void test1836 ( )
/******************************************************************************/
/*
Purpose:
TEST1836 tests SPHERE_EXP2IMP_ND.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
26 July 2011
Author:
John Burkardt
*/
{
# define N 3
int n = N;
double p[N*(N+1)] = {
4.0, 2.0, 3.0,
1.0, 5.0, 3.0,
1.0, 2.0, 6.0,
-2.0, 2.0, 3.0 };
double pc[N];
double pc_true[N] = { 1.0, 2.0, 3.0 };
double r;
double r_true = 3.0;
printf ( "\n" );
printf ( "TEST1836\n" );
printf ( " SPHERE_EXP2IMP_ND: explicit sphere => implicit form;\n" );
r8mat_transpose_print ( n, n + 1, p, " Initial form of explicit sphere:" );
sphere_exp2imp_nd ( n, p, &r, pc );
printf ( "\n" );
printf ( " Computed form of implicit sphere:\n" );
printf ( "\n" );
printf ( " Imputed radius = %f\n", r );
printf ( " True radius = %f\n", r_true );
r8vec_print ( n, pc, " Imputed center" );
r8vec_print ( n, pc_true, " True center" );
return;
# undef N
}
void test02 ( void )
/******************************************************************************/
/*
Purpose:
TEST02 prints the data for each problem.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
06 February 2012
Author:
John Burkardt
*/
{
int data_num;
int dim_num;
double *p;
int prob;
int prob_num;
printf ( "\n" );
printf ( "TEST02\n" );
printf ( " P00_DATA_NUM returns N, the number of data points.\n" );
printf ( " P00_DIM_NUM returns M, the dimension of data.\n" );
printf ( " P00_DATA returns the actual (MxN) data.\n" );
prob_num = p00_prob_num ( );
for ( prob = 1; prob <= prob_num; prob++ )
{
printf ( "\n" );
printf ( " Problem %d\n", prob );
data_num = p00_data_num ( prob );
printf ( " DATA_NUM %d\n", data_num );
dim_num = p00_dim_num ( prob );
printf ( " DIM_NUM %d\n", dim_num );
p = p00_data ( prob, dim_num, data_num );
r8mat_transpose_print ( dim_num, data_num, p, " Data array:" );
free ( p );
}
return;
}
void test171 ( )
/******************************************************************************/
/*
Purpose:
TEST171 tests QUAD_AREA_2D and QUAD_AREA2_2D;
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
09 May 2010
Author:
John Burkardt
*/
{
# define DIM_NUM 2
double area;
double quad[DIM_NUM*4] = {
0.0, 0.0,
1.0, 0.0,
1.0, 1.0,
0.0, 1.0 };
printf ( "\n" );
printf ( "TEST171\n" );
printf ( " For a quadrilateral in 2D:\n" );
printf ( " QUAD_AREA_2D finds the area;\n" );
printf ( " QUAD_AREA2_2D finds the area;\n" );
r8mat_transpose_print ( DIM_NUM, 4, quad, " The vertices:" );
area = quad_area_2d ( quad );
printf ( "\n" );
printf ( " QUAD_AREA_2D area is %f\n", area );
area = quad_area2_2d ( quad );
printf ( " QUAD_AREA2_2D area is %f\n", area );
return;
# undef DIM_NUM
}
void test0478 ( )
/******************************************************************************/
/*
Purpose:
TEST0478 tests PARALLELOGRAM_AREA_3D.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
09 May 2010
Author:
John Burkardt
*/
{
double area;
double p[3*4] = {
1.0, 2.0, 3.0,
2.4142137, 3.4142137, 3.0,
1.7071068, 2.7071068, 4.0,
0.2928931, 0.2928931, 4.0 };
printf ( "\n" );
printf ( "TEST0478\n" );
printf ( " PARALLELOGRAM_AREA_3D finds the area of a\n" );
printf ( " parallelogram in 3D.\n" );
r8mat_transpose_print ( 3, 4, p, " Vertices:" );
area = parallelogram_area_3d ( p );
printf ( "\n" );
printf ( " AREA = %f\n", area );
return;
}
void test0477 ( )
/******************************************************************************/
/*
Purpose:
