer *kd, 
+        integer *nrhs, complex *ab, integer *ldab, complex *afb, integer *
+        ldafb, char *equed, real *s, complex *b, integer *ldb, complex *x, 
+        integer *ldx, real *rcond, real *ferr, real *berr, complex *work, 
+        real *rwork, integer *info);
+ 
+/* Subroutine */ int cpbtf2_(char *uplo, integer *n, integer *kd, complex *ab,
+         integer *ldab, integer *info);
+ 
+/* Subroutine */ int cpbtrf_(char *uplo, integer *n, integer *kd, complex *ab,
+         integer *ldab, integer *info);
+ 
+/* Subroutine */ int cpbtrs_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, complex *ab, integer *ldab, complex *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int cpocon_(char *uplo, integer *n, complex *a, integer *lda,
+         real *anorm, real *rcond, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cpoequ_(integer *n, complex *a, integer *lda, real *s, 
+        real *scond, real *amax, integer *info);
+ 
+/* Subroutine */ int cporfs_(char *uplo, integer *n, integer *nrhs, complex *
+        a, integer *lda, complex *af, integer *ldaf, complex *b, integer *ldb,
+         complex *x, integer *ldx, real *ferr, real *berr, complex *work, 
+        real *rwork, integer *info);
+ 
+/* Subroutine */ int cposv_(char *uplo, integer *n, integer *nrhs, complex *a,
+         integer *lda, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cposvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, complex *a, integer *lda, complex *af, integer *ldaf, char *
+        equed, real *s, complex *b, integer *ldb, complex *x, integer *ldx, 
+        real *rcond, real *ferr, real *berr, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int cpotf2_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *info);
+ 
+/* Subroutine */ int cpotrf_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *info);
+ 
+/* Subroutine */ int cpotri_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *info);
+ 
+/* Subroutine */ int cpotrs_(char *uplo, integer *n, integer *nrhs, complex *
+        a, integer *lda, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cppcon_(char *uplo, integer *n, complex *ap, real *anorm,
+         real *rcond, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cppequ_(char *uplo, integer *n, complex *ap, real *s, 
+        real *scond, real *amax, integer *info);
+ 
+/* Subroutine */ int cpprfs_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, complex *afp, complex *b, integer *ldb, complex *x, integer *ldx, 
+        real *ferr, real *berr, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cppsv_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cppsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, complex *ap, complex *afp, char *equed, real *s, complex *b, 
+        integer *ldb, complex *x, integer *ldx, real *rcond, real *ferr, real 
+        *berr, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int cpptrf_(char *uplo, integer *n, complex *ap, integer *
+        info);
+ 
+/* Subroutine */ int cpptri_(char *uplo, integer *n, complex *ap, integer *
+        info);
+ 
+/* Subroutine */ int cpptrs_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cptcon_(integer *n, real *d__, complex *e, real *anorm, 
+        real *rcond, real *rwork, integer *info);
+ 
+/* Subroutine */ int cptrfs_(char *uplo, integer *n, integer *nrhs, real *d__,
+         complex *e, real *df, complex *ef, complex *b, integer *ldb, complex 
+        *x, integer *ldx, real *ferr, real *berr, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int cptsv_(integer *n, integer *nrhs, real *d__, complex *e, 
+        complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cptsvx_(char *fact, integer *n, integer *nrhs, real *d__,
+         complex *e, real *df, complex *ef, complex *b, integer *ldb, complex 
+        *x, integer *ldx, real *rcond, real *ferr, real *berr, complex *work, 
+        real *rwork, integer *info);
+ 
+/* Subroutine */ int cpttrf_(integer *n, real *d__, complex *e, integer *info);
+ 
+/* Subroutine */ int cpttrs_(char *uplo, integer *n, integer *nrhs, real *d__,
+         complex *e, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cptts2_(integer *iuplo, integer *n, integer *nrhs, real *
+        d__, complex *e, complex *b, integer *ldb);
+ 
+/* Subroutine */ int crot_(integer *n, complex *cx, integer *incx, complex *
+        cy, integer *incy, real *c__, complex *s);
+ 
+/* Subroutine */ int cspcon_(char *uplo, integer *n, complex *ap, integer *
+        ipiv, real *anorm, real *rcond, complex *work, integer *info);
+ 
+/* Subroutine */ int cspmv_(char *uplo, integer *n, complex *alpha, complex *
+        ap, complex *x, integer *incx, complex *beta, complex *y, integer *
+        incy);
+ 
+/* Subroutine */ int cspr_(char *uplo, integer *n, complex *alpha, complex *x,
+         integer *incx, complex *ap);
+ 
+/* Subroutine */ int csprfs_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, complex *afp, integer *ipiv, complex *b, integer *ldb, complex *x,
+         integer *ldx, real *ferr, real *berr, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int cspsv_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, integer *ipiv, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int cspsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, complex *ap, complex *afp, integer *ipiv, complex *b, integer *
+        ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int csptrf_(char *uplo, integer *n, complex *ap, integer *
+        ipiv, integer *info);
+ 
+/* Subroutine */ int csptri_(char *uplo, integer *n, complex *ap, integer *
+        ipiv, complex *work, integer *info);
+ 
+/* Subroutine */ int csptrs_(char *uplo, integer *n, integer *nrhs, complex *
+        ap, integer *ipiv, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int csrot_(integer *n, complex *cx, integer *incx, complex *
+        cy, integer *incy, real *c__, real *s);
+ 
+/* Subroutine */ int csrscl_(integer *n, real *sa, complex *sx, integer *incx);
+ 
+/* Subroutine */ int cstedc_(char *compz, integer *n, real *d__, real *e, 
+        complex *z__, integer *ldz, complex *work, integer *lwork, real *
+        rwork, integer *lrwork, integer *iwork, integer *liwork, integer *
+        info);
+ 
+/* Subroutine */ int cstein_(integer *n, real *d__, real *e, integer *m, real 
+        *w, integer *iblock, integer *isplit, complex *z__, integer *ldz, 
+        real *work, integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int csteqr_(char *compz, integer *n, real *d__, real *e, 
+        complex *z__, integer *ldz, real *work, integer *info);
+ 
+/* Subroutine */ int csycon_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *ipiv, real *anorm, real *rcond, complex *work, integer *
+        info);
+ 
+/* Subroutine */ int csymv_(char *uplo, integer *n, complex *alpha, complex *
+        a, integer *lda, complex *x, integer *incx, complex *beta, complex *y,
+         integer *incy);
+ 
+/* Subroutine */ int csyr_(char *uplo, integer *n, complex *alpha, complex *x,
+         integer *incx, complex *a, integer *lda);
+ 
+/* Subroutine */ int csyrfs_(char *uplo, integer *n, integer *nrhs, complex *
+        a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex *
+        b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int csysv_(char *uplo, integer *n, integer *nrhs, complex *a,
+         integer *lda, integer *ipiv, complex *b, integer *ldb, complex *work,
+         integer *lwork, integer *info);
+ 
+/* Subroutine */ int csysvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer *
+        ipiv, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond,
+         real *ferr, real *berr, complex *work, integer *lwork, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int csytf2_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *ipiv, integer *info);
+ 
+/* Subroutine */ int csytrf_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *ipiv, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int csytri_(char *uplo, integer *n, complex *a, integer *lda,
+         integer *ipiv, complex *work, integer *info);
+ 
+/* Subroutine */ int csytrs_(char *uplo, integer *n, integer *nrhs, complex *
+        a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int ctbcon_(char *norm, char *uplo, char *diag, integer *n, 
+        integer *kd, complex *ab, integer *ldab, real *rcond, complex *work, 
+        real *rwork, integer *info);
+ 
+/* Subroutine */ int ctbrfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *kd, integer *nrhs, complex *ab, integer *ldab, complex *b, 
+        integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, 
+        complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int ctbtrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *kd, integer *nrhs, complex *ab, integer *ldab, complex *b, 
+        integer *ldb, integer *info);
+ 
+/* Subroutine */ int ctgevc_(char *side, char *howmny, logical *select, 
+        integer *n, complex *a, integer *lda, complex *b, integer *ldb, 
+        complex *vl, integer *ldvl, complex *vr, integer *ldvr, integer *mm, 
+        integer *m, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int ctgex2_(logical *wantq, logical *wantz, integer *n, 
+        complex *a, integer *lda, complex *b, integer *ldb, complex *q, 
+        integer *ldq, complex *z__, integer *ldz, integer *j1, integer *info);
+ 
+/* Subroutine */ int ctgexc_(logical *wantq, logical *wantz, integer *n, 
+        complex *a, integer *lda, complex *b, integer *ldb, complex *q, 
+        integer *ldq, complex *z__, integer *ldz, integer *ifst, integer *
+        ilst, integer *info);
+ 
+/* Subroutine */ int ctgsen_(integer *ijob, logical *wantq, logical *wantz, 
+        logical *select, integer *n, complex *a, integer *lda, complex *b, 
+        integer *ldb, complex *alpha, complex *beta, complex *q, integer *ldq,
+         complex *z__, integer *ldz, integer *m, real *pl, real *pr, real *
+        dif, complex *work, integer *lwork, integer *iwork, integer *liwork, 
+        integer *info);
+ 
+/* Subroutine */ int ctgsja_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *p, integer *n, integer *k, integer *l, complex *a, integer *
+        lda, complex *b, integer *ldb, real *tola, real *tolb, real *alpha, 
+        real *beta, complex *u, integer *ldu, complex *v, integer *ldv, 
+        complex *q, integer *ldq, complex *work, integer *ncycle, integer *
+        info);
+ 
+/* Subroutine */ int ctgsna_(char *job, char *howmny, logical *select, 
+        integer *n, complex *a, integer *lda, complex *b, integer *ldb, 
+        complex *vl, integer *ldvl, complex *vr, integer *ldvr, real *s, real 
+        *dif, integer *mm, integer *m, complex *work, integer *lwork, integer 
+        *iwork, integer *info);
+ 
+/* Subroutine */ int ctgsy2_(char *trans, integer *ijob, integer *m, integer *
+        n, complex *a, integer *lda, complex *b, integer *ldb, complex *c__, 
+        integer *ldc, complex *d__, integer *ldd, complex *e, integer *lde, 
+        complex *f, integer *ldf, real *scale, real *rdsum, real *rdscal, 
+        integer *info);
+ 
+/* Subroutine */ int ctgsyl_(char *trans, integer *ijob, integer *m, integer *
+        n, complex *a, integer *lda, complex *b, integer *ldb, complex *c__, 
+        integer *ldc, complex *d__, integer *ldd, complex *e, integer *lde, 
+        complex *f, integer *ldf, real *scale, real *dif, complex *work, 
+        integer *lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int ctpcon_(char *norm, char *uplo, char *diag, integer *n, 
+        complex *ap, real *rcond, complex *work, real *rwork, integer *info);
+ 
+/* Subroutine */ int ctprfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, complex *ap, complex *b, integer *ldb, complex *x, 
+        integer *ldx, real *ferr, real *berr, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int ctptri_(char *uplo, char *diag, integer *n, complex *ap, 
+        integer *info);
+ 
+/* Subroutine */ int ctptrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, complex *ap, complex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int ctrcon_(char *norm, char *uplo, char *diag, integer *n, 
+        complex *a, integer *lda, real *rcond, complex *work, real *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int ctrevc_(char *side, char *howmny, logical *select, 
+        integer *n, complex *t, integer *ldt, complex *vl, integer *ldvl, 
+        complex *vr, integer *ldvr, integer *mm, integer *m, complex *work, 
+        real *rwork, integer *info);
+ 
+/* Subroutine */ int ctrexc_(char *compq, integer *n, complex *t, integer *
+        ldt, complex *q, integer *ldq, integer *ifst, integer *ilst, integer *
+        info);
+ 
+/* Subroutine */ int ctrrfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, complex *a, integer *lda, complex *b, integer *ldb, 
+        complex *x, integer *ldx, real *ferr, real *berr, complex *work, real 
+        *rwork, integer *info);
+ 
+/* Subroutine */ int ctrsen_(char *job, char *compq, logical *select, integer 
+        *n, complex *t, integer *ldt, complex *q, integer *ldq, complex *w, 
+        integer *m, real *s, real *sep, complex *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int ctrsna_(char *job, char *howmny, logical *select, 
+        integer *n, complex *t, integer *ldt, complex *vl, integer *ldvl, 
+        complex *vr, integer *ldvr, real *s, real *sep, integer *mm, integer *
+        m, complex *work, integer *ldwork, real *rwork, integer *info);
+ 
+/* Subroutine */ int ctrsyl_(char *trana, char *tranb, integer *isgn, integer 
+        *m, integer *n, complex *a, integer *lda, complex *b, integer *ldb, 
+        complex *c__, integer *ldc, real *scale, integer *info);
+ 
+/* Subroutine */ int ctrti2_(char *uplo, char *diag, integer *n, complex *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int ctrtri_(char *uplo, char *diag, integer *n, complex *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int ctrtrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, complex *a, integer *lda, complex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int ctzrqf_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, integer *info);
+ 
+/* Subroutine */ int ctzrzf_(integer *m, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cung2l_(integer *m, integer *n, integer *k, complex *a, 
+        integer *lda, complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cung2r_(integer *m, integer *n, integer *k, complex *a, 
+        integer *lda, complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cungbr_(char *vect, integer *m, integer *n, integer *k, 
+        complex *a, integer *lda, complex *tau, complex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int cunghr_(integer *n, integer *ilo, integer *ihi, complex *
+        a, integer *lda, complex *tau, complex *work, integer *lwork, integer 
+        *info);
+ 
+/* Subroutine */ int cungl2_(integer *m, integer *n, integer *k, complex *a, 
+        integer *lda, complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cunglq_(integer *m, integer *n, integer *k, complex *a, 
+        integer *lda, complex *tau, complex *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int cungql_(integer *m, integer *n, integer *k, complex *a, 
+        integer *lda, complex *tau, complex *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int cungqr_(integer *m, integer *n, integer *k, complex *a, 
+        integer *lda, complex *tau, complex *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int cungr2_(integer *m, integer *n, integer *k, complex *a, 
+        integer *lda, complex *tau, complex *work, integer *info);
+ 
+/* Subroutine */ int cungrq_(integer *m, integer *n, integer *k, complex *a, 
+        integer *lda, complex *tau, complex *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int cungtr_(char *uplo, integer *n, complex *a, integer *lda,
+         complex *tau, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cunm2l_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *info);
+ 
+/* Subroutine */ int cunm2r_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *info);
+ 
+/* Subroutine */ int cunmbr_(char *vect, char *side, char *trans, integer *m, 
+        integer *n, integer *k, complex *a, integer *lda, complex *tau, 
+        complex *c__, integer *ldc, complex *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int cunmhr_(char *side, char *trans, integer *m, integer *n, 
+        integer *ilo, integer *ihi, complex *a, integer *lda, complex *tau, 
+        complex *c__, integer *ldc, complex *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int cunml2_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *info);
+ 
+/* Subroutine */ int cunmlq_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cunmql_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cunmqr_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cunmr2_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *info);
+ 
+/* Subroutine */ int cunmr3_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, integer *l, complex *a, integer *lda, complex *tau, 
+        complex *c__, integer *ldc, complex *work, integer *info);
+ 
+/* Subroutine */ int cunmrq_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cunmrz_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, integer *l, complex *a, integer *lda, complex *tau, 
+        complex *c__, integer *ldc, complex *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int cunmtr_(char *side, char *uplo, char *trans, integer *m, 
+        integer *n, complex *a, integer *lda, complex *tau, complex *c__, 
+        integer *ldc, complex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int cupgtr_(char *uplo, integer *n, complex *ap, complex *
+        tau, complex *q, integer *ldq, complex *work, integer *info);
+ 
+/* Subroutine */ int cupmtr_(char *side, char *uplo, char *trans, integer *m, 
+        integer *n, complex *ap, complex *tau, complex *c__, integer *ldc, 
+        complex *work, integer *info);
+ 
+/* Subroutine */ int dbdsdc_(char *uplo, char *compq, integer *n, doublereal *
+        d__, doublereal *e, doublereal *u, integer *ldu, doublereal *vt, 
+        integer *ldvt, doublereal *q, integer *iq, doublereal *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer *
+        nru, integer *ncc, doublereal *d__, doublereal *e, doublereal *vt, 
+        integer *ldvt, doublereal *u, integer *ldu, doublereal *c__, integer *
+        ldc, doublereal *work, integer *info);
+ 
+/* Subroutine */ int ddisna_(char *job, integer *m, integer *n, doublereal *
+        d__, doublereal *sep, integer *info);
+ 
+/* Subroutine */ int dgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
+         integer *kl, integer *ku, doublereal *ab, integer *ldab, doublereal *
+        d__, doublereal *e, doublereal *q, integer *ldq, doublereal *pt, 
+        integer *ldpt, doublereal *c__, integer *ldc, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int dgbcon_(char *norm, integer *n, integer *kl, integer *ku,
+         doublereal *ab, integer *ldab, integer *ipiv, doublereal *anorm, 
+        doublereal *rcond, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dgbequ_(integer *m, integer *n, integer *kl, integer *ku,
+         doublereal *ab, integer *ldab, doublereal *r__, doublereal *c__, 
+        doublereal *rowcnd, doublereal *colcnd, doublereal *amax, integer *
+        info);
+ 
+/* Subroutine */ int dgbrfs_(char *trans, integer *n, integer *kl, integer *
+        ku, integer *nrhs, doublereal *ab, integer *ldab, doublereal *afb, 
+        integer *ldafb, integer *ipiv, doublereal *b, integer *ldb, 
+        doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+        doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dgbsv_(integer *n, integer *kl, integer *ku, integer *
+        nrhs, doublereal *ab, integer *ldab, integer *ipiv, doublereal *b, 
+        integer *ldb, integer *info);
+ 
+/* Subroutine */ int dgbsvx_(char *fact, char *trans, integer *n, integer *kl,
+         integer *ku, integer *nrhs, doublereal *ab, integer *ldab, 
+        doublereal *afb, integer *ldafb, integer *ipiv, char *equed, 
+        doublereal *r__, doublereal *c__, doublereal *b, integer *ldb, 
+        doublereal *x, integer *ldx, doublereal *rcond, doublereal *ferr, 
+        doublereal *berr, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dgbtf2_(integer *m, integer *n, integer *kl, integer *ku,
+         doublereal *ab, integer *ldab, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int dgbtrf_(integer *m, integer *n, integer *kl, integer *ku,
+         doublereal *ab, integer *ldab, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int dgbtrs_(char *trans, integer *n, integer *kl, integer *
+        ku, integer *nrhs, doublereal *ab, integer *ldab, integer *ipiv, 
+        doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dgebak_(char *job, char *side, integer *n, integer *ilo, 
+        integer *ihi, doublereal *scale, integer *m, doublereal *v, integer *
+        ldv, integer *info);
+ 
+/* Subroutine */ int dgebal_(char *job, integer *n, doublereal *a, integer *
+        lda, integer *ilo, integer *ihi, doublereal *scale, integer *info);
+ 
+/* Subroutine */ int dgebd2_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal *
+        taup, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dgebrd_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal *
+        taup, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgecon_(char *norm, integer *n, doublereal *a, integer *
+        lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dgeequ_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, doublereal 
+        *colcnd, doublereal *amax, integer *info);
+ 
+/* Subroutine */ int dgees_(char *jobvs, char *sort, L_fp select, integer *n, 
+        doublereal *a, integer *lda, integer *sdim, doublereal *wr, 
+        doublereal *wi, doublereal *vs, integer *ldvs, doublereal *work, 
+        integer *lwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int dgeesx_(char *jobvs, char *sort, L_fp select, char *
+        sense, integer *n, doublereal *a, integer *lda, integer *sdim, 
+        doublereal *wr, doublereal *wi, doublereal *vs, integer *ldvs, 
+        doublereal *rconde, doublereal *rcondv, doublereal *work, integer *
+        lwork, integer *iwork, integer *liwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int dgeev_(char *jobvl, char *jobvr, integer *n, doublereal *
+        a, integer *lda, doublereal *wr, doublereal *wi, doublereal *vl, 
+        integer *ldvl, doublereal *vr, integer *ldvr, doublereal *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgeevx_(char *balanc, char *jobvl, char *jobvr, char *
+        sense, integer *n, doublereal *a, integer *lda, doublereal *wr, 
+        doublereal *wi, doublereal *vl, integer *ldvl, doublereal *vr, 
+        integer *ldvr, integer *ilo, integer *ihi, doublereal *scale, 
+        doublereal *abnrm, doublereal *rconde, doublereal *rcondv, doublereal 
+        *work, integer *lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dgegs_(char *jobvsl, char *jobvsr, integer *n, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
+        alphar, doublereal *alphai, doublereal *beta, doublereal *vsl, 
+        integer *ldvsl, doublereal *vsr, integer *ldvsr, doublereal *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgegv_(char *jobvl, char *jobvr, integer *n, doublereal *
+        a, integer *lda, doublereal *b, integer *ldb, doublereal *alphar, 
+        doublereal *alphai, doublereal *beta, doublereal *vl, integer *ldvl, 
+        doublereal *vr, integer *ldvr, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dgehd2_(integer *n, integer *ilo, integer *ihi, 
+        doublereal *a, integer *lda, doublereal *tau, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int dgehrd_(integer *n, integer *ilo, integer *ihi, 
+        doublereal *a, integer *lda, doublereal *tau, doublereal *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgelq2_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dgelqf_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgels_(char *trans, integer *m, integer *n, integer *
+        nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
+        doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
+        s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork,
+         integer *iwork, integer *info);
+ 
+/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
+        s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int dgelsx_(integer *m, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
+        jpvt, doublereal *rcond, integer *rank, doublereal *work, integer *
+        info);
+ 
+/* Subroutine */ int dgelsy_(integer *m, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
+        jpvt, doublereal *rcond, integer *rank, doublereal *work, integer *
+        lwork, integer *info);
+ 
+/* Subroutine */ int dgeql2_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dgeqlf_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgeqp3_(integer *m, integer *n, doublereal *a, integer *
+        lda, integer *jpvt, doublereal *tau, doublereal *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int dgeqpf_(integer *m, integer *n, doublereal *a, integer *
+        lda, integer *jpvt, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dgeqr2_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dgeqrf_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgerfs_(char *trans, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, doublereal *af, integer *ldaf, integer *
+        ipiv, doublereal *b, integer *ldb, doublereal *x, integer *ldx, 
+        doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int dgerq2_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dgerqf_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgesc2_(integer *n, doublereal *a, integer *lda, 
+        doublereal *rhs, integer *ipiv, integer *jpiv, doublereal *scale);
+ 
+/* Subroutine */ int dgesdd_(char *jobz, integer *m, integer *n, doublereal *
+        a, integer *lda, doublereal *s, doublereal *u, integer *ldu, 
+        doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int dgesv_(integer *n, integer *nrhs, doublereal *a, integer 
+        *lda, integer *ipiv, doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dgesvd_(char *jobu, char *jobvt, integer *m, integer *n, 
+        doublereal *a, integer *lda, doublereal *s, doublereal *u, integer *
+        ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dgesvx_(char *fact, char *trans, integer *n, integer *
+        nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, 
+        integer *ipiv, char *equed, doublereal *r__, doublereal *c__, 
+        doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
+        rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dgetc2_(integer *n, doublereal *a, integer *lda, integer 
+        *ipiv, integer *jpiv, integer *info);
+ 
+/* Subroutine */ int dgetf2_(integer *m, integer *n, doublereal *a, integer *
+        lda, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int dgetrf_(integer *m, integer *n, doublereal *a, integer *
+        lda, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer 
+        *ipiv, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dgetrs_(char *trans, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer *
+        ldb, integer *info);
+ 
+/* Subroutine */ int dggbak_(char *job, char *side, integer *n, integer *ilo, 
+        integer *ihi, doublereal *lscale, doublereal *rscale, integer *m, 
+        doublereal *v, integer *ldv, integer *info);
+ 
+/* Subroutine */ int dggbal_(char *job, integer *n, doublereal *a, integer *
+        lda, doublereal *b, integer *ldb, integer *ilo, integer *ihi, 
