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Description | ||||||||||

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

Synopsis | ||||||||||

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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Solves a symmetric positive definite system of linear equations using a precomputed Cholesky factorization obtained by cholS.
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Solves a Hermitian positive definite system of linear equations using a precomputed Cholesky factorization obtained by cholH.
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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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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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Cholesky factorization of a real symmetric positive definite matrix, using LAPACK's dpotrf (Maybe version).
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Cholesky factorization of a complex Hermitian positive definite matrix, using LAPACK's zpotrf (Maybe version).
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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 2.6.1 |