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Manual

disna

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ddisna (character job, integer m, integer n, double precision,dimension( * ) d, double precision, dimension( * ) sep, integer info)
subroutine sdisna (character job, integer m, integer n, real, dimension( *) d, real, dimension( * ) sep, integer info)
Author

NAME

disna - disna: eig condition numbers

SYNOPSIS

Functions

subroutine ddisna (job, m, n, d, sep, info)
DDISNA
subroutine sdisna (job, m, n, d, sep, info)
SDISNA

Detailed Description

Function Documentation

subroutine ddisna (character job, integer m, integer n, double precision,dimension( * ) d, double precision, dimension( * ) sep, integer info)

DDISNA

Purpose:

DDISNA 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

DLAMCH( ’E’ ) * ( ANORM / SEP( I ) )

where ANORM = 2-norm(A) = max( abs( D(j) ) ). SEP(I) is not allowed
to be smaller than DLAMCH( ’E’ )*ANORM in order to limit the size of
the error bound.

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

Parameters

JOB

JOB is CHARACTER*1
Specifies for which problem the reciprocal condition numbers
should be computed:
= ’E’: the eigenvectors of a symmetric/Hermitian matrix;
= ’L’: the left singular vectors of a general matrix;
= ’R’: the right singular vectors of a general matrix.

M

M is INTEGER
The number of rows of the matrix. M >= 0.

N

N is INTEGER
If JOB = ’L’ or ’R’, the number of columns of the matrix,
in which case N >= 0. Ignored if JOB = ’E’.

D

D is DOUBLE PRECISION array, dimension (M) if JOB = ’E’
dimension (min(M,N)) if JOB = ’L’ or ’R’
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.

SEP

SEP is DOUBLE PRECISION array, dimension (M) if JOB = ’E’
dimension (min(M,N)) if JOB = ’L’ or ’R’
The reciprocal condition numbers of the vectors.

INFO

INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sdisna (character job, integer m, integer n, real, dimension( *) d, real, dimension( * ) sep, integer info)

SDISNA

Purpose:

SDISNA 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

SLAMCH( ’E’ ) * ( ANORM / SEP( I ) )

where ANORM = 2-norm(A) = max( abs( D(j) ) ). SEP(I) is not allowed
to be smaller than SLAMCH( ’E’ )*ANORM in order to limit the size of
the error bound.

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

Parameters

JOB

JOB is CHARACTER*1
Specifies for which problem the reciprocal condition numbers
should be computed:
= ’E’: the eigenvectors of a symmetric/Hermitian matrix;
= ’L’: the left singular vectors of a general matrix;
= ’R’: the right singular vectors of a general matrix.

M

M is INTEGER
The number of rows of the matrix. M >= 0.

N

N is INTEGER
If JOB = ’L’ or ’R’, the number of columns of the matrix,
in which case N >= 0. Ignored if JOB = ’E’.

D

D is REAL array, dimension (M) if JOB = ’E’
dimension (min(M,N)) if JOB = ’L’ or ’R’
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.

SEP

SEP is REAL array, dimension (M) if JOB = ’E’
dimension (min(M,N)) if JOB = ’L’ or ’R’
The reciprocal condition numbers of the vectors.

INFO

INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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