mat_mul_rect (complex)

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

Synopsis

#include <imsl.h>

f_complex *imsl_c_mat_mul_rect (char *string, …, 0)

The type d_complex function is imsl_z_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 an f_complex, 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>

f_complex *imsl_c_mat_mul_rect (char *string,

IMSL_A_MATRIX, int nrowa, int ncola, f_complex *a,

IMSL_A_COL_DIM, int a_col_dim,

IMSL_B_MATRIX, int nrowb, int ncolb, f_complex *b,

IMSL_B_COL_DIM, int b_col_dim,

IMSL_X_VECTOR, int nx, f_complex *x,

IMSL_Y_VECTOR, int ny, f_complex *y,

IMSL_RETURN_USER, f_complex ans[],

IMSL_RETURN_COL_DIM, int return_col_dim,

Optional Arguments

IMSL_A_MATRIX, int nrowa, int ncola, f_complex *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, f_complex *b (Input)
The nrowb × ncolb matrix B.

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

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

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

IMSL_RETURN_USER, f_complex 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, or with ctrans, indicating conjugate (or Hermitian) 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*ctrans(B)”, “x*trans(y)”, or “ctrans(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 AH, Ax, xTAT, AB, BHAT, xTy, and xyH are computed and printed.

#include <imsl.h>

int main()

{

f_complex A[] = {{1,4}, {2, 3}, {9,6},

{5,2}, {4,-3}, {7,1}};

f_complex B[] = {{3,-6}, {2, 4},

{7, 3}, {4,-5},

{9, 2}, {1, 3}};

f_complex x[] = {{7,4}, {2, 2}, {1,-5}};

f_complex y[] = {{3,4}, {4,-2}, {2, 3}};

f_complex *ans;

ans = imsl_c_mat_mul_rect("ctrans(A)",

IMSL_A_MATRIX, 2, 3, A,

0);

imsl_c_write_matrix("ctrans(A)", 3, 2, ans, 0);

ans = imsl_c_mat_mul_rect("A*x",

IMSL_A_MATRIX, 2, 3, A,

IMSL_X_VECTOR, 3, x,

0);

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

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

IMSL_A_MATRIX, 2, 3, A,

IMSL_X_VECTOR, 3, x,

0);

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

ans = imsl_c_mat_mul_rect("A*B",

IMSL_A_MATRIX, 2, 3, A,

IMSL_B_MATRIX, 3, 2, B,

0);

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

ans = imsl_c_mat_mul_rect("ctrans(B)*trans(A)",

IMSL_A_MATRIX, 2, 3, A,

IMSL_B_MATRIX, 3, 2, B,

0);

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

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

IMSL_X_VECTOR, 3, x,

IMSL_Y_VECTOR, 3, y,

0);

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

ans = imsl_c_mat_mul_rect("x*ctrans(y)",

IMSL_X_VECTOR, 3, x,

IMSL_Y_VECTOR, 3, y,

0);

imsl_c_write_matrix("x*ctrans(y)", 3, 3, ans, 0);

}

Output

ctrans(A)

1 2

1 ( 1, -4) ( 5, -2)

2 ( 2, -3) ( 4, 3)

3 ( 9, -6) ( 7, -1)

A*x

1 2

( 28, 3) ( 53, 2)

trans(x)*trans(A)

1 2

( 28, 3) ( 53, 2)

A*B

1 2

1 ( 101, 105) ( 0, 47)

2 ( 125, -10) ( 7, 14)

ctrans(B)*trans(A)

1 2

1 ( 95, 69) ( 87, -2)

2 ( 38, 5) ( 59, -28)

trans(x)*y

( 34, 37)

x*ctrans(y)

1 2 3

1 ( 37, -16) ( 20, 30) ( 26, -13)

2 ( 14, -2) ( 4, 12) ( 10, -2)

3 ( -17, -19) ( 14, -18) ( -13, -13)