void test03 ( int prob )
/******************************************************************************/
/*
Purpose:
TEST03 tests PWL_INTERP_2D_SCATTERED_VALUE.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
25 October 2012
Author:
John Burkardt
*/
{
int *element_neighbor;
int element_num;
int g;
int i;
int j;
int k;
int nd;
int ni = 25;
double rms;
int *triangle;
double x;
double *xd;
double xi[25];
double *xyd;
double xyi[2*25];
double y;
double *yd;
double yi[25];
double *zd;
double *ze;
double *zi;
g = 2;
nd = g00_size ( g );
printf ( "\n" );
printf ( "TEST03\n" );
printf ( " PWL_INTERP_2D_SCATTERED_VALUE evaluates a\n" );
printf ( " piecewise linear interpolant to scattered data.\n" );
printf ( " Here, we use grid number %d\n", g );
printf ( " with %d scattered points in the unit square\n", nd );
printf ( " on problem %d\n", prob );
/*
Get the data points and evaluate the function there.
*/
xd = ( double * ) malloc ( nd * sizeof ( double ) );
yd = ( double * ) malloc ( nd * sizeof ( double ) );
g00_xy ( g, nd, xd, yd );
zd = ( double * ) malloc ( nd * sizeof ( double ) );
f00_f0 ( prob, nd, xd, yd, zd );
xyd = ( double * ) malloc ( 2 * nd * sizeof ( double ) );
for ( i = 0; i < nd; i++ )
{
xyd[0+i*2] = xd[i];
xyd[1+i*2] = yd[i];
}
/*
Set up the Delaunay triangulation.
*/
element_neighbor = ( int * ) malloc ( 3 * 2 * nd * sizeof ( int ) );
triangle = ( int * ) malloc ( 3 * 2 * nd * sizeof ( int ) );
r8tris2 ( nd, xyd, &element_num, triangle, element_neighbor );
for ( j = 0; j < element_num; j++ )
{
for ( i = 0; i < 3; i++ )
{
if ( 0 < element_neighbor[i+j*3] )
{
element_neighbor[i+j*3] = element_neighbor[i+j*3] - 1;
}
}
}
/*
Define the interpolation points.
*/
k = 0;
for ( i = 1; i <= 5; i++ )
{
for ( j = 1; j <= 5; j++ )
{
xyi[0+k*2] = ( 2 * i - 1 ) / 10.0;
xyi[1+k*2] = ( 2 * j - 1 ) / 10.0;
k = k + 1;
}
}
for ( k = 0; k < ni; k++ )
{
xi[k] = xyi[0+k*2];
yi[k] = xyi[1+k*2];
}
ze = ( double * ) malloc ( ni * sizeof ( double ) );
f00_f0 ( prob, ni, xi, yi, ze );
/*
Evaluate the interpolant.
*/
zi = pwl_interp_2d_scattered_value ( nd, xyd, zd, element_num,
triangle, element_neighbor, ni, xyi );
rms = 0.0;
for ( k = 0; k < ni; k++ )
{
rms = rms + pow ( zi[k] - ze[k], 2 );
}
rms = sqrt ( rms / ( double ) ( ni ) );
printf ( "\n" );
printf ( " RMS error is %g\n", rms );
printf ( "\n" );
printf ( " K Xi(K) Yi(K) Zi(K) Z(X,Y)\n" );
printf ( "\n" );
for ( k = 0; k < ni; k++ )
{
printf ( " %4d %10.4f %10.4f %10.4f %10.4f\n",
k, xyi[0+k*2], xyi[1+k*2], zi[k], ze[k] );
}
free ( element_neighbor );
free ( triangle );
free ( xd );
free ( xyd );
free ( yd );
free ( zd );
free ( ze );
return;
}
void test01 ( int prob, int n )
/******************************************************************************/
/*
Purpose:
PWL_INTERP_2D_TEST01 tests PWL_INTERP_2D.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
15 October 2012
Author:
John Burkardt
Parameters:
Input, int PROB, the problem number.
