LAPACK Routines

oneMath provides a DPC++ interface to select routines from the Linear Algebra PACKage (LAPACK), as well as several LAPACK-like extension routines. LAPACK routines require column major layout of matrices.

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
geqrf	geqrf_scratchpad_size	Computes the QR factorization of a general m-by-n matrix.
gerqf	gerqf_scratchpad_size	Computes the RQ factorization of a general m-by-n matrix.
getrf	getrf_scratchpad_size	Computes the LU factorization of a general m-by-n matrix.
getri	getri_scratchpad_size	Computes the inverse of an LU-factored general matrix.
getrs	getrs_scratchpad_size	Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.
hetrf	hetrf_scratchpad_size	Computes the Bunch-Kaufman factorization of a complex Hermitian matrix.
orgqr	orgqr_scratchpad_size	Generates the real orthogonal matrix \(Q\) of the QR factorization formed by geqrf.
ormqr	ormqr_scratchpad_size	Multiplies a real matrix by the orthogonal matrix \(Q\) of the QR factorization formed by geqrf.
ormrq	ormrq_scratchpad_size	Multiplies a real matrix by the orthogonal matrix \(Q\) of the RQ factorization formed by gerqf.
potrf	potrf_scratchpad_size	Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.
potri	potri_scratchpad_size	Computes the inverse of a Cholesky-factored symmetric (Hermitian) positive-definite matrix.
potrs	potrs_scratchpad_size	Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix, with multiple right-hand sides.
sytrf	sytrf_scratchpad_size	Computes the Bunch-Kaufman factorization of a symmetric matrix.
trtrs	trtrs_scratchpad_size	Solves a system of linear equations with a triangular coefficient matrix, with multiple right-hand sides.
ungqr	ungqr_scratchpad_size	Generates the complex unitary matrix \(Q\) of the QR factorization formed by geqrf.
unmqr	unmqr_scratchpad_size	Multiplies a complex matrix by the unitary matrix \(Q\) of the QR factorization formed by geqrf.
unmrq	unmrq_scratchpad_size	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
gebrd	gebrd_scratchpad_size	Reduces a general matrix to bidiagonal form.
gesvd	gesvd_scratchpad_size	Computes the singular value decomposition of a general rectangular matrix.
heevd	heevd_scratchpad_size	Computes all eigenvalues and, optionally, all eigenvectors of a complex Hermitian matrix using divide and conquer algorithm.
hegvd	hegvd_scratchpad_size	Computes all eigenvalues and, optionally, all eigenvectors of a complex generalized Hermitian definite eigenproblem using divide and conquer algorithm.
hetrd	hetrd_scratchpad_size	Reduces a complex Hermitian matrix to tridiagonal form.
orgbr	orgbr_scratchpad_size	Generates the real orthogonal matrix \(Q\) or \(P^T\) determined by gebrd.
orgtr	orgtr_scratchpad_size	Generates the real orthogonal matrix \(Q\) determined by sytrd.
ormtr	ormtr_scratchpad_size	Multiplies a real matrix by the orthogonal matrix \(Q\) determined by sytrd.
syevd	syevd_scratchpad_size	Computes all eigenvalues and, optionally, all eigenvectors of a real symmetric matrix using divide and conquer algorithm.
sygvd	sygvd_scratchpad_size	Computes all eigenvalues and, optionally, all eigenvectors of a real generalized symmetric definite eigenproblem using divide and conquer algorithm.
sytrd	sytrd_scratchpad_size	Reduces a real symmetric matrix to tridiagonal form.
ungbr	ungbr_scratchpad_size	Generates the complex unitary matrix \(Q\) or \(P^T\) determined by gebrd.
ungtr	ungtr_scratchpad_size	Generates the complex unitary matrix \(Q\) determined by hetrd.
unmtr	unmtr_scratchpad_size	Multiplies a complex matrix by the unitary matrix \(Q\) determined by hetrd.

LAPACK-like Extensions Routines

oneAPI Math 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
geqrf_batch	geqrf_batch_scratchpad_size	Computes the QR factorizations of a batch of general matrices.
getrf_batch	getrf_batch_scratchpad_size	Computes the LU factorizations of a batch of general matrices.
getri_batch	getri_batch_scratchpad_size	Computes the inverses of a batch of LU-factored general matrices.
getrs_batch	getrs_batch_scratchpad_size	Solves systems of linear equations with a batch of LU-factored square coefficient matrices, with multiple right-hand sides.
orgqr_batch	orgqr_batch_scratchpad_size	Generates the real orthogonal/complex unitary matrix \(Q_i\) of the QR factorization formed by geqrf_batch.
potrf_batch	potrf_batch_scratchpad_size	Computes the Cholesky factorization of a batch of symmetric (Hermitian) positive-definite matrices.
potrs_batch	potrs_batch_scratchpad_size	Solves systems of linear equations with a batch of Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrices, with multiple right-hand sides.
ungqr_batch	ungqr_batch_scratchpad_size	Generates the complex unitary matrix \(Q_i\) with the QR factorization formed by geqrf_batch.

Note

Different arrays used as parameters to oneMath 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