NAG Toolbox: nag_linsys_real_square_solve_1rhs (f04at)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{a}\left(\mathit{lda},:\right)$ – double array

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

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

The $n$ by $n$ matrix $A$.

2:     $\mathrm{b}\left(:\right)$ – double array

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

The right-hand side vector $b$.

Optional Input Parameters

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

Default: the first dimension of the array a and the second dimension of the arrays a, b.

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

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

Output Parameters

1:     $\mathrm{c}\left(\mathbf{n}\right)$ – double array

The solution vector $x$.

2:     $\mathrm{aa}\left(\mathit{ldaa},\mathbf{n}\right)$ – double array

The first dimension of the array aa will be $\max \left(1,\mathbf{n}\right)$.

The second dimension of the array aa will be $\max \left(1,\mathbf{n}\right)$.

The triangular factors $L$ and $U$, except that the unit diagonal elements of $U$ are not stored.

3:     $\mathrm{ifail}$ – int64int32nag_int scalar

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

Error Indicators and Warnings

   $\mathbf{ifail}=1$

The matrix $A$ is singular, possibly due to rounding errors.

   $\mathbf{ifail}=2$

Iterative refinement fails to improve the solution, i.e., the matrix $A$ is too ill-conditioned.

   $\mathbf{ifail}=3$

On entry,	$\mathbf{n}<0$,
or	$\mathit{lda}<\max \left(1,\mathbf{n}\right)$,
or	$\mathit{ldaa}<\max \left(1,\mathbf{n}\right)$.

   $\mathbf{ifail}=-99$

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: f04at_example

function f04at_example


fprintf('f04at example results\n\n');

% Accurate solution to Ax = b, for general A
a = [  33,  16,  72;
      -24, -10, -57;
       -8,  -4, -17];
b = [-359;
      281;
      85];

[x, LU, ifail] = f04at(a, b);

disp('Solution');
disp(x);

f04at example results

Solution
     1
    -2
    -5