TEST0477 tests PARALLELOGRAM_AREA_2D.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
09 May 2010
Author:
John Burkardt
*/
{
double area;
double p[2*4] = {
2.0, 7.0,
5.0, 7.0,
6.0, 9.0,
3.0, 9.0 };
printf ( "\n" );
printf ( "TEST0477\n" );
printf ( " PARALLELOGRAM_AREA_2D finds the area of a\n" );
printf ( " parallelogram in 2D.\n" );
r8mat_transpose_print ( 2, 4, p, " Vertices:" );
area = parallelogram_area_2d ( p );
printf ( "\n" );
printf ( " AREA = %f\n", area );
return;
}
void test02 ( )
/******************************************************************************/
/*
Purpose:
TEST02 examines the sample points in the pyramid
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
14 April 2014
Author:
John Burkardt
*/
{
int m = 3;
int n = 20;
int seed;
double *x;
printf ( "\n" );
printf ( "TEST02\n" );
printf ( " Print sample points in the unit pyramid in 3D.\n" );
seed = 123456789;
x = pyramid01_sample ( n, &seed );
r8mat_transpose_print ( 3, n, x, " Unit pyramid points" );
free ( x );
return;
}
void test01 ( int prob )
/******************************************************************************/
/*
Purpose:
TEST01 tests CHEBYSHEV_VALUE_1D.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
27 September 2012
Author:
John Burkardt
*/
{
int i;
double int_error;
int nd;
int ni;
double *xd;
double *xi;
double *xy;
double *yd;
double *yi;
printf ( "\n" );
printf ( "CHEBYSHEV_INTERP_1D_TEST01:\n" );
printf ( " Interpolate data from TEST_INTERP problem #%d\n", prob );
nd = p00_data_num ( prob );
printf ( " Number of data points = %d\n", nd );
xy = p00_data ( prob, 2, nd );
r8mat_transpose_print ( 2, nd, xy, " Data array:" );
xd = ( double * ) malloc ( nd * sizeof ( double ) );
yd = ( double * ) malloc ( nd * sizeof ( double ) );
for ( i = 0; i < nd; i++ )
{
xd[i] = xy[0+i*2];
yd[i] = xy[1+i*2];
}
/*
#1: Does interpolant match function at interpolation points?
*/
ni = nd;
xi = ( double * ) malloc ( ni * sizeof ( double ) );
for ( i = 0; i < ni; i++ )
{
xi[i] = xd[i];
}
yi = chebyshev_interp_1d ( nd, xd, yd, ni, xi );
int_error = r8vec_norm_affine ( ni, yi, yd ) / ( double ) ( ni );
printf ( "\n" );
printf ( " L2 interpolation error averaged per interpolant node = %g\n", int_error );
free ( xd );
free ( xi );
free ( xy );
free ( yd );
free ( yi );
return;
}
void test1712 ( )
/******************************************************************************/
/*
Purpose:
TEST1712 tests QUAD_AREA_3D;
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
09 May 2010
Author:
John Burkardt
*/
{
double area;
double area1;
double area2;
int i;
int j;
double q[3*4] = {
2.0, 2.0, 0.0,
0.0, 0.0, 0.0,
1.0, 1.0, 1.0,
3.0, 3.0, 1.0 };
double t[3*3];
printf ( "\n" );
printf ( "TEST1712\n" );
printf ( " For a quadrilateral in 3D:\n" );
printf ( " QUAD_AREA_3D finds the area.\n" );
r8mat_transpose_print ( 3, 4, q, " The vertices:");
area = quad_area_3d ( q );
printf ( "\n" );
printf ( " QUAD_AREA_3D area is %f\n", area );
for ( j = 0; j < 3; j++ )
{
for ( i = 0; i < 3; i++ )
{
t[i+j*3] = q[i+j*3];
}
}
area1 = triangle_area_3d ( t );
for ( j = 0; j < 2; j++ )
{
for ( i = 0; i < 3; i++ )
{
t[i+j*3] = q[i+(j+2)*3];
}
}
for ( i = 0; i < 3; i++ )
{
t[i+2*3] = q[i+0*3];
}
area2 = triangle_area_3d ( t );
printf ( " Sum of TRIANGLE_AREA_3D: %f\n", area1 + area2 );
return;
}
void test2101 ( )
/******************************************************************************/
/*
Purpose:
TEST2101 tests TRIANGLE_CIRCUMCENTER_2D and others.
