NAG Toolbox: nag_lapack_zspcon (f07qu)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{uplo}$ – string (length ≥ 1)

Specifies how $A$ has been factorized.

$\mathbf{uplo}=\text{'U'}$

$A=PUD{U}^{\mathrm{T}}{P}^{\mathrm{T}}$, where $U$ is upper triangular.

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

$A=PLD{L}^{\mathrm{T}}{P}^{\mathrm{T}}$, where $L$ is lower triangular.

Constraint: $\mathbf{uplo}=\text{'U'}$ or $\text{'L'}$.

2:     $\mathrm{ap}\left(:\right)$ – complex array

The dimension of the array ap must be at least $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$

The factorization of $A$ stored in packed form, as returned by nag_lapack_zsptrf (f07qr).

3:     $\mathrm{ipiv}\left(:\right)$ – int64int32nag_int array

The dimension of the array ipiv must be at least $\max \left(1,\mathbf{n}\right)$

Details of the interchanges and the block structure of $D$, as returned by nag_lapack_zsptrf (f07qr).

4:     $\mathrm{anorm}$ – double scalar

The $1$-norm of the original matrix $A$. anorm must be computed either before calling nag_lapack_zsptrf (f07qr) or else from a copy of the original matrix $A$.

Constraint: $\mathbf{anorm}\ge 0.0$.

Optional Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

Default: the dimension of the array ipiv.

$n$, the order of the matrix $A$.

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

Output Parameters

1:     $\mathrm{rcond}$ – double scalar

An estimate of the reciprocal of the condition number of $A$. rcond is set to zero if exact singularity is detected or the estimate underflows. If rcond is less than machine precision, $A$ is singular to working precision.

2:     $\mathrm{info}$ – int64int32nag_int scalar

$\mathbf{info}=0$ unless the function detects an error (see Error Indicators and Warnings).

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.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f07qu_example

function f07qu_example


fprintf('f07qu example results\n\n');

% Estimate condition number of A, where A is complex symmetric matrix
% such that the lower triangular part is stored in packed format

% A in full format first to get 1-norm of A
n = int64(4);
a =  [ -0.39 - 0.71i   5.14 - 0.64i  -7.86 - 2.96i   3.80 + 0.92i;
        5.14 - 0.64i   8.86 + 1.81i  -3.52 + 0.58i   5.32 - 1.59i;
       -7.86 - 2.96i  -3.52 + 0.58i  -2.83 - 0.03i  -1.54 - 2.86i;
        3.80 + 0.92i   5.32 - 1.59i  -1.54 - 2.86i  -0.56 + 0.12i];
anorm = norm(a,1);

% pack A in array ap
uplo = 'L';
ap = [];
for j = 1:n
  ap = [ap; a(j:n,j)];
end

% Factorize packed form
[apf, ipiv, info] = f07qr( ...
                           uplo, n, ap);

% Get reciprocal condition number
[rcond, info] = f07qu( ...
                       uplo, apf, ipiv, anorm);

fprintf('Estimate of condition number = %9.2e\n', 1/rcond);

f07qu example results

Estimate of condition number =  2.06e+01