Input, int N, the grid size in each dimension.
*/
{
double app_error;
int i;
int ij;
double int_error;
int j;
int nd;
int ni;
int nxd;
int nyd;
double *xd;
double *xd_1d;
double *xi;
double *xi_1d;
double *yd;
double *yd_1d;
double *yi;
double *yi_1d;
double *zd;
double *zdm;
double *zi;
nxd = n;
nyd = n;
printf ( "\n" );
printf ( "PWL_INTERP_2D_TEST01:\n" );
printf ( " Interpolate data from TEST_INTERP_2D problem #%d\n", prob );
printf ( " Using polynomial interpolant of product degree %d x %d\n", nxd, nyd );
nd = nxd * nyd;
printf ( " Number of data points = %d\n", nd );
xd_1d = r8vec_linspace_new ( nxd, 0.0, 1.0 );
yd_1d = r8vec_linspace_new ( nyd, 0.0, 1.0 );
xd = ( double * ) malloc ( nxd * nyd * sizeof ( double ) );
yd = ( double * ) malloc ( nxd * nyd * sizeof ( double ) );
zd = ( double * ) malloc ( nxd * nyd * sizeof ( double ) );
ij = 0;
for ( j = 0; j < nyd; j++ )
{
for ( i = 0; i < nxd; i++ )
{
xd[ij] = xd_1d[i];
yd[ij] = yd_1d[j];
ij = ij + 1;
}
}
f00_f0 ( prob, nd, xd, yd, zd );
if ( nd <= 20 )
{
r8vec3_print ( nd, xd, yd, zd, " X, Y, Z data:" );
}
/*
#1: Does interpolant match function at data points?
*/
ni = nd;
xi = r8vec_copy_new ( ni, xd );
yi = r8vec_copy_new ( ni, yd );
zi = pwl_interp_2d ( nxd, nyd, xd_1d, yd_1d, zd, ni, xi, yi );
if ( ni <= 20 )
{
r8vec3_print ( ni, xi, yi, zi, " X, Y, Z interpolation:" );
}
int_error = r8vec_norm_affine ( ni, zi, zd ) / ( double ) ( ni );
printf ( "\n" );
printf ( " RMS data interpolation error = %g\n", int_error );
free ( xi );
free ( yi );
free ( zi );
/*
#2: Does interpolant approximate data at midpoints?
*/
if ( 1 < nd )
{
xi_1d = ( double * ) malloc ( ( nxd - 1 ) * sizeof ( double ) );
yi_1d = ( double * ) malloc ( ( nyd - 1 ) * sizeof ( double ) );
for ( i = 0; i < nxd - 1; i++ )
{
xi_1d[i] = 0.5 * ( xd_1d[i] + xd_1d[i+1] );
}
for ( i = 0; i < nyd - 1; i++ )
{
yi_1d[i] = 0.5 * ( yd_1d[i] + yd_1d[i+1] );
}
ni = ( nxd - 1 ) * ( nyd - 1 );
xi = ( double * ) malloc ( ni * sizeof ( double ) );
yi = ( double * ) malloc ( ni * sizeof ( double ) );
zdm = ( double * ) malloc ( ni * sizeof ( double ) );
ij = 0;
for ( j = 0; j < nyd - 1; j++ )
{
for ( i = 0; i < nxd - 1; i++ )
{
xi[ij] = xi_1d[i];
yi[ij] = yi_1d[j];
ij = ij + 1;
}
}
f00_f0 ( prob, ni, xi, yi, zdm );
zi = pwl_interp_2d ( nxd, nyd, xd_1d, yd_1d, zd, ni, xi, yi );
app_error = r8vec_norm_affine ( ni, zi, zdm ) / ( double ) ( ni );
printf ( " RMS data approximation error = %g\n", app_error );
free ( xi );
free ( xi_1d );
free ( yi );
free ( yi_1d );
free ( zdm );
free ( zi );
}
free ( xd );
free ( xd_1d );
free ( yd );
free ( yd_1d );
free ( zd );
return;
}
void test01 ( int prob, int grd, int m )
/******************************************************************************/
/*
Purpose:
VANDERMONDE_APPROX_2D_TEST01 tests VANDERMONDE_APPROX_2D_MATRIX.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
11 October 2012
Author:
John Burkardt
Parameters:
Input, int PROB, the problem number.
