NAG Toolbox: nag_sparse_direct_real_gen_matmul (f11mk)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

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

Specifies whether or not the matrix $A$ is transposed.

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

$\alpha AB+\beta C$ is computed.

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

$\alpha A^{\mathrm{T}}B+\beta C$ is computed.

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

2:     $\mathrm{alpha}$ – double scalar

$\alpha$, the scalar factor in the matrix multiplication.

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

The dimension of the array icolzp must be at least $\mathbf{n}+1$

$\mathbf{icolzp}\left(i\right)$ contains the index in $A$ of the start of a new column. See Compressed column storage (CCS) format in the F11 Chapter Introduction.

4:     $\mathrm{irowix}\left(:\right)$ – int64int32nag_int array

The dimension of the array irowix must be at least $\mathbf{icolzp}\left(\mathbf{n}+1\right)-1$, the number of nonzeros of the sparse matrix $A$

The row index array of sparse matrix $A$.

5:     $\mathrm{a}\left(:\right)$ – double array

The dimension of the array a must be at least $\mathbf{icolzp}\left(\mathbf{n}+1\right)-1$, the number of nonzeros of the sparse matrix $A$

The array of nonzero values in the sparse matrix $A$.

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

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

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

The $n$ by $m$ matrix $B$.

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

The scalar factor $\beta$.

8:     $\mathrm{c}\left(\mathit{ldc},:\right)$ – double array

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

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

The $n$ by $m$ matrix $C$.

Optional Input Parameters

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

Default: the first dimension of the arrays b, c. (An error is raised if these dimensions are not equal.)

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

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

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

Default: the second dimension of the arrays b, c. (An error is raised if these dimensions are not equal.)

$m$, the number of columns of matrices $B$ and $C$.

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

Output Parameters

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

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

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

$C$ stores $\alpha AB+\beta C$ or $\alpha A^{\mathrm{T}}B+\beta C$ depending on the value of trans.

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: $\mathit{ldb}\ge \max \left(1,\mathbf{n}\right)$.

Constraint: $\mathit{ldc}\ge \max \left(1,\mathbf{n}\right)$.

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

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

On entry, $\mathbf{trans}=\_$.
Constraint: $\mathbf{trans}=\text{'N'}$ 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: f11mk_example

function f11mk_example


fprintf('f11mk example results\n\n');

% Form C = AB and C = A^TB, for sparse A.

icolzp = [int64(1); 3; 5;  7; 9; 12];
irowix = [int64(1); 3; 1;  5; 2;  3;  2; 4; 3; 4; 5];
a      = [        2;  4; 1; -2; 1;  1; -1; 1; 1; 2; 3];
b = [0.70, 1.40;
     0.16, 0.32;
     0.52, 1.04;
     0.77, 1.54;
     0.28, 0.56];
c = [0, 0;
     0, 0;
     0, 0;
     0, 0;
     0, 0];

alpha = 1;
beta  = 0;

% Calculate matrix-matrix product
trans = 'N';
[c, ifail] = f11mk( ...
                    trans, alpha, icolzp, irowix, a, b, beta, c);
fprintf('Matrix-matrix product:\n');
disp(c);

% Calculate transposed matrix-matrix product
trans = 'T';
[c, ifail] = f11mk( ...
                    trans, alpha, icolzp, irowix, a, b, beta, c);
fprintf('\nTransposed matrix-matrix product:\n');
disp(c);

f11mk example results

Matrix-matrix product:
    1.5600    3.1200
   -0.2500   -0.5000
    3.6000    7.2000
    1.3300    2.6600
    0.5200    1.0400


Transposed matrix-matrix product:
    3.4800    6.9600
    0.1400    0.2800
    0.6800    1.3600
    0.6100    1.2200
    2.9000    5.8000