mat_add_coordinate (complex)

Performs element-wise addition on two complex matrices stored in coordinate format, C ←αAβB.

Synopsis

#include <imsl.h>

Imsl_c_sparse_elem *imsl_c_mat_add_coordinate (int n, int nz_a, f_complex alpha, Imsl_c_sparse_elem a[], int nz_b, f_complex beta, Imsl_c_sparse_elem b[], int *nz_c, ..., 0)

The type d_complex function is imsl_z_mat_add_coordinate.

Required Arguments

int n (Input)
The order of the matrices A and B.

int nz_a (Input)
Number of nonzeros in the matrix A.

f_complex alpha (Input)
Scalar multiplier for A.

Imsl_c_sparse_elem a[] (Input)
Vector of length nz_a containing the location and value of each nonzero entry in the matrix A.

int nz_b (Input)
Number of nonzeros in the matrix B.

f_complex beta (Input)
Scalar multiplier for B.

Imsl_c_sparse_elem b[] (Input)
Vector of length nz_b containing the location and value of each nonzero entry in the matrix B.

Int *nz_c (Output)
The number of nonzeros in the sum αA + βB.

Return Value

A pointer to an array of type Imsl_c_sparse_elem containing the computed sum. In the event of an error or if the return matrix has no nonzero elements, NULL is returned.

Synopsis with Optional Arguments

#include <imsl.h>

Imsl_c_sparse_elem *imsl_c_mat_add_coordinate (int n, int nz_a, f_complex alpha, Imsl_c_sparse_elem a[], int nz_b, f_complex beta, Imsl_c_sparse_elem b[], int *nz_c,

IMSL_A_TRANSPOSE,

IMSL_B_TRANSPOSE,

IMSL_A_CONJUGATE_TRANSPOSE,

IMSL_B_CONJUGATE_TRANSPOSE,

0)

Optional Arguments

IMSL_A_TRANSPOSE,
Replace A with AT in the expression αAβB.

IMSL_B_TRANSPOSE,
Replace B with BT in the expression αAβB.

IMSL_A_CONJUGATE_TRANSPOSE,
Replace A with AH in the expression αAβB.

IMSL_B_CONJUGATE_TRANSPOSE,
Replace B with BH in the expression αAβB.

Description

The function imsl_c_mat_add_coordinate forms the sum αA + βB, given the scalars αand β and the matrices A and B in coordinate format. The transpose or conjugate transpose of A and/or B may be used during the computation if optional arguments are specified. The method starts by storing A in a linked list data structure, and performs the multiply by α. Next the data in matrix B is traversed and if the coordinates of a nonzero element correspond to those of a nonzero element in A, that entry in the linked list is updated. Otherwise, a new node in the linked list is created. The multiply by β occurs at this time. Lastly, the linked list representation of C is converted to coordinate representation, omitting any elements that may have become zero through cancellation.

Examples

 

Example 1

Add two complex matrices of order 4 stored in coordinate format. Matrix A has five nonzero ele­ments. Matrix B has seven nonzero elements.

 

#include <imsl.h>

#include <stdio.h>

 

int main ()

{

Imsl_c_sparse_elem a[] = {0, 0, 3, 4,

0, 3, -1, 2,

1, 2, 5, -1,

2, 0, 1, 2,

3, 1, 3, 0};

 

Imsl_c_sparse_elem b[] = {0, 1, -2, 1,

0, 3, 1, -2,

1, 0, 3, 0,

2, 2, 5, 2,

2, 3, 1, 4,

3, 0, 4, 0,

3, 1, 3, -2};

 

int nz_a = 5, nz_b = 7, nz_c, n = 4, i;

f_complex alpha = {1.0, 0.0}, beta = {1.0, 0.0};

Imsl_c_sparse_elem *c;

 

c = imsl_c_mat_add_coordinate(n, nz_a, alpha, a, nz_b, beta,

b, &nz_c,

0);

 

printf(" row column value\n");

 

for (i = 0; i < nz_c; i++)

printf("%3d %5d %8.2f %8.2f\n",

c[i].row, c[i].col, c[i].val.re, c[i].val.im);

}

Output

 

row column value

0 0 3.00 4.00

0 1 -2.00 1.00

1 0 3.00 0.00

1 2 5.00 -1.00

2 0 1.00 2.00

2 2 5.00 2.00

2 3 1.00 4.00

3 0 4.00 0.00

3 1 6.00 -2.00

Example 2

Compute 2+3i*AT + 2-i*BT, where

 

 

#include <imsl.h>

#include <stdio.h>

 

int main ()

{

Imsl_c_sparse_elem a[] = {0, 0, 3, 4,

0, 3, -1, 2,

1, 2, 5, -1,

2, 0, 1, 2,

3, 1, 3, 0};

 

Imsl_c_sparse_elem b[] = {0, 1, -2, 1,

0, 3, 1, -2,

1, 0, 3, 0,

2, 2, 5, 2,

2, 3, 1, 4,

3, 0, 4, 0,

3, 1, 3, -2};

 

int nz_a = 5, nz_b = 7, nz_c, n = 4, i;

f_complex alpha = {2.0, 3.0}, beta = {2.0, -1.0};

Imsl_c_sparse_elem *c;

 

c = imsl_c_mat_add_coordinate(n, nz_a, alpha, a,

nz_b, beta, b, &nz_c,

IMSL_A_TRANSPOSE,

IMSL_B_TRANSPOSE,

0);

 

printf(" row column value\n");

for (i = 0; i < nz_c; i++)

printf("%3d %5d %8.2f %8.2f\n",

c[i].row, c[i].col, c[i].val.re, c[i].val.im);

}

Output

 

row column value

0 0 -6.00 17.00

0 1 6.00 -3.00

0 2 -4.00 7.00

0 3 8.00 -4.00

1 0 -3.00 4.00

1 3 10.00 2.00

2 1 13.00 13.00

2 2 12.00 -1.00

3 0 -8.00 -4.00

3 2 6.00 7.00