1 files changed, 259 insertions, 2 deletions

diff --git a/lib/LAPACK.hs b/lib/LAPACK.hs
index 0019fbe..e6249a1 100644
--- a/lib/LAPACK.hs
+++ b/lib/LAPACK.hs
@@ -1,3 +1,4 @@
+{-# OPTIONS_GHC -fglasgow-exts #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  LAPACK
@@ -13,11 +14,267 @@
 -----------------------------------------------------------------------------
 
 module LAPACK (
-    svdR, svdR', svdC, svdC',
+    svdR, svdR', svdRdd, svdRdd', svdC, svdC',
     eigC, eigR, eigS, eigH,
     linearSolveR, linearSolveC,
     linearSolveLSR, linearSolveLSC,
     linearSolveSVDR, linearSolveSVDC,
 ) where
 
-import LAPACK.Internal
+import Data.Packed.Internal.Vector
+import Data.Packed.Internal.Matrix
+import Complex
+import Foreign
+
+-----------------------------------------------------------------------------
+-- dgesvd
+foreign import ccall "LAPACK/lapack-aux.h svd_l_R"
+    dgesvd :: Double ::> Double ::> (Double :> Double ::> IO Int)
+
+-- | Wrapper for LAPACK's /dgesvd/, which computes the full svd decomposition of a real matrix.
+--
+-- @(u,s,v)=svdR m@ so that @m=u \<\> s \<\> 'trans' v@.
+svdR :: Matrix Double -> (Matrix Double, Matrix Double , Matrix Double)
+svdR x@M {rows = r, cols = c} = (u, diagRect s r c, v) where (u,s,v) = svdR' x
+
+svdR' x@M {rows = r, cols = c} = unsafePerformIO $ do
+    u <- createMatrix ColumnMajor r r
+    s <- createVector (min r c)
+    v <- createMatrix ColumnMajor c c
+    dgesvd // mat fdat x // mat dat u // vec s // mat dat v // check "svdR" [fdat x]
+    return (u,s,trans v)
+
+-----------------------------------------------------------------------------
+-- dgesdd
+foreign import ccall "LAPACK/lapack-aux.h svd_l_Rdd"
+    dgesdd :: Double ::> Double ::> (Double :> Double ::> IO Int)
+
+-- | Wrapper for LAPACK's /dgesvd/, which computes the full svd decomposition of a real matrix.
+--
+-- @(u,s,v)=svdRdd m@ so that @m=u \<\> s \<\> 'trans' v@.
+svdRdd :: Matrix Double -> (Matrix Double, Matrix Double , Matrix Double)
+svdRdd x@M {rows = r, cols = c} = (u, diagRect s r c, v) where (u,s,v) = svdRdd' x
+
+svdRdd' x@M {rows = r, cols = c} = unsafePerformIO $ do
+    u <- createMatrix ColumnMajor r r
+    s <- createVector (min r c)
+    v <- createMatrix ColumnMajor c c
+    dgesdd // mat fdat x // mat dat u // vec s // mat dat v // check "svdRdd" [fdat x]
+    return (u,s,trans v)
+
+-----------------------------------------------------------------------------
+-- zgesvd
+foreign import ccall "LAPACK/lapack-aux.h svd_l_C"
+    zgesvd :: (Complex Double) ::> (Complex Double) ::> (Double :> (Complex Double) ::> IO Int)
+
+-- | Wrapper for LAPACK's /zgesvd/, which computes the full svd decomposition of a complex matrix.
+--
+-- @(u,s,v)=svdC m@ so that @m=u \<\> s \<\> 'trans' v@.
+svdC :: Matrix (Complex Double)
+     -> (Matrix (Complex Double), Matrix Double, Matrix (Complex Double))
+svdC x@M {rows = r, cols = c} = (u, diagRect s r c, v) where (u,s,v) = svdC' x
+
+svdC' x@M {rows = r, cols = c} = unsafePerformIO $ do
+    u <- createMatrix ColumnMajor r r
+    s <- createVector (min r c)
+    v <- createMatrix ColumnMajor c c
+    zgesvd // mat fdat x // mat dat u // vec s // mat dat v // check "svdC" [fdat x]
+    return (u,s,trans v)
+
+-----------------------------------------------------------------------------
+-- zgeev
+foreign import ccall "LAPACK/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}) 
+    | r == 1 = (fromList [cdat m `at` 0], singleton 1)
+    | otherwise = 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/lapack-aux.h eig_l_R"
+    dgeev :: Double ::> Double ::> ((Complex Double) :> Double ::> IO Int)
+
+-- | Wrapper for LAPACK's /dgeev/, which computes the eigenvalues and right eigenvectors of a general real matrix:
+--
+-- if @(l,v)=eigR m@ then @m \<\> v = v \<\> diag l@.
