generate_test_coordinate

Generates test matrices of class D(n, c) and E(n, c). Returns in either coordinate format.

Synopsis

#include <imsl.h>

Imsl_f_sparse_elem *imsl_f_generate_test_coordinate (int n, int c, int *nz, ..., 0)

The function imsl_d_generate_test_coordinate is the double precision analogue.

Required Arguments

int n (Input)
Number of rows in the matrix.

int c (Input)
Parameter used to alter structure.

int *nz (Output)
Length of the return vector.

Return Value

A pointer to a vector of length nz of type Imsl_f_sparse_elem. To release this space, use imsl_free. If no test was generated, then NULL is returned.

Synopsis with Optional Arguments

#include <imsl.h>

void *imsl_f_generate_test_coordinate (int n, int c, int *nz,

IMSL_D_MATRIX,

IMSL_SYMMETRIC_STORAGE,

0)

Optional Arguments

IMSL_D_MATRIX
Return a matrix of class D(n, c).
Default: Return a matrix of class E(n, c).

IMSL_SYMMETRIC_STORAGE,
For coordinate representation, return only values for the diagonal and lower triangle. This option is not allowed if IMSL_D_MATRIX is specified.

Description

We use the same nomenclature as Østerby and Zlatev (1982).Test matrices of class E(n, c), to which we will generally refer to as E-matrices, are symmetric, positive definite matrices of order n with 4 in the diagonal and −1 in the superdiagonal and subdiagonal. In addition there are two bands with −1 at a distance c from the diagonal. More precisely

ai,i = 4	0 ≤ i < n
ai,i+1 = −1	0 ≤ i < n − 1
ai+1,i = −1	0 ≤ i < n − 1
ai,i+c = −1	0 ≤i < n − c
ai+c,i = −1	0 ≤ i < n − c

for any n ≥ 3 and 2 ≤ c ≤ n − 1.

E-matrices are similar to those obtained from the five-point formula in the discretization of elliptic partial differential equations.

Test matrices of class D(n, c) are square matrices of order n with a full diagonal, three bands at a distance c above the diagonal and reappearing cyclically under the diagonal, and a 10 ×10 triangle of elements in the upper right corner. More precisely:

ai,i = 1	0 ≤ i < n
ai,i+c = i + 2	0 ≤ i < n − c
ai,i-n+c = i + 2	n − c ≤ i < n
ai,i+c+1 = −(i + 1)	0 ≤ i < n − c − 1
ai,i-n+c+1 = −(i + 1)	n − c −1 ≤ i < n
ai,i+c+2 = 16	0 ≤ i < n − c − 2
ai,i-n+c+2 = 16	n − c − 2 ≤ i < n
ai,n-11+i+j = 100j	1 ≤ i< 11 − j, 0 ≤ j < 10

for any n ≥14 and 1 ≤ c ≤ n -13.

We now show the sparsity pattern of D(20, 5)

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By default imsl_f_generate_test_coordinate returns an E-matrix in coordinate representation. By specifying the IMSL_SYMMETRIC_STORAGE option, only the diagonal and lower triangle are returned. The scalar nz will contain the number of nonzeros in this representation.

The option IMSL_D_MATRIX will return a matrix of class D(n, c). Since D-matrices are not symmetric, the IMSL_SYMMETRIC_STORAGE option is not allowed.

Examples

 

Example 1

This example generates the matrix

 

and prints the result.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

int i;

int n = 5;

int c = 3;

int nz;

Imsl_f_sparse_elem *a;

 

a = imsl_f_generate_test_coordinate (n, c, &nz,

0);

 

printf ("row col val\n");

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

printf (" %d %d %5.1f\n",

a[i].row, a[i].col, a[i].val);

}

Output

 

row col val

0 0 4.0

1 1 4.0

2 2 4.0

3 3 4.0

4 4 4.0

1 0 -1.0

2 1 -1.0

3 2 -1.0

4 3 -1.0

0 1 -1.0

1 2 -1.0

2 3 -1.0

3 4 -1.0

3 0 -1.0

4 1 -1.0

0 3 -1.0

1 4 -1.0

Example 2

In this example, the matrix E(5, 3) is returned in symmetric storage and printed.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

int i;

int n = 5;

int c = 3;

int nz;

Imsl_f_sparse_elem *a;

 

a = imsl_f_generate_test_coordinate (n, c, &nz,

IMSL_SYMMETRIC_STORAGE,

0);

 

printf ("row col val\n");

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

printf (" %d %d %5.1f\n",

a[i].row, a[i].col, a[i].val);

}

Output

 

row col val

0 0 4.0

1 1 4.0

2 2 4.0

3 3 4.0

4 4 4.0

1 0 -1.0

2 1 -1.0

3 2 -1.0

4 3 -1.0

3 0 -1.0

4 1 -1.0