LAPACK Routines#
oneMKL provides a DPC++ interface to select routines from the Linear Algebra PACKage (LAPACK), as well as several LAPACK-like extension routines.
LAPACK Linear Equation Routines#
LAPACK Linear Equation routines are used for factoring a matrix, solving a system of linear equations, solving linear least squares problems, and inverting a matrix. The following table lists the LAPACK Linear Equation routine groups.
Routines |
Scratchpad Size Routines |
Description |
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Computes the QR factorization of a general m-by-n matrix. |
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Computes the RQ factorization of a general m-by-n matrix. |
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Computes the LU factorization of a general m-by-n matrix. |
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Computes the inverse of an LU-factored general matrix. |
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Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides. |
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Computes the Bunch-Kaufman factorization of a complex Hermitian matrix. |
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Generates the real orthogonal matrix \(Q\) of the QR factorization formed by geqrf. |
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Multiplies a real matrix by the orthogonal matrix \(Q\) of the QR factorization formed by geqrf. |
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Multiplies a real matrix by the orthogonal matrix \(Q\) of the RQ factorization formed by gerqf. |
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Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix. |
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Computes the inverse of a Cholesky-factored symmetric (Hermitian) positive-definite matrix. |
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Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix, with multiple right-hand sides. |
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Computes the Bunch-Kaufman factorization of a symmetric matrix. |
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Solves a system of linear equations with a triangular coefficient matrix, with multiple right-hand sides. |
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Generates the complex unitary matrix \(Q\) of the QR factorization formed by geqrf. |
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Multiplies a complex matrix by the unitary matrix \(Q\) of the QR factorization formed by geqrf. |
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Multiplies a complex matrix by the unitary matrix \(Q\) of the RQ factorization formed by gerqf. |
LAPACK Singular Value and Eigenvalue Problem Routines#
LAPACK Singular Value and Eigenvalue Problem routines are used for singular value and eigenvalue problems, and for performing a number of related computational tasks. The following table lists the LAPACK Singular Value and Eigenvalue Problem routine groups.
Routines |
Scratchpad Size Routines |
Description |
---|---|---|
Reduces a general matrix to bidiagonal form. |
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Computes the singular value decomposition of a general rectangular matrix. |
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Computes all eigenvalues and, optionally, all eigenvectors of a complex Hermitian matrix using divide and conquer algorithm. |
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Computes all eigenvalues and, optionally, all eigenvectors of a complex generalized Hermitian definite eigenproblem using divide and conquer algorithm. |
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Reduces a complex Hermitian matrix to tridiagonal form. |
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Generates the real orthogonal matrix \(Q\) or \(P^T\) determined by gebrd. |
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Generates the real orthogonal matrix \(Q\) determined by sytrd. |
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Multiplies a real matrix by the orthogonal matrix \(Q\) determined by sytrd. |
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Computes all eigenvalues and, optionally, all eigenvectors of a real symmetric matrix using divide and conquer algorithm. |
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Computes all eigenvalues and, optionally, all eigenvectors of a real generalized symmetric definite eigenproblem using divide and conquer algorithm. |
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Reduces a real symmetric matrix to tridiagonal form. |
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Generates the complex unitary matrix \(Q\) or \(P^T\) determined by gebrd. |
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Generates the complex unitary matrix \(Q\) determined by hetrd. |
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Multiplies a complex matrix by the unitary matrix \(Q\) determined by hetrd. |
LAPACK-like Extensions Routines#
oneAPI Math Kernel Library DPC++ provides additional routines to extend the functionality of the LAPACK routines. These include routines to compute many independent factorizations, linear equation solutions, and similar. The following table lists the LAPACK-like Extensions routine groups.
Routines |
Scratchpad Size Routines |
Description |
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Computes the QR factorizations of a batch of general matrices. |
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Computes the LU factorizations of a batch of general matrices. |
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Computes the inverses of a batch of LU-factored general matrices. |
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Solves systems of linear equations with a batch of LU-factored square coefficient matrices, with multiple right-hand sides. |
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Generates the real orthogonal/complex unitary matrix \(Q_i\) of the QR factorization formed by geqrf_batch. |
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Computes the Cholesky factorization of a batch of symmetric (Hermitian) positive-definite matrices. |
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Solves systems of linear equations with a batch of Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrices, with multiple right-hand sides. |
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Generates the complex unitary matrix \(Q_i\) with the QR factorization formed by geqrf_batch. |
Note
Different arrays used as parameters to oneMKL LAPACK routines must not overlap.
Warning
LAPACK routines assume that input matrices do not contain IEEE 754 special values such as INF or NaN values. Using these special values may cause LAPACK to return unexpected results or become unstable.
Parent topic: Dense Linear Algebra