# ddisna.f - Man Page

SRC/ddisna.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine 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

NAG Ltd.

Definition at line 116 of file ddisna.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ddisna(3) is an alias of ddisna.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK