void test04 ( )
/******************************************************************************/
/*
Purpose:
TEST04 works with a CC sparse matrix with many repeated index pairs.
Discussion:
To complete this test, I want to compare AST * X and ACC * X.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
23 July 2014
Author:
John Burkardt
*/
{
double *acc;
double *ast;
double *b1;
double *b2;
int *ccc;
int i_max;
int i_min;
int *icc;
int *ist;
int j_max;
int j_min;
int *jst;
int m;
int n;
int ncc;
int nst;
int nx;
int ny;
double r;
int seed;
double *x;
printf ( "\n" );
printf ( "TEST04\n" );
printf ( " Convert a sparse matrix from ST to CC format.\n" );
printf ( " ST: sparse triplet, I, J, A.\n" );
printf ( " CC: compressed column, I, CC, A.\n" );
printf ( " The ST matrix is the Wathen finite element matrix.\n" );
printf ( " It has many repeated index pairs.\n" );
printf ( " To check, compare ACC*X - AST*X for a random X.\n" );
/*
Get the size of the ST matrix.
*/
nx = 3;
ny = 3;
nst = wathen_st_size ( nx, ny );
printf ( "\n" );
printf ( " Number of ST values = %d\n", nst );
/*
Set the formal matrix size
*/
m = 3 * nx * ny + 2 * nx + 2 * ny + 1;
n = m;
/*
Set a random vector.
*/
seed = 123456789;
x = r8vec_uniform_01_new ( n, &seed );
/*
Allocate space.
*/
ist = ( int * ) malloc ( nst * sizeof ( int ) );
jst = ( int * ) malloc ( nst * sizeof ( int ) );
/*
Create the ST matrix.
*/
seed = 123456789;
ast = wathen_st ( nx, ny, nst, &seed, ist, jst );
i_min = i4vec_min ( nst, ist );
i_max = i4vec_max ( nst, ist );
j_min = i4vec_min ( nst, jst );
j_max = i4vec_max ( nst, jst );
st_header_print ( i_min, i_max, j_min, j_max, m, n, nst );
/*
Compute B1 = AST * X
*/
b1 = st_mv ( m, n, nst, ist, jst, ast, x );
/*
Get the CC size.
*/
ncc = st_to_cc_size ( nst, ist, jst );
printf ( " Number of CC values = %d\n", ncc );
/*
Create the CC indices.
*/
icc = ( int * ) malloc ( ncc * sizeof ( int ) );
ccc = ( int * ) malloc ( ( n + 1 ) * sizeof ( int ) );
st_to_cc_index ( nst, ist, jst, ncc, n, icc, ccc );
/*
Create the CC values.
*/
acc = st_to_cc_values ( nst, ist, jst, ast, ncc, n, icc, ccc );
/*
Compute B2 = ACC * X.
*/
b2 = cc_mv ( m, n, ncc, icc, ccc, acc, x );
/*
Compare B1 and B2.
*/
r = r8vec_diff_norm ( n, b1, b2 );
printf ( " || ACC*X - AST*X|| = %g\n", r );
/*
Free memory.
*/
free ( acc );
free ( ast );
free ( b1 );
free ( b2 );
free ( ccc );
free ( icc );
free ( ist );
free ( jst );
free ( x );
return;
}
void test01 ( )
/******************************************************************************/
/*
Purpose:
TEST01 tests ST_TO_CC using a tiny matrix.
