?disna

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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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

call sdisna(job, m, n, d, sep, info)

call ddisna(job, m, n, d, sep, info)

call disna(d, sep [,job] [,minmn] [,info])

Include Files

mkl.fi, lapack.f90

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

CHARACTER*1. 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

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

n

INTEGER.

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

d

REAL for sdisna

DOUBLE PRECISION for ddisna.

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

REAL for sdisna

DOUBLE PRECISION for ddisna.

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.

info

INTEGER.

If info = 0, the execution is successful.

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

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine disna interface are the following:

d

Holds the vector of length min(m,n).

sep

Holds the vector of length min(m,n).

job

Must be 'E', 'L', or 'R'. The default value is 'E'.

minmn

Indicates which of the values m or n is smaller. Must be either 'M' or 'N', the default is 'M'.

If job = 'E', this argument is superfluous, If job = 'L' or 'R', this argument is used by the routine.

Parent topic: Symmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?disna