+        doublereal *lscale, doublereal *rscale, doublereal *work, integer *
+        info);
+ 
+/* Subroutine */ int dgges_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+        delctg, integer *n, doublereal *a, integer *lda, doublereal *b, 
+        integer *ldb, integer *sdim, doublereal *alphar, doublereal *alphai, 
+        doublereal *beta, doublereal *vsl, integer *ldvsl, doublereal *vsr, 
+        integer *ldvsr, doublereal *work, integer *lwork, logical *bwork, 
+        integer *info);
+ 
+/* Subroutine */ int dggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+        delctg, char *sense, integer *n, doublereal *a, integer *lda, 
+        doublereal *b, integer *ldb, integer *sdim, doublereal *alphar, 
+        doublereal *alphai, doublereal *beta, doublereal *vsl, integer *ldvsl,
+         doublereal *vsr, integer *ldvsr, doublereal *rconde, doublereal *
+        rcondv, doublereal *work, integer *lwork, integer *iwork, integer *
+        liwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int dggev_(char *jobvl, char *jobvr, integer *n, doublereal *
+        a, integer *lda, doublereal *b, integer *ldb, doublereal *alphar, 
+        doublereal *alphai, doublereal *beta, doublereal *vl, integer *ldvl, 
+        doublereal *vr, integer *ldvr, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dggevx_(char *balanc, char *jobvl, char *jobvr, char *
+        sense, integer *n, doublereal *a, integer *lda, doublereal *b, 
+        integer *ldb, doublereal *alphar, doublereal *alphai, doublereal *
+        beta, doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, 
+        integer *ilo, integer *ihi, doublereal *lscale, doublereal *rscale, 
+        doublereal *abnrm, doublereal *bbnrm, doublereal *rconde, doublereal *
+        rcondv, doublereal *work, integer *lwork, integer *iwork, logical *
+        bwork, integer *info);
+ 
+/* Subroutine */ int dggglm_(integer *n, integer *m, integer *p, doublereal *
+        a, integer *lda, doublereal *b, integer *ldb, doublereal *d__, 
+        doublereal *x, doublereal *y, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dgghrd_(char *compq, char *compz, integer *n, integer *
+        ilo, integer *ihi, doublereal *a, integer *lda, doublereal *b, 
+        integer *ldb, doublereal *q, integer *ldq, doublereal *z__, integer *
+        ldz, integer *info);
+ 
+/* Subroutine */ int dgglse_(integer *m, integer *n, integer *p, doublereal *
+        a, integer *lda, doublereal *b, integer *ldb, doublereal *c__, 
+        doublereal *d__, doublereal *x, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dggqrf_(integer *n, integer *m, integer *p, doublereal *
+        a, integer *lda, doublereal *taua, doublereal *b, integer *ldb, 
+        doublereal *taub, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dggrqf_(integer *m, integer *p, integer *n, doublereal *
+        a, integer *lda, doublereal *taua, doublereal *b, integer *ldb, 
+        doublereal *taub, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dggsvd_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *n, integer *p, integer *k, integer *l, doublereal *a, 
+        integer *lda, doublereal *b, integer *ldb, doublereal *alpha, 
+        doublereal *beta, doublereal *u, integer *ldu, doublereal *v, integer 
+        *ldv, doublereal *q, integer *ldq, doublereal *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int dggsvp_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *p, integer *n, doublereal *a, integer *lda, doublereal *b, 
+        integer *ldb, doublereal *tola, doublereal *tolb, integer *k, integer 
+        *l, doublereal *u, integer *ldu, doublereal *v, integer *ldv, 
+        doublereal *q, integer *ldq, integer *iwork, doublereal *tau, 
+        doublereal *work, integer *info);
+ 
+/* Subroutine */ int dgtcon_(char *norm, integer *n, doublereal *dl, 
+        doublereal *d__, doublereal *du, doublereal *du2, integer *ipiv, 
+        doublereal *anorm, doublereal *rcond, doublereal *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dgtrfs_(char *trans, integer *n, integer *nrhs, 
+        doublereal *dl, doublereal *d__, doublereal *du, doublereal *dlf, 
+        doublereal *df, doublereal *duf, doublereal *du2, integer *ipiv, 
+        doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
+        ferr, doublereal *berr, doublereal *work, integer *iwork, integer *
+        info);
+ 
+/* Subroutine */ int dgtsv_(integer *n, integer *nrhs, doublereal *dl, 
+        doublereal *d__, doublereal *du, doublereal *b, integer *ldb, integer 
+        *info);
+ 
+/* Subroutine */ int dgtsvx_(char *fact, char *trans, integer *n, integer *
+        nrhs, doublereal *dl, doublereal *d__, doublereal *du, doublereal *
+        dlf, doublereal *df, doublereal *duf, doublereal *du2, integer *ipiv, 
+        doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
+        rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dgttrf_(integer *n, doublereal *dl, doublereal *d__, 
+        doublereal *du, doublereal *du2, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int dgttrs_(char *trans, integer *n, integer *nrhs, 
+        doublereal *dl, doublereal *d__, doublereal *du, doublereal *du2, 
+        integer *ipiv, doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dgtts2_(integer *itrans, integer *n, integer *nrhs, 
+        doublereal *dl, doublereal *d__, doublereal *du, doublereal *du2, 
+        integer *ipiv, doublereal *b, integer *ldb);
+ 
+/* Subroutine */ int dhgeqz_(char *job, char *compq, char *compz, integer *n, 
+        integer *ilo, integer *ihi, doublereal *a, integer *lda, doublereal *
+        b, integer *ldb, doublereal *alphar, doublereal *alphai, doublereal *
+        beta, doublereal *q, integer *ldq, doublereal *z__, integer *ldz, 
+        doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dhsein_(char *side, char *eigsrc, char *initv, logical *
+        select, integer *n, doublereal *h__, integer *ldh, doublereal *wr, 
+        doublereal *wi, doublereal *vl, integer *ldvl, doublereal *vr, 
+        integer *ldvr, integer *mm, integer *m, doublereal *work, integer *
+        ifaill, integer *ifailr, integer *info);
+ 
+/* Subroutine */ int dhseqr_(char *job, char *compz, integer *n, integer *ilo,
+         integer *ihi, doublereal *h__, integer *ldh, doublereal *wr, 
+        doublereal *wi, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int dlabad_(doublereal *small, doublereal *large);
+ 
+/* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal *
+        a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, 
+        doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer 
+        *ldy);
+ 
+/* Subroutine */ int dlacon_(integer *n, doublereal *v, doublereal *x, 
+        integer *isgn, doublereal *est, integer *kase);
+ 
+/* Subroutine */ int dlacpy_(char *uplo, integer *m, integer *n, doublereal *
+        a, integer *lda, doublereal *b, integer *ldb);
+ 
+/* Subroutine */ int dladiv_(doublereal *a, doublereal *b, doublereal *c__, 
+        doublereal *d__, doublereal *p, doublereal *q);
+ 
+/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__, 
+        doublereal *rt1, doublereal *rt2);
+ 
+/* Subroutine */ int dlaebz_(integer *ijob, integer *nitmax, integer *n, 
+        integer *mmax, integer *minp, integer *nbmin, doublereal *abstol, 
+        doublereal *reltol, doublereal *pivmin, doublereal *d__, doublereal *
+        e, doublereal *e2, integer *nval, doublereal *ab, doublereal *c__, 
+        integer *mout, integer *nab, doublereal *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, 
+        doublereal *d__, doublereal *e, doublereal *q, integer *ldq, 
+        doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q, 
+        integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt, 
+        doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dlaed2_(integer *k, integer *n, integer *n1, doublereal *
+        d__, doublereal *q, integer *ldq, integer *indxq, doublereal *rho, 
+        doublereal *z__, doublereal *dlamda, doublereal *w, doublereal *q2, 
+        integer *indx, integer *indxc, integer *indxp, integer *coltyp, 
+        integer *info);
+ 
+/* Subroutine */ int dlaed3_(integer *k, integer *n, integer *n1, doublereal *
+        d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda,
+         doublereal *q2, integer *indx, integer *ctot, doublereal *w, 
+        doublereal *s, integer *info);
+ 
+/* Subroutine */ int dlaed4_(integer *n, integer *i__, doublereal *d__, 
+        doublereal *z__, doublereal *delta, doublereal *rho, doublereal *dlam,
+         integer *info);
+ 
+/* Subroutine */ int dlaed5_(integer *i__, doublereal *d__, doublereal *z__, 
+        doublereal *delta, doublereal *rho, doublereal *dlam);
+ 
+/* Subroutine */ int dlaed6_(integer *kniter, logical *orgati, doublereal *
+        rho, doublereal *d__, doublereal *z__, doublereal *finit, doublereal *
+        tau, integer *info);
+ 
+/* Subroutine */ int dlaed7_(integer *icompq, integer *n, integer *qsiz, 
+        integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, 
+        doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer 
+        *cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer *
+        perm, integer *givptr, integer *givcol, doublereal *givnum, 
+        doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer 
+        *qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, 
+        doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda,
+         doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer 
+        *givptr, integer *givcol, doublereal *givnum, integer *indxp, integer 
+        *indx, integer *info);
+ 
+/* Subroutine */ int dlaed9_(integer *k, integer *kstart, integer *kstop, 
+        integer *n, doublereal *d__, doublereal *q, integer *ldq, doublereal *
+        rho, doublereal *dlamda, doublereal *w, doublereal *s, integer *lds, 
+        integer *info);
+ 
+/* Subroutine */ int dlaeda_(integer *n, integer *tlvls, integer *curlvl, 
+        integer *curpbm, integer *prmptr, integer *perm, integer *givptr, 
+        integer *givcol, doublereal *givnum, doublereal *q, integer *qptr, 
+        doublereal *z__, doublereal *ztemp, integer *info);
+ 
+/* Subroutine */ int dlaein_(logical *rightv, logical *noinit, integer *n, 
+        doublereal *h__, integer *ldh, doublereal *wr, doublereal *wi, 
+        doublereal *vr, doublereal *vi, doublereal *b, integer *ldb, 
+        doublereal *work, doublereal *eps3, doublereal *smlnum, doublereal *
+        bignum, integer *info);
+ 
+/* Subroutine */ int dlaev2_(doublereal *a, doublereal *b, doublereal *c__, 
+        doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1);
+ 
+/* Subroutine */ int dlaexc_(logical *wantq, integer *n, doublereal *t, 
+        integer *ldt, doublereal *q, integer *ldq, integer *j1, integer *n1, 
+        integer *n2, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dlag2_(doublereal *a, integer *lda, doublereal *b, 
+        integer *ldb, doublereal *safmin, doublereal *scale1, doublereal *
+        scale2, doublereal *wr1, doublereal *wr2, doublereal *wi);
+ 
+/* Subroutine */ int dlags2_(logical *upper, doublereal *a1, doublereal *a2, 
+        doublereal *a3, doublereal *b1, doublereal *b2, doublereal *b3, 
+        doublereal *csu, doublereal *snu, doublereal *csv, doublereal *snv, 
+        doublereal *csq, doublereal *snq);
+ 
+/* Subroutine */ int dlagtf_(integer *n, doublereal *a, doublereal *lambda, 
+        doublereal *b, doublereal *c__, doublereal *tol, doublereal *d__, 
+        integer *in, integer *info);
+ 
+/* Subroutine */ int dlagtm_(char *trans, integer *n, integer *nrhs, 
+        doublereal *alpha, doublereal *dl, doublereal *d__, doublereal *du, 
+        doublereal *x, integer *ldx, doublereal *beta, doublereal *b, integer 
+        *ldb);
+ 
+/* Subroutine */ int dlagts_(integer *job, integer *n, doublereal *a, 
+        doublereal *b, doublereal *c__, doublereal *d__, integer *in, 
+        doublereal *y, doublereal *tol, integer *info);
+ 
+/* Subroutine */ int dlagv2_(doublereal *a, integer *lda, doublereal *b, 
+        integer *ldb, doublereal *alphar, doublereal *alphai, doublereal *
+        beta, doublereal *csl, doublereal *snl, doublereal *csr, doublereal *
+        snr);
+ 
+/* Subroutine */ int dlahqr_(logical *wantt, logical *wantz, integer *n, 
+        integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal 
+        *wr, doublereal *wi, integer *iloz, integer *ihiz, doublereal *z__, 
+        integer *ldz, integer *info);
+ 
+/* Subroutine */ int dlahrd_(integer *n, integer *k, integer *nb, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *t, integer *ldt, 
+        doublereal *y, integer *ldy);
+ 
+/* Subroutine */ int dlaic1_(integer *job, integer *j, doublereal *x, 
+        doublereal *sest, doublereal *w, doublereal *gamma, doublereal *
+        sestpr, doublereal *s, doublereal *c__);
+ 
+/* Subroutine */ int dlaln2_(logical *ltrans, integer *na, integer *nw, 
+        doublereal *smin, doublereal *ca, doublereal *a, integer *lda, 
+        doublereal *d1, doublereal *d2, doublereal *b, integer *ldb, 
+        doublereal *wr, doublereal *wi, doublereal *x, integer *ldx, 
+        doublereal *scale, doublereal *xnorm, integer *info);
+ 
+/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr, 
+        integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal 
+        *bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol, 
+        integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal *
+        poles, doublereal *difl, doublereal *difr, doublereal *z__, integer *
+        k, doublereal *c__, doublereal *s, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n, 
+        integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer *
+        ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k, 
+        doublereal *difl, doublereal *difr, doublereal *z__, doublereal *
+        poles, integer *givptr, integer *givcol, integer *ldgcol, integer *
+        perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal *
+        work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer 
+        *nrhs, doublereal *d__, doublereal *e, doublereal *b, integer *ldb, 
+        doublereal *rcond, integer *rank, doublereal *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int dlamc1_(integer *beta, integer *t, logical *rnd, logical 
+        *ieee1);
+ 
+/* Subroutine */ int dlamc2_(integer *beta, integer *t, logical *rnd, 
+        doublereal *eps, integer *emin, doublereal *rmin, integer *emax, 
+        doublereal *rmax);
+ 
+/* Subroutine */ int dlamc4_(integer *emin, doublereal *start, integer *base);
+ 
+/* Subroutine */ int dlamc5_(integer *beta, integer *p, integer *emin, 
+        logical *ieee, integer *emax, doublereal *rmax);
+ 
+/* Subroutine */ int dlamrg_(integer *n1, integer *n2, doublereal *a, integer 
+        *dtrd1, integer *dtrd2, integer *index);
+ 
+/* Subroutine */ int dlanv2_(doublereal *a, doublereal *b, doublereal *c__, 
+        doublereal *d__, doublereal *rt1r, doublereal *rt1i, doublereal *rt2r,
+         doublereal *rt2i, doublereal *cs, doublereal *sn);
+ 
+/* Subroutine */ int dlapll_(integer *n, doublereal *x, integer *incx, 
+        doublereal *y, integer *incy, doublereal *ssmin);
+ 
+/* Subroutine */ int dlapmt_(logical *forwrd, integer *m, integer *n, 
+        doublereal *x, integer *ldx, integer *k);
+ 
+/* Subroutine */ int dlaqgb_(integer *m, integer *n, integer *kl, integer *ku,
+         doublereal *ab, integer *ldab, doublereal *r__, doublereal *c__, 
+        doublereal *rowcnd, doublereal *colcnd, doublereal *amax, char *equed);
+ 
+/* Subroutine */ int dlaqge_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, doublereal 
+        *colcnd, doublereal *amax, char *equed);
+ 
+/* Subroutine */ int dlaqp2_(integer *m, integer *n, integer *offset, 
+        doublereal *a, integer *lda, integer *jpvt, doublereal *tau, 
+        doublereal *vn1, doublereal *vn2, doublereal *work);
+ 
+/* Subroutine */ int dlaqps_(integer *m, integer *n, integer *offset, integer 
+        *nb, integer *kb, doublereal *a, integer *lda, integer *jpvt, 
+        doublereal *tau, doublereal *vn1, doublereal *vn2, doublereal *auxv, 
+        doublereal *f, integer *ldf);
+ 
+/* Subroutine */ int dlaqsb_(char *uplo, integer *n, integer *kd, doublereal *
+        ab, integer *ldab, doublereal *s, doublereal *scond, doublereal *amax,
+         char *equed);
+ 
+/* Subroutine */ int dlaqsp_(char *uplo, integer *n, doublereal *ap, 
+        doublereal *s, doublereal *scond, doublereal *amax, char *equed);
+ 
+/* Subroutine */ int dlaqsy_(char *uplo, integer *n, doublereal *a, integer *
+        lda, doublereal *s, doublereal *scond, doublereal *amax, char *equed);
+ 
+/* Subroutine */ int dlaqtr_(logical *ltran, logical *lreal, integer *n, 
+        doublereal *t, integer *ldt, doublereal *b, doublereal *w, doublereal 
+        *scale, doublereal *x, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dlar1v_(integer *n, integer *b1, integer *bn, doublereal 
+        *sigma, doublereal *d__, doublereal *l, doublereal *ld, doublereal *
+        lld, doublereal *gersch, doublereal *z__, doublereal *ztz, doublereal 
+        *mingma, integer *r__, integer *isuppz, doublereal *work);
+ 
+/* Subroutine */ int dlar2v_(integer *n, doublereal *x, doublereal *y, 
+        doublereal *z__, integer *incx, doublereal *c__, doublereal *s, 
+        integer *incc);
+ 
+/* Subroutine */ int dlarf_(char *side, integer *m, integer *n, doublereal *v,
+         integer *incv, doublereal *tau, doublereal *c__, integer *ldc, 
+        doublereal *work);
+ 
+/* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char *
+        storev, integer *m, integer *n, integer *k, doublereal *v, integer *
+        ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc, 
+        doublereal *work, integer *ldwork);
+ 
+/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x, 
+        integer *incx, doublereal *tau);
+ 
+/* Subroutine */ int dlarft_(char *direct, char *storev, integer *n, integer *
+        k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, 
+        integer *ldt);
+ 
+/* Subroutine */ int dlarfx_(char *side, integer *m, integer *n, doublereal *
+        v, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work);
+ 
+/* Subroutine */ int dlargv_(integer *n, doublereal *x, integer *incx, 
+        doublereal *y, integer *incy, doublereal *c__, integer *incc);
+ 
+/* Subroutine */ int dlarnv_(integer *idist, integer *iseed, integer *n, 
+        doublereal *x);
+ 
+/* Subroutine */ int dlarrb_(integer *n, doublereal *d__, doublereal *l, 
+        doublereal *ld, doublereal *lld, integer *ifirst, integer *ilast, 
+        doublereal *sigma, doublereal *reltol, doublereal *w, doublereal *
+        wgap, doublereal *werr, doublereal *work, integer *iwork, integer *
+        info);
+ 
+/* Subroutine */ int dlarre_(integer *n, doublereal *d__, doublereal *e, 
+        doublereal *tol, integer *nsplit, integer *isplit, integer *m, 
+        doublereal *w, doublereal *woff, doublereal *gersch, doublereal *work,
+         integer *info);
+ 
+/* Subroutine */ int dlarrf_(integer *n, doublereal *d__, doublereal *l, 
+        doublereal *ld, doublereal *lld, integer *ifirst, integer *ilast, 
+        doublereal *w, doublereal *dplus, doublereal *lplus, doublereal *work,
+         integer *iwork, integer *info);
+ 
+/* Subroutine */ int dlarrv_(integer *n, doublereal *d__, doublereal *l, 
+        integer *isplit, integer *m, doublereal *w, integer *iblock, 
+        doublereal *gersch, doublereal *tol, doublereal *z__, integer *ldz, 
+        integer *isuppz, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dlartg_(doublereal *f, doublereal *g, doublereal *cs, 
+        doublereal *sn, doublereal *r__);
+ 
+/* Subroutine */ int dlartv_(integer *n, doublereal *x, integer *incx, 
+        doublereal *y, integer *incy, doublereal *c__, doublereal *s, integer 
+        *incc);
+ 
+/* Subroutine */ int dlaruv_(integer *iseed, integer *n, doublereal *x);
+ 
+/* Subroutine */ int dlarz_(char *side, integer *m, integer *n, integer *l, 
+        doublereal *v, integer *incv, doublereal *tau, doublereal *c__, 
+        integer *ldc, doublereal *work);
+ 
+/* Subroutine */ int dlarzb_(char *side, char *trans, char *direct, char *
+        storev, integer *m, integer *n, integer *k, integer *l, doublereal *v,
+         integer *ldv, doublereal *t, integer *ldt, doublereal *c__, integer *
+        ldc, doublereal *work, integer *ldwork);
+ 
+/* Subroutine */ int dlarzt_(char *direct, char *storev, integer *n, integer *
+        k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, 
+        integer *ldt);
+ 
+/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__, 
+        doublereal *ssmin, doublereal *ssmax);
+ 
+/* Subroutine */ int dlascl_(char *type__, integer *kl, integer *ku, 
+        doublereal *cfrom, doublereal *cto, integer *m, integer *n, 
+        doublereal *a, integer *lda, integer *info);
+ 
+/* Subroutine */ int dlasd0_(integer *n, integer *sqre, doublereal *d__, 
+        doublereal *e, doublereal *u, integer *ldu, doublereal *vt, integer *
+        ldvt, integer *smlsiz, integer *iwork, doublereal *work, integer *
+        info);
+ 
+/* Subroutine */ int dlasd1_(integer *nl, integer *nr, integer *sqre, 
+        doublereal *d__, doublereal *alpha, doublereal *beta, doublereal *u, 
+        integer *ldu, doublereal *vt, integer *ldvt, integer *idxq, integer *
+        iwork, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dlasd2_(integer *nl, integer *nr, integer *sqre, integer 
+        *k, doublereal *d__, doublereal *z__, doublereal *alpha, doublereal *
+        beta, doublereal *u, integer *ldu, doublereal *vt, integer *ldvt, 
+        doublereal *dsigma, doublereal *u2, integer *ldu2, doublereal *vt2, 
+        integer *ldvt2, integer *idxp, integer *idx, integer *idxc, integer *
+        idxq, integer *coltyp, integer *info);
+ 
+/* Subroutine */ int dlasd3_(integer *nl, integer *nr, integer *sqre, integer 
+        *k, doublereal *d__, doublereal *q, integer *ldq, doublereal *dsigma, 
+        doublereal *u, integer *ldu, doublereal *u2, integer *ldu2, 
+        doublereal *vt, integer *ldvt, doublereal *vt2, integer *ldvt2, 
+        integer *idxc, integer *ctot, doublereal *z__, integer *info);
+ 
+/* Subroutine */ int dlasd4_(integer *n, integer *i__, doublereal *d__, 
+        doublereal *z__, doublereal *delta, doublereal *rho, doublereal *
+        sigma, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dlasd5_(integer *i__, doublereal *d__, doublereal *z__, 
+        doublereal *delta, doublereal *rho, doublereal *dsigma, doublereal *
+        work);
+ 
+/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr, 
+        integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl, 
+        doublereal *alpha, doublereal *beta, integer *idxq, integer *perm, 
+        integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
+         integer *ldgnum, doublereal *poles, doublereal *difl, doublereal *
+        difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s, 
+        doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dlasd7_(integer *icompq, integer *nl, integer *nr, 
+        integer *sqre, integer *k, doublereal *d__, doublereal *z__, 
+        doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl, 
+        doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal *
+        dsigma, integer *idx, integer *idxp, integer *idxq, integer *perm, 
+        integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
+         integer *ldgnum, doublereal *c__, doublereal *s, integer *info);
+ 
+/* Subroutine */ int dlasd8_(integer *icompq, integer *k, doublereal *d__, 
+        doublereal *z__, doublereal *vf, doublereal *vl, doublereal *difl, 
+        doublereal *difr, integer *lddifr, doublereal *dsigma, doublereal *
+        work, integer *info);
+ 
+/* Subroutine */ int dlasd9_(integer *icompq, integer *ldu, integer *k, 
+        doublereal *d__, doublereal *z__, doublereal *vf, doublereal *vl, 
+        doublereal *difl, doublereal *difr, doublereal *dsigma, doublereal *
+        work, integer *info);
+ 
+/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n, 
+        integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer 
+        *ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr, 
+        doublereal *z__, doublereal *poles, integer *givptr, integer *givcol, 
+        integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__, 
+        doublereal *s, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer *
+        ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e, 
+        doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, 
+        doublereal *c__, integer *ldc, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dlasdt_(integer *n, integer *lvl, integer *nd, integer *
+        inode, integer *ndiml, integer *ndimr, integer *msub);
+ 
+/* Subroutine */ int dlaset_(char *uplo, integer *m, integer *n, doublereal *
+        alpha, doublereal *beta, doublereal *a, integer *lda);
+ 
+/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e, 
+        doublereal *work, integer *info);
+ 
+/* Subroutine */ int dlasq2_(integer *n, doublereal *z__, integer *info);
+ 
+/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__, 
+        integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
+         doublereal *qmax, integer *nfail, integer *iter, integer *ndiv, 
+        logical *ieee);
+ 
+/* Subroutine */ int dlasq4_(integer *i0, integer *n0, doublereal *z__, 
+        integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1, 
+        doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2, 
+        doublereal *tau, integer *ttype);
+ 
+/* Subroutine */ int dlasq5_(integer *i0, integer *n0, doublereal *z__, 
+        integer *pp, doublereal *tau, doublereal *dmin__, doublereal *dmin1, 
+        doublereal *dmin2, doublereal *dn, doublereal *dnm1, doublereal *dnm2,
+         logical *ieee);
+ 
+/* Subroutine */ int dlasq6_(integer *i0, integer *n0, doublereal *z__, 
+        integer *pp, doublereal *dmin__, doublereal *dmin1, doublereal *dmin2,
+         doublereal *dn, doublereal *dnm1, doublereal *dnm2);
+ 
+/* Subroutine */ int dlasr_(char *side, char *pivot, char *direct, integer *m,
+         integer *n, doublereal *c__, doublereal *s, doublereal *a, integer *
+        lda);
+ 
+/* Subroutine */ int dlasrt_(char *id, integer *n, doublereal *d__, integer *
+        info);
+ 
+/* Subroutine */ int dlassq_(integer *n, doublereal *x, integer *incx, 
+        doublereal *scale, doublereal *sumsq);
+ 
+/* Subroutine */ int dlasv2_(doublereal *f, doublereal *g, doublereal *h__, 
+        doublereal *ssmin, doublereal *ssmax, doublereal *snr, doublereal *
+        csr, doublereal *snl, doublereal *csl);
+ 
+/* Subroutine */ int dlaswp_(integer *n, doublereal *a, integer *lda, integer 
+        *k1, integer *k2, integer *ipiv, integer *incx);
+ 
+/* Subroutine */ int dlasy2_(logical *ltranl, logical *ltranr, integer *isgn, 
+        integer *n1, integer *n2, doublereal *tl, integer *ldtl, doublereal *
+        tr, integer *ldtr, doublereal *b, integer *ldb, doublereal *scale, 
+        doublereal *x, integer *ldx, doublereal *xnorm, integer *info);
+ 
+/* Subroutine */ int dlasyf_(char *uplo, integer *n, integer *nb, integer *kb,
+         doublereal *a, integer *lda, integer *ipiv, doublereal *w, integer *
+        ldw, integer *info);
+ 
+/* Subroutine */ int dlatbs_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, integer *kd, doublereal *ab, integer *ldab, 
