5 files changed, 120 insertions, 15 deletions

diff --git a/examples/tests.hs b/examples/tests.hs
index 9388671..e91b9f1 100644
--- a/examples/tests.hs
+++ b/examples/tests.hs
@@ -189,12 +189,12 @@ pinvTest m =  m <> p <> m |~| m
 
 square m = rows m == cols m
 
-orthonormal m = square m && m <> ctrans m |~| ident (rows m)
+unitary m = square m && m <> ctrans m |~| ident (rows m)
 
 hermitian m = m |~| ctrans m
 
 svdTest svd m = u <> real d <> trans v |~| m
-          && orthonormal u && orthonormal v
+          && unitary u && unitary v
     where (u,d,v) = full svd m
 
 svdTest' svd m = m |~| 0 || u <> real (diag s) <> trans v |~| m
@@ -204,7 +204,7 @@ eigTest m = complex m <> v |~| v <> diag s
     where (s, v) = eig m
 
 eigTestSH m = m <> v |~| v <> real (diag s)
-              && orthonormal v
+              && unitary v
               && m |~| v <> real (diag s) <> ctrans v
     where (s, v) = eigSH m
 
@@ -274,11 +274,16 @@ cholCTest = chol ((2><2) [1,2,2,9::Complex Double]) == (2><2) [1,2,0,2.236067977
 
 ---------------------------------------------------------------------
 
-qrTest qr m = q <> r |~| m && q <> ctrans q |~| ident (rows m)
+qrTest qr m = q <> r |~| m && unitary q
     where (q,r) = qr m
 
 ---------------------------------------------------------------------
 
+hessTest m = m |~| p <> h <> ctrans p && unitary p
+    where (p,h) = hess m
+
+---------------------------------------------------------------------
+
 asFortran m = (rows m >|< cols m) $ toList (fdat m)
 asC m = (rows m >< cols m) $ toList (cdat m)
 
@@ -338,6 +343,9 @@ tests = do
     quickCheck (qrTest (    unpackQR . GSL.qrPacked))
     quickCheck (qrTest qr ::RM->Bool)
     quickCheck (qrTest qr ::CM->Bool)
+    putStrLn "--------- hess --------"
+    quickCheck (hessTest . sqm ::SqM Double->Bool)
+    quickCheck (hessTest . sqm ::SqM (Complex Double) -> Bool)
     putStrLn "--------- nullspace ------"
     quickCheck (nullspaceTest :: RM -> Bool)
     quickCheck (nullspaceTest :: CM -> Bool)
diff --git a/lib/Numeric/LinearAlgebra/Algorithms.hs b/lib/Numeric/LinearAlgebra/Algorithms.hs
index 84c399a..1345975 100644
--- a/lib/Numeric/LinearAlgebra/Algorithms.hs
+++ b/lib/Numeric/LinearAlgebra/Algorithms.hs
@@ -33,6 +33,8 @@ module Numeric.LinearAlgebra.Algorithms (
     qr,
 -- ** Cholesky
     chol,
+-- ** Hessenberg
+    hess,
 -- * Nullspace
     nullspacePrec,
     nullVector,
@@ -42,7 +44,9 @@ module Numeric.LinearAlgebra.Algorithms (
     ctrans,
     eps, i,
 -- * Util
-    GenMat(linearSolveSVD,lu,eigSH',cholSH), unpackQR, haussholder
+    GenMat(linearSolveSVD,lu,eigSH',cholSH), 
+    haussholder,
+    unpackQR, unpackHess
 ) where
 
 
@@ -64,7 +68,8 @@ class (Linear Matrix t) => GenMat t where
     --  See also other versions of linearSolve in "Numeric.LinearAlgebra.LAPACK".
     linearSolve :: Matrix t -> Matrix t -> Matrix t
     linearSolveSVD :: Matrix t -> Matrix t -> Matrix t
-    -- | Eigenvalues and eigenvectors of a general square matrix using lapack's dgeev or zgeev. If @(s,v) = eig m@ then @m \<> v == v \<> diag s@
+    -- | Eigenvalues and eigenvectors of a general square matrix using lapack's dgeev or zgeev.
+    -- If @(s,v) = eig m@ then @m \<> v == v \<> diag s@
     eig         :: Matrix t -> (Vector (Complex Double), Matrix (Complex Double))
     -- | Similar to eigSH without checking that the input matrix is hermitian or symmetric.
     eigSH'      :: Matrix t -> (Vector Double, Matrix t)
@@ -72,6 +77,8 @@ class (Linear Matrix t) => GenMat t where
     cholSH      :: Matrix t -> Matrix t
     -- | QR factorization using lapack's dgeqr2 or zgeqr2.
     qr          :: Matrix t -> (Matrix t, Matrix t)
+    -- | Hessenberg factorization using lapack's dgehrd or zgehrd.
+    hess        :: Matrix t -> (Matrix t, Matrix t)
     -- | Conjugate transpose.
     ctrans :: Matrix t -> Matrix t
 
