Portability | portable (uses FFI) |
---|---|

Stability | provisional |

Maintainer | Alberto Ruiz (aruiz at um dot es) |

Functional interface to selected LAPACK functions (http://www.netlib.org/lapack).

- multiplyR :: Matrix Double -> Matrix Double -> Matrix Double
- multiplyC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)
- multiplyF :: Matrix Float -> Matrix Float -> Matrix Float
- multiplyQ :: Matrix (Complex Float) -> Matrix (Complex Float) -> Matrix (Complex Float)
- linearSolveR :: Matrix Double -> Matrix Double -> Matrix Double
- linearSolveC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)
- lusR :: Matrix Double -> [Int] -> Matrix Double -> Matrix Double
- lusC :: Matrix (Complex Double) -> [Int] -> Matrix (Complex Double) -> Matrix (Complex Double)
- cholSolveR :: Matrix Double -> Matrix Double -> Matrix Double
- cholSolveC :: 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)
- svR :: Matrix Double -> Vector Double
- svRd :: Matrix Double -> Vector Double
- svC :: Matrix (Complex Double) -> Vector Double
- svCd :: Matrix (Complex Double) -> Vector Double
- svdR :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double)
- svdRd :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double)
- svdC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double))
- svdCd :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double))
- thinSVDR :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double)
- thinSVDRd :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double)
- thinSVDC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double))
- thinSVDCd :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double))
- rightSVR :: Matrix Double -> (Vector Double, Matrix Double)
- rightSVC :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double))
- leftSVR :: Matrix Double -> (Matrix Double, Vector Double)
- leftSVC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double)
- eigR :: Matrix Double -> (Vector (Complex Double), Matrix (Complex Double))
- eigC :: Matrix (Complex Double) -> (Vector (Complex Double), Matrix (Complex Double))
- eigS :: Matrix Double -> (Vector Double, Matrix Double)
- eigS' :: Matrix Double -> (Vector Double, Matrix Double)
- eigH :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double))
- eigH' :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double))
- eigOnlyR :: Matrix Double -> Vector (Complex Double)
- eigOnlyC :: Matrix (Complex Double) -> Vector (Complex Double)
- eigOnlyS :: Matrix Double -> Vector Double
- eigOnlyH :: Matrix (Complex Double) -> Vector 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)
- mbCholS :: Matrix Double -> Maybe (Matrix Double)
- mbCholH :: Matrix (Complex Double) -> Maybe (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))

# Matrix product

multiplyR :: Matrix Double -> Matrix Double -> Matrix DoubleSource

Matrix product based on BLAS's *dgemm*.

multiplyC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)Source

Matrix product based on BLAS's *zgemm*.

multiplyF :: Matrix Float -> Matrix Float -> Matrix FloatSource

Matrix product based on BLAS's *sgemm*.

multiplyQ :: Matrix (Complex Float) -> Matrix (Complex Float) -> Matrix (Complex Float)Source

Matrix product based on BLAS's *cgemm*.

# Linear systems

linearSolveR :: Matrix Double -> Matrix Double -> Matrix DoubleSource

Solve a real linear system (for square coefficient matrix and several right-hand sides) using the LU decomposition, based on LAPACK's *dgesv*. For underconstrained or overconstrained systems use `linearSolveLSR`

or `linearSolveSVDR`

. See also `lusR`

.

linearSolveC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)Source

Solve a complex linear system (for square coefficient matrix and several right-hand sides) using the LU decomposition, based on LAPACK's *zgesv*. For underconstrained or overconstrained systems use `linearSolveLSC`

or `linearSolveSVDC`

. See also `lusC`

.

lusR :: Matrix Double -> [Int] -> Matrix Double -> Matrix DoubleSource

Solve a real linear system from a precomputed LU decomposition (`luR`

), using LAPACK's *dgetrs*.

lusC :: Matrix (Complex Double) -> [Int] -> Matrix (Complex Double) -> Matrix (Complex Double)Source