+        doublereal *x, doublereal *scale, doublereal *cnorm, integer *info);
+ 
+/* Subroutine */ int dlatdf_(integer *ijob, integer *n, doublereal *z__, 
+        integer *ldz, doublereal *rhs, doublereal *rdsum, doublereal *rdscal, 
+        integer *ipiv, integer *jpiv);
+ 
+/* Subroutine */ int dlatps_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, doublereal *ap, doublereal *x, doublereal *scale, 
+        doublereal *cnorm, integer *info);
+ 
+/* Subroutine */ int dlatrd_(char *uplo, integer *n, integer *nb, doublereal *
+        a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, 
+        integer *ldw);
+ 
+/* Subroutine */ int dlatrs_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, doublereal *a, integer *lda, doublereal *x, 
+        doublereal *scale, doublereal *cnorm, integer *info);
+ 
+/* Subroutine */ int dlatrz_(integer *m, integer *n, integer *l, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work);
+ 
+/* Subroutine */ int dlatzm_(char *side, integer *m, integer *n, doublereal *
+        v, integer *incv, doublereal *tau, doublereal *c1, doublereal *c2, 
+        integer *ldc, doublereal *work);
+ 
+/* Subroutine */ int dlauu2_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *info);
+ 
+/* Subroutine */ int dlauum_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *info);
+ 
+/* Subroutine */ int dopgtr_(char *uplo, integer *n, doublereal *ap, 
+        doublereal *tau, doublereal *q, integer *ldq, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int dopmtr_(char *side, char *uplo, char *trans, integer *m, 
+        integer *n, doublereal *ap, doublereal *tau, doublereal *c__, integer 
+        *ldc, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dorg2l_(integer *m, integer *n, integer *k, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dorg2r_(integer *m, integer *n, integer *k, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k, 
+        doublereal *a, integer *lda, doublereal *tau, doublereal *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int dorghr_(integer *n, integer *ilo, integer *ihi, 
+        doublereal *a, integer *lda, doublereal *tau, doublereal *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int dorgl2_(integer *m, integer *n, integer *k, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dorglq_(integer *m, integer *n, integer *k, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dorgql_(integer *m, integer *n, integer *k, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dorgqr_(integer *m, integer *n, integer *k, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dorgr2_(integer *m, integer *n, integer *k, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dorgrq_(integer *m, integer *n, integer *k, doublereal *
+        a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dorgtr_(char *uplo, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dorm2l_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dorm2r_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, 
+        integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, 
+        doublereal *c__, integer *ldc, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dormhr_(char *side, char *trans, integer *m, integer *n, 
+        integer *ilo, integer *ihi, doublereal *a, integer *lda, doublereal *
+        tau, doublereal *c__, integer *ldc, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dorml2_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dormlq_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dormql_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dormqr_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dormr2_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dormr3_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, integer *l, doublereal *a, integer *lda, doublereal *tau, 
+        doublereal *c__, integer *ldc, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dormrq_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dormrz_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, integer *l, doublereal *a, integer *lda, doublereal *tau, 
+        doublereal *c__, integer *ldc, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dormtr_(char *side, char *uplo, char *trans, integer *m, 
+        integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal *
+        c__, integer *ldc, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dpbcon_(char *uplo, integer *n, integer *kd, doublereal *
+        ab, integer *ldab, doublereal *anorm, doublereal *rcond, doublereal *
+        work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dpbequ_(char *uplo, integer *n, integer *kd, doublereal *
+        ab, integer *ldab, doublereal *s, doublereal *scond, doublereal *amax,
+         integer *info);
+ 
+/* Subroutine */ int dpbrfs_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb, 
+        doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
+        ferr, doublereal *berr, doublereal *work, integer *iwork, integer *
+        info);
+ 
+/* Subroutine */ int dpbstf_(char *uplo, integer *n, integer *kd, doublereal *
+        ab, integer *ldab, integer *info);
+ 
+/* Subroutine */ int dpbsv_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, doublereal *ab, integer *ldab, doublereal *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int dpbsvx_(char *fact, char *uplo, integer *n, integer *kd, 
+        integer *nrhs, doublereal *ab, integer *ldab, doublereal *afb, 
+        integer *ldafb, char *equed, doublereal *s, doublereal *b, integer *
+        ldb, doublereal *x, integer *ldx, doublereal *rcond, doublereal *ferr,
+         doublereal *berr, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dpbtf2_(char *uplo, integer *n, integer *kd, doublereal *
+        ab, integer *ldab, integer *info);
+ 
+/* Subroutine */ int dpbtrf_(char *uplo, integer *n, integer *kd, doublereal *
+        ab, integer *ldab, integer *info);
+ 
+/* Subroutine */ int dpbtrs_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, doublereal *ab, integer *ldab, doublereal *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int dpocon_(char *uplo, integer *n, doublereal *a, integer *
+        lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dpoequ_(integer *n, doublereal *a, integer *lda, 
+        doublereal *s, doublereal *scond, doublereal *amax, integer *info);
+ 
+/* Subroutine */ int dporfs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, doublereal *af, integer *ldaf, 
+        doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
+        ferr, doublereal *berr, doublereal *work, integer *iwork, integer *
+        info);
+ 
+/* Subroutine */ int dposv_(char *uplo, integer *n, integer *nrhs, doublereal 
+        *a, integer *lda, doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dposvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, 
+        char *equed, doublereal *s, doublereal *b, integer *ldb, doublereal *
+        x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *
+        berr, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dpotf2_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *info);
+ 
+/* Subroutine */ int dpotrf_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *info);
+ 
+/* Subroutine */ int dpotri_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *info);
+ 
+/* Subroutine */ int dpotrs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int dppcon_(char *uplo, integer *n, doublereal *ap, 
+        doublereal *anorm, doublereal *rcond, doublereal *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dppequ_(char *uplo, integer *n, doublereal *ap, 
+        doublereal *s, doublereal *scond, doublereal *amax, integer *info);
+ 
+/* Subroutine */ int dpprfs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *ap, doublereal *afp, doublereal *b, integer *ldb, 
+        doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+        doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dppsv_(char *uplo, integer *n, integer *nrhs, doublereal 
+        *ap, doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dppsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublereal *ap, doublereal *afp, char *equed, doublereal *s, 
+        doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
+        rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dpptrf_(char *uplo, integer *n, doublereal *ap, integer *
+        info);
+ 
+/* Subroutine */ int dpptri_(char *uplo, integer *n, doublereal *ap, integer *
+        info);
+ 
+/* Subroutine */ int dpptrs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *ap, doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dptcon_(integer *n, doublereal *d__, doublereal *e, 
+        doublereal *anorm, doublereal *rcond, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dpteqr_(char *compz, integer *n, doublereal *d__, 
+        doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int dptrfs_(integer *n, integer *nrhs, doublereal *d__, 
+        doublereal *e, doublereal *df, doublereal *ef, doublereal *b, integer 
+        *ldb, doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr,
+         doublereal *work, integer *info);
+ 
+/* Subroutine */ int dptsv_(integer *n, integer *nrhs, doublereal *d__, 
+        doublereal *e, doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dptsvx_(char *fact, integer *n, integer *nrhs, 
+        doublereal *d__, doublereal *e, doublereal *df, doublereal *ef, 
+        doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
+        rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *
+        info);
+ 
+/* Subroutine */ int dpttrf_(integer *n, doublereal *d__, doublereal *e, 
+        integer *info);
+ 
+/* Subroutine */ int dpttrs_(integer *n, integer *nrhs, doublereal *d__, 
+        doublereal *e, doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dptts2_(integer *n, integer *nrhs, doublereal *d__, 
+        doublereal *e, doublereal *b, integer *ldb);
+ 
+/* Subroutine */ int drscl_(integer *n, doublereal *sa, doublereal *sx, 
+        integer *incx);
+ 
+/* Subroutine */ int dsbev_(char *jobz, char *uplo, integer *n, integer *kd, 
+        doublereal *ab, integer *ldab, doublereal *w, doublereal *z__, 
+        integer *ldz, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dsbevd_(char *jobz, char *uplo, integer *n, integer *kd, 
+        doublereal *ab, integer *ldab, doublereal *w, doublereal *z__, 
+        integer *ldz, doublereal *work, integer *lwork, integer *iwork, 
+        integer *liwork, integer *info);
+ 
+/* Subroutine */ int dsbevx_(char *jobz, char *range, char *uplo, integer *n, 
+        integer *kd, doublereal *ab, integer *ldab, doublereal *q, integer *
+        ldq, doublereal *vl, doublereal *vu, integer *il, integer *iu, 
+        doublereal *abstol, integer *m, doublereal *w, doublereal *z__, 
+        integer *ldz, doublereal *work, integer *iwork, integer *ifail, 
+        integer *info);
+ 
+/* Subroutine */ int dsbgst_(char *vect, char *uplo, integer *n, integer *ka, 
+        integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer *
+        ldbb, doublereal *x, integer *ldx, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dsbgv_(char *jobz, char *uplo, integer *n, integer *ka, 
+        integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer *
+        ldbb, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int dsbgvd_(char *jobz, char *uplo, integer *n, integer *ka, 
+        integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer *
+        ldbb, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int dsbgvx_(char *jobz, char *range, char *uplo, integer *n, 
+        integer *ka, integer *kb, doublereal *ab, integer *ldab, doublereal *
+        bb, integer *ldbb, doublereal *q, integer *ldq, doublereal *vl, 
+        doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer 
+        *m, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int dsbtrd_(char *vect, char *uplo, integer *n, integer *kd, 
+        doublereal *ab, integer *ldab, doublereal *d__, doublereal *e, 
+        doublereal *q, integer *ldq, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dspcon_(char *uplo, integer *n, doublereal *ap, integer *
+        ipiv, doublereal *anorm, doublereal *rcond, doublereal *work, integer 
+        *iwork, integer *info);
+ 
+/* Subroutine */ int dspev_(char *jobz, char *uplo, integer *n, doublereal *
+        ap, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int dspevd_(char *jobz, char *uplo, integer *n, doublereal *
+        ap, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int dspevx_(char *jobz, char *range, char *uplo, integer *n, 
+        doublereal *ap, doublereal *vl, doublereal *vu, integer *il, integer *
+        iu, doublereal *abstol, integer *m, doublereal *w, doublereal *z__, 
+        integer *ldz, doublereal *work, integer *iwork, integer *ifail, 
+        integer *info);
+ 
+/* Subroutine */ int dspgst_(integer *itype, char *uplo, integer *n, 
+        doublereal *ap, doublereal *bp, integer *info);
+ 
+/* Subroutine */ int dspgv_(integer *itype, char *jobz, char *uplo, integer *
+        n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__, 
+        integer *ldz, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dspgvd_(integer *itype, char *jobz, char *uplo, integer *
+        n, doublereal *ap, doublereal *bp, doublereal *w, doublereal *z__, 
+        integer *ldz, doublereal *work, integer *lwork, integer *iwork, 
+        integer *liwork, integer *info);
+ 
+/* Subroutine */ int dspgvx_(integer *itype, char *jobz, char *range, char *
+        uplo, integer *n, doublereal *ap, doublereal *bp, doublereal *vl, 
+        doublereal *vu, integer *il, integer *iu, doublereal *abstol, integer 
+        *m, doublereal *w, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int dsprfs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b, 
+        integer *ldb, doublereal *x, integer *ldx, doublereal *ferr, 
+        doublereal *berr, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dspsv_(char *uplo, integer *n, integer *nrhs, doublereal 
+        *ap, integer *ipiv, doublereal *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dspsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublereal *ap, doublereal *afp, integer *ipiv, doublereal *b, 
+        integer *ldb, doublereal *x, integer *ldx, doublereal *rcond, 
+        doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int dsptrd_(char *uplo, integer *n, doublereal *ap, 
+        doublereal *d__, doublereal *e, doublereal *tau, integer *info);
+ 
+/* Subroutine */ int dsptrf_(char *uplo, integer *n, doublereal *ap, integer *
+        ipiv, integer *info);
+ 
+/* Subroutine */ int dsptri_(char *uplo, integer *n, doublereal *ap, integer *
+        ipiv, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dsptrs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *ap, integer *ipiv, doublereal *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int dstebz_(char *range, char *order, integer *n, doublereal 
+        *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, 
+        doublereal *d__, doublereal *e, integer *m, integer *nsplit, 
+        doublereal *w, integer *iblock, integer *isplit, doublereal *work, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int dstedc_(char *compz, integer *n, doublereal *d__, 
+        doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int dstegr_(char *jobz, char *range, integer *n, doublereal *
+        d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, 
+        integer *iu, doublereal *abstol, integer *m, doublereal *w, 
+        doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int dstein_(integer *n, doublereal *d__, doublereal *e, 
+        integer *m, doublereal *w, integer *iblock, integer *isplit, 
+        doublereal *z__, integer *ldz, doublereal *work, integer *iwork, 
+        integer *ifail, integer *info);
+ 
+/* Subroutine */ int dsteqr_(char *compz, integer *n, doublereal *d__, 
+        doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e, 
+        integer *info);
+ 
+/* Subroutine */ int dstev_(char *jobz, integer *n, doublereal *d__, 
+        doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int dstevd_(char *jobz, integer *n, doublereal *d__, 
+        doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int dstevr_(char *jobz, char *range, integer *n, doublereal *
+        d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, 
+        integer *iu, doublereal *abstol, integer *m, doublereal *w, 
+        doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int dstevx_(char *jobz, char *range, integer *n, doublereal *
+        d__, doublereal *e, doublereal *vl, doublereal *vu, integer *il, 
+        integer *iu, doublereal *abstol, integer *m, doublereal *w, 
+        doublereal *z__, integer *ldz, doublereal *work, integer *iwork, 
+        integer *ifail, integer *info);
+ 
+/* Subroutine */ int dsycon_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *ipiv, doublereal *anorm, doublereal *rcond, doublereal *
+        work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dsyev_(char *jobz, char *uplo, integer *n, doublereal *a,
+         integer *lda, doublereal *w, doublereal *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int dsyevd_(char *jobz, char *uplo, integer *n, doublereal *
+        a, integer *lda, doublereal *w, doublereal *work, integer *lwork, 
+        integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int dsyevr_(char *jobz, char *range, char *uplo, integer *n, 
+        doublereal *a, integer *lda, doublereal *vl, doublereal *vu, integer *
+        il, integer *iu, doublereal *abstol, integer *m, doublereal *w, 
+        doublereal *z__, integer *ldz, integer *isuppz, doublereal *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int dsyevx_(char *jobz, char *range, char *uplo, integer *n, 
+        doublereal *a, integer *lda, doublereal *vl, doublereal *vu, integer *
+        il, integer *iu, doublereal *abstol, integer *m, doublereal *w, 
+        doublereal *z__, integer *ldz, doublereal *work, integer *lwork, 
+        integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int dsygst_(integer *itype, char *uplo, integer *n, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int dsygv_(integer *itype, char *jobz, char *uplo, integer *
+        n, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
+        doublereal *w, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dsygvd_(integer *itype, char *jobz, char *uplo, integer *
+        n, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
+        doublereal *w, doublereal *work, integer *lwork, integer *iwork, 
+        integer *liwork, integer *info);
+ 
+/* Subroutine */ int dsygvx_(integer *itype, char *jobz, char *range, char *
+        uplo, integer *n, doublereal *a, integer *lda, doublereal *b, integer 
+        *ldb, doublereal *vl, doublereal *vu, integer *il, integer *iu, 
+        doublereal *abstol, integer *m, doublereal *w, doublereal *z__, 
+        integer *ldz, doublereal *work, integer *lwork, integer *iwork, 
+        integer *ifail, integer *info);
+ 
+/* Subroutine */ int dsyrfs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, doublereal *af, integer *ldaf, integer *
+        ipiv, doublereal *b, integer *ldb, doublereal *x, integer *ldx, 
+        doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int dsysv_(char *uplo, integer *n, integer *nrhs, doublereal 
+        *a, integer *lda, integer *ipiv, doublereal *b, integer *ldb, 
+        doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dsysvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf, 
+        integer *ipiv, doublereal *b, integer *ldb, doublereal *x, integer *
+        ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, 
+        doublereal *work, integer *lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dsytd2_(char *uplo, integer *n, doublereal *a, integer *
+        lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info);
+ 
+/* Subroutine */ int dsytf2_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int dsytrd_(char *uplo, integer *n, doublereal *a, integer *
+        lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dsytrf_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *ipiv, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dsytri_(char *uplo, integer *n, doublereal *a, integer *
+        lda, integer *ipiv, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dsytrs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer *
+        ldb, integer *info);
+ 
+/* Subroutine */ int dtbcon_(char *norm, char *uplo, char *diag, integer *n, 
+        integer *kd, doublereal *ab, integer *ldab, doublereal *rcond, 
+        doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dtbrfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *kd, integer *nrhs, doublereal *ab, integer *ldab, doublereal 
+        *b, integer *ldb, doublereal *x, integer *ldx, doublereal *ferr, 
+        doublereal *berr, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dtbtrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *kd, integer *nrhs, doublereal *ab, integer *ldab, doublereal 
+        *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int dtgevc_(char *side, char *howmny, logical *select, 
+        integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
+        doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, integer 
+        *mm, integer *m, doublereal *work, integer *info);
+ 
+/* Subroutine */ int dtgex2_(logical *wantq, logical *wantz, integer *n, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
+        q, integer *ldq, doublereal *z__, integer *ldz, integer *j1, integer *
+        n1, integer *n2, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dtgexc_(logical *wantq, logical *wantz, integer *n, 
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
+        q, integer *ldq, doublereal *z__, integer *ldz, integer *ifst, 
+        integer *ilst, doublereal *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int dtgsen_(integer *ijob, logical *wantq, logical *wantz, 
+        logical *select, integer *n, doublereal *a, integer *lda, doublereal *
+        b, integer *ldb, doublereal *alphar, doublereal *alphai, doublereal *
+        beta, doublereal *q, integer *ldq, doublereal *z__, integer *ldz, 
+        integer *m, doublereal *pl, doublereal *pr, doublereal *dif, 
+        doublereal *work, integer *lwork, integer *iwork, integer *liwork, 
+        integer *info);
+ 
+/* Subroutine */ int dtgsja_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *p, integer *n, integer *k, integer *l, doublereal *a, 
+        integer *lda, doublereal *b, integer *ldb, doublereal *tola, 
+        doublereal *tolb, doublereal *alpha, doublereal *beta, doublereal *u, 
+        integer *ldu, doublereal *v, integer *ldv, doublereal *q, integer *
+        ldq, doublereal *work, integer *ncycle, integer *info);
+ 
+/* Subroutine */ int dtgsna_(char *job, char *howmny, logical *select, 
+        integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
+        doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, 
+        doublereal *s, doublereal *dif, integer *mm, integer *m, doublereal *
+        work, integer *lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dtgsy2_(char *trans, integer *ijob, integer *m, integer *
+        n, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
+        doublereal *c__, integer *ldc, doublereal *d__, integer *ldd, 
+        doublereal *e, integer *lde, doublereal *f, integer *ldf, doublereal *
+        scale, doublereal *rdsum, doublereal *rdscal, integer *iwork, integer 
+        *pq, integer *info);
+ 
+/* Subroutine */ int dtgsyl_(char *trans, integer *ijob, integer *m, integer *
+        n, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
+        doublereal *c__, integer *ldc, doublereal *d__, integer *ldd, 
+        doublereal *e, integer *lde, doublereal *f, integer *ldf, doublereal *
+        scale, doublereal *dif, doublereal *work, integer *lwork, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dtpcon_(char *norm, char *uplo, char *diag, integer *n, 
+        doublereal *ap, doublereal *rcond, doublereal *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int dtprfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, doublereal *ap, doublereal *b, integer *ldb, 
+        doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+        doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dtptri_(char *uplo, char *diag, integer *n, doublereal *
+        ap, integer *info);
+ 
+/* Subroutine */ int dtptrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, doublereal *ap, doublereal *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int dtrcon_(char *norm, char *uplo, char *diag, integer *n, 
+        doublereal *a, integer *lda, doublereal *rcond, doublereal *work, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int dtrevc_(char *side, char *howmny, logical *select, 
+        integer *n, doublereal *t, integer *ldt, doublereal *vl, integer *
+        ldvl, doublereal *vr, integer *ldvr, integer *mm, integer *m, 
+        doublereal *work, integer *info);
+ 
+/* Subroutine */ int dtrexc_(char *compq, integer *n, doublereal *t, integer *
+        ldt, doublereal *q, integer *ldq, integer *ifst, integer *ilst, 
+        doublereal *work, integer *info);
+ 
+/* Subroutine */ int dtrrfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, doublereal *a, integer *lda, doublereal *b, integer *
+        ldb, doublereal *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+        doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int dtrsen_(char *job, char *compq, logical *select, integer 
+        *n, doublereal *t, integer *ldt, doublereal *q, integer *ldq, 
+        doublereal *wr, doublereal *wi, integer *m, doublereal *s, doublereal 
+        *sep, doublereal *work, integer *lwork, integer *iwork, integer *
+        liwork, integer *info);
+ 
+/* Subroutine */ int dtrsna_(char *job, char *howmny, logical *select, 
+        integer *n, doublereal *t, integer *ldt, doublereal *vl, integer *
+        ldvl, doublereal *vr, integer *ldvr, doublereal *s, doublereal *sep, 
+        integer *mm, integer *m, doublereal *work, integer *ldwork, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int dtrsyl_(char *trana, char *tranb, integer *isgn, integer 
+        *m, integer *n, doublereal *a, integer *lda, doublereal *b, integer *
+        ldb, doublereal *c__, integer *ldc, doublereal *scale, integer *info);
+ 
+/* Subroutine */ int dtrti2_(char *uplo, char *diag, integer *n, doublereal *
+        a, integer *lda, integer *info);
+ 
+/* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal *
+        a, integer *lda, integer *info);
+ 
+/* Subroutine */ int dtrtrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, doublereal *a, integer *lda, doublereal *b, integer *
+        ldb, integer *info);
+ 
+/* Subroutine */ int dtzrqf_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, integer *info);
+ 
+/* Subroutine */ int dtzrzf_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublereal *tau, doublereal *work, integer *lwork, integer *info);
+ 
+integer icmax1_(integer *n, complex *cx, integer *incx);
+ 
+integer ieeeck_(integer *ispec, real *zero, real *one);
+ 
+integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, 
+        integer *n2, integer *n3, integer *n4, ftnlen name_len, ftnlen 
+        opts_len);
+ 
+integer izmax1_(integer *n, doublecomplex *cx, integer *incx);
+ 
+/* Subroutine */ int sbdsdc_(char *uplo, char *compq, integer *n, real *d__, 
+        real *e, real *u, integer *ldu, real *vt, integer *ldvt, real *q, 