@@ -85,6 +92,7 @@ instance GenMat Double where
     eigSH' = eigS
     cholSH = cholS
     qr = GSL.unpackQR . qrR
+    hess = unpackHess hessR
 
 instance GenMat (Complex Double) where
     svd = svdC
@@ -96,6 +104,7 @@ instance GenMat (Complex Double) where
     eigSH' = eigH
     cholSH = cholH
     qr = unpackQR . qrC
+    hess = unpackHess hessC
 
 -- | Eigenvalues and Eigenvectors of a complex hermitian or real symmetric matrix using lapack's dsyev or zheev. If @(s,v) = eigSH m@ then @m == v \<> diag s \<> ctrans v@
 eigSH :: GenMat t => Matrix t -> (Vector Double, Matrix t)
@@ -277,6 +286,14 @@ haussholder :: (GenMat a) => a -> Vector a -> Matrix a
 haussholder tau v = ident (dim v) `sub` (tau `scale` (w `mXm` ctrans w))
     where w = asColumn v
 
+
+zh k v = fromList $ replicate (k-1) 0 ++ (1:drop k xs)
+              where xs = toList v
+
+zt 0 v = v
+zt k v = join [subVector 0 (dim v - k) v, constant 0 k]
+
+
 unpackQR :: (GenMat t) => (Matrix t, Vector t) -> (Matrix t, Matrix t)
 unpackQR (pq, tau) = (q,r)
     where cs = toColumns pq
@@ -288,8 +305,17 @@ unpackQR (pq, tau) = (q,r)
           hs = zipWith haussholder (toList tau) vs
           q = foldl1' mXm hs
 
-          zh k v = fromList $ replicate (k-1) 0 ++ (1:drop k xs)
-              where xs = toList v
+unpackHess :: (GenMat t) => (Matrix t -> (Matrix t,Vector t)) -> Matrix t -> (Matrix t, Matrix t)
+unpackHess hf m
+    | rows m == 1 = ((1><1)[1],m)
+    | otherwise = (uH . hf) m
 
-          zt 0 v = v
-          zt k v = join [subVector 0 (dim v - k) v, constant 0 k]
+uH (pq, tau) = (p,h)
+    where cs = toColumns pq
+          m = rows pq
+          n = cols pq
+          mn = min m n
+          h = fromColumns $ zipWith zt ([m-2, m-3 .. 1] ++ repeat 0) cs
+          vs = zipWith zh [2..mn] cs
+          hs = zipWith haussholder (toList tau) vs
+          p = foldl1' mXm hs
diff --git a/lib/Numeric/LinearAlgebra/LAPACK.hs b/lib/Numeric/LinearAlgebra/LAPACK.hs
index 648e59f..a84a17e 100644
--- a/lib/Numeric/LinearAlgebra/LAPACK.hs
+++ b/lib/Numeric/LinearAlgebra/LAPACK.hs
@@ -20,7 +20,8 @@ module Numeric.LinearAlgebra.LAPACK (
     linearSolveLSR, linearSolveLSC,
     linearSolveSVDR, linearSolveSVDC,
     cholS, cholH,
-    qrR, qrC
+    qrR, qrC,
+    hessR, hessC
 ) where
 
 import Data.Packed.Internal
@@ -284,7 +285,7 @@ linearSolveSVDC_l rcond  a b = unsafePerformIO $ do
 -----------------------------------------------------------------------------------
 foreign import ccall "LAPACK/lapack-aux.h chol_l_H" zpotrf :: TCMCM
 
--- | Wrapper for LAPACK's /zpotrf/,which computes the Cholesky factorization of a
+-- | Wrapper for LAPACK's /zpotrf/, which computes the Cholesky factorization of a
 -- complex Hermitian positive definite matrix.
 cholH :: Matrix (Complex Double) -> Matrix (Complex Double)
 cholH a = unsafePerformIO $ do
@@ -296,7 +297,7 @@ cholH a = unsafePerformIO $ do
 -----------------------------------------------------------------------------------
 foreign import ccall "LAPACK/lapack-aux.h chol_l_S" dpotrf :: TMM
 
--- | Wrapper for LAPACK's /dpotrf/,which computes the Cholesky factorization of a
+-- | Wrapper for LAPACK's /dpotrf/, which computes the Cholesky factorization of a
 -- real symmetric positive definite matrix.
 cholS :: Matrix Double -> Matrix Double
 cholS a = unsafePerformIO $ do
@@ -308,7 +309,7 @@ cholS a = unsafePerformIO $ do
 -----------------------------------------------------------------------------------
 foreign import ccall "LAPACK/lapack-aux.h qr_l_R" dgeqr2 :: TMVM
 
--- | Wrapper for LAPACK's /dgeqr2/,which computes a QR factorization of a real matrix.
+-- | Wrapper for LAPACK's /dgeqr2/, which computes a QR factorization of a real matrix.
 qrR :: Matrix Double -> (Matrix Double, Vector Double)
 qrR a = unsafePerformIO $ do
     r <- createMatrix ColumnMajor m n
@@ -322,7 +323,7 @@ qrR a = unsafePerformIO $ do
 -----------------------------------------------------------------------------------
 foreign import ccall "LAPACK/lapack-aux.h qr_l_C" zgeqr2 :: TCMCVCM
 
