NAG Toolbox: nag_linsys_real_blkdiag_fac_solve (f04lh)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Specifies the equations to be solved.

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

Solve $AX=B$.

$\mathbf{trans}=\text{'T'}$

Solve $A^{\mathrm{T}}X=B$.

Constraint: $\mathbf{trans}=\text{'N'}$ or $\text{'T'}$.

2:     $\mathrm{blkstr}\left(3,\mathbf{nbloks}\right)$ – int64int32nag_int array

Information which describes the block structure of $A$, as supplied to nag_linsys_real_blkdiag_fac_solve (f04lh).

3:     $\mathrm{a}\left(\mathbf{lena}\right)$ – double array

The elements in the factorization of $A$, as returned by nag_linsys_real_blkdiag_fac_solve (f04lh).

4:     $\mathrm{pivot}\left(\mathbf{n}\right)$ – int64int32nag_int array

Details of the interchanges in the factorization, as returned by nag_linsys_real_blkdiag_fac_solve (f04lh).

5:     $\mathrm{b}\left(\mathit{ldb},\mathbf{ir}\right)$ – double array

ldb, the first dimension of the array, must satisfy the constraint $\mathit{ldb}\ge \mathbf{n}$.

The $n$ by $r$ right-hand side matrix $B$.

Optional Input Parameters

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

Default: the dimension of the array pivot and the first dimension of the array b. (An error is raised if these dimensions are not equal.)

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

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

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

Default: the dimension of the array blkstr.

The total number of blocks of the matrix $A$, as supplied to nag_linsys_real_blkdiag_fac_solve (f04lh).

Constraint: $0<\mathbf{nbloks}\le \mathbf{n}$.

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

Default: the dimension of the array a.

The dimension of the array a.

Constraint: $\mathbf{lena}\ge {\displaystyle \sum _{k=1}^{\mathbf{nbloks}}}\mathbf{blkstr}\left(1,k\right)\times \mathbf{blkstr}\left(2,k\right)$.

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

Default: the second dimension of the array b.

$r$, the number of right-hand sides.

Constraint: $\mathbf{ir}>0$.

Output Parameters

1:     $\mathrm{b}\left(\mathit{ldb},\mathbf{ir}\right)$ – double array

b stores the $n$ by $r$ solution matrix $X$.

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

   $\mathbf{ifail}=1$

On entry,	$\mathbf{n}<1$,
or	$\mathbf{nbloks}<1$,
or	$\mathbf{ir}<1$,
or	$\mathit{ldb}<\mathbf{n}$,
or	$\mathbf{n}<\mathbf{nbloks}$,
or	lena is too small,
or	illegal values detected in blkstr,
or	$\mathbf{trans}\ne \text{'N'}$ or $\text{'T'}$.

   $\mathbf{ifail}=-99$

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: f04lh_example

function f04lh_example


fprintf('f04lh example results\n\n');

% Block structure of A
n = int64(18);
blkstr = [int64(2),4,5,3,4;
                  4, 7,8,6,5;
                  3, 4,2,3,0];
a1 = [-1.00  -0.98  -0.79  -0.15;
      -1.00   0.25  -0.87   0.35];
a2 = [ 0.78   0.31  -0.85   0.89  -0.69  -0.98 -0.76;
      -0.82   0.12  -0.01   0.75   0.32  -1.00 -0.53;
      -0.83  -0.98  -0.58   0.04   0.87   0.38 -1.00;
      -0.21  -0.93  -0.84   0.37  -0.94  -0.96 -1.00];
a3 = [-0.99  -0.91  -0.28   0.90   0.78  -0.93  -0.76   0.48;
      -0.87  -0.14  -1.00  -0.59  -0.99   0.21  -0.73  -0.48;
      -0.93  -0.91   0.10  -0.89  -0.68  -0.09  -0.58  -0.21;
       0.85  -0.39   0.79  -0.71   0.39  -0.99  -0.12  -0.75;
       0.17  -1.37   1.29  -1.59   1.10  -1.63  -1.01  -0.27];
a4 = [ 0.08   0.61   0.54  -0.41   0.16  -0.46;
      -0.67   0.56  -0.99   0.16  -0.16   0.98;
      -0.24  -0.41   0.40  -0.93   0.70   0.43];
a5 = [ 0.71  -0.97  -0.60  -0.30   0.18; 
      -0.47  -0.98  -0.73   0.07   0.04; 
      -0.25  -0.92  -0.52  -0.46  -0.58; 
       0.89  -0.94  -0.54  -1.00  -0.36];
% Flatten A
a = [reshape(a1,[ 8,1]);
     reshape(a2,[28,1]);
     reshape(a3,[40,1]);
     reshape(a4,[18,1]);
     reshape(a5,[20,1])];

% Right hand side     
b  = [-2.92;  -1.27;  -1.30;  -1.17;  -2.10;  -4.51;  -1.71;  -4.59;
      -4.19;  -0.93;  -3.31;   0.52;  -0.12;  -0.05;  -0.98;  -2.07;
      -2.73;  -1.95];
    
% Factorize A
tol = 0;
[AF, pivot, tol, index, ifail] = ...
f01lh(n, blkstr, a, tol);

% Solve system
trans = 'N';
[x, ifail] = f04lh( ...
                    trans, blkstr, AF, pivot, b);
disp('Component solution');
disp(x);

f04lh example results

Component solution
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000