+        integer *iq, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sbdsqr_(char *uplo, integer *n, integer *ncvt, integer *
+        nru, integer *ncc, real *d__, real *e, real *vt, integer *ldvt, real *
+        u, integer *ldu, real *c__, integer *ldc, real *work, integer *info);
+ 
+/* Subroutine */ int sdisna_(char *job, integer *m, integer *n, real *d__, 
+        real *sep, integer *info);
+ 
+/* Subroutine */ int sgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
+         integer *kl, integer *ku, real *ab, integer *ldab, real *d__, real *
+        e, real *q, integer *ldq, real *pt, integer *ldpt, real *c__, integer 
+        *ldc, real *work, integer *info);
+ 
+/* Subroutine */ int sgbcon_(char *norm, integer *n, integer *kl, integer *ku,
+         real *ab, integer *ldab, integer *ipiv, real *anorm, real *rcond, 
+        real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgbequ_(integer *m, integer *n, integer *kl, integer *ku,
+         real *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real *
+        colcnd, real *amax, integer *info);
+ 
+/* Subroutine */ int sgbrfs_(char *trans, integer *n, integer *kl, integer *
+        ku, integer *nrhs, real *ab, integer *ldab, real *afb, integer *ldafb,
+         integer *ipiv, real *b, integer *ldb, real *x, integer *ldx, real *
+        ferr, real *berr, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgbsv_(integer *n, integer *kl, integer *ku, integer *
+        nrhs, real *ab, integer *ldab, integer *ipiv, real *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int sgbsvx_(char *fact, char *trans, integer *n, integer *kl,
+         integer *ku, integer *nrhs, real *ab, integer *ldab, real *afb, 
+        integer *ldafb, integer *ipiv, char *equed, real *r__, real *c__, 
+        real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *ferr,
+         real *berr, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgbtf2_(integer *m, integer *n, integer *kl, integer *ku,
+         real *ab, integer *ldab, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int sgbtrf_(integer *m, integer *n, integer *kl, integer *ku,
+         real *ab, integer *ldab, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int sgbtrs_(char *trans, integer *n, integer *kl, integer *
+        ku, integer *nrhs, real *ab, integer *ldab, integer *ipiv, real *b, 
+        integer *ldb, integer *info);
+ 
+/* Subroutine */ int sgebak_(char *job, char *side, integer *n, integer *ilo, 
+        integer *ihi, real *scale, integer *m, real *v, integer *ldv, integer 
+        *info);
+ 
+/* Subroutine */ int sgebal_(char *job, integer *n, real *a, integer *lda, 
+        integer *ilo, integer *ihi, real *scale, integer *info);
+ 
+/* Subroutine */ int sgebd2_(integer *m, integer *n, real *a, integer *lda, 
+        real *d__, real *e, real *tauq, real *taup, real *work, integer *info);
+ 
+/* Subroutine */ int sgebrd_(integer *m, integer *n, real *a, integer *lda, 
+        real *d__, real *e, real *tauq, real *taup, real *work, integer *
+        lwork, integer *info);
+ 
+/* Subroutine */ int sgecon_(char *norm, integer *n, real *a, integer *lda, 
+        real *anorm, real *rcond, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgeequ_(integer *m, integer *n, real *a, integer *lda, 
+        real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, integer 
+        *info);
+ 
+/* Subroutine */ int sgees_(char *jobvs, char *sort, L_fp select, integer *n, 
+        real *a, integer *lda, integer *sdim, real *wr, real *wi, real *vs, 
+        integer *ldvs, real *work, integer *lwork, logical *bwork, integer *
+        info);
+ 
+/* Subroutine */ int sgeesx_(char *jobvs, char *sort, L_fp select, char *
+        sense, integer *n, real *a, integer *lda, integer *sdim, real *wr, 
+        real *wi, real *vs, integer *ldvs, real *rconde, real *rcondv, real *
+        work, integer *lwork, integer *iwork, integer *liwork, logical *bwork,
+         integer *info);
+ 
+/* Subroutine */ int sgeev_(char *jobvl, char *jobvr, integer *n, real *a, 
+        integer *lda, real *wr, real *wi, real *vl, integer *ldvl, real *vr, 
+        integer *ldvr, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgeevx_(char *balanc, char *jobvl, char *jobvr, char *
+        sense, integer *n, real *a, integer *lda, real *wr, real *wi, real *
+        vl, integer *ldvl, real *vr, integer *ldvr, integer *ilo, integer *
+        ihi, real *scale, real *abnrm, real *rconde, real *rcondv, real *work,
+         integer *lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgegs_(char *jobvsl, char *jobvsr, integer *n, real *a, 
+        integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real 
+        *beta, real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgegv_(char *jobvl, char *jobvr, integer *n, real *a, 
+        integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real 
+        *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgehd2_(integer *n, integer *ilo, integer *ihi, real *a, 
+        integer *lda, real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sgehrd_(integer *n, integer *ilo, integer *ihi, real *a, 
+        integer *lda, real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgelq2_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sgelqf_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgels_(char *trans, integer *m, integer *n, integer *
+        nrhs, real *a, integer *lda, real *b, integer *ldb, real *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgelsd_(integer *m, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *b, integer *ldb, real *s, real *rcond, integer *
+        rank, real *work, integer *lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgelss_(integer *m, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *b, integer *ldb, real *s, real *rcond, integer *
+        rank, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgelsx_(integer *m, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *b, integer *ldb, integer *jpvt, real *rcond, 
+        integer *rank, real *work, integer *info);
+ 
+/* Subroutine */ int sgelsy_(integer *m, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *b, integer *ldb, integer *jpvt, real *rcond, 
+        integer *rank, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgeql2_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sgeqlf_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgeqp3_(integer *m, integer *n, real *a, integer *lda, 
+        integer *jpvt, real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgeqpf_(integer *m, integer *n, real *a, integer *lda, 
+        integer *jpvt, real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sgeqr2_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sgeqrf_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgerfs_(char *trans, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *af, integer *ldaf, integer *ipiv, real *b, 
+        integer *ldb, real *x, integer *ldx, real *ferr, real *berr, real *
+        work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgerq2_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sgerqf_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgesc2_(integer *n, real *a, integer *lda, real *rhs, 
+        integer *ipiv, integer *jpiv, real *scale);
+ 
+/* Subroutine */ int sgesdd_(char *jobz, integer *m, integer *n, real *a, 
+        integer *lda, real *s, real *u, integer *ldu, real *vt, integer *ldvt,
+         real *work, integer *lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgesv_(integer *n, integer *nrhs, real *a, integer *lda, 
+        integer *ipiv, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sgesvd_(char *jobu, char *jobvt, integer *m, integer *n, 
+        real *a, integer *lda, real *s, real *u, integer *ldu, real *vt, 
+        integer *ldvt, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgesvx_(char *fact, char *trans, integer *n, integer *
+        nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, 
+        char *equed, real *r__, real *c__, real *b, integer *ldb, real *x, 
+        integer *ldx, real *rcond, real *ferr, real *berr, real *work, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgetc2_(integer *n, real *a, integer *lda, integer *ipiv,
+         integer *jpiv, integer *info);
+ 
+/* Subroutine */ int sgetf2_(integer *m, integer *n, real *a, integer *lda, 
+        integer *ipiv, integer *info);
+ 
+/* Subroutine */ int sgetrf_(integer *m, integer *n, real *a, integer *lda, 
+        integer *ipiv, integer *info);
+ 
+/* Subroutine */ int sgetri_(integer *n, real *a, integer *lda, integer *ipiv,
+         real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgetrs_(char *trans, integer *n, integer *nrhs, real *a, 
+        integer *lda, integer *ipiv, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sggbak_(char *job, char *side, integer *n, integer *ilo, 
+        integer *ihi, real *lscale, real *rscale, integer *m, real *v, 
+        integer *ldv, integer *info);
+ 
+/* Subroutine */ int sggbal_(char *job, integer *n, real *a, integer *lda, 
+        real *b, integer *ldb, integer *ilo, integer *ihi, real *lscale, real 
+        *rscale, real *work, integer *info);
+ 
+/* Subroutine */ int sgges_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+        selctg, integer *n, real *a, integer *lda, real *b, integer *ldb, 
+        integer *sdim, real *alphar, real *alphai, real *beta, real *vsl, 
+        integer *ldvsl, real *vsr, integer *ldvsr, real *work, integer *lwork,
+         logical *bwork, integer *info);
+ 
+/* Subroutine */ int sggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+        selctg, char *sense, integer *n, real *a, integer *lda, real *b, 
+        integer *ldb, integer *sdim, real *alphar, real *alphai, real *beta, 
+        real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *rconde, 
+        real *rcondv, real *work, integer *lwork, integer *iwork, integer *
+        liwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int sggev_(char *jobvl, char *jobvr, integer *n, real *a, 
+        integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real 
+        *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int sggevx_(char *balanc, char *jobvl, char *jobvr, char *
+        sense, integer *n, real *a, integer *lda, real *b, integer *ldb, real 
+        *alphar, real *alphai, real *beta, real *vl, integer *ldvl, real *vr, 
+        integer *ldvr, integer *ilo, integer *ihi, real *lscale, real *rscale,
+         real *abnrm, real *bbnrm, real *rconde, real *rcondv, real *work, 
+        integer *lwork, integer *iwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int sggglm_(integer *n, integer *m, integer *p, real *a, 
+        integer *lda, real *b, integer *ldb, real *d__, real *x, real *y, 
+        real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sgghrd_(char *compq, char *compz, integer *n, integer *
+        ilo, integer *ihi, real *a, integer *lda, real *b, integer *ldb, real 
+        *q, integer *ldq, real *z__, integer *ldz, integer *info);
+ 
+/* Subroutine */ int sgglse_(integer *m, integer *n, integer *p, real *a, 
+        integer *lda, real *b, integer *ldb, real *c__, real *d__, real *x, 
+        real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sggqrf_(integer *n, integer *m, integer *p, real *a, 
+        integer *lda, real *taua, real *b, integer *ldb, real *taub, real *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sggrqf_(integer *m, integer *p, integer *n, real *a, 
+        integer *lda, real *taua, real *b, integer *ldb, real *taub, real *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sggsvd_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *n, integer *p, integer *k, integer *l, real *a, integer *lda,
+         real *b, integer *ldb, real *alpha, real *beta, real *u, integer *
+        ldu, real *v, integer *ldv, real *q, integer *ldq, real *work, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int sggsvp_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb, 
+        real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu,
+         real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real *
+        tau, real *work, integer *info);
+ 
+/* Subroutine */ int sgtcon_(char *norm, integer *n, real *dl, real *d__, 
+        real *du, real *du2, integer *ipiv, real *anorm, real *rcond, real *
+        work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgtrfs_(char *trans, integer *n, integer *nrhs, real *dl,
+         real *d__, real *du, real *dlf, real *df, real *duf, real *du2, 
+        integer *ipiv, real *b, integer *ldb, real *x, integer *ldx, real *
+        ferr, real *berr, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sgtsv_(integer *n, integer *nrhs, real *dl, real *d__, 
+        real *du, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sgtsvx_(char *fact, char *trans, integer *n, integer *
+        nrhs, real *dl, real *d__, real *du, real *dlf, real *df, real *duf, 
+        real *du2, integer *ipiv, real *b, integer *ldb, real *x, integer *
+        ldx, real *rcond, real *ferr, real *berr, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int sgttrf_(integer *n, real *dl, real *d__, real *du, real *
+        du2, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int sgttrs_(char *trans, integer *n, integer *nrhs, real *dl,
+         real *d__, real *du, real *du2, integer *ipiv, real *b, integer *ldb,
+         integer *info);
+ 
+/* Subroutine */ int sgtts2_(integer *itrans, integer *n, integer *nrhs, real 
+        *dl, real *d__, real *du, real *du2, integer *ipiv, real *b, integer *
+        ldb);
+ 
+/* Subroutine */ int shgeqz_(char *job, char *compq, char *compz, integer *n, 
+        integer *ilo, integer *ihi, real *a, integer *lda, real *b, integer *
+        ldb, real *alphar, real *alphai, real *beta, real *q, integer *ldq, 
+        real *z__, integer *ldz, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int shsein_(char *side, char *eigsrc, char *initv, logical *
+        select, integer *n, real *h__, integer *ldh, real *wr, real *wi, real 
+        *vl, integer *ldvl, real *vr, integer *ldvr, integer *mm, integer *m, 
+        real *work, integer *ifaill, integer *ifailr, integer *info);
+ 
+/* Subroutine */ int shseqr_(char *job, char *compz, integer *n, integer *ilo,
+         integer *ihi, real *h__, integer *ldh, real *wr, real *wi, real *z__,
+         integer *ldz, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int slabad_(real *small, real *large);
+ 
+/* Subroutine */ int slabrd_(integer *m, integer *n, integer *nb, real *a, 
+        integer *lda, real *d__, real *e, real *tauq, real *taup, real *x, 
+        integer *ldx, real *y, integer *ldy);
+ 
+/* Subroutine */ int slacon_(integer *n, real *v, real *x, integer *isgn, 
+        real *est, integer *kase);
+ 
+/* Subroutine */ int slacpy_(char *uplo, integer *m, integer *n, real *a, 
+        integer *lda, real *b, integer *ldb);
+ 
+/* Subroutine */ int sladiv_(real *a, real *b, real *c__, real *d__, real *p, 
+        real *q);
+ 
+/* Subroutine */ int slae2_(real *a, real *b, real *c__, real *rt1, real *rt2);
+ 
+/* Subroutine */ int slaebz_(integer *ijob, integer *nitmax, integer *n, 
+        integer *mmax, integer *minp, integer *nbmin, real *abstol, real *
+        reltol, real *pivmin, real *d__, real *e, real *e2, integer *nval, 
+        real *ab, real *c__, integer *mout, integer *nab, real *work, integer 
+        *iwork, integer *info);
+ 
+/* Subroutine */ int slaed0_(integer *icompq, integer *qsiz, integer *n, real 
+        *d__, real *e, real *q, integer *ldq, real *qstore, integer *ldqs, 
+        real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int slaed1_(integer *n, real *d__, real *q, integer *ldq, 
+        integer *indxq, real *rho, integer *cutpnt, real *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int slaed2_(integer *k, integer *n, integer *n1, real *d__, 
+        real *q, integer *ldq, integer *indxq, real *rho, real *z__, real *
+        dlamda, real *w, real *q2, integer *indx, integer *indxc, integer *
+        indxp, integer *coltyp, integer *info);
+ 
+/* Subroutine */ int slaed3_(integer *k, integer *n, integer *n1, real *d__, 
+        real *q, integer *ldq, real *rho, real *dlamda, real *q2, integer *
+        indx, integer *ctot, real *w, real *s, integer *info);
+ 
+/* Subroutine */ int slaed4_(integer *n, integer *i__, real *d__, real *z__, 
+        real *delta, real *rho, real *dlam, integer *info);
+ 
+/* Subroutine */ int slaed5_(integer *i__, real *d__, real *z__, real *delta, 
+        real *rho, real *dlam);
+ 
+/* Subroutine */ int slaed6_(integer *kniter, logical *orgati, real *rho, 
+        real *d__, real *z__, real *finit, real *tau, integer *info);
+ 
+/* Subroutine */ int slaed7_(integer *icompq, integer *n, integer *qsiz, 
+        integer *tlvls, integer *curlvl, integer *curpbm, real *d__, real *q, 
+        integer *ldq, integer *indxq, real *rho, integer *cutpnt, real *
+        qstore, integer *qptr, integer *prmptr, integer *perm, integer *
+        givptr, integer *givcol, real *givnum, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int slaed8_(integer *icompq, integer *k, integer *n, integer 
+        *qsiz, real *d__, real *q, integer *ldq, integer *indxq, real *rho, 
+        integer *cutpnt, real *z__, real *dlamda, real *q2, integer *ldq2, 
+        real *w, integer *perm, integer *givptr, integer *givcol, real *
+        givnum, integer *indxp, integer *indx, integer *info);
+ 
+/* Subroutine */ int slaed9_(integer *k, integer *kstart, integer *kstop, 
+        integer *n, real *d__, real *q, integer *ldq, real *rho, real *dlamda,
+         real *w, real *s, integer *lds, integer *info);
+ 
+/* Subroutine */ int slaeda_(integer *n, integer *tlvls, integer *curlvl, 
+        integer *curpbm, integer *prmptr, integer *perm, integer *givptr, 
+        integer *givcol, real *givnum, real *q, integer *qptr, real *z__, 
+        real *ztemp, integer *info);
+ 
+/* Subroutine */ int slaein_(logical *rightv, logical *noinit, integer *n, 
+        real *h__, integer *ldh, real *wr, real *wi, real *vr, real *vi, real 
+        *b, integer *ldb, real *work, real *eps3, real *smlnum, real *bignum, 
+        integer *info);
+ 
+/* Subroutine */ int slaev2_(real *a, real *b, real *c__, real *rt1, real *
+        rt2, real *cs1, real *sn1);
+ 
+/* Subroutine */ int slaexc_(logical *wantq, integer *n, real *t, integer *
+        ldt, real *q, integer *ldq, integer *j1, integer *n1, integer *n2, 
+        real *work, integer *info);
+ 
+/* Subroutine */ int slag2_(real *a, integer *lda, real *b, integer *ldb, 
+        real *safmin, real *scale1, real *scale2, real *wr1, real *wr2, real *
+        wi);
+ 
+/* Subroutine */ int slags2_(logical *upper, real *a1, real *a2, real *a3, 
+        real *b1, real *b2, real *b3, real *csu, real *snu, real *csv, real *
+        snv, real *csq, real *snq);
+ 
+/* Subroutine */ int slagtf_(integer *n, real *a, real *lambda, real *b, real 
+        *c__, real *tol, real *d__, integer *in, integer *info);
+ 
+/* Subroutine */ int slagtm_(char *trans, integer *n, integer *nrhs, real *
+        alpha, real *dl, real *d__, real *du, real *x, integer *ldx, real *
+        beta, real *b, integer *ldb);
+ 
+/* Subroutine */ int slagts_(integer *job, integer *n, real *a, real *b, real 
+        *c__, real *d__, integer *in, real *y, real *tol, integer *info);
+ 
+/* Subroutine */ int slagv2_(real *a, integer *lda, real *b, integer *ldb, 
+        real *alphar, real *alphai, real *beta, real *csl, real *snl, real *
+        csr, real *snr);
+ 
+/* Subroutine */ int slahqr_(logical *wantt, logical *wantz, integer *n, 
+        integer *ilo, integer *ihi, real *h__, integer *ldh, real *wr, real *
+        wi, integer *iloz, integer *ihiz, real *z__, integer *ldz, integer *
+        info);
+ 
+/* Subroutine */ int slahrd_(integer *n, integer *k, integer *nb, real *a, 
+        integer *lda, real *tau, real *t, integer *ldt, real *y, integer *ldy);
+ 
+/* Subroutine */ int slaic1_(integer *job, integer *j, real *x, real *sest, 
+        real *w, real *gamma, real *sestpr, real *s, real *c__);
+ 
+/* Subroutine */ int slaln2_(logical *ltrans, integer *na, integer *nw, real *
+        smin, real *ca, real *a, integer *lda, real *d1, real *d2, real *b, 
+        integer *ldb, real *wr, real *wi, real *x, integer *ldx, real *scale, 
+        real *xnorm, integer *info);
+ 
+/* Subroutine */ int slals0_(integer *icompq, integer *nl, integer *nr, 
+        integer *sqre, integer *nrhs, real *b, integer *ldb, real *bx, 
+        integer *ldbx, integer *perm, integer *givptr, integer *givcol, 
+        integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
+        difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
+        work, integer *info);
+ 
+/* Subroutine */ int slalsa_(integer *icompq, integer *smlsiz, integer *n, 
+        integer *nrhs, real *b, integer *ldb, real *bx, integer *ldbx, real *
+        u, integer *ldu, real *vt, integer *k, real *difl, real *difr, real *
+        z__, real *poles, integer *givptr, integer *givcol, integer *ldgcol, 
+        integer *perm, real *givnum, real *c__, real *s, real *work, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int slalsd_(char *uplo, integer *smlsiz, integer *n, integer 
+        *nrhs, real *d__, real *e, real *b, integer *ldb, real *rcond, 
+        integer *rank, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int slamc1_(integer *beta, integer *t, logical *rnd, logical 
+        *ieee1);
+ 
+/* Subroutine */ int slamc2_(integer *beta, integer *t, logical *rnd, real *
+        eps, integer *emin, real *rmin, integer *emax, real *rmax);
+ 
+/* Subroutine */ int slamc4_(integer *emin, real *start, integer *base);
+ 
+/* Subroutine */ int slamc5_(integer *beta, integer *p, integer *emin, 
+        logical *ieee, integer *emax, real *rmax);
+ 
+/* Subroutine */ int slamrg_(integer *n1, integer *n2, real *a, integer *
+        strd1, integer *strd2, integer *index);
+ 
+/* Subroutine */ int slanv2_(real *a, real *b, real *c__, real *d__, real *
+        rt1r, real *rt1i, real *rt2r, real *rt2i, real *cs, real *sn);
+ 
+/* Subroutine */ int slapll_(integer *n, real *x, integer *incx, real *y, 
+        integer *incy, real *ssmin);
+ 
+/* Subroutine */ int slapmt_(logical *forwrd, integer *m, integer *n, real *x,
+         integer *ldx, integer *k);
+ 
+/* Subroutine */ int slaqgb_(integer *m, integer *n, integer *kl, integer *ku,
+         real *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real *
+        colcnd, real *amax, char *equed);
+ 
+/* Subroutine */ int slaqge_(integer *m, integer *n, real *a, integer *lda, 
+        real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, char *
+        equed);
+ 
+/* Subroutine */ int slaqp2_(integer *m, integer *n, integer *offset, real *a,
+         integer *lda, integer *jpvt, real *tau, real *vn1, real *vn2, real *
+        work);
+ 
+/* Subroutine */ int slaqps_(integer *m, integer *n, integer *offset, integer 
+        *nb, integer *kb, real *a, integer *lda, integer *jpvt, real *tau, 
+        real *vn1, real *vn2, real *auxv, real *f, integer *ldf);
+ 
+/* Subroutine */ int slaqsb_(char *uplo, integer *n, integer *kd, real *ab, 
+        integer *ldab, real *s, real *scond, real *amax, char *equed);
+ 
+/* Subroutine */ int slaqsp_(char *uplo, integer *n, real *ap, real *s, real *
+        scond, real *amax, char *equed);
+ 
+/* Subroutine */ int slaqsy_(char *uplo, integer *n, real *a, integer *lda, 
+        real *s, real *scond, real *amax, char *equed);
+ 
+/* Subroutine */ int slaqtr_(logical *ltran, logical *lreal, integer *n, real 
+        *t, integer *ldt, real *b, real *w, real *scale, real *x, real *work, 
+        integer *info);
+ 
+/* Subroutine */ int slar1v_(integer *n, integer *b1, integer *bn, real *
+        sigma, real *d__, real *l, real *ld, real *lld, real *gersch, real *
+        z__, real *ztz, real *mingma, integer *r__, integer *isuppz, real *
+        work);
+ 
+/* Subroutine */ int slar2v_(integer *n, real *x, real *y, real *z__, integer 
+        *incx, real *c__, real *s, integer *incc);
+ 
+/* Subroutine */ int slarf_(char *side, integer *m, integer *n, real *v, 
+        integer *incv, real *tau, real *c__, integer *ldc, real *work);
+ 
+/* Subroutine */ int slarfb_(char *side, char *trans, char *direct, char *
+        storev, integer *m, integer *n, integer *k, real *v, integer *ldv, 
+        real *t, integer *ldt, real *c__, integer *ldc, real *work, integer *
+        ldwork);
+ 
+/* Subroutine */ int slarfg_(integer *n, real *alpha, real *x, integer *incx, 
+        real *tau);
+ 
+/* Subroutine */ int slarft_(char *direct, char *storev, integer *n, integer *
+        k, real *v, integer *ldv, real *tau, real *t, integer *ldt);
+ 
+/* Subroutine */ int slarfx_(char *side, integer *m, integer *n, real *v, 
+        real *tau, real *c__, integer *ldc, real *work);
+ 
+/* Subroutine */ int slargv_(integer *n, real *x, integer *incx, real *y, 
+        integer *incy, real *c__, integer *incc);
+ 
+/* Subroutine */ int slarnv_(integer *idist, integer *iseed, integer *n, real 
+        *x);
+ 
+/* Subroutine */ int slarrb_(integer *n, real *d__, real *l, real *ld, real *
+        lld, integer *ifirst, integer *ilast, real *sigma, real *reltol, real 
+        *w, real *wgap, real *werr, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int slarre_(integer *n, real *d__, real *e, real *tol, 
+        integer *nsplit, integer *isplit, integer *m, real *w, real *woff, 
+        real *gersch, real *work, integer *info);
+ 
+/* Subroutine */ int slarrf_(integer *n, real *d__, real *l, real *ld, real *
+        lld, integer *ifirst, integer *ilast, real *w, real *dplus, real *
+        lplus, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int slarrv_(integer *n, real *d__, real *l, integer *isplit, 
+        integer *m, real *w, integer *iblock, real *gersch, real *tol, real *
+        z__, integer *ldz, integer *isuppz, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int slartg_(real *f, real *g, real *cs, real *sn, real *r__);
+ 
+/* Subroutine */ int slartv_(integer *n, real *x, integer *incx, real *y, 
+        integer *incy, real *c__, real *s, integer *incc);
+ 
+/* Subroutine */ int slaruv_(integer *iseed, integer *n, real *x);
+ 
+/* Subroutine */ int slarz_(char *side, integer *m, integer *n, integer *l, 
+        real *v, integer *incv, real *tau, real *c__, integer *ldc, real *
+        work);
+ 
+/* Subroutine */ int slarzb_(char *side, char *trans, char *direct, char *
+        storev, integer *m, integer *n, integer *k, integer *l, real *v, 
+        integer *ldv, real *t, integer *ldt, real *c__, integer *ldc, real *
+        work, integer *ldwork);
+ 
+/* Subroutine */ int slarzt_(char *direct, char *storev, integer *n, integer *
+        k, real *v, integer *ldv, real *tau, real *t, integer *ldt);
+ 
+/* Subroutine */ int slas2_(real *f, real *g, real *h__, real *ssmin, real *
+        ssmax);
+ 
+/* Subroutine */ int slascl_(char *type__, integer *kl, integer *ku, real *
+        cfrom, real *cto, integer *m, integer *n, real *a, integer *lda, 
+        integer *info);
+ 
+/* Subroutine */ int slasd0_(integer *n, integer *sqre, real *d__, real *e, 
+        real *u, integer *ldu, real *vt, integer *ldvt, integer *smlsiz, 
+        integer *iwork, real *work, integer *info);
+ 
+/* Subroutine */ int slasd1_(integer *nl, integer *nr, integer *sqre, real *
+        d__, real *alpha, real *beta, real *u, integer *ldu, real *vt, 
+        integer *ldvt, integer *idxq, integer *iwork, real *work, integer *
+        info);
+ 
+/* Subroutine */ int slasd2_(integer *nl, integer *nr, integer *sqre, integer 