+--
+-- The eigenvectors are the columns of v.
+-- The eigenvalues are not sorted.
+eigR :: Matrix Double -> (Vector (Complex Double), Matrix (Complex Double))
+eigR (m@M {rows = r}) = (s', v'')
+    where (s,v) = eigRaux m
+          s' = toComplex (subVector 0 r (asReal s), subVector r r (asReal s))
+          v' = toRows $ trans v
+          v'' = fromColumns $ fixeig (toList s') v'
+
+eigRaux :: Matrix Double -> (Vector (Complex Double), Matrix Double)
+eigRaux (m@M {rows = r})
+    | r == 1 = (fromList [(cdat m `at` 0):+0], singleton 1)
+    | otherwise = unsafePerformIO $ do
+        l <- createVector r
+        v <- createMatrix ColumnMajor r r
+        dummy <- createMatrix ColumnMajor 1 1
+        dgeev // mat fdat m // mat dat dummy // vec l // mat dat v // check "eigR" [fdat m]
+        return (l,v)
+
+fixeig  []  _ =  []
+fixeig [r] [v] = [comp v]
+fixeig ((r1:+i1):(r2:+i2):r) (v1:v2:vs)
+    | r1 == r2 && i1 == (-i2) = toComplex (v1,v2) : toComplex (v1,scale (-1) v2) : fixeig r vs
+    | otherwise = comp v1 : fixeig ((r2:+i2):r) (v2:vs)
+
+scale r v = fromList [r] `outer` v
+
+-----------------------------------------------------------------------------
+-- dsyev
+foreign import ccall "LAPACK/lapack-aux.h eig_l_S"
+    dsyev :: Double ::> (Double :> Double ::> IO Int)
+
+-- | Wrapper for LAPACK's /dsyev/, which computes the eigenvalues and right eigenvectors of a symmetric real matrix:
+--
+-- if @(l,v)=eigSl m@ then @m \<\> v = v \<\> diag l@.
+--
+-- The eigenvectors are the columns of v.
+-- The eigenvalues are sorted in descending order (use eigS' for ascending order).
+eigS :: Matrix Double -> (Vector Double, Matrix Double)
+eigS m = (s', fliprl v)
+    where (s,v) = eigS' m
+          s' = fromList . reverse . toList $  s
+
+eigS' (m@M {rows = r})
+    | r == 1 = (fromList [cdat m `at` 0], singleton 1)
+    | otherwise = unsafePerformIO $ do
+        l <- createVector r
+        v <- createMatrix ColumnMajor r r
+        dsyev // mat fdat m // vec l // mat dat v // check "eigS" [fdat m]
+        return (l,v)
+
+-----------------------------------------------------------------------------
+-- zheev
+foreign import ccall "LAPACK/lapack-aux.h eig_l_H"
+    zheev :: (Complex Double) ::> (Double :> (Complex Double) ::> IO Int)
+
+-- | Wrapper for LAPACK's /zheev/, which computes the eigenvalues and right eigenvectors of a hermitian complex matrix:
+--
+-- if @(l,v)=eigH m@ then @m \<\> s v = v \<\> diag l@.
+--
+-- The eigenvectors are the columns of v.
+-- The eigenvalues are sorted in descending order.
+eigH :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double))
+eigH m = (s', fliprl v)
+    where (s,v) = eigH' m
+          s' = fromList . reverse . toList $  s
+
+eigH' (m@M {rows = r})
+    | r == 1 = (fromList [realPart (cdat m `at` 0)], singleton 1)
+    | otherwise = unsafePerformIO $ do
+        l <- createVector r
+        v <- createMatrix ColumnMajor r r
+        zheev // mat fdat m // vec l // mat dat v // check "eigH" [fdat m]
+        return (l,v)
+
+-----------------------------------------------------------------------------
+-- dgesv
+foreign import ccall "LAPACK/lapack-aux.h linearSolveR_l"
+    dgesv :: Double ::> Double ::> Double ::> IO Int
+
+-- | Wrapper for LAPACK's /dgesv/, which solves a general real linear system (for several right-hand sides) internally using the lu decomposition.
+linearSolveR :: Matrix Double -> Matrix Double -> Matrix Double
+linearSolveR  a@(M {rows = n1, cols = n2}) b@(M {rows = r, cols = c})
+    | n1==n2 && n1==r = unsafePerformIO $ do
+        s <- createMatrix ColumnMajor r c
+        dgesv // mat fdat a // mat fdat b // mat dat s // check "linearSolveR" [fdat a, fdat b]
+        return s
+    | otherwise = error "linearSolveR of nonsquare matrix"
+
+-----------------------------------------------------------------------------
+-- zgesv
+foreign import ccall "LAPACK/lapack-aux.h linearSolveC_l"
+    zgesv :: (Complex Double) ::> (Complex Double) ::> (Complex Double) ::> IO Int
+
+-- | Wrapper for LAPACK's /zgesv/, which solves a general complex linear system (for several right-hand sides) internally using the lu decomposition.