Discussion:
The functions tested include
* TRIANGLE_CIRCUMCENTER_2D;
* TRIANGLE_CIRCUMCENTER_2D_2;
* TRIANGLE_CIRCUMCENTER.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
28 October 2010
Author:
John Burkardt
*/
{
# define M 2
# define TEST_NUM 4
int i;
int j;
int m = M;
double *pc;
double t[M*3];
double t_test[M*3*TEST_NUM] = {
10.0, 5.0,
11.0, 5.0,
10.0, 6.0,
10.0, 5.0,
11.0, 5.0,
10.5, 5.86602539,
10.0, 5.0,
11.0, 5.0,
10.5, 15.0,
10.0, 5.0,
11.0, 5.0,
20.0, 7.0 };
int test;
int test_num = TEST_NUM;
printf ( "\n" );
printf ( "TEST2101\n" );
printf ( " For a triangle in 2D, the circumenter can be computed by:\n" );
printf ( " TRIANGLE_CIRCUMCENTER_2D;\n" );
printf ( " TRIANGLE_CIRCUMCENTER_2D_2;\n" );
printf ( " TRIANGLE_CIRCUMCENTER (any dimension);\n" );
for ( test = 0; test < test_num; test++ )
{
for ( j = 0; j < 3; j++ )
{
for ( i = 0; i < m; i++ )
{
t[i+j*m] = t_test[i+j*m+test*m*3];
}
}
r8mat_transpose_print ( m, 3, t, " Triangle vertices:" );
pc = triangle_circumcenter_2d ( t );
r8vec_print ( m, pc, " Circumcenter by TRIANGLE_CIRCUMCENTER_2D:" );
free ( pc );
pc = triangle_circumcenter_2d_2 ( t );
r8vec_print ( m, pc, " Circumcenter by TRIANGLE_CIRCUMCENTER_2D_2:" );
free ( pc );
pc = triangle_circumcenter ( m, t );
r8vec_print ( m, pc, " Circumcenter by TRIANGLE_CIRCUMCENTER:" );
free ( pc );
}
return;
# undef M
# undef TEST_NUM
}
void rbf_interp_nd_test01 ( void )
/******************************************************************************/
/*
Purpose:
RBF_INTERP_ND_TEST01 tests RBF_WEIGHTS and RBF_INTERP_ND with PHI1.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
01 July 2012
Author:
John Burkardt
*/
{
double a;
double app_error;
double b;
int debug = 0;
double *fd;
double *fe;
double *fi;
int i;
double int_error;
int j;
int m = 2;
int n1d = 5;
int nd;
int ni;
double r0;
int seed;
double *w;
double *x1d;
double *xd;
double *xi;
printf ( "\n" );
printf ( "RBF_INTERP_ND_TEST01:\n" );
printf ( " RBF_WEIGHT computes weights for RBF interpolation.\n" );
printf ( " RBF_INTERP_ND evaluates the RBF interpolant.\n" );
printf ( " Use the multiquadratic basis function PHI1(R).\n" );
a = 0.0;
b = 2.0;
r0 = ( b - a ) / ( double ) ( n1d );
printf ( " Scale factor R0 = %g\n", r0 );
x1d = r8vec_linspace_new ( n1d, a, b );
nd = i4_power ( n1d, m );
xd = ( double * ) malloc ( m * nd * sizeof ( double ) );
for ( i = 0; i < m; i++ )
{
r8vec_direct_product ( i, n1d, x1d, m, nd, xd );
}
if ( debug )
{
r8mat_transpose_print ( m, nd, xd, " The product points:" );
}
fd = ( double * ) malloc ( nd * sizeof ( double ) );
for ( j = 0; j < nd; j++ )
{
fd[j] = xd[0+j*m] * xd[1+j*m] * exp ( - xd[0+j*m] * xd[1+j*m] );
}
if ( debug )
{
r8vec_print ( nd, fd, " Function data:" );
}
w = rbf_weight ( m, nd, xd, r0, phi1, fd );
if ( debug )
{
r8vec_print ( nd, w, " Weight vector:" );
}
/*
#1: Interpolation test. Does interpolant match function at interpolation points?
