# 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

Description

gebrd

Reduces a general matrix to bidiagonal form.

gesvd

Computes the singular value decomposition of a general rectangular matrix.

heevd

Computes all eigenvalues and, optionally, all eigenvectors of a complex Hermitian matrix using divide and conquer algorithm.

hegvd

Computes all eigenvalues and, optionally, all eigenvectors of a complex generalized Hermitian definite eigenproblem using divide and conquer algorithm.

hetrd

Reduces a complex Hermitian matrix to tridiagonal form.

orgbr

Generates the real orthogonal matrix $$Q$$ or $$P^T$$ determined by gebrd.

orgtr

Generates the real orthogonal matrix $$Q$$ determined by sytrd.

ormtr

Multiplies a real matrix by the orthogonal matrix $$Q$$ determined by sytrd.

syevd

Computes all eigenvalues and, optionally, all eigenvectors of a real symmetric matrix using divide and conquer algorithm.

sygvd

Computes all eigenvalues and, optionally, all eigenvectors of a real generalized symmetric definite eigenproblem using divide and conquer algorithm.

sytrd

Reduces a real symmetric matrix to tridiagonal form.

ungbr

Generates the complex unitary matrix $$Q$$ or $$P^T$$ determined by gebrd.

ungtr

Generates the complex unitary matrix $$Q$$ determined by hetrd.

unmtr

Multiplies a complex matrix by the unitary matrix $$Q$$ determined by hetrd.