?disna

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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?disna

Computes the reciprocal condition numbers for the eigenvectors of a symmetric/ Hermitian matrix or for the left or right singular vectors of a general matrix.

Syntax

lapack_int LAPACKE_sdisna (char job, lapack_int m, lapack_int n, const float* d, float* sep);

lapack_int LAPACKE_ddisna (char job, lapack_int m, lapack_int n, const double* d, double* sep);

Include Files

mkl.h

Description

The routine computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix.

The reciprocal condition number is the 'gap' between the corresponding eigenvalue or singular value and the nearest other one.

The bound on the error, measured by angle in radians, in the i-th computed vector is given by

?lamch('E')*(anorm/sep(i))

where anorm = ||A||₂ = max( |d(j)| ). sep(i) is not allowed to be smaller than slamch('E')*anorm in order to limit the size of the error bound.

?disna may also be used to compute error bounds for eigenvectors of the generalized symmetric definite eigenproblem.

Input Parameters

job

Must be 'E','L', or 'R'. Specifies for which problem the reciprocal condition numbers should be computed:

job = 'E': for the eigenvectors of a symmetric/Hermitian matrix;

job = 'L': for the left singular vectors of a general matrix;

job = 'R': for the right singular vectors of a general matrix.

m

The number of rows of the matrix (m≥ 0).

n

If job = 'L', or 'R', the number of columns of the matrix (n≥ 0). Ignored if job = 'E'.

d

Array, dimension at least max(1,m) if job = 'E', and at least max(1, min(m,n)) if job = 'L' or 'R'.

This array must contain the eigenvalues (if job = 'E') or singular values (if job = 'L' or 'R') of the matrix, in either increasing or decreasing order.

If singular values, they must be non-negative.

Output Parameters

sep: Array, dimension at least max(1,m) if job = 'E', and at least max(1, min(m,n)) if job = 'L' or 'R'. The reciprocal condition numbers of the vectors.

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

Parent topic: Symmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?disna