 | hmatrix-0.2.1.0: Linear algebra and numerical computations | Contents | Index |
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| Numeric.LinearAlgebra.LAPACK | | Portability | portable (uses FFI) | | Stability | provisional | | Maintainer | Alberto Ruiz (aruiz at um dot es) |
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| Description |
| Wrappers for a few LAPACK functions (http://www.netlib.org/lapack).
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| Synopsis |
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| svdR :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double) | | | svdRdd :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double) | | | svdC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double)) | | | eigC :: Matrix (Complex Double) -> (Vector (Complex Double), Matrix (Complex Double)) | | | eigR :: Matrix Double -> (Vector (Complex Double), Matrix (Complex Double)) | | | eigS :: Matrix Double -> (Vector Double, Matrix Double) | | | eigH :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double)) | | | linearSolveR :: Matrix Double -> Matrix Double -> Matrix Double | | | linearSolveC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double) | | | linearSolveLSR :: Matrix Double -> Matrix Double -> Matrix Double | | | linearSolveLSC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double) | | | linearSolveSVDR :: Maybe Double -> Matrix Double -> Matrix Double -> Matrix Double | | | linearSolveSVDC :: Maybe Double -> Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double) | | | luR :: Matrix Double -> (Matrix Double, [Int]) | | | luC :: Matrix (Complex Double) -> (Matrix (Complex Double), [Int]) | | | cholS :: Matrix Double -> Matrix Double | | | cholH :: Matrix (Complex Double) -> Matrix (Complex Double) | | | qrR :: Matrix Double -> (Matrix Double, Vector Double) | | | qrC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double)) | | | hessR :: Matrix Double -> (Matrix Double, Vector Double) | | | hessC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double)) | | | schurR :: Matrix Double -> (Matrix Double, Matrix Double) | | | schurC :: Matrix (Complex Double) -> (Matrix (Complex Double), Matrix (Complex Double)) |
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| Documentation |
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| svdR :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double) |
Wrapper for LAPACK's dgesvd, which computes the full svd decomposition of a real matrix.
(u,s,v)=full svdR m so that m=u <> s <> trans v.
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| svdRdd :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double) |
Wrapper for LAPACK's dgesvd, which computes the full svd decomposition of a real matrix.
(u,s,v)=full svdRdd m so that m=u <> s <> trans v.
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| svdC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double)) |
Wrapper for LAPACK's zgesvd, which computes the full svd decomposition of a complex matrix.
(u,s,v)=full svdC m so that m=u <> comp s <> trans v.
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| eigC :: Matrix (Complex Double) -> (Vector (Complex Double), Matrix (Complex Double)) |
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.
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| eigR :: Matrix Double -> (Vector (Complex Double), Matrix (Complex Double)) |
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.
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| eigS :: Matrix Double -> (Vector Double, Matrix Double) |
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).
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| eigH :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double)) |
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 (use eigH' for ascending order).
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| linearSolveR :: Matrix Double -> Matrix Double -> Matrix Double |
| Wrapper for LAPACK's dgesv, which solves a general real linear system (for several right-hand sides) internally using the lu decomposition.
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| linearSolveC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double) |
| Wrapper for LAPACK's zgesv, which solves a general complex linear system (for several right-hand sides) internally using the lu decomposition.
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| linearSolveLSR :: Matrix Double -> Matrix Double -> Matrix Double |
| 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.
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| linearSolveLSC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double) |
| 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.
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| linearSolveSVDR |
| :: Maybe Double | rcond
| | -> Matrix Double | coefficient matrix
| | -> Matrix Double | right hand sides (as columns)
| | -> Matrix Double | solution vectors (as columns)
| | 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.
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| linearSolveSVDC |
| :: Maybe Double | rcond
| | -> Matrix (Complex Double) | coefficient matrix
| | -> Matrix (Complex Double) | right hand sides (as columns)
| | -> Matrix (Complex Double) | solution vectors (as columns)
| | 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.
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| luR :: Matrix Double -> (Matrix Double, [Int]) |
| Wrapper for LAPACK's dgetrf, which computes a LU factorization of a general real matrix.
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| luC :: Matrix (Complex Double) -> (Matrix (Complex Double), [Int]) |
| Wrapper for LAPACK's zgees, which computes a Schur factorization of a square complex matrix.
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| cholS :: Matrix Double -> Matrix Double |
| Wrapper for LAPACK's dpotrf, which computes the Cholesky factorization of a
real symmetric positive definite matrix.
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| cholH :: Matrix (Complex Double) -> Matrix (Complex Double) |
| Wrapper for LAPACK's zpotrf, which computes the Cholesky factorization of a
complex Hermitian positive definite matrix.
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| qrR :: Matrix Double -> (Matrix Double, Vector Double) |
| Wrapper for LAPACK's dgeqr2, which computes a QR factorization of a real matrix.
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| qrC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double)) |
| Wrapper for LAPACK's zgeqr2, which computes a QR factorization of a complex matrix.
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| hessR :: Matrix Double -> (Matrix Double, Vector Double) |
| Wrapper for LAPACK's dgehrd, which computes a Hessenberg factorization of a square real matrix.
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| hessC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double)) |
| Wrapper for LAPACK's zgehrd, which computes a Hessenberg factorization of a square complex matrix.
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| schurR :: Matrix Double -> (Matrix Double, Matrix Double) |
| Wrapper for LAPACK's dgees, which computes a Schur factorization of a square real matrix.
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| schurC :: Matrix (Complex Double) -> (Matrix (Complex Double), Matrix (Complex Double)) |
| Wrapper for LAPACK's zgees, which computes a Schur factorization of a square complex matrix.
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| Produced by Haddock version 2.1.0 |