NAG Toolbox: nag_sparse_direct_real_gen_cond (f11mg)

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 to be 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:     $\mathrm{n}$ – int64int32nag_int scalar

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

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

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

The dimension of the array il must be at least as large as the dimension of the array of the same name in nag_sparse_direct_real_gen_lu (f11me)

Records the sparsity pattern of matrix $L$ as computed by nag_sparse_direct_real_gen_lu (f11me).

4:     $\mathrm{lval}\left(:\right)$ – double array

The dimension of the array lval must be at least as large as the dimension of the array of the same name in nag_sparse_direct_real_gen_lu (f11me)

Records the nonzero values of matrix $L$ and some nonzero values of matrix $U$ as computed by nag_sparse_direct_real_gen_lu (f11me).

5:     $\mathrm{iu}\left(:\right)$ – int64int32nag_int array

The dimension of the array iu must be at least as large as the dimension of the array of the same name in nag_sparse_direct_real_gen_lu (f11me)

Records the sparsity pattern of matrix $U$ as computed by nag_sparse_direct_real_gen_lu (f11me).

6:     $\mathrm{uval}\left(:\right)$ – double array

The dimension of the array uval must be at least as large as the dimension of the array of the same name in nag_sparse_direct_real_gen_lu (f11me)

Records some nonzero values of matrix $U$ as computed by nag_sparse_direct_real_gen_lu (f11me).

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

If $\mathbf{norm\_p}=\text{'1'}$ or $\text{'O'}$, the $1$-norm of the matrix $A$.

If $\mathbf{norm\_p}=\text{'I'}$, the $\infty$-norm of the matrix $A$.

anorm may be computed by calling nag_sparse_direct_real_gen_norm (f11ml) with the same value for the argument norm_p.

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

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:     $\mathrm{ifail}$ – int64int32nag_int scalar

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

Error Indicators and Warnings

   $\mathbf{ifail}=1$

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

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

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

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: f11mg_example

function f11mg_example


fprintf('f11mg example results\n\n');

% Sparse matrix A
n      = int64(5);
a      = [        2;  4; 1; -2; 1;  1; -1; 1; 1; 2; 3];
icolzp = [int64(1); 3; 5;  7; 9; 12];
irowix = [int64(1); 3; 1;  5; 2;  3;  2; 4; 3; 4; 5];
nz     = icolzp(n+1) - 1;

% Calculate COLAMD permutation
spec   = 'M';
iprm   = zeros(7*n, 1, 'int64');

[iprm, ifail] = f11md( ...
                       spec, n, icolzp, irowix, iprm);


% Factorise
thresh = 1;
nzlmx  = int64(8*nz);
nzlumx = int64(8*nz);
nzumx  = int64(8*nz);

[iprm, nzlumx, il, lval, iu, uval, nnzl, nnzu, flop, ifail] = ...
  f11me( ...
         n, irowix, a, iprm, thresh, nzlmx, nzlumx, nzumx);

% Calculate Norm
norm_p = '1';
[anorm, ifail] = f11ml( ...
                        norm_p, n, icolzp, irowix, a);

% Calculate condition number
[rcond, ifail] = f11mg( ...
                        norm_p, n, il, lval, iu, uval, anorm);

fprintf('Norm             = %7.3f\n', anorm);
fprintf('Condition number = %7.3f\n', 1/rcond);

f11mg example results

Norm             =   6.000
Condition number =  20.250