mat_mul_rect

Computes the transpose of a matrix, a matrix-vector product, a matrix-matrix product, the bilinear form, or any triple product.

Synopsis

#include <imsl.h>

float *imsl_f_mat_mul_rect (char *string, …, 0)

The type double function is imsl_d_mat_mul_rect.

Required Arguments

char *string (Input)
String indicating matrix multiplication to be performed.

Return Value

The result of the multiplication. This is always a pointer to a float, even if the result is a single number. To release this space, use imsl_free. If no answer was computed, then NULL is returned.

Synopsis with Optional Arguments

#include <imsl.h>

float *imsl_f_mat_mul_rect (char *string,

IMSL_A_MATRIX, int nrowa, int ncola, float a[],

IMSL_A_COL_DIM, int a_col_dim,

IMSL_B_MATRIX, int nrowb, int ncolb, float b[],

IMSL_B_COL_DIM, int b_col_dim,

IMSL_X_VECTOR, int nx, float *x,

IMSL_Y_VECTOR, int ny, float *y,

IMSL_RETURN_USER, float ans[],

IMSL_RETURN_COL_DIM, int return_col_dim,

Optional Arguments

IMSL_A_MATRIX, int nrowa, int ncola, float a[] (Input)
The nrowa ×ncola matrix A.

IMSL_A_COL_DIM, int a_col_dim (Input)
The column dimension of A.
Default: a_col_dim = ncola

IMSL_B_MATRIX, int nrowb, int ncolb, float b[] (Input)
The nrowb × ncolb matrix A.

IMSL_B_COL_DIM, int b_col_dim (Input)
The column dimension of B.
Default: b_col_dim = ncolb

IMSL_X_VECTOR, int nx, float *x (Input)
The vector x of size nx.

IMSL_Y_VECTOR, int ny, float *y (Input)
The vector y of size ny.

IMSL_RETURN_USER, float ans[] (Output)
A user-allocated array containing the result.

IMSL_RETURN_COL_DIM, int return_col_dim (Input)
The column dimension of the answer.
Default: return_col_dim = the number of columns in the answer

Description

This function computes a matrix-vector product, a matrix-matrix product, a bilinear form of a matrix, or a triple product according to the specification given by string. For example, if “A*x” is given, Ax is computed. In string, the matrices A and B and the vectors x and y can be used. Any of these four names can be used with trans, indicating transpose. The vectors x and y are treated as n × 1 matrices.

If string contains only one item, such as “x” or “trans(A)”, then a copy of the array, or its transpose, is returned. If string contains one multiplication, such as “A*x” or “B*A”, then the indicated product is returned. Some other legal values for string are “trans(y)*A”, “A*trans(B)”, “x*trans(y)”, or “trans(x)*y”.

The matrices and/or vectors referred to in string must be given as optional arguments. If string is “B*x”, then IMSL_B_MATRIX and IMSL_X_VECTOR must be given.

Example

Let

The arrays AT, Ax, xTAT, AB, BTAT, xTy, xyT, and xTAy are computed and printed.

#include <imsl.h>

int main()

{

float A[] = {1, 2, 9,

5, 4, 7};

float B[] = {3, 2,

7, 4,

9, 1};

float x[] = {7, 2, 1};

float y[] = {3, 4, 2};

float *ans;

ans = imsl_f_mat_mul_rect("trans(A)",

IMSL_A_MATRIX, 2, 3, A,

0);

imsl_f_write_matrix("trans(A)", 3, 2, ans, 0);

ans = imsl_f_mat_mul_rect("A*x",

IMSL_A_MATRIX, 2, 3, A,

IMSL_X_VECTOR, 3, x,

0);

imsl_f_write_matrix("A*x", 1, 2, ans, 0);

ans = imsl_f_mat_mul_rect("trans(x)*trans(A)",

IMSL_A_MATRIX, 2, 3, A,

IMSL_X_VECTOR, 3, x,

0);

imsl_f_write_matrix("trans(x)*trans(A)", 1, 2, ans, 0);

ans = imsl_f_mat_mul_rect("A*B",

IMSL_A_MATRIX, 2, 3, A,

IMSL_B_MATRIX, 3, 2, B,

0);

imsl_f_write_matrix("A*B", 2, 2, ans, 0);

ans = imsl_f_mat_mul_rect("trans(B)*trans(A)",

IMSL_A_MATRIX, 2, 3, A,

IMSL_B_MATRIX, 3, 2, B,

0);

imsl_f_write_matrix("trans(B)*trans(A)", 2, 2, ans, 0);

ans = imsl_f_mat_mul_rect("trans(x)*y",

IMSL_X_VECTOR, 3, x,

IMSL_Y_VECTOR, 3, y,

0);

imsl_f_write_matrix("trans(x)*y", 1, 1, ans, 0);

ans = imsl_f_mat_mul_rect("x*trans(y)",

IMSL_X_VECTOR, 3, x,

IMSL_Y_VECTOR, 3, y,

0);

imsl_f_write_matrix("x*trans(y)", 3, 3, ans, 0);

ans = imsl_f_mat_mul_rect("trans(x)*A*y",

IMSL_A_MATRIX, 2, 3, A,

/* use only the first 2 components of x */

IMSL_X_VECTOR, 2, x,

IMSL_Y_VECTOR, 3, y,

0);

imsl_f_write_matrix("trans(x)*A*y", 1, 1, ans, 0);

}

Output

trans(A)

1 2

1 1 5

2 2 4

3 9 7

A*x

1 2

20 50

trans(x)*trans(A)

1 2

20 50

A*B

1 2

1 98 19

2 106 33

trans(B)*trans(A)

1 2

1 98 106

2 19 33

trans(x)*y

x*trans(y)

1 2 3

1 21 28 14

2 6 8 4

3 3 4 2

trans(x)*A*y

293