naginterfaces.library.lapackeig.ddisna

naginterfaces.library.lapackeig.ddisna(job, m, n, d)

ddisna computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian $m\times m$ matrix $A$, or for the left or right singular vectors of a general $m\times n$ matrix $A$.

For full information please refer to the NAG Library document for f08fl

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08flf.html

Parameters

jobstr, length 1

Specifies for which problem the reciprocal condition number should be computed.

$job=\text{'E'}$

The eigenvectors of a symmetric or Hermitian matrix.

$job=\text{'L'}$

The left singular vectors of a general matrix.

$job=\text{'R'}$

The right singular vectors of a general matrix.

mint

$m$, the number of rows of the matrix $A$.

nint

$n$, the number of columns of the matrix when $job=\text{'L'}$ or $\text{'R'}$.

If $job=\text{'E'}$, $n$ is not referenced.

dfloat, array-like, shape $(:)$

Note: the required length for this argument is determined as follows: if $job=\text{'E'}$: $m$; if $job\text{in}(\text{'L'},\text{'R'})$: $min(m,n)$; otherwise: $0$.

The eigenvalues if $job=\text{'E'}$, or singular values if $job=\text{'L'}$ or $\text{'R'}$ of the matrix $A$.

Returns

sepfloat, ndarray, shape $(:)$

The reciprocal condition numbers of the vectors.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $job$.

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

(errno $-2$)

On entry, error in parameter $m$.

Constraint: $m\ge 0$.

(errno $-3$)

On entry, error in parameter $n$.

Constraint: $n\ge 0$.

(errno $-4$)

On entry, error in parameter $d$.

Constraint: the elements of the array must be in increasing or decreasing order.

(errno $-4$)

On entry, error in parameter $d$.

Constraint: the elements of the array must not be negative.

Notes

The bound on the error, measured by the angle in radians, for the $i$th computed vector is given by $ϵ{\parallel A\parallel }_2/{sep}_i$, where $ϵ$ is the machine precision and ${sep}_i$ is the reciprocal condition number for the vectors, returned in the array element $sep[i-1]$. $sep[i-1]$ is restricted to be at least $ϵ{\parallel A\parallel }_2$ in order to limit the size of the error bound.

References

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