+linearSolveC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)
+linearSolveC  a@(M {rows = n1, cols = n2}) b@(M {rows = r, cols = c})
+    | n1==n2 && n1==r = unsafePerformIO $ do
+        s <- createMatrix ColumnMajor r c
+        zgesv // mat fdat a // mat fdat b // mat dat s // check "linearSolveC" [fdat a, fdat b]
+        return s
+    | otherwise = error "linearSolveC of nonsquare matrix"
+
+-----------------------------------------------------------------------------------
+-- dgels
+foreign import ccall "LAPACK/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/lapack-aux.h linearSolveLSC_l"
+    zgels :: (Complex Double) ::> (Complex Double) ::> (Complex Double) ::> IO Int
+
+-- | Wrapper for LAPACK's /zgels/, which obtains the least squared error solution of an overconstrained complex linear system or the minimum norm solution of an underdetermined system, for several right-hand sides. For rank deficient systems use 'linearSolveSVDC'.
+linearSolveLSC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)
+linearSolveLSC a b = subMatrix (0,0) (cols a, cols b) $ linearSolveLSC_l a b
+
+linearSolveLSC_l a@(M {rows = m, cols = n}) b@(M {cols = nrhs}) = unsafePerformIO $ do
+    r <- createMatrix ColumnMajor (max m n) nrhs
+    zgels // mat fdat a // mat fdat b // mat dat r // check "linearSolveLSC" [fdat a, fdat b]
+    return r
+
+-----------------------------------------------------------------------------------
+-- dgelss
+foreign import ccall "LAPACK/lapack-aux.h linearSolveSVDR_l"
+    dgelss :: Double -> Double ::> Double ::> Double ::> IO Int
+
+-- | Wrapper for LAPACK's /dgelss/, which obtains the minimum norm solution to a real linear least squares problem Ax=B using the svd, for several right-hand sides. Admits rank deficient systems but it is slower than 'linearSolveLSR'. The effective rank of A is determined by treating as zero those singular valures which are less than rcond times the largest singular value. If rcond == Nothing machine precision is used.
+linearSolveSVDR :: Maybe Double   -- ^ rcond
+                -> Matrix Double  -- ^ coefficient matrix
+                -> Matrix Double  -- ^ right hand sides (as columns)
+                -> Matrix Double  -- ^ solution vectors (as columns)
+linearSolveSVDR (Just rcond) a b = subMatrix (0,0) (cols a, cols b) $ linearSolveSVDR_l rcond a b
+linearSolveSVDR Nothing a b = linearSolveSVDR (Just (-1)) a b
+
+linearSolveSVDR_l rcond a@(M {rows = m, cols = n}) b@(M {cols = nrhs}) = unsafePerformIO $ do
+    r <- createMatrix ColumnMajor (max m n) nrhs
+    dgelss rcond // mat fdat a // mat fdat b // mat dat r // check "linearSolveSVDR" [fdat a, fdat b]
+    return r
+
+-----------------------------------------------------------------------------------
+-- zgelss
+foreign import ccall "LAPACK/lapack-aux.h linearSolveSVDC_l"
+    zgelss :: Double -> (Complex Double) ::> (Complex Double) ::> (Complex Double) ::> IO Int
+
+-- | Wrapper for LAPACK's /zgelss/, which obtains the minimum norm solution to a complex linear least squares problem Ax=B using the svd, for several right-hand sides. Admits rank deficient systems but it is slower than 'linearSolveLSC'. The effective rank of A is determined by treating as zero those singular valures which are less than rcond times the largest singular value. If rcond == Nothing machine precision is used.
+linearSolveSVDC :: Maybe Double            -- ^ rcond
+                -> Matrix (Complex Double) -- ^ coefficient matrix
+                -> Matrix (Complex Double) -- ^ right hand sides (as columns)
+                -> Matrix (Complex Double) -- ^ solution vectors (as columns)
+linearSolveSVDC (Just rcond) a b = subMatrix (0,0) (cols a, cols b) $ linearSolveSVDC_l rcond a b
+linearSolveSVDC Nothing a b = linearSolveSVDC (Just (-1)) a b
+
+linearSolveSVDC_l rcond  a@(M {rows = m, cols = n}) b@(M {cols = nrhs}) = unsafePerformIO $ do
+    r <- createMatrix ColumnMajor (max m n) nrhs
+    zgelss rcond // mat fdat a // mat fdat b // mat dat r // check "linearSolveSVDC" [fdat a, fdat b]
+    return r
+