NAG Library Routine Document

F08FLF (DDISNA)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{JOB}$ – CHARACTER(1)Input

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

$\mathbf{JOB}=\text{'E'}$

The eigenvectors of a symmetric or Hermitian matrix.

$\mathbf{JOB}=\text{'L'}$

The left singular vectors of a general matrix.

$\mathbf{JOB}=\text{'R'}$

The right singular vectors of a general matrix.

Constraint: $\mathbf{JOB}=\text{'E'}$, $\text{'L'}$ or $\text{'R'}$.

2:     $\mathrm{M}$ – INTEGERInput

On entry: $m$, the number of rows of the matrix $A$.

Constraint: $\mathbf{M}\ge 0$.

3:     $\mathrm{N}$ – INTEGERInput

On entry: $n$, the number of columns of the matrix when $\mathbf{JOB}=\text{'L'}$ or $\text{'R'}$.

If $\mathbf{JOB}=\text{'E'}$, N is not referenced.

Constraint: if $\mathbf{JOB}=\text{'L'}$ or $\text{'R'}$, $\mathbf{N}\ge 0$.

4:     $\mathrm{D}\left(*\right)$ – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array D must be at least $\max \left(1,\mathbf{M}\right)$ if $\mathbf{JOB}=\text{'E'}$ and at least $\max \left(1,\min \left(\mathbf{M},\mathbf{N}\right)\right)$ if $\mathbf{JOB}=\text{'L'}$ or $\text{'R'}$.

On entry: the eigenvalues if $\mathbf{JOB}=\text{'E'}$, or singular values if $\mathbf{JOB}=\text{'L'}$ or $\text{'R'}$ of the matrix $A$.

Constraints:

• the elements of the array D must be in either increasing or decreasing order;
• if $\mathbf{JOB}=\text{'L'}$ or $\text{'R'}$ the elements of D must be non-negative.

5:     $\mathrm{SEP}\left(*\right)$ – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array SEP must be at least $\max \left(1,\mathbf{M}\right)$ if $\mathbf{JOB}=\text{'E'}$ and at least $\max \left(1,\min \left(\mathbf{M},\mathbf{N}\right)\right)$ if $\mathbf{JOB}=\text{'L'}$ or $\text{'R'}$.

On exit: the reciprocal condition numbers of the vectors.

6:     $\mathrm{INFO}$ – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

If $\mathbf{INFO}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example