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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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multiplyR :: Matrix Double -> Matrix Double -> Matrix Double | | multiplyC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double) | | 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)) | | eigS' | | eigH' | | 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]) | | lusR :: Matrix Double -> [Int] -> Matrix Double -> Matrix Double | | lusC :: Matrix (Complex Double) -> [Int] -> Matrix (Complex Double) -> Matrix (Complex Double) | | 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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Matrix product based on BLAS's dgemm.
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Matrix product based on BLAS's zgemm.
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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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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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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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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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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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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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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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eigS' |
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eigH' |
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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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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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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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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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:: 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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:: 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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Wrapper for LAPACK's dgetrf, which computes a LU factorization of a general real matrix.
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Wrapper for LAPACK's zgees, which computes a Schur factorization of a square complex matrix.
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Wrapper for LAPACK's dgetrs, which solves a general real linear system (for several right-hand sides) from a precomputed LU decomposition.
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Wrapper for LAPACK's zgetrs, which solves a general real linear system (for several right-hand sides) from a precomputed LU decomposition.
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Wrapper for LAPACK's dpotrf, which computes the Cholesky factorization of a
real symmetric positive definite matrix.
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Wrapper for LAPACK's zpotrf, which computes the Cholesky factorization of a
complex Hermitian positive definite matrix.
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Wrapper for LAPACK's dgeqr2, which computes a QR factorization of a real matrix.
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Wrapper for LAPACK's zgeqr2, which computes a QR factorization of a complex matrix.
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Wrapper for LAPACK's dgehrd, which computes a Hessenberg factorization of a square real matrix.
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Wrapper for LAPACK's zgehrd, which computes a Hessenberg factorization of a square complex matrix.
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Wrapper for LAPACK's dgees, which computes a Schur factorization of a square real matrix.
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Wrapper for LAPACK's zgees, which computes a Schur factorization of a square complex matrix.
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Produced by Haddock version 2.4.2 |