+        *k, real *d__, real *z__, real *alpha, real *beta, real *u, integer *
+        ldu, real *vt, integer *ldvt, real *dsigma, real *u2, integer *ldu2, 
+        real *vt2, integer *ldvt2, integer *idxp, integer *idx, integer *idxc,
+         integer *idxq, integer *coltyp, integer *info);
+ 
+/* Subroutine */ int slasd3_(integer *nl, integer *nr, integer *sqre, integer 
+        *k, real *d__, real *q, integer *ldq, real *dsigma, real *u, integer *
+        ldu, real *u2, integer *ldu2, real *vt, integer *ldvt, real *vt2, 
+        integer *ldvt2, integer *idxc, integer *ctot, real *z__, integer *
+        info);
+ 
+/* Subroutine */ int slasd4_(integer *n, integer *i__, real *d__, real *z__, 
+        real *delta, real *rho, real *sigma, real *work, integer *info);
+ 
+/* Subroutine */ int slasd5_(integer *i__, real *d__, real *z__, real *delta, 
+        real *rho, real *dsigma, real *work);
+ 
+/* Subroutine */ int slasd6_(integer *icompq, integer *nl, integer *nr, 
+        integer *sqre, real *d__, real *vf, real *vl, real *alpha, real *beta,
+         integer *idxq, integer *perm, integer *givptr, integer *givcol, 
+        integer *ldgcol, real *givnum, integer *ldgnum, real *poles, real *
+        difl, real *difr, real *z__, integer *k, real *c__, real *s, real *
+        work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int slasd7_(integer *icompq, integer *nl, integer *nr, 
+        integer *sqre, integer *k, real *d__, real *z__, real *zw, real *vf, 
+        real *vfw, real *vl, real *vlw, real *alpha, real *beta, real *dsigma,
+         integer *idx, integer *idxp, integer *idxq, integer *perm, integer *
+        givptr, integer *givcol, integer *ldgcol, real *givnum, integer *
+        ldgnum, real *c__, real *s, integer *info);
+ 
+/* Subroutine */ int slasd8_(integer *icompq, integer *k, real *d__, real *
+        z__, real *vf, real *vl, real *difl, real *difr, integer *lddifr, 
+        real *dsigma, real *work, integer *info);
+ 
+/* Subroutine */ int slasd9_(integer *icompq, integer *ldu, integer *k, real *
+        d__, real *z__, real *vf, real *vl, real *difl, real *difr, real *
+        dsigma, real *work, integer *info);
+ 
+/* Subroutine */ int slasda_(integer *icompq, integer *smlsiz, integer *n, 
+        integer *sqre, real *d__, real *e, real *u, integer *ldu, real *vt, 
+        integer *k, real *difl, real *difr, real *z__, real *poles, integer *
+        givptr, integer *givcol, integer *ldgcol, integer *perm, real *givnum,
+         real *c__, real *s, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int slasdq_(char *uplo, integer *sqre, integer *n, integer *
+        ncvt, integer *nru, integer *ncc, real *d__, real *e, real *vt, 
+        integer *ldvt, real *u, integer *ldu, real *c__, integer *ldc, real *
+        work, integer *info);
+ 
+/* Subroutine */ int slasdt_(integer *n, integer *lvl, integer *nd, integer *
+        inode, integer *ndiml, integer *ndimr, integer *msub);
+ 
+/* Subroutine */ int slaset_(char *uplo, integer *m, integer *n, real *alpha, 
+        real *beta, real *a, integer *lda);
+ 
+/* Subroutine */ int slasq1_(integer *n, real *d__, real *e, real *work, 
+        integer *info);
+ 
+/* Subroutine */ int slasq2_(integer *n, real *z__, integer *info);
+ 
+/* Subroutine */ int slasq3_(integer *i0, integer *n0, real *z__, integer *pp,
+         real *dmin__, real *sigma, real *desig, real *qmax, integer *nfail, 
+        integer *iter, integer *ndiv, logical *ieee);
+ 
+/* Subroutine */ int slasq4_(integer *i0, integer *n0, real *z__, integer *pp,
+         integer *n0in, real *dmin__, real *dmin1, real *dmin2, real *dn, 
+        real *dn1, real *dn2, real *tau, integer *ttype);
+ 
+/* Subroutine */ int slasq5_(integer *i0, integer *n0, real *z__, integer *pp,
+         real *tau, real *dmin__, real *dmin1, real *dmin2, real *dn, real *
+        dnm1, real *dnm2, logical *ieee);
+ 
+/* Subroutine */ int slasq6_(integer *i0, integer *n0, real *z__, integer *pp,
+         real *dmin__, real *dmin1, real *dmin2, real *dn, real *dnm1, real *
+        dnm2);
+ 
+/* Subroutine */ int slasr_(char *side, char *pivot, char *direct, integer *m,
+         integer *n, real *c__, real *s, real *a, integer *lda);
+ 
+/* Subroutine */ int slasrt_(char *id, integer *n, real *d__, integer *info);
+ 
+/* Subroutine */ int slassq_(integer *n, real *x, integer *incx, real *scale, 
+        real *sumsq);
+ 
+/* Subroutine */ int slasv2_(real *f, real *g, real *h__, real *ssmin, real *
+        ssmax, real *snr, real *csr, real *snl, real *csl);
+ 
+/* Subroutine */ int slaswp_(integer *n, real *a, integer *lda, integer *k1, 
+        integer *k2, integer *ipiv, integer *incx);
+ 
+/* Subroutine */ int slasy2_(logical *ltranl, logical *ltranr, integer *isgn, 
+        integer *n1, integer *n2, real *tl, integer *ldtl, real *tr, integer *
+        ldtr, real *b, integer *ldb, real *scale, real *x, integer *ldx, real 
+        *xnorm, integer *info);
+ 
+/* Subroutine */ int slasyf_(char *uplo, integer *n, integer *nb, integer *kb,
+         real *a, integer *lda, integer *ipiv, real *w, integer *ldw, integer 
+        *info);
+ 
+/* Subroutine */ int slatbs_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, integer *kd, real *ab, integer *ldab, real *x, 
+        real *scale, real *cnorm, integer *info);
+ 
+/* Subroutine */ int slatdf_(integer *ijob, integer *n, real *z__, integer *
+        ldz, real *rhs, real *rdsum, real *rdscal, integer *ipiv, integer *
+        jpiv);
+ 
+/* Subroutine */ int slatps_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, real *ap, real *x, real *scale, real *cnorm, 
+        integer *info);
+ 
+/* Subroutine */ int slatrd_(char *uplo, integer *n, integer *nb, real *a, 
+        integer *lda, real *e, real *tau, real *w, integer *ldw);
+ 
+/* Subroutine */ int slatrs_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, real *a, integer *lda, real *x, real *scale, real 
+        *cnorm, integer *info);
+ 
+/* Subroutine */ int slatrz_(integer *m, integer *n, integer *l, real *a, 
+        integer *lda, real *tau, real *work);
+ 
+/* Subroutine */ int slatzm_(char *side, integer *m, integer *n, real *v, 
+        integer *incv, real *tau, real *c1, real *c2, integer *ldc, real *
+        work);
+ 
+/* Subroutine */ int slauu2_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *info);
+ 
+/* Subroutine */ int slauum_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *info);
+ 
+/* Subroutine */ int sopgtr_(char *uplo, integer *n, real *ap, real *tau, 
+        real *q, integer *ldq, real *work, integer *info);
+ 
+/* Subroutine */ int sopmtr_(char *side, char *uplo, char *trans, integer *m, 
+        integer *n, real *ap, real *tau, real *c__, integer *ldc, real *work, 
+        integer *info);
+ 
+/* Subroutine */ int sorg2l_(integer *m, integer *n, integer *k, real *a, 
+        integer *lda, real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sorg2r_(integer *m, integer *n, integer *k, real *a, 
+        integer *lda, real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sorgbr_(char *vect, integer *m, integer *n, integer *k, 
+        real *a, integer *lda, real *tau, real *work, integer *lwork, integer 
+        *info);
+ 
+/* Subroutine */ int sorghr_(integer *n, integer *ilo, integer *ihi, real *a, 
+        integer *lda, real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sorgl2_(integer *m, integer *n, integer *k, real *a, 
+        integer *lda, real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sorglq_(integer *m, integer *n, integer *k, real *a, 
+        integer *lda, real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sorgql_(integer *m, integer *n, integer *k, real *a, 
+        integer *lda, real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sorgqr_(integer *m, integer *n, integer *k, real *a, 
+        integer *lda, real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sorgr2_(integer *m, integer *n, integer *k, real *a, 
+        integer *lda, real *tau, real *work, integer *info);
+ 
+/* Subroutine */ int sorgrq_(integer *m, integer *n, integer *k, real *a, 
+        integer *lda, real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sorgtr_(char *uplo, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sorm2l_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *info);
+ 
+/* Subroutine */ int sorm2r_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *info);
+ 
+/* Subroutine */ int sormbr_(char *vect, char *side, char *trans, integer *m, 
+        integer *n, integer *k, real *a, integer *lda, real *tau, real *c__, 
+        integer *ldc, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sormhr_(char *side, char *trans, integer *m, integer *n, 
+        integer *ilo, integer *ihi, real *a, integer *lda, real *tau, real *
+        c__, integer *ldc, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sorml2_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *info);
+ 
+/* Subroutine */ int sormlq_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sormql_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sormqr_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sormr2_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *info);
+ 
+/* Subroutine */ int sormr3_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, integer *l, real *a, integer *lda, real *tau, real *c__, 
+        integer *ldc, real *work, integer *info);
+ 
+/* Subroutine */ int sormrq_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sormrz_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, integer *l, real *a, integer *lda, real *tau, real *c__, 
+        integer *ldc, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int sormtr_(char *side, char *uplo, char *trans, integer *m, 
+        integer *n, real *a, integer *lda, real *tau, real *c__, integer *ldc,
+         real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int spbcon_(char *uplo, integer *n, integer *kd, real *ab, 
+        integer *ldab, real *anorm, real *rcond, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int spbequ_(char *uplo, integer *n, integer *kd, real *ab, 
+        integer *ldab, real *s, real *scond, real *amax, integer *info);
+ 
+/* Subroutine */ int spbrfs_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, real *ab, integer *ldab, real *afb, integer *ldafb, real *b, 
+        integer *ldb, real *x, integer *ldx, real *ferr, real *berr, real *
+        work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int spbstf_(char *uplo, integer *n, integer *kd, real *ab, 
+        integer *ldab, integer *info);
+ 
+/* Subroutine */ int spbsv_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, real *ab, integer *ldab, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int spbsvx_(char *fact, char *uplo, integer *n, integer *kd, 
+        integer *nrhs, real *ab, integer *ldab, real *afb, integer *ldafb, 
+        char *equed, real *s, real *b, integer *ldb, real *x, integer *ldx, 
+        real *rcond, real *ferr, real *berr, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int spbtf2_(char *uplo, integer *n, integer *kd, real *ab, 
+        integer *ldab, integer *info);
+ 
+/* Subroutine */ int spbtrf_(char *uplo, integer *n, integer *kd, real *ab, 
+        integer *ldab, integer *info);
+ 
+/* Subroutine */ int spbtrs_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, real *ab, integer *ldab, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int spocon_(char *uplo, integer *n, real *a, integer *lda, 
+        real *anorm, real *rcond, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int spoequ_(integer *n, real *a, integer *lda, real *s, real 
+        *scond, real *amax, integer *info);
+ 
+/* Subroutine */ int sporfs_(char *uplo, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *af, integer *ldaf, real *b, integer *ldb, real *x,
+         integer *ldx, real *ferr, real *berr, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int sposv_(char *uplo, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sposvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, real *a, integer *lda, real *af, integer *ldaf, char *equed, 
+        real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond, 
+        real *ferr, real *berr, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int spotf2_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *info);
+ 
+/* Subroutine */ int spotrf_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *info);
+ 
+/* Subroutine */ int spotri_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *info);
+ 
+/* Subroutine */ int spotrs_(char *uplo, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sppcon_(char *uplo, integer *n, real *ap, real *anorm, 
+        real *rcond, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sppequ_(char *uplo, integer *n, real *ap, real *s, real *
+        scond, real *amax, integer *info);
+ 
+/* Subroutine */ int spprfs_(char *uplo, integer *n, integer *nrhs, real *ap, 
+        real *afp, real *b, integer *ldb, real *x, integer *ldx, real *ferr, 
+        real *berr, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sppsv_(char *uplo, integer *n, integer *nrhs, real *ap, 
+        real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sppsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, real *ap, real *afp, char *equed, real *s, real *b, integer *
+        ldb, real *x, integer *ldx, real *rcond, real *ferr, real *berr, real 
+        *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int spptrf_(char *uplo, integer *n, real *ap, integer *info);
+ 
+/* Subroutine */ int spptri_(char *uplo, integer *n, real *ap, integer *info);
+ 
+/* Subroutine */ int spptrs_(char *uplo, integer *n, integer *nrhs, real *ap, 
+        real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sptcon_(integer *n, real *d__, real *e, real *anorm, 
+        real *rcond, real *work, integer *info);
+ 
+/* Subroutine */ int spteqr_(char *compz, integer *n, real *d__, real *e, 
+        real *z__, integer *ldz, real *work, integer *info);
+ 
+/* Subroutine */ int sptrfs_(integer *n, integer *nrhs, real *d__, real *e, 
+        real *df, real *ef, real *b, integer *ldb, real *x, integer *ldx, 
+        real *ferr, real *berr, real *work, integer *info);
+ 
+/* Subroutine */ int sptsv_(integer *n, integer *nrhs, real *d__, real *e, 
+        real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sptsvx_(char *fact, integer *n, integer *nrhs, real *d__,
+         real *e, real *df, real *ef, real *b, integer *ldb, real *x, integer 
+        *ldx, real *rcond, real *ferr, real *berr, real *work, integer *info);
+ 
+/* Subroutine */ int spttrf_(integer *n, real *d__, real *e, integer *info);
+ 
+/* Subroutine */ int spttrs_(integer *n, integer *nrhs, real *d__, real *e, 
+        real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sptts2_(integer *n, integer *nrhs, real *d__, real *e, 
+        real *b, integer *ldb);
+ 
+/* Subroutine */ int srscl_(integer *n, real *sa, real *sx, integer *incx);
+ 
+/* Subroutine */ int ssbev_(char *jobz, char *uplo, integer *n, integer *kd, 
+        real *ab, integer *ldab, real *w, real *z__, integer *ldz, real *work,
+         integer *info);
+ 
+/* Subroutine */ int ssbevd_(char *jobz, char *uplo, integer *n, integer *kd, 
+        real *ab, integer *ldab, real *w, real *z__, integer *ldz, real *work,
+         integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int ssbevx_(char *jobz, char *range, char *uplo, integer *n, 
+        integer *kd, real *ab, integer *ldab, real *q, integer *ldq, real *vl,
+         real *vu, integer *il, integer *iu, real *abstol, integer *m, real *
+        w, real *z__, integer *ldz, real *work, integer *iwork, integer *
+        ifail, integer *info);
+ 
+/* Subroutine */ int ssbgst_(char *vect, char *uplo, integer *n, integer *ka, 
+        integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real *
+        x, integer *ldx, real *work, integer *info);
+ 
+/* Subroutine */ int ssbgv_(char *jobz, char *uplo, integer *n, integer *ka, 
+        integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real *
+        w, real *z__, integer *ldz, real *work, integer *info);
+ 
+/* Subroutine */ int ssbgvd_(char *jobz, char *uplo, integer *n, integer *ka, 
+        integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real *
+        w, real *z__, integer *ldz, real *work, integer *lwork, integer *
+        iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int ssbgvx_(char *jobz, char *range, char *uplo, integer *n, 
+        integer *ka, integer *kb, real *ab, integer *ldab, real *bb, integer *
+        ldbb, real *q, integer *ldq, real *vl, real *vu, integer *il, integer 
+        *iu, real *abstol, integer *m, real *w, real *z__, integer *ldz, real 
+        *work, integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int ssbtrd_(char *vect, char *uplo, integer *n, integer *kd, 
+        real *ab, integer *ldab, real *d__, real *e, real *q, integer *ldq, 
+        real *work, integer *info);
+ 
+/* Subroutine */ int sspcon_(char *uplo, integer *n, real *ap, integer *ipiv, 
+        real *anorm, real *rcond, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sspev_(char *jobz, char *uplo, integer *n, real *ap, 
+        real *w, real *z__, integer *ldz, real *work, integer *info);
+ 
+/* Subroutine */ int sspevd_(char *jobz, char *uplo, integer *n, real *ap, 
+        real *w, real *z__, integer *ldz, real *work, integer *lwork, integer 
+        *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int sspevx_(char *jobz, char *range, char *uplo, integer *n, 
+        real *ap, real *vl, real *vu, integer *il, integer *iu, real *abstol, 
+        integer *m, real *w, real *z__, integer *ldz, real *work, integer *
+        iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int sspgst_(integer *itype, char *uplo, integer *n, real *ap,
+         real *bp, integer *info);
+ 
+/* Subroutine */ int sspgv_(integer *itype, char *jobz, char *uplo, integer *
+        n, real *ap, real *bp, real *w, real *z__, integer *ldz, real *work, 
+        integer *info);
+ 
+/* Subroutine */ int sspgvd_(integer *itype, char *jobz, char *uplo, integer *
+        n, real *ap, real *bp, real *w, real *z__, integer *ldz, real *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int sspgvx_(integer *itype, char *jobz, char *range, char *
+        uplo, integer *n, real *ap, real *bp, real *vl, real *vu, integer *il,
+         integer *iu, real *abstol, integer *m, real *w, real *z__, integer *
+        ldz, real *work, integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int ssprfs_(char *uplo, integer *n, integer *nrhs, real *ap, 
+        real *afp, integer *ipiv, real *b, integer *ldb, real *x, integer *
+        ldx, real *ferr, real *berr, real *work, integer *iwork, integer *
+        info);
+ 
+/* Subroutine */ int sspsv_(char *uplo, integer *n, integer *nrhs, real *ap, 
+        integer *ipiv, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sspsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, real *ap, real *afp, integer *ipiv, real *b, integer *ldb, real 
+        *x, integer *ldx, real *rcond, real *ferr, real *berr, real *work, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int ssptrd_(char *uplo, integer *n, real *ap, real *d__, 
+        real *e, real *tau, integer *info);
+ 
+/* Subroutine */ int ssptrf_(char *uplo, integer *n, real *ap, integer *ipiv, 
+        integer *info);
+ 
+/* Subroutine */ int ssptri_(char *uplo, integer *n, real *ap, integer *ipiv, 
+        real *work, integer *info);
+ 
+/* Subroutine */ int ssptrs_(char *uplo, integer *n, integer *nrhs, real *ap, 
+        integer *ipiv, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int sstebz_(char *range, char *order, integer *n, real *vl, 
+        real *vu, integer *il, integer *iu, real *abstol, real *d__, real *e, 
+        integer *m, integer *nsplit, real *w, integer *iblock, integer *
+        isplit, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int sstedc_(char *compz, integer *n, real *d__, real *e, 
+        real *z__, integer *ldz, real *work, integer *lwork, integer *iwork, 
+        integer *liwork, integer *info);
+ 
+/* Subroutine */ int sstegr_(char *jobz, char *range, integer *n, real *d__, 
+        real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol, 
+        integer *m, real *w, real *z__, integer *ldz, integer *isuppz, real *
+        work, integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int sstein_(integer *n, real *d__, real *e, integer *m, real 
+        *w, integer *iblock, integer *isplit, real *z__, integer *ldz, real *
+        work, integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int ssteqr_(char *compz, integer *n, real *d__, real *e, 
+        real *z__, integer *ldz, real *work, integer *info);
+ 
+/* Subroutine */ int ssterf_(integer *n, real *d__, real *e, integer *info);
+ 
+/* Subroutine */ int sstev_(char *jobz, integer *n, real *d__, real *e, real *
+        z__, integer *ldz, real *work, integer *info);
+ 
+/* Subroutine */ int sstevd_(char *jobz, integer *n, real *d__, real *e, real 
+        *z__, integer *ldz, real *work, integer *lwork, integer *iwork, 
+        integer *liwork, integer *info);
+ 
+/* Subroutine */ int sstevr_(char *jobz, char *range, integer *n, real *d__, 
+        real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol, 
+        integer *m, real *w, real *z__, integer *ldz, integer *isuppz, real *
+        work, integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int sstevx_(char *jobz, char *range, integer *n, real *d__, 
+        real *e, real *vl, real *vu, integer *il, integer *iu, real *abstol, 
+        integer *m, real *w, real *z__, integer *ldz, real *work, integer *
+        iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int ssycon_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *ipiv, real *anorm, real *rcond, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int ssyev_(char *jobz, char *uplo, integer *n, real *a, 
+        integer *lda, real *w, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int ssyevd_(char *jobz, char *uplo, integer *n, real *a, 
+        integer *lda, real *w, real *work, integer *lwork, integer *iwork, 
+        integer *liwork, integer *info);
+ 
+/* Subroutine */ int ssyevr_(char *jobz, char *range, char *uplo, integer *n, 
+        real *a, integer *lda, real *vl, real *vu, integer *il, integer *iu, 
+        real *abstol, integer *m, real *w, real *z__, integer *ldz, integer *
+        isuppz, real *work, integer *lwork, integer *iwork, integer *liwork, 
+        integer *info);
+ 
+/* Subroutine */ int ssyevx_(char *jobz, char *range, char *uplo, integer *n, 
+        real *a, integer *lda, real *vl, real *vu, integer *il, integer *iu, 
+        real *abstol, integer *m, real *w, real *z__, integer *ldz, real *
+        work, integer *lwork, integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int ssygs2_(integer *itype, char *uplo, integer *n, real *a, 
+        integer *lda, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int ssygst_(integer *itype, char *uplo, integer *n, real *a, 
+        integer *lda, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int ssygv_(integer *itype, char *jobz, char *uplo, integer *
+        n, real *a, integer *lda, real *b, integer *ldb, real *w, real *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int ssygvd_(integer *itype, char *jobz, char *uplo, integer *
+        n, real *a, integer *lda, real *b, integer *ldb, real *w, real *work, 
+        integer *lwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int ssygvx_(integer *itype, char *jobz, char *range, char *
+        uplo, integer *n, real *a, integer *lda, real *b, integer *ldb, real *
+        vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, 
+        real *w, real *z__, integer *ldz, real *work, integer *lwork, integer 
+        *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int ssyrfs_(char *uplo, integer *n, integer *nrhs, real *a, 
+        integer *lda, real *af, integer *ldaf, integer *ipiv, real *b, 
+        integer *ldb, real *x, integer *ldx, real *ferr, real *berr, real *
+        work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int ssysv_(char *uplo, integer *n, integer *nrhs, real *a, 
+        integer *lda, integer *ipiv, real *b, integer *ldb, real *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int ssysvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, 
+        real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *ferr,
+         real *berr, real *work, integer *lwork, integer *iwork, integer *
+        info);
+ 
+/* Subroutine */ int ssytd2_(char *uplo, integer *n, real *a, integer *lda, 
+        real *d__, real *e, real *tau, integer *info);
+ 
+/* Subroutine */ int ssytf2_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *ipiv, integer *info);
+ 
+/* Subroutine */ int ssytrd_(char *uplo, integer *n, real *a, integer *lda, 
+        real *d__, real *e, real *tau, real *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int ssytrf_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *ipiv, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int ssytri_(char *uplo, integer *n, real *a, integer *lda, 
+        integer *ipiv, real *work, integer *info);
+ 
+/* Subroutine */ int ssytrs_(char *uplo, integer *n, integer *nrhs, real *a, 
+        integer *lda, integer *ipiv, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int stbcon_(char *norm, char *uplo, char *diag, integer *n, 
+        integer *kd, real *ab, integer *ldab, real *rcond, real *work, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int stbrfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *kd, integer *nrhs, real *ab, integer *ldab, real *b, integer 
+        *ldb, real *x, integer *ldx, real *ferr, real *berr, real *work, 
+        integer *iwork, integer *info);
+ 
+/* Subroutine */ int stbtrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *kd, integer *nrhs, real *ab, integer *ldab, real *b, integer 
+        *ldb, integer *info);
+ 
+/* Subroutine */ int stgevc_(char *side, char *howmny, logical *select, 
+        integer *n, real *a, integer *lda, real *b, integer *ldb, real *vl, 
+        integer *ldvl, real *vr, integer *ldvr, integer *mm, integer *m, real 
+        *work, integer *info);
+ 
+/* Subroutine */ int stgex2_(logical *wantq, logical *wantz, integer *n, real 
+        *a, integer *lda, real *b, integer *ldb, real *q, integer *ldq, real *
+        z__, integer *ldz, integer *j1, integer *n1, integer *n2, real *work, 
+        integer *lwork, integer *info);
+ 
+/* Subroutine */ int stgexc_(logical *wantq, logical *wantz, integer *n, real 
+        *a, integer *lda, real *b, integer *ldb, real *q, integer *ldq, real *
+        z__, integer *ldz, integer *ifst, integer *ilst, real *work, integer *
+        lwork, integer *info);
+ 
+/* Subroutine */ int stgsen_(integer *ijob, logical *wantq, logical *wantz, 
+        logical *select, integer *n, real *a, integer *lda, real *b, integer *
+        ldb, real *alphar, real *alphai, real *beta, real *q, integer *ldq, 
+        real *z__, integer *ldz, integer *m, real *pl, real *pr, real *dif, 
+        real *work, integer *lwork, integer *iwork, integer *liwork, integer *
+        info);
+ 
+/* Subroutine */ int stgsja_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *p, integer *n, integer *k, integer *l, real *a, integer *lda,
+         real *b, integer *ldb, real *tola, real *tolb, real *alpha, real *
+        beta, real *u, integer *ldu, real *v, integer *ldv, real *q, integer *
+        ldq, real *work, integer *ncycle, integer *info);
+ 
+/* Subroutine */ int stgsna_(char *job, char *howmny, logical *select, 
