NAG Toolbox: nag_lapack_ztpcon (f07uu)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Indicates whether ${\kappa }_1\left(A\right)$ or ${\kappa }_{\infty }\left(A\right)$ is estimated.

$\mathbf{norm\_p}=\text{'1'}$ or $\text{'O'}$

${\kappa }_1\left(A\right)$ is estimated.

$\mathbf{norm\_p}=\text{'I'}$

${\kappa }_{\infty }\left(A\right)$ is estimated.

Constraint: $\mathbf{norm\_p}=\text{'1'}$, $\text{'O'}$ or $\text{'I'}$.

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

Specifies whether $A$ is upper or lower triangular.

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

$A$ is upper triangular.

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

$A$ is lower triangular.

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

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

Indicates whether $A$ is a nonunit or unit triangular matrix.

$\mathbf{diag}=\text{'N'}$

$A$ is a nonunit triangular matrix.

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

$A$ is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be $1$.

Constraint: $\mathbf{diag}=\text{'N'}$ or $\text{'U'}$.

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

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

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

5:     $\mathrm{ap}\left(:\right)$ – 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 $n$ by $n$ triangular matrix $A$, packed by columns.

More precisely,

• if $\mathbf{uplo}=\text{'U'}$, the upper triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{ap}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if $\mathbf{uplo}=\text{'L'}$, the lower triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{ap}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.

If $\mathbf{diag}=\text{'U'}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced; the same storage scheme is used whether $\mathbf{diag}=\text{'N'}$ or ‘U’.

Optional Input Parameters

None.

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: f07uu_example

function f07uu_example


fprintf('f07uu example results\n\n');

% Condition number of A, where A is Complex Lower triangular and packed.
n = int64(4);
ap = [ 4.78 + 4.56i;  2.00 - 0.30i;  2.89 - 1.34i; -1.89 + 1.15i;
                     -4.11 + 1.25i;  2.36 - 4.25i;  0.04 - 3.69i;
                                     4.15 + 0.80i; -0.02 + 0.46i;
                                                    0.33 - 0.26i];

norm_p = '1';
uplo   = 'L';
diag   = 'N';

% Resciprocal condition estimate
[rcond, info] = f07uu( ...
                       norm_p, uplo, diag, n, ap);

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

f07uu example results

Estimate of condition number =  3.74e+01