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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.