+        integer *n, real *a, integer *lda, real *b, integer *ldb, real *vl, 
+        integer *ldvl, real *vr, integer *ldvr, real *s, real *dif, integer *
+        mm, integer *m, real *work, integer *lwork, integer *iwork, integer *
+        info);
+ 
+/* Subroutine */ int stgsy2_(char *trans, integer *ijob, integer *m, integer *
+        n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer *
+        ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer 
+        *ldf, real *scale, real *rdsum, real *rdscal, integer *iwork, integer 
+        *pq, integer *info);
+ 
+/* Subroutine */ int stgsyl_(char *trans, integer *ijob, integer *m, integer *
+        n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer *
+        ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer 
+        *ldf, real *scale, real *dif, real *work, integer *lwork, integer *
+        iwork, integer *info);
+ 
+/* Subroutine */ int stpcon_(char *norm, char *uplo, char *diag, integer *n, 
+        real *ap, real *rcond, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int stprfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, real *ap, real *b, integer *ldb, real *x, integer *ldx,
+         real *ferr, real *berr, real *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int stptri_(char *uplo, char *diag, integer *n, real *ap, 
+        integer *info);
+ 
+/* Subroutine */ int stptrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, real *ap, real *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int strcon_(char *norm, char *uplo, char *diag, integer *n, 
+        real *a, integer *lda, real *rcond, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int strevc_(char *side, char *howmny, logical *select, 
+        integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr, 
+        integer *ldvr, integer *mm, integer *m, real *work, integer *info);
+ 
+/* Subroutine */ int strexc_(char *compq, integer *n, real *t, integer *ldt, 
+        real *q, integer *ldq, integer *ifst, integer *ilst, real *work, 
+        integer *info);
+ 
+/* Subroutine */ int strrfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, real *a, integer *lda, real *b, integer *ldb, real *x, 
+        integer *ldx, real *ferr, real *berr, real *work, integer *iwork, 
+        integer *info);
+ 
+/* Subroutine */ int strsen_(char *job, char *compq, logical *select, integer 
+        *n, real *t, integer *ldt, real *q, integer *ldq, real *wr, real *wi, 
+        integer *m, real *s, real *sep, real *work, integer *lwork, integer *
+        iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int strsna_(char *job, char *howmny, logical *select, 
+        integer *n, real *t, integer *ldt, real *vl, integer *ldvl, real *vr, 
+        integer *ldvr, real *s, real *sep, integer *mm, integer *m, real *
+        work, integer *ldwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int strsyl_(char *trana, char *tranb, integer *isgn, integer 
+        *m, integer *n, real *a, integer *lda, real *b, integer *ldb, real *
+        c__, integer *ldc, real *scale, integer *info);
+ 
+/* Subroutine */ int strti2_(char *uplo, char *diag, integer *n, real *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int strtri_(char *uplo, char *diag, integer *n, real *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int strtrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, real *a, integer *lda, real *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int stzrqf_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, integer *info);
+ 
+/* Subroutine */ int stzrzf_(integer *m, integer *n, real *a, integer *lda, 
+        real *tau, real *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int xerbla_(char *srname, integer *info);
+ 
+/* Subroutine */ int zbdsqr_(char *uplo, integer *n, integer *ncvt, integer *
+        nru, integer *ncc, doublereal *d__, doublereal *e, doublecomplex *vt, 
+        integer *ldvt, doublecomplex *u, integer *ldu, doublecomplex *c__, 
+        integer *ldc, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zdrot_(integer *n, doublecomplex *cx, integer *incx, 
+        doublecomplex *cy, integer *incy, doublereal *c__, doublereal *s);
+ 
+/* Subroutine */ int zdrscl_(integer *n, doublereal *sa, doublecomplex *sx, 
+        integer *incx);
+ 
+/* Subroutine */ int zgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
+         integer *kl, integer *ku, doublecomplex *ab, integer *ldab, 
+        doublereal *d__, doublereal *e, doublecomplex *q, integer *ldq, 
+        doublecomplex *pt, integer *ldpt, doublecomplex *c__, integer *ldc, 
+        doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgbcon_(char *norm, integer *n, integer *kl, integer *ku,
+         doublecomplex *ab, integer *ldab, integer *ipiv, doublereal *anorm, 
+        doublereal *rcond, doublecomplex *work, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zgbequ_(integer *m, integer *n, integer *kl, integer *ku,
+         doublecomplex *ab, integer *ldab, doublereal *r__, doublereal *c__, 
+        doublereal *rowcnd, doublereal *colcnd, doublereal *amax, integer *
+        info);
+ 
+/* Subroutine */ int zgbrfs_(char *trans, integer *n, integer *kl, integer *
+        ku, integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex *
+        afb, integer *ldafb, integer *ipiv, doublecomplex *b, integer *ldb, 
+        doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+        doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgbsv_(integer *n, integer *kl, integer *ku, integer *
+        nrhs, doublecomplex *ab, integer *ldab, integer *ipiv, doublecomplex *
+        b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int zgbsvx_(char *fact, char *trans, integer *n, integer *kl,
+         integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab, 
+        doublecomplex *afb, integer *ldafb, integer *ipiv, char *equed, 
+        doublereal *r__, doublereal *c__, doublecomplex *b, integer *ldb, 
+        doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, 
+        doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zgbtf2_(integer *m, integer *n, integer *kl, integer *ku,
+         doublecomplex *ab, integer *ldab, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int zgbtrf_(integer *m, integer *n, integer *kl, integer *ku,
+         doublecomplex *ab, integer *ldab, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int zgbtrs_(char *trans, integer *n, integer *kl, integer *
+        ku, integer *nrhs, doublecomplex *ab, integer *ldab, integer *ipiv, 
+        doublecomplex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int zgebak_(char *job, char *side, integer *n, integer *ilo, 
+        integer *ihi, doublereal *scale, integer *m, doublecomplex *v, 
+        integer *ldv, integer *info);
+ 
+/* Subroutine */ int zgebal_(char *job, integer *n, doublecomplex *a, integer 
+        *lda, integer *ilo, integer *ihi, doublereal *scale, integer *info);
+ 
+/* Subroutine */ int zgebd2_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *d__, doublereal *e, doublecomplex *tauq, 
+        doublecomplex *taup, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zgebrd_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *d__, doublereal *e, doublecomplex *tauq, 
+        doublecomplex *taup, doublecomplex *work, integer *lwork, integer *
+        info);
+ 
+/* Subroutine */ int zgecon_(char *norm, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *anorm, doublereal *rcond, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgeequ_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, 
+        doublereal *colcnd, doublereal *amax, integer *info);
+ 
+/* Subroutine */ int zgees_(char *jobvs, char *sort, L_fp select, integer *n, 
+        doublecomplex *a, integer *lda, integer *sdim, doublecomplex *w, 
+        doublecomplex *vs, integer *ldvs, doublecomplex *work, integer *lwork,
+         doublereal *rwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int zgeesx_(char *jobvs, char *sort, L_fp select, char *
+        sense, integer *n, doublecomplex *a, integer *lda, integer *sdim, 
+        doublecomplex *w, doublecomplex *vs, integer *ldvs, doublereal *
+        rconde, doublereal *rcondv, doublecomplex *work, integer *lwork, 
+        doublereal *rwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int zgeev_(char *jobvl, char *jobvr, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *w, doublecomplex *vl, 
+        integer *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, 
+        integer *lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgeevx_(char *balanc, char *jobvl, char *jobvr, char *
+        sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w, 
+        doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, 
+        integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm, 
+        doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer *
+        lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgegs_(char *jobvsl, char *jobvsr, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, 
+        integer *ldvsl, doublecomplex *vsr, integer *ldvsr, doublecomplex *
+        work, integer *lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgegv_(char *jobvl, char *jobvr, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *alpha, doublecomplex *beta, doublecomplex *vl, integer 
+        *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, integer 
+        *lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgehd2_(integer *n, integer *ilo, integer *ihi, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *info);
+ 
+/* Subroutine */ int zgehrd_(integer *n, integer *ilo, integer *ihi, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zgelq2_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zgelqf_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zgels_(char *trans, integer *m, integer *n, integer *
+        nrhs, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zgelsx_(integer *m, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        integer *jpvt, doublereal *rcond, integer *rank, doublecomplex *work, 
+        doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgelsy_(integer *m, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        integer *jpvt, doublereal *rcond, integer *rank, doublecomplex *work, 
+        integer *lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgeql2_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zgeqlf_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zgeqp3_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, integer *jpvt, doublecomplex *tau, doublecomplex *work, 
+        integer *lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgeqpf_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, integer *jpvt, doublecomplex *tau, doublecomplex *work, 
+        doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgeqr2_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zgerfs_(char *trans, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, 
+        integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, 
+        integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work,
+         doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgerq2_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zgerqf_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zgesc2_(integer *n, doublecomplex *a, integer *lda, 
+        doublecomplex *rhs, integer *ipiv, integer *jpiv, doublereal *scale);
+ 
+/* Subroutine */ int zgesv_(integer *n, integer *nrhs, doublecomplex *a, 
+        integer *lda, integer *ipiv, doublecomplex *b, integer *ldb, integer *
+        info);
+ 
+/* Subroutine */ int zgesvx_(char *fact, char *trans, integer *n, integer *
+        nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
+        ldaf, integer *ipiv, char *equed, doublereal *r__, doublereal *c__, 
+        doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+        doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgetc2_(integer *n, doublecomplex *a, integer *lda, 
+        integer *ipiv, integer *jpiv, integer *info);
+ 
+/* Subroutine */ int zgetf2_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int zgetrf_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int zgetri_(integer *n, doublecomplex *a, integer *lda, 
+        integer *ipiv, doublecomplex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zgetrs_(char *trans, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, 
+        integer *ldb, integer *info);
+ 
+/* Subroutine */ int zggbak_(char *job, char *side, integer *n, integer *ilo, 
+        integer *ihi, doublereal *lscale, doublereal *rscale, integer *m, 
+        doublecomplex *v, integer *ldv, integer *info);
+ 
+/* Subroutine */ int zggbal_(char *job, integer *n, doublecomplex *a, integer 
+        *lda, doublecomplex *b, integer *ldb, integer *ilo, integer *ihi, 
+        doublereal *lscale, doublereal *rscale, doublereal *work, integer *
+        info);
+ 
+/* Subroutine */ int zgges_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+        delctg, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, 
+        integer *ldb, integer *sdim, doublecomplex *alpha, doublecomplex *
+        beta, doublecomplex *vsl, integer *ldvsl, doublecomplex *vsr, integer 
+        *ldvsr, doublecomplex *work, integer *lwork, doublereal *rwork, 
+        logical *bwork, integer *info);
+ 
+/* Subroutine */ int zggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+        delctg, char *sense, integer *n, doublecomplex *a, integer *lda, 
+        doublecomplex *b, integer *ldb, integer *sdim, doublecomplex *alpha, 
+        doublecomplex *beta, doublecomplex *vsl, integer *ldvsl, 
+        doublecomplex *vsr, integer *ldvsr, doublereal *rconde, doublereal *
+        rcondv, doublecomplex *work, integer *lwork, doublereal *rwork, 
+        integer *iwork, integer *liwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int zggev_(char *jobvl, char *jobvr, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *alpha, doublecomplex *beta, doublecomplex *vl, integer 
+        *ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, integer 
+        *lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zggevx_(char *balanc, char *jobvl, char *jobvr, char *
+        sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, 
+        integer *ldb, doublecomplex *alpha, doublecomplex *beta, 
+        doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, 
+        integer *ilo, integer *ihi, doublereal *lscale, doublereal *rscale, 
+        doublereal *abnrm, doublereal *bbnrm, doublereal *rconde, doublereal *
+        rcondv, doublecomplex *work, integer *lwork, doublereal *rwork, 
+        integer *iwork, logical *bwork, integer *info);
+ 
+/* Subroutine */ int zggglm_(integer *n, integer *m, integer *p, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *d__, doublecomplex *x, doublecomplex *y, doublecomplex 
+        *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zgghrd_(char *compq, char *compz, integer *n, integer *
+        ilo, integer *ihi, doublecomplex *a, integer *lda, doublecomplex *b, 
+        integer *ldb, doublecomplex *q, integer *ldq, doublecomplex *z__, 
+        integer *ldz, integer *info);
+ 
+/* Subroutine */ int zgglse_(integer *m, integer *n, integer *p, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *c__, doublecomplex *d__, doublecomplex *x, 
+        doublecomplex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zggqrf_(integer *n, integer *m, integer *p, 
+        doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b,
+         integer *ldb, doublecomplex *taub, doublecomplex *work, integer *
+        lwork, integer *info);
+ 
+/* Subroutine */ int zggrqf_(integer *m, integer *p, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *taua, doublecomplex *b,
+         integer *ldb, doublecomplex *taub, doublecomplex *work, integer *
+        lwork, integer *info);
+ 
+/* Subroutine */ int zggsvd_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *n, integer *p, integer *k, integer *l, doublecomplex *a, 
+        integer *lda, doublecomplex *b, integer *ldb, doublereal *alpha, 
+        doublereal *beta, doublecomplex *u, integer *ldu, doublecomplex *v, 
+        integer *ldv, doublecomplex *q, integer *ldq, doublecomplex *work, 
+        doublereal *rwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int zggsvp_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *p, integer *n, doublecomplex *a, integer *lda, doublecomplex 
+        *b, integer *ldb, doublereal *tola, doublereal *tolb, integer *k, 
+        integer *l, doublecomplex *u, integer *ldu, doublecomplex *v, integer 
+        *ldv, doublecomplex *q, integer *ldq, integer *iwork, doublereal *
+        rwork, doublecomplex *tau, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zgtcon_(char *norm, integer *n, doublecomplex *dl, 
+        doublecomplex *d__, doublecomplex *du, doublecomplex *du2, integer *
+        ipiv, doublereal *anorm, doublereal *rcond, doublecomplex *work, 
+        integer *info);
+ 
+/* Subroutine */ int zgtrfs_(char *trans, integer *n, integer *nrhs, 
+        doublecomplex *dl, doublecomplex *d__, doublecomplex *du, 
+        doublecomplex *dlf, doublecomplex *df, doublecomplex *duf, 
+        doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb, 
+        doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+        doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zgtsv_(integer *n, integer *nrhs, doublecomplex *dl, 
+        doublecomplex *d__, doublecomplex *du, doublecomplex *b, integer *ldb,
+         integer *info);
+ 
+/* Subroutine */ int zgtsvx_(char *fact, char *trans, integer *n, integer *
+        nrhs, doublecomplex *dl, doublecomplex *d__, doublecomplex *du, 
+        doublecomplex *dlf, doublecomplex *df, doublecomplex *duf, 
+        doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb, 
+        doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, 
+        doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zgttrf_(integer *n, doublecomplex *dl, doublecomplex *
+        d__, doublecomplex *du, doublecomplex *du2, integer *ipiv, integer *
+        info);
+ 
+/* Subroutine */ int zgttrs_(char *trans, integer *n, integer *nrhs, 
+        doublecomplex *dl, doublecomplex *d__, doublecomplex *du, 
+        doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zgtts2_(integer *itrans, integer *n, integer *nrhs, 
+        doublecomplex *dl, doublecomplex *d__, doublecomplex *du, 
+        doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb);
+ 
+/* Subroutine */ int zhbev_(char *jobz, char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, doublereal *w, doublecomplex *z__, 
+        integer *ldz, doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zhbevd_(char *jobz, char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, doublereal *w, doublecomplex *z__, 
+        integer *ldz, doublecomplex *work, integer *lwork, doublereal *rwork, 
+        integer *lrwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int zhbevx_(char *jobz, char *range, char *uplo, integer *n, 
+        integer *kd, doublecomplex *ab, integer *ldab, doublecomplex *q, 
+        integer *ldq, doublereal *vl, doublereal *vu, integer *il, integer *
+        iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__,
+         integer *ldz, doublecomplex *work, doublereal *rwork, integer *iwork,
+         integer *ifail, integer *info);
+ 
+/* Subroutine */ int zhbgst_(char *vect, char *uplo, integer *n, integer *ka, 
+        integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb, 
+        integer *ldbb, doublecomplex *x, integer *ldx, doublecomplex *work, 
+        doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zhbgv_(char *jobz, char *uplo, integer *n, integer *ka, 
+        integer *kb, doublecomplex *ab, integer *ldab, doublecomplex *bb, 
+        integer *ldbb, doublereal *w, doublecomplex *z__, integer *ldz, 
+        doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zhbgvx_(char *jobz, char *range, char *uplo, integer *n, 
+        integer *ka, integer *kb, doublecomplex *ab, integer *ldab, 
+        doublecomplex *bb, integer *ldbb, doublecomplex *q, integer *ldq, 
+        doublereal *vl, doublereal *vu, integer *il, integer *iu, doublereal *
+        abstol, integer *m, doublereal *w, doublecomplex *z__, integer *ldz, 
+        doublecomplex *work, doublereal *rwork, integer *iwork, integer *
+        ifail, integer *info);
+ 
+/* Subroutine */ int zhbtrd_(char *vect, char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, doublereal *d__, doublereal *e, 
+        doublecomplex *q, integer *ldq, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zhecon_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, doublereal *anorm, doublereal *rcond, 
+        doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zheev_(char *jobz, char *uplo, integer *n, doublecomplex 
+        *a, integer *lda, doublereal *w, doublecomplex *work, integer *lwork, 
+        doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n, 
+        doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work, 
+        integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, 
+        integer *liwork, integer *info);
+ 
+/* Subroutine */ int zheevr_(char *jobz, char *range, char *uplo, integer *n, 
+        doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, 
+        integer *il, integer *iu, doublereal *abstol, integer *m, doublereal *
+        w, doublecomplex *z__, integer *ldz, integer *isuppz, doublecomplex *
+        work, integer *lwork, doublereal *rwork, integer *lrwork, integer *
+        iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int zheevx_(char *jobz, char *range, char *uplo, integer *n, 
+        doublecomplex *a, integer *lda, doublereal *vl, doublereal *vu, 
+        integer *il, integer *iu, doublereal *abstol, integer *m, doublereal *
+        w, doublecomplex *z__, integer *ldz, doublecomplex *work, integer *
+        lwork, doublereal *rwork, integer *iwork, integer *ifail, integer *
+        info);
+ 
+/* Subroutine */ int zhegs2_(integer *itype, char *uplo, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zhegst_(integer *itype, char *uplo, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zhegv_(integer *itype, char *jobz, char *uplo, integer *
+        n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork,
+         integer *info);
+ 
+/* Subroutine */ int zhegvd_(integer *itype, char *jobz, char *uplo, integer *
+        n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublereal *w, doublecomplex *work, integer *lwork, doublereal *rwork,
+         integer *lrwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int zhegvx_(integer *itype, char *jobz, char *range, char *
+        uplo, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, 
+        integer *ldb, doublereal *vl, doublereal *vu, integer *il, integer *
+        iu, doublereal *abstol, integer *m, doublereal *w, doublecomplex *z__,
+         integer *ldz, doublecomplex *work, integer *lwork, doublereal *rwork,
+         integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int zherfs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, 
+        integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, 
+        integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work,
+         doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zhesv_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, 
+        integer *ldb, doublecomplex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zhesvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
+        ldaf, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x,
+         integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, 
+        doublecomplex *work, integer *lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zhetf2_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int zhetrd_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, 
+        doublecomplex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zhetrf_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, doublecomplex *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int zhetri_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zhetrs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, 
+        integer *ldb, integer *info);
+ 
+/* Subroutine */ int zhgeqz_(char *job, char *compq, char *compz, integer *n, 
+        integer *ilo, integer *ihi, doublecomplex *a, integer *lda, 
+        doublecomplex *b, integer *ldb, doublecomplex *alpha, doublecomplex *
+        beta, doublecomplex *q, integer *ldq, doublecomplex *z__, integer *
+        ldz, doublecomplex *work, integer *lwork, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zhpcon_(char *uplo, integer *n, doublecomplex *ap, 
+        integer *ipiv, doublereal *anorm, doublereal *rcond, doublecomplex *
+        work, integer *info);
+ 
+/* Subroutine */ int zhpev_(char *jobz, char *uplo, integer *n, doublecomplex 
+        *ap, doublereal *w, doublecomplex *z__, integer *ldz, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zhpevd_(char *jobz, char *uplo, integer *n, 
+        doublecomplex *ap, doublereal *w, doublecomplex *z__, integer *ldz, 
+        doublecomplex *work, integer *lwork, doublereal *rwork, integer *
+        lrwork, integer *iwork, integer *liwork, integer *info);
+ 
+/* Subroutine */ int zhpevx_(char *jobz, char *range, char *uplo, integer *n, 
+        doublecomplex *ap, doublereal *vl, doublereal *vu, integer *il, 
+        integer *iu, doublereal *abstol, integer *m, doublereal *w, 
+        doublecomplex *z__, integer *ldz, doublecomplex *work, doublereal *
+        rwork, integer *iwork, integer *ifail, integer *info);
+ 
+/* Subroutine */ int zhpgst_(integer *itype, char *uplo, integer *n, 
+        doublecomplex *ap, doublecomplex *bp, integer *info);
+ 
+/* Subroutine */ int zhpgv_(integer *itype, char *jobz, char *uplo, integer *
+        n, doublecomplex *ap, doublecomplex *bp, doublereal *w, doublecomplex 
+        *z__, integer *ldz, doublecomplex *work, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zhpgvd_(integer *itype, char *jobz, char *uplo, integer *
+        n, doublecomplex *ap, doublecomplex *bp, doublereal *w, doublecomplex 
+        *z__, integer *ldz, doublecomplex *work, integer *lwork, doublereal *
+        rwork, integer *lrwork, integer *iwork, integer *liwork, integer *
+        info);
+ 
+/* Subroutine */ int zhpgvx_(integer *itype, char *jobz, char *range, char *
+        uplo, integer *n, doublecomplex *ap, doublecomplex *bp, doublereal *
+        vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol, 
+        integer *m, doublereal *w, doublecomplex *z__, integer *ldz, 
+        doublecomplex *work, doublereal *rwork, integer *iwork, integer *
+        ifail, integer *info);
+ 
+/* Subroutine */ int zhprfs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, doublecomplex *afp, integer *ipiv, doublecomplex *
+        b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, 
+        doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zhpsv_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zhpsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublecomplex *ap, doublecomplex *afp, integer *ipiv, 
+        doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+        doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zhptrd_(char *uplo, integer *n, doublecomplex *ap, 
+        doublereal *d__, doublereal *e, doublecomplex *tau, integer *info);
+ 
+/* Subroutine */ int zhptrf_(char *uplo, integer *n, doublecomplex *ap, 
+        integer *ipiv, integer *info);
+ 
+/* Subroutine */ int zhptri_(char *uplo, integer *n, doublecomplex *ap, 