--- | Wrapper for LAPACK's /zgeqr2/,which computes a QR factorization of a complex matrix.
+-- | Wrapper for LAPACK's /zgeqr2/, which computes a QR factorization of a complex matrix.
 qrC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double))
 qrC a = unsafePerformIO $ do
     r <- createMatrix ColumnMajor m n
@@ -333,3 +334,31 @@ qrC a = unsafePerformIO $ do
         n = cols a
         mn = min m n
 
+-----------------------------------------------------------------------------------
+foreign import ccall "LAPACK/lapack-aux.h hess_l_R" dgehrd :: TMVM
+
+-- | Wrapper for LAPACK's /dgehrd/, which computes a Hessenberg factorization of a square real matrix.
+hessR :: Matrix Double -> (Matrix Double, Vector Double)
+hessR a = unsafePerformIO $ do
+    r <- createMatrix ColumnMajor m n
+    tau <- createVector (mn-1)
+    dgehrd // mat fdat a // vec tau // mat dat r // check "hessR" [fdat a]
+    return (r,tau)
+  where m = rows a
+        n = cols a
+        mn = min m n
+
+-----------------------------------------------------------------------------------
+foreign import ccall "LAPACK/lapack-aux.h hess_l_C" zgehrd :: TCMCVCM
+
+-- | Wrapper for LAPACK's /zgeqr2/, which computes a Hessenberg factorization of a square complex matrix.
+hessC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double))
+hessC a = unsafePerformIO $ do
+    r <- createMatrix ColumnMajor m n
+    tau <- createVector (mn-1)
+    zgehrd // mat fdat a // vec tau // mat dat r // check "hessC" [fdat a]
+    return (r,tau)
+  where m = rows a
+        n = cols a
+        mn = min m n
+
diff --git a/lib/Numeric/LinearAlgebra/LAPACK/lapack-aux.c b/lib/Numeric/LinearAlgebra/LAPACK/lapack-aux.c
index 9b6c1db..04ef416 100644
--- a/lib/Numeric/LinearAlgebra/LAPACK/lapack-aux.c
+++ b/lib/Numeric/LinearAlgebra/LAPACK/lapack-aux.c
@@ -663,3 +663,41 @@ int qr_l_C(KCMAT(a), CVEC(tau), CMAT(r)) {
     free(WORK);
     OK
 }
+
+//////////////////// Hessenberg factorization /////////////////////////
+
+int hess_l_R(KDMAT(a), DVEC(tau), DMAT(r)) {
+    integer m = ar;
+    integer n = ac;
+    integer mn = MIN(m,n);
+    REQUIRES(m>=1 && n == m && rr== m && rc == n && taun == mn-1, BAD_SIZE);
+    DEBUGMSG("hess_l_R");
+    integer lwork = 5*n; // fixme
+    double *WORK = (double*)malloc(lwork*sizeof(double));
+    CHECK(!WORK,MEM);
+    memcpy(rp,ap,m*n*sizeof(double));
+    integer res;
+    integer one = 1;
+    dgehrd_ (&n,&one,&n,rp,&n,taup,WORK,&lwork,&res);
+    CHECK(res,res);
+    free(WORK);
+    OK
+}
+
+int hess_l_C(KCMAT(a), CVEC(tau), CMAT(r)) {
+    integer m = ar;
+    integer n = ac;
+    integer mn = MIN(m,n);
+    REQUIRES(m>=1 && n == m && rr== m && rc == n && taun == mn-1, BAD_SIZE);
+    DEBUGMSG("hess_l_C");
+    integer lwork = 5*n; // fixme
+    doublecomplex *WORK = (doublecomplex*)malloc(lwork*sizeof(doublecomplex));
+    CHECK(!WORK,MEM);
+    memcpy(rp,ap,m*n*sizeof(doublecomplex));
+    integer res;
+    integer one = 1;
+    zgehrd_ (&n,&one,&n,(doublecomplex*)rp,&n,(doublecomplex*)taup,WORK,&lwork,&res);
+    CHECK(res,res);
+    free(WORK);
+    OK
+}
diff --git a/lib/Numeric/LinearAlgebra/LAPACK/lapack-aux.h b/lib/Numeric/LinearAlgebra/LAPACK/lapack-aux.h
index ea71847..52ac41e 100644
--- a/lib/Numeric/LinearAlgebra/LAPACK/lapack-aux.h
+++ b/lib/Numeric/LinearAlgebra/LAPACK/lapack-aux.h
@@ -44,3 +44,7 @@ int chol_l_S(KDMAT(a),DMAT(r));
 int qr_l_R(KDMAT(a), DVEC(tau), DMAT(r));
 
 int qr_l_C(KCMAT(a), CVEC(tau), CMAT(r));
+
+int hess_l_R(KDMAT(a), DVEC(tau), DMAT(r));
+
+int hess_l_C(KCMAT(a), CVEC(tau), CMAT(r));