Discussion:
This test uses a trivial matrix whose full representation is:
2 3 0 0 0
3 0 4 0 6
A = 0 -1 -3 2 0
0 0 1 0 0
0 4 2 0 1
A (1-based) ST representation, reading in order by rows is:
I J A
-- -- --
1 1 2
1 2 3
2 1 3
2 3 4
2 5 6
3 2 -1
3 3 -3
3 4 2
4 3 1
5 2 4
5 3 2
5 5 1
The CC representation (which goes in order by columns) is
# I JC A
-- -- -- --
1 1 1 2
2 2 3
3 1 3 3
4 3 -1
5 5 4
6 2 6 4
7 3 -3
8 4 1
9 5 2
10 3 10 2
11 2 11 6
12 5 1
13 * 13
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
23 July 2014
Author:
John Burkardt
*/
{
# define NST 12
double *acc;
double ast[NST] = {
2.0, 3.0,
3.0, 4.0, 6.0,
-1.0, -3.0, 2.0,
1.0,
4.0, 2.0, 1.0 };
int *ccc;
int i_max;
int i_min;
int *icc;
int ist[NST] = {
1, 1,
2, 2, 2,
3, 3, 3,
4,
5, 5, 5 };
int j_max;
int j_min;
int jst[NST] = {
1, 2,
1, 3, 5,
2, 3, 4,
3,
2, 3, 5 };
int m = 5;
int n = 5;
int ncc;
int nst = NST;
printf ( "\n" );
printf ( "TEST01\n" );
printf ( " Convert a sparse matrix from ST to CC format.\n" );
printf ( " ST: sparse triplet, I, J, A.\n" );
printf ( " CC: compressed column, I, CC, A.\n" );
i_min = i4vec_min ( nst, ist );
i_max = i4vec_max ( nst, ist );
j_min = i4vec_min ( nst, jst );
j_max = i4vec_max ( nst, jst );
st_header_print ( i_min, i_max, j_min, j_max, m, n, nst );
/*
Decrement the 1-based data.
*/
i4vec_dec ( nst, ist );
i4vec_dec ( nst, jst );
/*
Print the ST matrix.
*/
st_print ( m, n, nst, ist, jst, ast, " The matrix in ST format:" );
/*
Get the CC size.
*/
ncc = st_to_cc_size ( nst, ist, jst );
printf ( "\n" );
printf ( " Number of CC values = %d\n", ncc );
/*
Create the CC indices.
*/
icc = ( int * ) malloc ( ncc * sizeof ( int ) );
ccc = ( int * ) malloc ( ( n + 1 ) * sizeof ( int ) );
st_to_cc_index ( nst, ist, jst, ncc, n, icc, ccc );
/*
Create the CC values.
*/
acc = st_to_cc_values ( nst, ist, jst, ast, ncc, n, icc, ccc );
/*
Print the CC matrix.
*/
cc_print ( m, n, ncc, icc, ccc, acc, " CC Matrix:" );
/*
Free memory.
*/
free ( acc );
free ( ccc );
free ( icc );
return;
# undef NST
}
void perm_inverse ( int n, int p[] )
{
int base;
int i;
int i0;
int i1;
int i2;
int is;
int p_min;
if ( n <= 0 )
{
std::cout << "\n";
std::cout << "PERM_INVERSE - Fatal error!\n";
std::cout << " Input value of N = " << n << "\n";
exit ( 1 );
}
//
// Find the least value, and shift data so it begins at 1.
//
p_min = i4vec_min ( n, p );
base = 1;
for ( i = 0; i < n; i++ )
{
p[i] = p[i] - p_min + base;
}
//
// Now we can safely check the permutation.
//
if ( !perm_check ( n, p, base ) )
{
std::cerr << "\n";
std::cerr << "PERM_INVERSE - Fatal error!\n";
std::cerr << " PERM_CHECK rejects this permutation.\n";
exit ( 1 );
}
//
// Now we can invert the permutation.
//
is = 1;
for ( i = 1; i <= n; i++ )
{
i1 = p[i-1];
while ( i < i1 )
{
i2 = p[i1-1];
p[i1-1] = -i2;
i1 = i2;
}
is = - i4_sign ( p[i-1] );
p[i-1] = i4_sign ( is ) * abs ( p[i-1] );
}
for ( i = 1; i <= n; i++ )
{
i1 = - p[i-1];
if ( 0 <= i1 )
{
i0 = i;
for ( ; ; )
{
i2 = p[i1-1];
p[i1-1] = i0;
if ( i2 < 0 )
{
break;
}
i0 = i1;
i1 = i2;
}
}
}
//
// Now we can restore the permutation.
//
for ( i = 0; i < n; i++ )
{
p[i] = p[i] + p_min - base;
}
return;
}