+        integer *ipiv, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zhptrs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zhsein_(char *side, char *eigsrc, char *initv, logical *
+        select, integer *n, doublecomplex *h__, integer *ldh, doublecomplex *
+        w, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr,
+         integer *mm, integer *m, doublecomplex *work, doublereal *rwork, 
+        integer *ifaill, integer *ifailr, integer *info);
+ 
+/* Subroutine */ int zhseqr_(char *job, char *compz, integer *n, integer *ilo,
+         integer *ihi, doublecomplex *h__, integer *ldh, doublecomplex *w, 
+        doublecomplex *z__, integer *ldz, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zlabrd_(integer *m, integer *n, integer *nb, 
+        doublecomplex *a, integer *lda, doublereal *d__, doublereal *e, 
+        doublecomplex *tauq, doublecomplex *taup, doublecomplex *x, integer *
+        ldx, doublecomplex *y, integer *ldy);
+ 
+/* Subroutine */ int zlacgv_(integer *n, doublecomplex *x, integer *incx);
+ 
+/* Subroutine */ int zlacon_(integer *n, doublecomplex *v, doublecomplex *x, 
+        doublereal *est, integer *kase);
+ 
+/* Subroutine */ int zlacp2_(char *uplo, integer *m, integer *n, doublereal *
+        a, integer *lda, doublecomplex *b, integer *ldb);
+ 
+/* Subroutine */ int zlacpy_(char *uplo, integer *m, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb);
+ 
+/* Subroutine */ int zlacrm_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *b, integer *ldb, doublecomplex *c__, 
+        integer *ldc, doublereal *rwork);
+ 
+/* Subroutine */ int zlacrt_(integer *n, doublecomplex *cx, integer *incx, 
+        doublecomplex *cy, integer *incy, doublecomplex *c__, doublecomplex *
+        s);
+ 
+/* Subroutine */ int zlaed0_(integer *qsiz, integer *n, doublereal *d__, 
+        doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore, 
+        integer *ldqs, doublereal *rwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int zlaed7_(integer *n, integer *cutpnt, integer *qsiz, 
+        integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, 
+        doublecomplex *q, integer *ldq, doublereal *rho, integer *indxq, 
+        doublereal *qstore, integer *qptr, integer *prmptr, integer *perm, 
+        integer *givptr, integer *givcol, doublereal *givnum, doublecomplex *
+        work, doublereal *rwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz, 
+        doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho, 
+        integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex *
+        q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx, 
+        integer *indxq, integer *perm, integer *givptr, integer *givcol, 
+        doublereal *givnum, integer *info);
+ 
+/* Subroutine */ int zlaein_(logical *rightv, logical *noinit, integer *n, 
+        doublecomplex *h__, integer *ldh, doublecomplex *w, doublecomplex *v, 
+        doublecomplex *b, integer *ldb, doublereal *rwork, doublereal *eps3, 
+        doublereal *smlnum, integer *info);
+ 
+/* Subroutine */ int zlaesy_(doublecomplex *a, doublecomplex *b, 
+        doublecomplex *c__, doublecomplex *rt1, doublecomplex *rt2, 
+        doublecomplex *evscal, doublecomplex *cs1, doublecomplex *sn1);
+ 
+/* Subroutine */ int zlaev2_(doublecomplex *a, doublecomplex *b, 
+        doublecomplex *c__, doublereal *rt1, doublereal *rt2, doublereal *cs1,
+         doublecomplex *sn1);
+ 
+/* Subroutine */ int zlags2_(logical *upper, doublereal *a1, doublecomplex *
+        a2, doublereal *a3, doublereal *b1, doublecomplex *b2, doublereal *b3,
+         doublereal *csu, doublecomplex *snu, doublereal *csv, doublecomplex *
+        snv, doublereal *csq, doublecomplex *snq);
+ 
+/* Subroutine */ int zlagtm_(char *trans, integer *n, integer *nrhs, 
+        doublereal *alpha, doublecomplex *dl, doublecomplex *d__, 
+        doublecomplex *du, doublecomplex *x, integer *ldx, doublereal *beta, 
+        doublecomplex *b, integer *ldb);
+ 
+/* Subroutine */ int zlahef_(char *uplo, integer *n, integer *nb, integer *kb,
+         doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *w, 
+        integer *ldw, integer *info);
+ 
+/* Subroutine */ int zlahqr_(logical *wantt, logical *wantz, integer *n, 
+        integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh, 
+        doublecomplex *w, integer *iloz, integer *ihiz, doublecomplex *z__, 
+        integer *ldz, integer *info);
+ 
+/* Subroutine */ int zlahrd_(integer *n, integer *k, integer *nb, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *t, 
+        integer *ldt, doublecomplex *y, integer *ldy);
+ 
+/* Subroutine */ int zlaic1_(integer *job, integer *j, doublecomplex *x, 
+        doublereal *sest, doublecomplex *w, doublecomplex *gamma, doublereal *
+        sestpr, doublecomplex *s, doublecomplex *c__);
+ 
+/* Subroutine */ int zlals0_(integer *icompq, integer *nl, integer *nr, 
+        integer *sqre, integer *nrhs, doublecomplex *b, integer *ldb, 
+        doublecomplex *bx, integer *ldbx, integer *perm, integer *givptr, 
+        integer *givcol, integer *ldgcol, doublereal *givnum, integer *ldgnum,
+         doublereal *poles, doublereal *difl, doublereal *difr, doublereal *
+        z__, integer *k, doublereal *c__, doublereal *s, doublereal *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int zlalsa_(integer *icompq, integer *smlsiz, integer *n, 
+        integer *nrhs, doublecomplex *b, integer *ldb, doublecomplex *bx, 
+        integer *ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *
+        k, doublereal *difl, doublereal *difr, doublereal *z__, doublereal *
+        poles, integer *givptr, integer *givcol, integer *ldgcol, integer *
+        perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal *
+        rwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int zlapll_(integer *n, doublecomplex *x, integer *incx, 
+        doublecomplex *y, integer *incy, doublereal *ssmin);
+ 
+/* Subroutine */ int zlapmt_(logical *forwrd, integer *m, integer *n, 
+        doublecomplex *x, integer *ldx, integer *k);
+ 
+/* Subroutine */ int zlaqgb_(integer *m, integer *n, integer *kl, integer *ku,
+         doublecomplex *ab, integer *ldab, doublereal *r__, doublereal *c__, 
+        doublereal *rowcnd, doublereal *colcnd, doublereal *amax, char *equed);
+ 
+/* Subroutine */ int zlaqge_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *r__, doublereal *c__, doublereal *rowcnd, 
+        doublereal *colcnd, doublereal *amax, char *equed);
+ 
+/* Subroutine */ int zlaqhb_(char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, doublereal *s, doublereal *scond, 
+        doublereal *amax, char *equed);
+ 
+/* Subroutine */ int zlaqhe_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *s, doublereal *scond, doublereal *amax, 
+        char *equed);
+ 
+/* Subroutine */ int zlaqhp_(char *uplo, integer *n, doublecomplex *ap, 
+        doublereal *s, doublereal *scond, doublereal *amax, char *equed);
+ 
+/* Subroutine */ int zlaqp2_(integer *m, integer *n, integer *offset, 
+        doublecomplex *a, integer *lda, integer *jpvt, doublecomplex *tau, 
+        doublereal *vn1, doublereal *vn2, doublecomplex *work);
+ 
+/* Subroutine */ int zlaqps_(integer *m, integer *n, integer *offset, integer 
+        *nb, integer *kb, doublecomplex *a, integer *lda, integer *jpvt, 
+        doublecomplex *tau, doublereal *vn1, doublereal *vn2, doublecomplex *
+        auxv, doublecomplex *f, integer *ldf);
+ 
+/* Subroutine */ int zlaqsb_(char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, doublereal *s, doublereal *scond, 
+        doublereal *amax, char *equed);
+ 
+/* Subroutine */ int zlaqsp_(char *uplo, integer *n, doublecomplex *ap, 
+        doublereal *s, doublereal *scond, doublereal *amax, char *equed);
+ 
+/* Subroutine */ int zlaqsy_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *s, doublereal *scond, doublereal *amax, 
+        char *equed);
+ 
+/* Subroutine */ int zlar1v_(integer *n, integer *b1, integer *bn, doublereal 
+        *sigma, doublereal *d__, doublereal *l, doublereal *ld, doublereal *
+        lld, doublereal *gersch, doublecomplex *z__, doublereal *ztz, 
+        doublereal *mingma, integer *r__, integer *isuppz, doublereal *work);
+ 
+/* Subroutine */ int zlar2v_(integer *n, doublecomplex *x, doublecomplex *y, 
+        doublecomplex *z__, integer *incx, doublereal *c__, doublecomplex *s, 
+        integer *incc);
+ 
+/* Subroutine */ int zlarcm_(integer *m, integer *n, doublereal *a, integer *
+        lda, doublecomplex *b, integer *ldb, doublecomplex *c__, integer *ldc,
+         doublereal *rwork);
+ 
+/* Subroutine */ int zlarf_(char *side, integer *m, integer *n, doublecomplex 
+        *v, integer *incv, doublecomplex *tau, doublecomplex *c__, integer *
+        ldc, doublecomplex *work);
+ 
+/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char *
+        storev, integer *m, integer *n, integer *k, doublecomplex *v, integer 
+        *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer *
+        ldc, doublecomplex *work, integer *ldwork);
+ 
+/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex *
+        x, integer *incx, doublecomplex *tau);
+ 
+/* Subroutine */ int zlarft_(char *direct, char *storev, integer *n, integer *
+        k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex *
+        t, integer *ldt);
+ 
+/* Subroutine */ int zlarfx_(char *side, integer *m, integer *n, 
+        doublecomplex *v, doublecomplex *tau, doublecomplex *c__, integer *
+        ldc, doublecomplex *work);
+ 
+/* Subroutine */ int zlargv_(integer *n, doublecomplex *x, integer *incx, 
+        doublecomplex *y, integer *incy, doublereal *c__, integer *incc);
+ 
+/* Subroutine */ int zlarnv_(integer *idist, integer *iseed, integer *n, 
+        doublecomplex *x);
+ 
+/* Subroutine */ int zlarrv_(integer *n, doublereal *d__, doublereal *l, 
+        integer *isplit, integer *m, doublereal *w, integer *iblock, 
+        doublereal *gersch, doublereal *tol, doublecomplex *z__, integer *ldz,
+         integer *isuppz, doublereal *work, integer *iwork, integer *info);
+ 
+/* Subroutine */ int zlartg_(doublecomplex *f, doublecomplex *g, doublereal *
+        cs, doublecomplex *sn, doublecomplex *r__);
+ 
+/* Subroutine */ int zlartv_(integer *n, doublecomplex *x, integer *incx, 
+        doublecomplex *y, integer *incy, doublereal *c__, doublecomplex *s, 
+        integer *incc);
+ 
+/* Subroutine */ int zlarz_(char *side, integer *m, integer *n, integer *l, 
+        doublecomplex *v, integer *incv, doublecomplex *tau, doublecomplex *
+        c__, integer *ldc, doublecomplex *work);
+ 
+/* Subroutine */ int zlarzb_(char *side, char *trans, char *direct, char *
+        storev, integer *m, integer *n, integer *k, integer *l, doublecomplex 
+        *v, integer *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, 
+        integer *ldc, doublecomplex *work, integer *ldwork);
+ 
+/* Subroutine */ int zlarzt_(char *direct, char *storev, integer *n, integer *
+        k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex *
+        t, integer *ldt);
+ 
+/* Subroutine */ int zlascl_(char *type__, integer *kl, integer *ku, 
+        doublereal *cfrom, doublereal *cto, integer *m, integer *n, 
+        doublecomplex *a, integer *lda, integer *info);
+ 
+/* Subroutine */ int zlaset_(char *uplo, integer *m, integer *n, 
+        doublecomplex *alpha, doublecomplex *beta, doublecomplex *a, integer *
+        lda);
+ 
+/* Subroutine */ int zlasr_(char *side, char *pivot, char *direct, integer *m,
+         integer *n, doublereal *c__, doublereal *s, doublecomplex *a, 
+        integer *lda);
+ 
+/* Subroutine */ int zlassq_(integer *n, doublecomplex *x, integer *incx, 
+        doublereal *scale, doublereal *sumsq);
+ 
+/* Subroutine */ int zlaswp_(integer *n, doublecomplex *a, integer *lda, 
+        integer *k1, integer *k2, integer *ipiv, integer *incx);
+ 
+/* Subroutine */ int zlasyf_(char *uplo, integer *n, integer *nb, integer *kb,
+         doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *w, 
+        integer *ldw, integer *info);
+ 
+/* Subroutine */ int zlatbs_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, integer *kd, doublecomplex *ab, integer *ldab, 
+        doublecomplex *x, doublereal *scale, doublereal *cnorm, integer *info);
+ 
+/* Subroutine */ int zlatdf_(integer *ijob, integer *n, doublecomplex *z__, 
+        integer *ldz, doublecomplex *rhs, doublereal *rdsum, doublereal *
+        rdscal, integer *ipiv, integer *jpiv);
+ 
+/* Subroutine */ int zlatps_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, doublecomplex *ap, doublecomplex *x, doublereal *
+        scale, doublereal *cnorm, integer *info);
+ 
+/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb, 
+        doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau, 
+        doublecomplex *w, integer *ldw);
+ 
+/* Subroutine */ int zlatrs_(char *uplo, char *trans, char *diag, char *
+        normin, integer *n, doublecomplex *a, integer *lda, doublecomplex *x, 
+        doublereal *scale, doublereal *cnorm, integer *info);
+ 
+/* Subroutine */ int zlatrz_(integer *m, integer *n, integer *l, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work);
+ 
+/* Subroutine */ int zlatzm_(char *side, integer *m, integer *n, 
+        doublecomplex *v, integer *incv, doublecomplex *tau, doublecomplex *
+        c1, doublecomplex *c2, integer *ldc, doublecomplex *work);
+ 
+/* Subroutine */ int zlauu2_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int zlauum_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int zpbcon_(char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, doublereal *anorm, doublereal *
+        rcond, doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zpbequ_(char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, doublereal *s, doublereal *scond, 
+        doublereal *amax, integer *info);
+ 
+/* Subroutine */ int zpbrfs_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *
+        ldafb, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx,
+         doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *
+        rwork, integer *info);
+ 
+/* Subroutine */ int zpbstf_(char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, integer *info);
+ 
+/* Subroutine */ int zpbsv_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, doublecomplex *ab, integer *ldab, doublecomplex *b, integer *
+        ldb, integer *info);
+ 
+/* Subroutine */ int zpbsvx_(char *fact, char *uplo, integer *n, integer *kd, 
+        integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex *afb, 
+        integer *ldafb, char *equed, doublereal *s, doublecomplex *b, integer 
+        *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *
+        ferr, doublereal *berr, doublecomplex *work, doublereal *rwork, 
+        integer *info);
+ 
+/* Subroutine */ int zpbtf2_(char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, integer *info);
+ 
+/* Subroutine */ int zpbtrf_(char *uplo, integer *n, integer *kd, 
+        doublecomplex *ab, integer *ldab, integer *info);
+ 
+/* Subroutine */ int zpbtrs_(char *uplo, integer *n, integer *kd, integer *
+        nrhs, doublecomplex *ab, integer *ldab, doublecomplex *b, integer *
+        ldb, integer *info);
+ 
+/* Subroutine */ int zpocon_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, doublereal *anorm, doublereal *rcond, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zpoequ_(integer *n, doublecomplex *a, integer *lda, 
+        doublereal *s, doublereal *scond, doublereal *amax, integer *info);
+ 
+/* Subroutine */ int zporfs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, 
+        doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+        doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *
+        rwork, integer *info);
+ 
+/* Subroutine */ int zposv_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zposvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
+        ldaf, char *equed, doublereal *s, doublecomplex *b, integer *ldb, 
+        doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, 
+        doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zpotf2_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int zpotrf_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int zpotri_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *info);
+ 
+/* Subroutine */ int zpotrs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zppcon_(char *uplo, integer *n, doublecomplex *ap, 
+        doublereal *anorm, doublereal *rcond, doublecomplex *work, doublereal 
+        *rwork, integer *info);
+ 
+/* Subroutine */ int zppequ_(char *uplo, integer *n, doublecomplex *ap, 
+        doublereal *s, doublereal *scond, doublereal *amax, integer *info);
+ 
+/* Subroutine */ int zpprfs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, doublecomplex *afp, doublecomplex *b, integer *ldb,
+         doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+        doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zppsv_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, doublecomplex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int zppsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublecomplex *ap, doublecomplex *afp, char *equed, doublereal *
+        s, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+        doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zpptrf_(char *uplo, integer *n, doublecomplex *ap, 
+        integer *info);
+ 
+/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap, 
+        integer *info);
+ 
+/* Subroutine */ int zpptrs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, doublecomplex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int zptcon_(integer *n, doublereal *d__, doublecomplex *e, 
+        doublereal *anorm, doublereal *rcond, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zptrfs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef, 
+        doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+        doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *
+        rwork, integer *info);
+ 
+/* Subroutine */ int zptsv_(integer *n, integer *nrhs, doublereal *d__, 
+        doublecomplex *e, doublecomplex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int zptsvx_(char *fact, integer *n, integer *nrhs, 
+        doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef, 
+        doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+        doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zpttrf_(integer *n, doublereal *d__, doublecomplex *e, 
+        integer *info);
+ 
+/* Subroutine */ int zpttrs_(char *uplo, integer *n, integer *nrhs, 
+        doublereal *d__, doublecomplex *e, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zptts2_(integer *iuplo, integer *n, integer *nrhs, 
+        doublereal *d__, doublecomplex *e, doublecomplex *b, integer *ldb);
+ 
+/* Subroutine */ int zrot_(integer *n, doublecomplex *cx, integer *incx, 
+        doublecomplex *cy, integer *incy, doublereal *c__, doublecomplex *s);
+ 
+/* Subroutine */ int zspcon_(char *uplo, integer *n, doublecomplex *ap, 
+        integer *ipiv, doublereal *anorm, doublereal *rcond, doublecomplex *
+        work, integer *info);
+ 
+/* Subroutine */ int zspmv_(char *uplo, integer *n, doublecomplex *alpha, 
+        doublecomplex *ap, doublecomplex *x, integer *incx, doublecomplex *
+        beta, doublecomplex *y, integer *incy);
+ 
+/* Subroutine */ int zspr_(char *uplo, integer *n, doublecomplex *alpha, 
+        doublecomplex *x, integer *incx, doublecomplex *ap);
+ 
+/* Subroutine */ int zsprfs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, doublecomplex *afp, integer *ipiv, doublecomplex *
+        b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, 
+        doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int zspsv_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zspsvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublecomplex *ap, doublecomplex *afp, integer *ipiv, 
+        doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+        doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zsptrf_(char *uplo, integer *n, doublecomplex *ap, 
+        integer *ipiv, integer *info);
+ 
+/* Subroutine */ int zsptri_(char *uplo, integer *n, doublecomplex *ap, 
+        integer *ipiv, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zsptrs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *ap, integer *ipiv, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int zstedc_(char *compz, integer *n, doublereal *d__, 
+        doublereal *e, doublecomplex *z__, integer *ldz, doublecomplex *work, 
+        integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, 
+        integer *liwork, integer *info);
+ 
+/* Subroutine */ int zstein_(integer *n, doublereal *d__, doublereal *e, 
+        integer *m, doublereal *w, integer *iblock, integer *isplit, 
+        doublecomplex *z__, integer *ldz, doublereal *work, integer *iwork, 
+        integer *ifail, integer *info);
+ 
+/* Subroutine */ int zsteqr_(char *compz, integer *n, doublereal *d__, 
+        doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work, 
+        integer *info);
+ 
+/* Subroutine */ int zsycon_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, doublereal *anorm, doublereal *rcond, 
+        doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zsymv_(char *uplo, integer *n, doublecomplex *alpha, 
+        doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, 
+        doublecomplex *beta, doublecomplex *y, integer *incy);
+ 
+/* Subroutine */ int zsyr_(char *uplo, integer *n, doublecomplex *alpha, 
+        doublecomplex *x, integer *incx, doublecomplex *a, integer *lda);
+ 
+/* Subroutine */ int zsyrfs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, doublecomplex *af, integer *ldaf, 
+        integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x, 
+        integer *ldx, doublereal *ferr, doublereal *berr, doublecomplex *work,
+         doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zsysv_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, 
+        integer *ldb, doublecomplex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zsysvx_(char *fact, char *uplo, integer *n, integer *
+        nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
+        ldaf, integer *ipiv, doublecomplex *b, integer *ldb, doublecomplex *x,
+         integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, 
+        doublecomplex *work, integer *lwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int zsytf2_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, integer *info);
+ 
+/* Subroutine */ int zsytrf_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, doublecomplex *work, integer *lwork, 
+        integer *info);
+ 
+/* Subroutine */ int zsytri_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, integer *ipiv, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zsytrs_(char *uplo, integer *n, integer *nrhs, 
+        doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b, 
+        integer *ldb, integer *info);
+ 
+/* Subroutine */ int ztbcon_(char *norm, char *uplo, char *diag, integer *n, 
+        integer *kd, doublecomplex *ab, integer *ldab, doublereal *rcond, 
+        doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int ztbrfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *kd, integer *nrhs, doublecomplex *ab, integer *ldab, 
+        doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, 
+        doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *
+        rwork, integer *info);
+ 
+/* Subroutine */ int ztbtrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *kd, integer *nrhs, doublecomplex *ab, integer *ldab, 
+        doublecomplex *b, integer *ldb, integer *info);
+ 
+/* Subroutine */ int ztgevc_(char *side, char *howmny, logical *select, 
+        integer *n, doublecomplex *a, integer *lda, doublecomplex *b, integer 
+        *ldb, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *
+        ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork,
+         integer *info);
+ 
+/* Subroutine */ int ztgex2_(logical *wantq, logical *wantz, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *q, integer *ldq, doublecomplex *z__, integer *ldz, 
+        integer *j1, integer *info);
+ 
+/* Subroutine */ int ztgexc_(logical *wantq, logical *wantz, integer *n, 
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *q, integer *ldq, doublecomplex *z__, integer *ldz, 
+        integer *ifst, integer *ilst, integer *info);
+ 
+/* Subroutine */ int ztgsen_(integer *ijob, logical *wantq, logical *wantz, 
+        logical *select, integer *n, doublecomplex *a, integer *lda, 
+        doublecomplex *b, integer *ldb, doublecomplex *alpha, doublecomplex *
+        beta, doublecomplex *q, integer *ldq, doublecomplex *z__, integer *
+        ldz, integer *m, doublereal *pl, doublereal *pr, doublereal *dif, 
+        doublecomplex *work, integer *lwork, integer *iwork, integer *liwork, 
+        integer *info);
+ 
+/* Subroutine */ int ztgsja_(char *jobu, char *jobv, char *jobq, integer *m, 
+        integer *p, integer *n, integer *k, integer *l, doublecomplex *a, 
+        integer *lda, doublecomplex *b, integer *ldb, doublereal *tola, 
+        doublereal *tolb, doublereal *alpha, doublereal *beta, doublecomplex *
+        u, integer *ldu, doublecomplex *v, integer *ldv, doublecomplex *q, 
+        integer *ldq, doublecomplex *work, integer *ncycle, integer *info);
+ 
+/* Subroutine */ int ztgsna_(char *job, char *howmny, logical *select, 
+        integer *n, doublecomplex *a, integer *lda, doublecomplex *b, integer 
+        *ldb, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *
+        ldvr, doublereal *s, doublereal *dif, integer *mm, integer *m, 
+        doublecomplex *work, integer *lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int ztgsy2_(char *trans, integer *ijob, integer *m, integer *
+        n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *c__, integer *ldc, doublecomplex *d__, integer *ldd, 
+        doublecomplex *e, integer *lde, doublecomplex *f, integer *ldf, 
+        doublereal *scale, doublereal *rdsum, doublereal *rdscal, integer *
+        info);
+ 
+/* Subroutine */ int ztgsyl_(char *trans, integer *ijob, integer *m, integer *
+        n, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
+        doublecomplex *c__, integer *ldc, doublecomplex *d__, integer *ldd, 
+        doublecomplex *e, integer *lde, doublecomplex *f, integer *ldf, 
+        doublereal *scale, doublereal *dif, doublecomplex *work, integer *
+        lwork, integer *iwork, integer *info);
+ 
+/* Subroutine */ int ztpcon_(char *norm, char *uplo, char *diag, integer *n, 
+        doublecomplex *ap, doublereal *rcond, doublecomplex *work, doublereal 
+        *rwork, integer *info);
+ 
+/* Subroutine */ int ztprfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, doublecomplex *ap, doublecomplex *b, integer *ldb, 
+        doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr, 
+        doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int ztptri_(char *uplo, char *diag, integer *n, 
+        doublecomplex *ap, integer *info);
+ 
+/* Subroutine */ int ztptrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, doublecomplex *ap, doublecomplex *b, integer *ldb, 
+        integer *info);
+ 
+/* Subroutine */ int ztrcon_(char *norm, char *uplo, char *diag, integer *n, 
+        doublecomplex *a, integer *lda, doublereal *rcond, doublecomplex *
+        work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int ztrevc_(char *side, char *howmny, logical *select, 
+        integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl, 
