NAG Library Function Document

nag_ddisna (f08flc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{job}$ – Nag_JobTypeInput

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

$\mathbf{job}=\mathrm{Nag\_EigVecs}$

The eigenvectors of a symmetric or Hermitian matrix.

$\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$

The left singular vectors of a general matrix.

$\mathbf{job}=\mathrm{Nag\_RightSingVecs}$

The right singular vectors of a general matrix.

Constraint: $\mathbf{job}=\mathrm{Nag\_EigVecs}$, $\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$.

2:    $\mathbf{m}$ – IntegerInput

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

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

3:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix when $\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$.

If $\mathbf{job}=\mathrm{Nag\_EigVecs}$, n is not referenced.

Constraint: if $\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$, $\mathbf{n}\ge 0$.

4:    $\mathbf{d}\left[\mathit{dim}\right]$ – const doubleInput

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

• $\max \left(1,\mathbf{m}\right)$ when $\mathbf{job}=\mathrm{Nag\_EigVecs}$;
• $\max \left(1,\min \left(\mathbf{m},\mathbf{n}\right)\right)$ when $\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$.

On entry: the eigenvalues if $\mathbf{job}=\mathrm{Nag\_EigVecs}$, or singular values if $\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$ of the matrix $A$.

Constraints:

• the elements of the array d must be in either increasing or decreasing order;
• if $\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$ the elements of d must be non-negative.

5:    $\mathbf{sep}\left[\mathit{dim}\right]$ – doubleOutput

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

• $\max \left(1,\mathbf{m}\right)$ when $\mathbf{job}=\mathrm{Nag\_EigVecs}$;
• $\max \left(1,\min \left(\mathbf{m},\mathbf{n}\right)\right)$ when $\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$.

On exit: the reciprocal condition numbers of the vectors.

6:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_ENUM_INT

On entry, $\mathbf{job}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$, $\mathbf{n}\ge 0$.

NE_INT

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

NE_NOT_MONOTONIC

Constraint: the elements of the array d must be in either increasing or decreasing order.
if $\mathbf{job}=\mathrm{Nag\_LeftSingVecs}$ or $\mathrm{Nag\_RightSingVecs}$ the elements of d must be non-negative.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example