Input, int GRD, the grid number.
(Can't use GRID as the name because that's also a plotting function.)
Input, int M, the total polynomial degree.
*/
{
double *a;
double app_error;
double *c;
int nd;
int ni;
int tm;
double *xd;
double *xi;
double *yd;
double *yi;
double *zd;
double *zi;
printf ( "\n" );
printf ( "TEST01:\n" );
printf ( " Approximate data from TEST_INTERP_2D problem #%d\n", prob );
printf ( " Use grid from TEST_INTERP_2D with index #%d\n", grd );
printf ( " Using polynomial approximant of total degree %d\n", m );
nd = g00_size ( grd );
printf ( " Number of data points = %d\n", nd );
xd = ( double * ) malloc ( nd * sizeof ( double ) );
yd = ( double * ) malloc ( nd * sizeof ( double ) );
g00_xy ( grd, nd, xd, yd );
zd = ( double * ) malloc ( nd * sizeof ( double ) );
f00_f0 ( prob, nd, xd, yd, zd );
if ( nd < 10 )
{
r8vec3_print ( nd, xd, yd, zd, " X, Y, Z data:" );
}
/*
Compute the Vandermonde matrix.
*/
tm = triangle_num ( m + 1 );
a = vandermonde_approx_2d_matrix ( nd, m, tm, xd, yd );
/*
Solve linear system.
*/
c = qr_solve ( nd, tm, a, zd );
/*
#1: Does approximant match function at data points?
*/
ni = nd;
xi = r8vec_copy_new ( ni, xd );
yi = r8vec_copy_new ( ni, yd );
zi = r8poly_value_2d ( m, c, ni, xi, yi );
app_error = r8vec_norm_affine ( ni, zi, zd ) / ( double ) ( ni );
printf ( "\n" );
printf ( " L2 data approximation error = %g\n", app_error );
free ( a );
free ( c );
free ( xd );
free ( xi );
free ( yd );
free ( yi );
free ( zd );
free ( zi );
return;
}
void test02 ( void )
/******************************************************************************/
/*
Purpose:
TEST02 samples each function using each grid.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
30 January 2012
Author:
John Burkardt
*/
{
double *f;
double f_ave;
double f_max;
double f_min;
int f_num;
int fi;
char ft[100];
int g_num;
int gi;
int gn;
char gt[100];
double *gx;
double *gy;
printf ( "\n" );
printf ( "TEST02\n" );
printf ( " Sample each function over each grid.\n" );
g_num = g00_num ( );
f_num = f00_num ( );
for ( fi = 1; fi <= f_num; fi++ )
{
f00_title ( fi, ft );
printf ( "\n" );
printf ( " %2d %s\n", fi, ft );
printf ( " Grid Title " );
printf ( "Min(F) Ave(F) Max(F)\n" );
printf ( "\n" );
for ( gi = 1; gi <= g_num; gi++ )
{
g00_title ( gi, gt );
gn = g00_size ( gi );
gx = ( double * ) malloc ( gn * sizeof ( double ) );
gy = ( double * ) malloc ( gn * sizeof ( double ) );
g00_xy ( gi, gn, gx, gy );
f = ( double * ) malloc ( gn * sizeof ( double ) );
f00_f0 ( fi, gn, gx, gy, f );
f_max = r8vec_max ( gn, f );
f_min = r8vec_min ( gn, f );
f_ave = r8vec_sum ( gn, f );
f_ave = f_ave / ( double ) ( gn );
printf ( " %4d %25s %14g %14g %14g\n", gi, gt, f_min, f_ave, f_max );
free ( f );
free ( gx );
free ( gy );
}
}
return;
}