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 a 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,
0)
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)