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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 |
| Functional interface to selected 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) | | | 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) | | | 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) | | | 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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| Matrix product
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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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| Linear systems
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| 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.
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| 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.
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| Solve a real linear system from a precomputed LU decomposition (luR), using LAPACK's dgetrs.
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| Solve a real linear system from a precomputed LU decomposition (luC), using LAPACK's zgetrs.
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| 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.
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| 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.
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| :: 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.
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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)
| | 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.
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| SVD
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| Singular values of a real matrix, using LAPACK's dgesvd with jobu == jobvt == 'N'.
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| Singular values of a real matrix, using LAPACK's dgesdd with jobz == 'N'.
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| Singular values of a complex matrix, using LAPACK's zgesvd with jobu == jobvt == 'N'.
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| Singular values of a complex matrix, using LAPACK's zgesdd with jobz == 'N'.
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| Full SVD of a real matrix using LAPACK's dgesvd.
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| Full SVD of a real matrix using LAPACK's dgesdd.
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| Full SVD of a complex matrix using LAPACK's zgesvd.
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| Full SVD of a complex matrix using LAPACK's zgesdd.
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| Thin SVD of a real matrix, using LAPACK's dgesvd with jobu == jobvt == 'S'.
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| Thin SVD of a real matrix, using LAPACK's dgesdd with jobz == 'S'.
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| Thin SVD of a complex matrix, using LAPACK's zgesvd with jobu == jobvt == 'S'.
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| Thin SVD of a complex matrix, using LAPACK's zgesdd with jobz == 'S'.
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| Singular values and all right singular vectors of a real matrix, using LAPACK's dgesvd with jobu == 'N' and jobvt == 'A'.
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| Singular values and all right singular vectors of a complex matrix, using LAPACK's zgesvd with jobu == 'N' and jobvt == 'A'.
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| Singular values and all left singular vectors of a real matrix, using LAPACK's dgesvd with jobu == 'A' and jobvt == 'N'.
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| Singular values and all left singular vectors of a complex matrix, using LAPACK's zgesvd with jobu == 'A' and jobvt == 'N'.
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| Eigensystems
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| 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.
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| 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.
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| 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).
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| eigS in ascending order
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| 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).
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| eigH in ascending order
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| Eigenvalues of a general real matrix, using LAPACK's dgeev with jobz == 'N'.
The eigenvalues are not sorted.
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| Eigenvalues of a general complex matrix, using LAPACK's zgeev with jobz == 'N'.
The eigenvalues are not sorted.
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| Eigenvalues of a symmetric real matrix, using LAPACK's dsyev with jobz == 'N'.
The eigenvalues are sorted in descending order.
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| Eigenvalues of a hermitian complex matrix, using LAPACK's zheev with jobz == 'N'.
The eigenvalues are sorted in descending order.
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| LU
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| LU factorization of a general real matrix, using LAPACK's dgetrf.
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| LU factorization of a general complex matrix, using LAPACK's zgetrf.
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| Cholesky
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| Cholesky factorization of a real symmetric positive definite matrix, using LAPACK's dpotrf.
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| Cholesky factorization of a complex Hermitian positive definite matrix, using LAPACK's zpotrf.
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| QR
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| QR factorization of a real matrix, using LAPACK's dgeqr2.
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| QR factorization of a complex matrix, using LAPACK's zgeqr2.
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| Hessenberg
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| Hessenberg factorization of a square real matrix, using LAPACK's dgehrd.
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| Hessenberg factorization of a square complex matrix, using LAPACK's zgehrd.
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| Schur
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| Schur factorization of a square real matrix, using LAPACK's dgees.
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| Schur factorization of a square complex matrix, using LAPACK's zgees.
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| Produced by Haddock version 2.6.0 |
