Integer, Intent (In)	::	m, n
Integer, Intent (Out)	::	info
Real (Kind=nag_wp), Intent (In)	::	d(*)
Real (Kind=nag_wp), Intent (Inout)	::	sep(*)
Character (1), Intent (In)	::	job

C Header Interface

#include <nag.h>

void	f08flf_ (const char job, const Integer m, const Integer n, const double d[], double sep[], Integer info, const Charlen length_job)

The routine may be called by the names f08flf, nagf_lapackeig_ddisna or its LAPACK name ddisna.

3 Description

The bound on the error, measured by the angle in radians, for the

i

th computed vector is given by

ε {‖ A ‖}_{2} / {sep}_{i}

, where

ε

is the machine precision and

{sep}_{i}

is the reciprocal condition number for the vectors, returned in the array element

sep (i)

sep (i)

is restricted to be at least

ε {‖ A ‖}_{2}

in order to limit the size of the error bound.

4 References

Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

5 Arguments

1: $job$ – Character(1) Input

On entry: specifies for which problem the reciprocal condition number should be computed.

$job ='E'$: The eigenvectors of a symmetric or Hermitian matrix.
$job ='L'$: The left singular vectors of a general matrix.
$job ='R'$: The right singular vectors of a general matrix.

Constraint:

job ='E'

'L'

'R'

2: $m$ – Integer Input

On entry:

m

, the number of rows of the matrix

A

Constraint:

m \geq 0

3: $n$ – Integer Input

On entry:

n

, the number of columns of the matrix when

job ='L'

'R'

job ='E'

, n is not referenced.

Constraint: if

job ='L'

'R'

n \geq 0

4: $d (*)$ – Real (Kind=nag_wp) array Input

Note: the dimension of the array d must be at least

\max (1, m)

job ='E'

and at least

\max (1, \min (m, n))

job ='L'

'R'

On entry: the eigenvalues if

job ='E'

, or singular values if

job ='L'

'R'

of the matrix

A

Constraints:

the elements of the array d must be in either increasing or decreasing order;
if $job ='L'$ or $'R'$ the elements of d must be non-negative.

5: $sep (*)$ – Real (Kind=nag_wp) array Output

Note: the dimension of the array sep must be at least

\max (1, m)

job ='E'

and at least

\max (1, \min (m, n))

job ='L'

'R'

On exit: the reciprocal condition numbers of the vectors.

6: $info$ – Integer Output

On exit:

info = 0

unless the routine detects an error (see Section 6).

6 Error Indicators and Warnings

$info < 0$: If $info = - i$ , argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

7 Accuracy

The reciprocal condition numbers are computed to machine precision relative to the size of the eigenvalues, or singular values.

8 Parallelism and Performance

f08flf is not threaded in any implementation.

9 Further Comments

f08flf may also be used towards computing error bounds for the eigenvectors of the generalized symmetric or Hermitian definite eigenproblem. See Golub and Van Loan (1996) for further details on the error bounds.

10 Example

The use of f08flf in computing error bounds for eigenvectors of the symmetric eigenvalue problem is illustrated in f08faf; its use in computing error bounds for singular vectors is illustrated in f08kbf; and its use in computing error bounds for eigenvectors of the generalized symmetric definite eigenvalue problem is illustrated in f08saf.

NAG Library Manual, Mark 27.3

Interfaces: FL CL CPP AD

NAG FL Interface Introduction

F08 (Lapackeig) Chapter Contents

F08 (Lapackeig) Chapter Introduction

f08fl: FL CL CPP AD

NAG FL Interfacef08flf (ddisna)

▸▿ Contents

1 Purpose

2 Specification