Solve a real linear system from a precomputed LU decomposition (`luC`

), using LAPACK's *zgetrs*.

cholSolveR :: Matrix Double -> Matrix Double -> Matrix DoubleSource

Solves a symmetric positive definite system of linear equations using a precomputed Cholesky factorization obtained by `cholS`

.

cholSolveC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)Source

Solves a Hermitian positive definite system of linear equations using a precomputed Cholesky factorization obtained by `cholH`

.

linearSolveLSR :: Matrix Double -> Matrix Double -> Matrix DoubleSource

Least squared error solution of an overconstrained real linear system, or the minimum norm solution of an underconstrained system, using LAPACK's *dgels*. For rank-deficient systems use `linearSolveSVDR`

.

linearSolveLSC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)Source

Least squared error solution of an overconstrained complex linear system, or the minimum norm solution of an underconstrained system, using LAPACK's *zgels*. For rank-deficient systems use `linearSolveSVDC`

.

:: Maybe Double | rcond |

-> Matrix Double | coefficient matrix |

-> Matrix Double | right hand sides (as columns) |

-> Matrix Double | solution vectors (as columns) |

Minimum norm solution of a general real linear least squares problem Ax=B using the SVD, based on LAPACK's *dgelss*. 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.

:: Maybe Double | rcond |

-> Matrix (Complex Double) | coefficient matrix |

-> Matrix (Complex Double) | right hand sides (as columns) |

-> Matrix (Complex Double) | solution vectors (as columns) |

Minimum norm solution of a general complex linear least squares problem Ax=B using the SVD, based on LAPACK's *zgelss*. 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.

# SVD

svR :: Matrix Double -> Vector DoubleSource

Singular values of a real matrix, using LAPACK's *dgesvd* with jobu == jobvt == 'N'.

svRd :: Matrix Double -> Vector DoubleSource

Singular values of a real matrix, using LAPACK's *dgesdd* with jobz == 'N'.

svC :: Matrix (Complex Double) -> Vector DoubleSource

Singular values of a complex matrix, using LAPACK's *zgesvd* with jobu == jobvt == 'N'.

svCd :: Matrix (Complex Double) -> Vector DoubleSource

Singular values of a complex matrix, using LAPACK's *zgesdd* with jobz == 'N'.

svdR :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double)Source

Full SVD of a real matrix using LAPACK's *dgesvd*.

svdRd :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double)Source

Full SVD of a real matrix using LAPACK's *dgesdd*.

svdC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double))Source

Full SVD of a complex matrix using LAPACK's *zgesvd*.

svdCd :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double))Source

Full SVD of a complex matrix using LAPACK's *zgesdd*.

thinSVDR :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double)Source

Thin SVD of a real matrix, using LAPACK's *dgesvd* with jobu == jobvt == 'S'.

thinSVDRd :: Matrix Double -> (Matrix Double, Vector Double, Matrix Double)Source

Thin SVD of a real matrix, using LAPACK's *dgesdd* with jobz == 'S'.

thinSVDC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double))Source

Thin SVD of a complex matrix, using LAPACK's *zgesvd* with jobu == jobvt == 'S'.

thinSVDCd :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double, Matrix (Complex Double))Source

Thin SVD of a complex matrix, using LAPACK's *zgesdd* with jobz == 'S'.

rightSVR :: Matrix Double -> (Vector Double, Matrix Double)Source

Singular values and all right singular vectors of a real matrix, using LAPACK's *dgesvd* with jobu == 'N' and jobvt == 'A'.

rightSVC :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double))Source

Singular values and all right singular vectors of a complex matrix, using LAPACK's *zgesvd* with jobu == 'N' and jobvt == 'A'.

leftSVR :: Matrix Double -> (Matrix Double, Vector Double)Source

Singular values and all left singular vectors of a real matrix, using LAPACK's *dgesvd* with jobu == 'A' and jobvt == 'N'.

leftSVC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector Double)Source

Singular values and all left singular vectors of a complex matrix, using LAPACK's *zgesvd* with jobu == 'A' and jobvt == 'N'.