+        integer *ldvl, doublecomplex *vr, integer *ldvr, integer *mm, integer 
+        *m, doublecomplex *work, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int ztrexc_(char *compq, integer *n, doublecomplex *t, 
+        integer *ldt, doublecomplex *q, integer *ldq, integer *ifst, integer *
+        ilst, integer *info);
+ 
+/* Subroutine */ int ztrrfs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, doublecomplex *a, integer *lda, doublecomplex *b, 
+        integer *ldb, doublecomplex *x, integer *ldx, doublereal *ferr, 
+        doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
+        info);
+ 
+/* Subroutine */ int ztrsen_(char *job, char *compq, logical *select, integer 
+        *n, doublecomplex *t, integer *ldt, doublecomplex *q, integer *ldq, 
+        doublecomplex *w, integer *m, doublereal *s, doublereal *sep, 
+        doublecomplex *work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int ztrsna_(char *job, char *howmny, logical *select, 
+        integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl, 
+        integer *ldvl, doublecomplex *vr, integer *ldvr, doublereal *s, 
+        doublereal *sep, integer *mm, integer *m, doublecomplex *work, 
+        integer *ldwork, doublereal *rwork, integer *info);
+ 
+/* Subroutine */ int ztrsyl_(char *trana, char *tranb, integer *isgn, integer 
+        *m, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, 
+        integer *ldb, doublecomplex *c__, integer *ldc, doublereal *scale, 
+        integer *info);
+ 
+/* Subroutine */ int ztrti2_(char *uplo, char *diag, integer *n, 
+        doublecomplex *a, integer *lda, integer *info);
+ 
+/* Subroutine */ int ztrtri_(char *uplo, char *diag, integer *n, 
+        doublecomplex *a, integer *lda, integer *info);
+ 
+/* Subroutine */ int ztrtrs_(char *uplo, char *trans, char *diag, integer *n, 
+        integer *nrhs, doublecomplex *a, integer *lda, doublecomplex *b, 
+        integer *ldb, integer *info);
+ 
+/* Subroutine */ int ztzrqf_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, integer *info);
+ 
+/* Subroutine */ int ztzrzf_(integer *m, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zung2l_(integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *info);
+ 
+/* Subroutine */ int zung2r_(integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *info);
+ 
+/* Subroutine */ int zungbr_(char *vect, integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zunghr_(integer *n, integer *ilo, integer *ihi, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zungl2_(integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *info);
+ 
+/* Subroutine */ int zunglq_(integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zungql_(integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zungr2_(integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *info);
+ 
+/* Subroutine */ int zungrq_(integer *m, integer *n, integer *k, 
+        doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zungtr_(char *uplo, integer *n, doublecomplex *a, 
+        integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zunm2l_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zunm2r_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zunmbr_(char *vect, char *side, char *trans, integer *m, 
+        integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex 
+        *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, integer *
+        lwork, integer *info);
+ 
+/* Subroutine */ int zunmhr_(char *side, char *trans, integer *m, integer *n, 
+        integer *ilo, integer *ihi, doublecomplex *a, integer *lda, 
+        doublecomplex *tau, doublecomplex *c__, integer *ldc, doublecomplex *
+        work, integer *lwork, integer *info);
+ 
+/* Subroutine */ int zunml2_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zunmlq_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zunmql_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zunmqr_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zunmr2_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info);
+ 
+/* Subroutine */ int zunmr3_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, integer *l, doublecomplex *a, integer *lda, doublecomplex 
+        *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, integer *
+        info);
+ 
+/* Subroutine */ int zunmrq_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zunmrz_(char *side, char *trans, integer *m, integer *n, 
+        integer *k, integer *l, doublecomplex *a, integer *lda, doublecomplex 
+        *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, integer *
+        lwork, integer *info);
+ 
+/* Subroutine */ int zunmtr_(char *side, char *uplo, char *trans, integer *m, 
+        integer *n, doublecomplex *a, integer *lda, doublecomplex *tau, 
+        doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork,
+         integer *info);
+ 
+/* Subroutine */ int zupgtr_(char *uplo, integer *n, doublecomplex *ap, 
+        doublecomplex *tau, doublecomplex *q, integer *ldq, doublecomplex *
+        work, integer *info);
+ 
+/* Subroutine */ int zupmtr_(char *side, char *uplo, char *trans, integer *m, 
+        integer *n, doublecomplex *ap, doublecomplex *tau, doublecomplex *c__,
+         integer *ldc, doublecomplex *work, integer *info);
+
+#endif /* __CLAPACK_H */
diff --git a/lib/LAPACK/f2c.h b/lib/LAPACK/f2c.h
new file mode 100644
index 0000000..b94ee7c
--- /dev/null
+++ b/lib/LAPACK/f2c.h
@@ -0,0 +1,223 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+        - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+typedef long int integer;
+typedef unsigned long int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+typedef long int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+#ifdef INTEGER_STAR_8   /* Adjust for integer*8. */
+typedef long long longint;              /* system-dependent */
+typedef unsigned long long ulongint;    /* system-dependent */
+#define qbit_clear(a,b) ((a) & ~((ulongint)1 << (b)))
+#define qbit_set(a,b)   ((a) |  ((ulongint)1 << (b)))
+#endif
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+#ifdef f2c_i2
+/* for -i2 */
+typedef short flag;
+typedef short ftnlen;
+typedef short ftnint;
+#else
+typedef long int flag;
+typedef long int ftnlen;
+typedef long int ftnint;
+#endif
+
+/*external read, write*/
+typedef struct
+{       flag cierr;
+        ftnint ciunit;
+        flag ciend;
+        char *cifmt;
+        ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{       flag icierr;
+        char *iciunit;
+        flag iciend;
+        char *icifmt;
+        ftnint icirlen;
+        ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{       flag oerr;
+        ftnint ounit;
+        char *ofnm;
+        ftnlen ofnmlen;
+        char *osta;
+        char *oacc;
+        char *ofm;
+        ftnint orl;
+        char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{       flag cerr;
+        ftnint cunit;
+        char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{       flag aerr;
+        ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{       flag inerr;
+        ftnint inunit;
+        char *infile;
+        ftnlen infilen;
+        ftnint  *inex;  /*parameters in standard's order*/
+        ftnint  *inopen;
+        ftnint  *innum;
+        ftnint  *innamed;
+        char    *inname;
+        ftnlen  innamlen;
+        char    *inacc;
+        ftnlen  inacclen;
+        char    *inseq;
+        ftnlen  inseqlen;
+        char    *indir;
+        ftnlen  indirlen;
+        char    *infmt;
+        ftnlen  infmtlen;
+        char    *inform;
+        ftnint  informlen;
+        char    *inunf;
+        ftnlen  inunflen;
+        ftnint  *inrecl;
+        ftnint  *innrec;
+        char    *inblank;
+        ftnlen  inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {       /* for multiple entry points */
+        integer1 g;
+        shortint h;
+        integer i;
+        /* longint j; */
+        real r;
+        doublereal d;
+        complex c;
+        doublecomplex z;
+        };
+
+typedef union Multitype Multitype;
+
+/*typedef long int Long;*/      /* No longer used; formerly in Namelist */
+
+struct Vardesc {        /* for Namelist */
+        char *name;
+        char *addr;
+        ftnlen *dims;
+        int  type;
+        };
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+        char *name;
+        Vardesc **vars;
+        int nvars;
+        };
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (doublereal)abs(x)
+#define min(a,b) ((a) <= (b) ? (a) : (b))
+#define max(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (doublereal)min(a,b)
+#define dmax(a,b) (doublereal)max(a,b)
+#define bit_test(a,b)   ((a) >> (b) & 1)
+#define bit_clear(a,b)  ((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)    ((a) |  ((uinteger)1 << (b)))
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef int /* Unknown procedure type */ (*U_fp)(...);
+typedef shortint (*J_fp)(...);
+typedef integer (*I_fp)(...);
+typedef real (*R_fp)(...);
+typedef doublereal (*D_fp)(...), (*E_fp)(...);
+typedef /* Complex */ VOID (*C_fp)(...);
+typedef /* Double Complex */ VOID (*Z_fp)(...);
+typedef logical (*L_fp)(...);
+typedef shortlogical (*K_fp)(...);
+typedef /* Character */ VOID (*H_fp)(...);
+typedef /* Subroutine */ int (*S_fp)(...);
+#else
+typedef int /* Unknown procedure type */ (*U_fp)();
+typedef shortint (*J_fp)();
+typedef integer (*I_fp)();
+typedef real (*R_fp)();
+typedef doublereal (*D_fp)(), (*E_fp)();
+typedef /* Complex */ VOID (*C_fp)();
+typedef /* Double Complex */ VOID (*Z_fp)();
+typedef logical (*L_fp)();
+typedef shortlogical (*K_fp)();
+typedef /* Character */ VOID (*H_fp)();
+typedef /* Subroutine */ int (*S_fp)();
+#endif
+/* E_fp is for real functions when -R is not specified */
+typedef VOID C_f;       /* complex function */
+typedef VOID H_f;       /* character function */
+typedef VOID Z_f;       /* double complex function */
+typedef doublereal E_f; /* real function with -R not specified */
+
+/* undef any lower-case symbols that your C compiler predefines, e.g.: */
+
+#ifndef Skip_f2c_Undefs
+#undef cray
+#undef gcos
+#undef mc68010
+#undef mc68020
+#undef mips
+#undef pdp11
+#undef sgi
+#undef sparc
+#undef sun
+#undef sun2
+#undef sun3
+#undef sun4
+#undef u370
+#undef u3b
+#undef u3b2
+#undef u3b5
+#undef unix
+#undef vax
+#endif
+#endif
diff --git a/lib/LAPACK/lapack-aux.c b/lib/LAPACK/lapack-aux.c
new file mode 100644
index 0000000..3e8c015
--- /dev/null
+++ b/lib/LAPACK/lapack-aux.c
@@ -0,0 +1,579 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include <time.h>
+#include "lapack-aux.h"
+
+#define MACRO(B) do {B} while (0)
+#define ERROR(CODE) MACRO(return CODE;)
+#define REQUIRES(COND, CODE) MACRO(if(!(COND)) {ERROR(CODE);})
+
+#define MIN(A,B) ((A)<(B)?(A):(B))
+#define MAX(A,B) ((A)>(B)?(A):(B))
+ 
+#ifdef DBGL
+#define DEBUGMSG(M) printf("LAPACK Wrapper "M"\n: "); size_t t0 = time(NULL);
+#define OK MACRO(printf("%ld s\n",time(0)-t0); return 0;);
+#else
+#define DEBUGMSG(M)
+#define OK return 0;
+#endif
+
+#define CHECK(RES,CODE) MACRO(if(RES) return CODE;)
+
+#define BAD_SIZE 1000
+#define BAD_CODE 1001
+#define MEM      1002
+#define BAD_FILE 1003
+#define SINGULAR 1004
+#define NOCONVER 1005
+
+//////////////////// real svd ////////////////////////////////////
+
+int svd_l_R(KDMAT(a),DMAT(u), DVEC(s),DMAT(v)) {
+    integer m = ar;
+    integer n = ac;
+    integer q = MIN(m,n);
+    REQUIRES(ur==m && uc==m && sn==q && vr==n && vc==n,BAD_SIZE);
+    DEBUGMSG("svd_l_R");
+    double *B = (double*)malloc(m*n*sizeof(double));
+    CHECK(!B,MEM);
+    memcpy(B,ap,m*n*sizeof(double));
+    integer lwork = -1;
+    integer res;
+    // ask for optimal lwork
+    double ans;
+    //printf("ask zgesvd\n");
+    char* job = "A";
+    dgesvd_ (job,job,
+             &m,&n,B,&m,
+             sp,
+             up,&m,
+             vp,&n,
+             &ans, &lwork,
+             &res);
+    lwork = ceil(ans);
+    //printf("ans = %d\n",lwork);
+    double * work = (double*)malloc(lwork*sizeof(double));
+    CHECK(!work,MEM);
+    //printf("dgesdd\n");
+    dgesvd_ (job,job,
+             &m,&n,B,&m,
+             sp,
+             up,&m,
+             vp,&n,
+             work, &lwork,
+             &res);
+    CHECK(res,res);
+    free(work);
+    free(B);
+    OK
+}
+
+// (alternative version)
+
+int svd_l_Rdd(KDMAT(a),DMAT(u), DVEC(s),DMAT(v)) {
+    integer m = ar;
+    integer n = ac;
+    integer q = MIN(m,n);
+    REQUIRES(ur==m && uc==m && sn==q && vr==n && vc==n,BAD_SIZE);
+    DEBUGMSG("svd_l_Rdd");
+    double *B = (double*)malloc(m*n*sizeof(double));
+    CHECK(!B,MEM);
+    memcpy(B,ap,m*n*sizeof(double));
+    integer* iwk = (integer*) malloc(8*q*sizeof(int));
+    CHECK(!iwk,MEM);
+    integer lwk = -1;
+    integer res;
+    // ask for optimal lwk
+    double ans;
+    //printf("ask dgesdd\n");
+    dgesdd_ ("A",&m,&n,B,&m,sp,up,&m,vp,&n,&ans,&lwk,iwk,&res);
+    lwk = 2*ceil(ans); // ????? otherwise 50x100 rejects lwk
+    //printf("lwk = %d\n",lwk);
+    double * workv = (double*)malloc(lwk*sizeof(double));
+    CHECK(!workv,MEM);
+    //printf("dgesdd\n");
+    dgesdd_ ("A",&m,&n,B,&m,sp,up,&m,vp,&n,workv,&lwk,iwk,&res);
+    CHECK(res,res);
+    free(iwk);
+    free(workv);
+    free(B);
+    OK
+}
+
+//////////////////// complex svd ////////////////////////////////////
+
+// not in clapack.h
+
+int zgesvd_(char *jobu, char *jobvt, integer *m, integer *n, 
+    doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u, 
+    integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work, 
+    integer *lwork, doublereal *rwork, integer *info);
+
+int svd_l_C(KCMAT(a),CMAT(u), DVEC(s),CMAT(v)) {
+    integer m = ar;
+    integer n = ac;
+    integer q = MIN(m,n);
+    REQUIRES(ur==m && uc==m && sn==q && vr==n && vc==n,BAD_SIZE);
+    DEBUGMSG("svd_l_C");
+    double *B = (double*)malloc(2*m*n*sizeof(double));
+    CHECK(!B,MEM);
+    memcpy(B,ap,m*n*2*sizeof(double));
+
+    double *rwork = (double*) malloc(5*q*sizeof(double));
+    CHECK(!rwork,MEM);
+    integer lwork = -1;
+    integer res;
+    // ask for optimal lwork
+    doublecomplex ans;
+    //printf("ask zgesvd\n");
+    char* job = "A";
+    zgesvd_ (job,job,
+             &m,&n,(doublecomplex*)B,&m,
+             sp,
+             (doublecomplex*)up,&m,
+             (doublecomplex*)vp,&n,
+             &ans, &lwork,
+             rwork,
+             &res);
+    lwork = ceil(ans.r);
+    //printf("ans = %d\n",lwork);
+    doublecomplex * work = (doublecomplex*)malloc(lwork*2*sizeof(double));
+    CHECK(!work,MEM);
+    //printf("zgesvd\n");
+    zgesvd_ (job,job,
+             &m,&n,(doublecomplex*)B,&m,
+             sp,
+             (doublecomplex*)up,&m,
+             (doublecomplex*)vp,&n,
+             work, &lwork,
+             rwork,
+             &res);
+    CHECK(res,res);
+    free(work);
+    free(rwork);
+    free(B);
+    OK
+}
+
+
+
+//////////////////// general complex eigensystem ////////////
+
+int eig_l_C(KCMAT(a),CMAT(u), CVEC(s),CMAT(v)) {
+    integer n = ar;
+    REQUIRES(n>=2 && (ur==1 || (ur==n && uc==n)) && sn==n && (vr==1 || (vr==n && vc==n)),BAD_SIZE);
+    DEBUGMSG("eig_l_C");
+    double *B = (double*)malloc(2*n*n*sizeof(double));
+    CHECK(!B,MEM);
+    memcpy(B,ap,n*n*2*sizeof(double));
+
+    double *rwork = (double*) malloc(2*n*sizeof(double));
+    CHECK(!rwork,MEM);
+    integer lwork = -1;
+    char jobvl = ur==1?'N':'V';
+    char jobvr = vr==1?'N':'V';
+    integer res;
+    // ask for optimal lwork
+    doublecomplex ans;
+    //printf("ask zgeev\n");
+    zgeev_  (&jobvl,&jobvr,
+             &n,(doublecomplex*)B,&n,
+             (doublecomplex*)sp,
+             (doublecomplex*)up,&n,
+             (doublecomplex*)vp,&n,
+             &ans, &lwork,
+             rwork,
+             &res);
+    lwork = ceil(ans.r);
+    //printf("ans = %d\n",lwork);
+    doublecomplex * work = (doublecomplex*)malloc(lwork*2*sizeof(double));
+    CHECK(!work,MEM);
+    //printf("zgeev\n");
+    zgeev_  (&jobvl,&jobvr,
+             &n,(doublecomplex*)B,&n,
+             (doublecomplex*)sp,
+             (doublecomplex*)up,&n,
+             (doublecomplex*)vp,&n,
+             work, &lwork,
+             rwork,
+             &res);
+    CHECK(res,res);
+    free(work);
+    free(rwork);
+    free(B);
+    OK
+}
+
+
+
+//////////////////// general real eigensystem ////////////
+
+int eig_l_R(KDMAT(a),DMAT(u), CVEC(s),DMAT(v)) {
+    integer n = ar;
+    REQUIRES(n>=2 && (ur==1 || (ur==n && uc==n)) && sn==n && (vr==1 || (vr==n && vc==n)),BAD_SIZE);
+    DEBUGMSG("eig_l_R");
+    double *B = (double*)malloc(n*n*sizeof(double));
+    CHECK(!B,MEM);
+    memcpy(B,ap,n*n*sizeof(double));
+    integer lwork = -1;
+    char jobvl = ur==1?'N':'V';
+    char jobvr = vr==1?'N':'V';
+    integer res;
+    // ask for optimal lwork
+    double ans;
+    //printf("ask dgeev\n");
+    dgeev_  (&jobvl,&jobvr,
+             &n,B,&n,
+             sp, sp+n,
+             up,&n,
+             vp,&n,
+             &ans, &lwork,
+             &res);
+    lwork = ceil(ans);
+    //printf("ans = %d\n",lwork);
+    double * work = (double*)malloc(lwork*sizeof(double));
+    CHECK(!work,MEM);
+    //printf("dgeev\n");
+    dgeev_  (&jobvl,&jobvr,
+             &n,B,&n,
+             sp, sp+n,
+             up,&n,
+             vp,&n,
+             work, &lwork,
+             &res);
+    CHECK(res,res);
+    free(work);
+    free(B);
+    OK
+}
+
+
+//////////////////// symmetric real eigensystem ////////////
+
+
+int eig_l_S(KDMAT(a),DVEC(s),DMAT(v)) {
+    integer n = ar;
+    REQUIRES(n>=2 && sn==n && (vr==1 || (vr==n && vc==n)),BAD_SIZE);
+    DEBUGMSG("eig_l_S");
+    memcpy(vp,ap,n*n*sizeof(double));
+    integer lwork = -1;
+    char jobz = vr==1?'N':'V';
+    char uplo = 'U';
+    integer res;
+    // ask for optimal lwork
+    double ans;
+    //printf("ask dsyev\n");
+    dsyev_  (&jobz,&uplo,
+             &n,vp,&n,
+             sp,
+             &ans, &lwork,
+             &res);
+    lwork = ceil(ans);
+    //printf("ans = %d\n",lwork);
+    double * work = (double*)malloc(lwork*sizeof(double));
+    CHECK(!work,MEM);
+    dsyev_  (&jobz,&uplo,
+             &n,vp,&n,
+             sp,
+             work, &lwork,
+             &res);
+    CHECK(res,res);
+    free(work);
+    OK
+}
+
+//////////////////// hermitian complex eigensystem ////////////
+
+int eig_l_H(KCMAT(a),DVEC(s),CMAT(v)) {
+    integer n = ar;
+    REQUIRES(n>=2 && sn==n && (vr==1 || (vr==n && vc==n)),BAD_SIZE);
+    DEBUGMSG("eig_l_H");
+    memcpy(vp,ap,2*n*n*sizeof(double));
+    double *rwork = (double*) malloc((3*n-2)*sizeof(double));
+    CHECK(!rwork,MEM);
+    integer lwork = -1;
+    char jobz = vr==1?'N':'V';
+    char uplo = 'U';
+    integer res;
+    // ask for optimal lwork
+    doublecomplex ans;
+    //printf("ask zheev\n");
+    zheev_  (&jobz,&uplo,
+             &n,(doublecomplex*)vp,&n,
+             sp,
+             &ans, &lwork,
+             rwork,
+             &res);
+    lwork = ceil(ans.r);
+    //printf("ans = %d\n",lwork);
+    doublecomplex * work = (doublecomplex*)malloc(lwork*2*sizeof(double));
+    CHECK(!work,MEM);
+    zheev_  (&jobz,&uplo,
+             &n,(doublecomplex*)vp,&n,
+             sp,
+             work, &lwork,
+             rwork,
+             &res);
+    CHECK(res,res);
+    free(work);
+    free(rwork);
+    OK
+}
+
+//////////////////// general real linear system ////////////
+
+int linearSolveR_l(KDMAT(a),KDMAT(b),DMAT(x)) {
+    integer n = ar;
+    integer nhrs = bc;
+    REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE);
+    DEBUGMSG("linearSolveR_l");
+    double*AC = (double*)malloc(n*n*sizeof(double));
+    memcpy(AC,ap,n*n*sizeof(double));
+    memcpy(xp,bp,n*nhrs*sizeof(double));
+    integer * ipiv = (integer*)malloc(n*sizeof(integer));
+    integer res;
+    dgesv_  (&n,&nhrs,
+             AC, &n,
+             ipiv,
+             xp, &n,
+             &res);
+    if(res>0) {
+        return SINGULAR;
+    }
+    CHECK(res,res);
+    free(ipiv);
+    free(AC);
+    OK
+}
+
+//////////////////// general complex linear system ////////////
+
+int linearSolveC_l(KCMAT(a),KCMAT(b),CMAT(x)) {
+    integer n = ar;
+    integer nhrs = bc;
+    REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE);
+    DEBUGMSG("linearSolveC_l");
+    double*AC = (double*)malloc(2*n*n*sizeof(double));
+    memcpy(AC,ap,2*n*n*sizeof(double));
+    memcpy(xp,bp,2*n*nhrs*sizeof(double));
+    integer * ipiv = (integer*)malloc(n*sizeof(integer));
+    integer res;
+    zgesv_  (&n,&nhrs,
+             (doublecomplex*)AC, &n,
+             ipiv,
+             (doublecomplex*)xp, &n,
+             &res);
+    if(res>0) {
+        return SINGULAR;
+    }
+    CHECK(res,res);
+    free(ipiv);
+    free(AC);
+    OK
+}
+
+//////////////////// least squares real linear system ////////////
+
+int linearSolveLSR_l(KDMAT(a),KDMAT(b),DMAT(x)) {
+    integer m = ar;
+    integer n = ac;
+    integer nrhs = bc;
+    integer ldb = xr;
+    REQUIRES(m>=1 && n>=1 && ar==br && xr==MAX(m,n) && xc == bc, BAD_SIZE);
+    DEBUGMSG("linearSolveLSR_l");
+    double*AC = (double*)malloc(m*n*sizeof(double));
+    memcpy(AC,ap,m*n*sizeof(double));
+    if (m>=n) {
+        memcpy(xp,bp,m*nrhs*sizeof(double));
+    } else {
+        int k;
+        for(k = 0; k<nrhs; k++) {
+            memcpy(xp+ldb*k,bp+m*k,m*sizeof(double));
+        }
+    }
+    integer res;
+    integer lwork = -1;
+    double ans;
+    dgels_  ("N",&m,&n,&nrhs,
+             AC,&m,
+             xp,&ldb,
+             &ans,&lwork,
+             &res);
+    lwork = ceil(ans);
+    //printf("ans = %d\n",lwork);
+    double * work = (double*)malloc(lwork*sizeof(double));
+    dgels_  ("N",&m,&n,&nrhs,
+             AC,&m,
+             xp,&ldb,
+             work,&lwork,
+             &res);
+    if(res>0) {
+        return SINGULAR;
+    }
+    CHECK(res,res);
+    free(work);
+    free(AC);
+    OK
+}
+
+//////////////////// least squares complex linear system ////////////
+
+int linearSolveLSC_l(KCMAT(a),KCMAT(b),CMAT(x)) {
+    integer m = ar;
+    integer n = ac;
+    integer nrhs = bc;
+    integer ldb = xr;
+    REQUIRES(m>=1 && n>=1 && ar==br && xr==MAX(m,n) && xc == bc, BAD_SIZE);
+    DEBUGMSG("linearSolveLSC_l");
+    double*AC = (double*)malloc(2*m*n*sizeof(double));
+    memcpy(AC,ap,2*m*n*sizeof(double));
+    memcpy(AC,ap,2*m*n*sizeof(double));
+    if (m>=n) {
+        memcpy(xp,bp,2*m*nrhs*sizeof(double));
+    } else {
+        int k;
+        for(k = 0; k<nrhs; k++) {
+            memcpy(xp+2*ldb*k,bp+2*m*k,m*2*sizeof(double));
+        }
+    }
+    integer res;
+    integer lwork = -1;
+    doublecomplex ans;
+    zgels_  ("N",&m,&n,&nrhs,
+             (doublecomplex*)AC,&m,
+             (doublecomplex*)xp,&ldb,
+             &ans,&lwork,
+             &res);
+    lwork = ceil(ans.r);
+    //printf("ans = %d\n",lwork);
+    doublecomplex * work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex));
+    zgels_  ("N",&m,&n,&nrhs,
+             (doublecomplex*)AC,&m,
+             (doublecomplex*)xp,&ldb,
+             work,&lwork,
+             &res);
+    if(res>0) {
+        return SINGULAR;
+    }
+    CHECK(res,res);
+    free(work);
+    free(AC);
+    OK
+}
+
+//////////////////// least squares real linear system using SVD ////////////
+
+int linearSolveSVDR_l(double rcond,KDMAT(a),KDMAT(b),DMAT(x)) {
+    integer m = ar;
+    integer n = ac;
+    integer nrhs = bc;
+    integer ldb = xr;
+    REQUIRES(m>=1 && n>=1 && ar==br && xr==MAX(m,n) && xc == bc, BAD_SIZE);
+    DEBUGMSG("linearSolveSVDR_l");
+    double*AC = (double*)malloc(m*n*sizeof(double));
+    double*S = (double*)malloc(MIN(m,n)*sizeof(double));
+    memcpy(AC,ap,m*n*sizeof(double));
+    if (m>=n) {
+        memcpy(xp,bp,m*nrhs*sizeof(double));
+    } else {
+        int k;
+        for(k = 0; k<nrhs; k++) {
+            memcpy(xp+ldb*k,bp+m*k,m*sizeof(double));
+        }
+    }
+    integer res;
+    integer lwork = -1;
+    integer rank;
+    double ans;
+    dgelss_  (&m,&n,&nrhs,
+             AC,&m,
+             xp,&ldb,
+             S,
+             &rcond,&rank,
+             &ans,&lwork,
+             &res);
+    lwork = ceil(ans);
+    //printf("ans = %d\n",lwork);
+    double * work = (double*)malloc(lwork*sizeof(double));
+    dgelss_  (&m,&n,&nrhs,
+             AC,&m,
+             xp,&ldb,
+             S,
+             &rcond,&rank,
+             work,&lwork,
+             &res);
+    if(res>0) {
+        return NOCONVER;
+    }
+    CHECK(res,res);
+    free(work);
+    free(S);
+    free(AC);
+    OK
+}
+
+//////////////////// least squares complex linear system using SVD ////////////
+
+// not in clapack.h
+
+int zgelss_(integer *m, integer *n, integer *nhrs,
+    doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublereal *s,
+    doublereal *rcond, integer* rank,
+    doublecomplex *work, integer* lwork, doublereal* rwork,
+    integer *info);
+
+int linearSolveSVDC_l(double rcond, KCMAT(a),KCMAT(b),CMAT(x)) {
+    integer m = ar;
+    integer n = ac;
+    integer nrhs = bc;
+    integer ldb = xr;
+    REQUIRES(m>=1 && n>=1 && ar==br && xr==MAX(m,n) && xc == bc, BAD_SIZE);
+    DEBUGMSG("linearSolveSVDC_l");
+    double*AC = (double*)malloc(2*m*n*sizeof(double));
+    double*S = (double*)malloc(MIN(m,n)*sizeof(double));
+    double*RWORK = (double*)malloc(5*MIN(m,n)*sizeof(double));
+    memcpy(AC,ap,2*m*n*sizeof(double));
+    if (m>=n) {
+        memcpy(xp,bp,2*m*nrhs*sizeof(double));
+    } else {
+        int k;
+        for(k = 0; k<nrhs; k++) {
+            memcpy(xp+2*ldb*k,bp+2*m*k,m*2*sizeof(double));
+        }
+    }
+    integer res;
+    integer lwork = -1;
+    integer rank;
+    doublecomplex ans;
+    zgelss_  (&m,&n,&nrhs,
+             (doublecomplex*)AC,&m,
+             (doublecomplex*)xp,&ldb,
+             S,
+             &rcond,&rank,
+             &ans,&lwork,
+             RWORK,
+             &res);
+    lwork = ceil(ans.r);
+    //printf("ans = %d\n",lwork);
+    doublecomplex * work = (doublecomplex*)malloc(lwork*sizeof(doublecomplex));
+    zgelss_  (&m,&n,&nrhs,
+             (doublecomplex*)AC,&m,
+             (doublecomplex*)xp,&ldb,
+             S,
+             &rcond,&rank,
+             work,&lwork,
+             RWORK,
+             &res);
+    if(res>0) {
+        return NOCONVER;
+    }
+    CHECK(res,res);
+    free(work);
+    free(RWORK);
+    free(S);
+    free(AC);
+    OK
+}
diff --git a/lib/LAPACK/lapack-aux.h b/lib/LAPACK/lapack-aux.h
new file mode 100644
index 0000000..869eabb
--- /dev/null
+++ b/lib/LAPACK/lapack-aux.h
@@ -0,0 +1,38 @@
+#include "f2c.h"
+#include "clapack.h"
+
+#define DVEC(A) int A##n, double*A##p
+#define CVEC(A) int A##n, double*A##p
+#define DMAT(A) int A##r, int A##c, double* A##p
+#define CMAT(A) int A##r, int A##c, double* A##p
+
+// const pointer versions for the parameters 
+#define KDVEC(A) int A##n, const double*A##p
+#define KCVEC(A) int A##n, const double*A##p
+#define KDMAT(A) int A##r, int A##c, const double* A##p
+#define KCMAT(A) int A##r, int A##c, const double* A##p 
+
+int svd_l_R(KDMAT(x),DMAT(u),DVEC(s),DMAT(v));
+int svd_l_Rdd(KDMAT(x),DMAT(u),DVEC(s),DMAT(v));
+
+int svd_l_C(KCMAT(a),CMAT(u),DVEC(s),CMAT(v));
+
+int eig_l_C(KCMAT(a),CMAT(u),CVEC(s),CMAT(v));
+
+int eig_l_R(KDMAT(a),DMAT(u),CVEC(s),DMAT(v));
+
+int eig_l_S(KDMAT(a),DVEC(s),DMAT(v));
+
+int eig_l_H(KCMAT(a),DVEC(s),CMAT(v));
+
+int linearSolveR_l(KDMAT(a),KDMAT(b),DMAT(x));
+
+int linearSolveC_l(KCMAT(a),KCMAT(b),CMAT(x));
+
+int linearSolveLSR_l(KDMAT(a),KDMAT(b),DMAT(x));
+
+int linearSolveLSC_l(KCMAT(a),KCMAT(b),CMAT(x));
+
+int linearSolveSVDR_l(double,KDMAT(a),KDMAT(b),DMAT(x));
+
+int linearSolveSVDC_l(double,KCMAT(a),KCMAT(b),CMAT(x));