# Eigensystems

eigR :: Matrix Double -> (Vector (Complex Double), Matrix (Complex Double))Source

Eigenvalues and right eigenvectors of a general real matrix, using LAPACK's *dgeev*.
The eigenvectors are the columns of v. The eigenvalues are not sorted.

eigC :: Matrix (Complex Double) -> (Vector (Complex Double), Matrix (Complex Double))Source

Eigenvalues and right eigenvectors of a general complex matrix, using LAPACK's *zgeev*.
The eigenvectors are the columns of v. The eigenvalues are not sorted.

eigS :: Matrix Double -> (Vector Double, Matrix Double)Source

Eigenvalues and right eigenvectors of a symmetric real matrix, using LAPACK's *dsyev*.
The eigenvectors are the columns of v.
The eigenvalues are sorted in descending order (use `eigS'`

for ascending order).

eigH :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double))Source

Eigenvalues and right eigenvectors of a hermitian complex matrix, using LAPACK's *zheev*.
The eigenvectors are the columns of v.
The eigenvalues are sorted in descending order (use `eigH'`

for ascending order).

eigH' :: Matrix (Complex Double) -> (Vector Double, Matrix (Complex Double))Source

`eigH`

in ascending order

eigOnlyR :: Matrix Double -> Vector (Complex Double)Source

Eigenvalues of a general real matrix, using LAPACK's *dgeev* with jobz == 'N'.
The eigenvalues are not sorted.

eigOnlyC :: Matrix (Complex Double) -> Vector (Complex Double)Source

Eigenvalues of a general complex matrix, using LAPACK's *zgeev* with jobz == 'N'.
The eigenvalues are not sorted.

eigOnlyS :: Matrix Double -> Vector DoubleSource

Eigenvalues of a symmetric real matrix, using LAPACK's *dsyev* with jobz == 'N'.
The eigenvalues are sorted in descending order.

eigOnlyH :: Matrix (Complex Double) -> Vector DoubleSource

Eigenvalues of a hermitian complex matrix, using LAPACK's *zheev* with jobz == 'N'.
The eigenvalues are sorted in descending order.

# LU

luR :: Matrix Double -> (Matrix Double, [Int])Source

LU factorization of a general real matrix, using LAPACK's *dgetrf*.

luC :: Matrix (Complex Double) -> (Matrix (Complex Double), [Int])Source

LU factorization of a general complex matrix, using LAPACK's *zgetrf*.

# Cholesky

cholS :: Matrix Double -> Matrix DoubleSource

Cholesky factorization of a real symmetric positive definite matrix, using LAPACK's *dpotrf*.

cholH :: Matrix (Complex Double) -> Matrix (Complex Double)Source

Cholesky factorization of a complex Hermitian positive definite matrix, using LAPACK's *zpotrf*.

mbCholS :: Matrix Double -> Maybe (Matrix Double)Source

Cholesky factorization of a real symmetric positive definite matrix, using LAPACK's *dpotrf* (`Maybe`

version).

mbCholH :: Matrix (Complex Double) -> Maybe (Matrix (Complex Double))Source

Cholesky factorization of a complex Hermitian positive definite matrix, using LAPACK's *zpotrf* (`Maybe`

version).

# QR

qrR :: Matrix Double -> (Matrix Double, Vector Double)Source

QR factorization of a real matrix, using LAPACK's *dgeqr2*.

qrC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double))Source

QR factorization of a complex matrix, using LAPACK's *zgeqr2*.

# Hessenberg

hessR :: Matrix Double -> (Matrix Double, Vector Double)Source

Hessenberg factorization of a square real matrix, using LAPACK's *dgehrd*.

hessC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double))Source

Hessenberg factorization of a square complex matrix, using LAPACK's *zgehrd*.