*/
ni = nd;
xi = r8mat_copy_new ( m, ni, xd );
fi = rbf_interp_nd ( m, nd, xd, r0, phi1, w, ni, xi );
int_error = r8vec_norm_affine ( nd, fd, fi ) / ( double ) ( nd );
printf ( "\n" );
printf ( " L2 interpolation error averaged per interpolant node = %g\n", int_error );
free ( fi );
free ( xi );
/*
#2: Approximation test. Estimate the integral (f-interp(f))^2.
*/
ni = 1000;
seed = 123456789;
xi = r8mat_uniform_ab_new ( m, ni, a, b, &seed );
fi = rbf_interp_nd ( m, nd, xd, r0, phi1, w, ni, xi );
fe = ( double * ) malloc ( ni * sizeof ( double ) );
for ( j = 0; j < ni; j++ )
{
fe[j] = xi[0+j*m] * xi[1+j*m] * exp ( - xi[0+j*m] * xi[1+j*m] );
}
app_error = pow ( b - a, m ) * r8vec_norm_affine ( ni, fi, fe ) / ( double ) ( ni );
printf ( " L2 approximation error averaged per 1000 samples = %g\n", app_error );
free ( fd );
free ( fe );
free ( fi );
free ( w );
free ( x1d );
free ( xd );
free ( xi );
return;
}
void test005 ( )
/******************************************************************************/
/*
Purpose:
TEST005 tests DIAEDG.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
23 October 2012
Author:
John Burkardt
*/
{
int node_num = 4;
int triangle_num = 2;
int triangle_order = 3;
double alpha_area;
double alpha_ave;
double alpha_min_swapped;
double alpha_min_unswapped;
double node_xy[2*4];
int seed = 123456789;
int swap;
int test;
int test_num = 10;
int triangle_node[3*2];
int value;
printf ( "\n" );
printf ( "TEST005\n" );
printf ( " DIAEDG determines whether two triangles\n" );
printf ( " with a common edge need to \"swap\" diagonals.\n" );
printf ( " If swapping is indicated, then ALPHA_MIN should increase.\n" );
printf ( "\n" );
printf ( " Swap ALPHA_MIN ALPHA_MIN\n" );
printf ( " Unswapped Swapped\n" );
printf ( "\n" );
for ( test = 1; test <= test_num; test++ )
{
/*
Generate a random quadrilateral (1,2,3,4).
*/
quad_convex_random ( &seed, node_xy );
/*
Does it need swapping?
*/
value = diaedg (
node_xy[0+0*2], node_xy[1+0*2],
node_xy[0+1*2], node_xy[1+1*2],
node_xy[0+2*2], node_xy[1+2*2],
node_xy[0+3*2], node_xy[1+3*2] );
if ( value == +1 )
{
swap = 0;
}
else
{
swap = 1;
}
/*
Compute ALPHA_MIN unswapped.
*/
triangle_node[0+0*3] = 1;
triangle_node[1+0*3] = 2;
triangle_node[2+0*3] = 3;
triangle_node[0+1*3] = 1;
triangle_node[1+1*3] = 3;
triangle_node[2+1*3] = 4;
alpha_measure ( node_num, node_xy, triangle_order, triangle_num,
triangle_node, &alpha_min_unswapped, &alpha_ave, &alpha_area );
/*
Compute ALPHA_MIN swapped.
*/
triangle_node[0+0*3] = 1;
triangle_node[1+0*3] = 2;
triangle_node[2+0*3] = 4;
triangle_node[0+1*3] = 2;
triangle_node[1+1*3] = 3;
triangle_node[2+1*3] = 4;
alpha_measure ( node_num, node_xy, triangle_order, triangle_num,
triangle_node, &alpha_min_swapped, &alpha_ave, &alpha_area );
if ( 0 )
{
r8mat_transpose_print ( 2, node_num, node_xy, " Quadrilateral" );
}
printf ( " %1d %10g %10g\n",
swap, alpha_min_unswapped, alpha_min_swapped );
}
return;
}
void test06 ( )
/******************************************************************************/
/*
Purpose:
TEST06 tests TRIANGLE_CIRCUMCENTER_2D;
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
23 October 2012
Author:
John Burkardt
*/
{
# define DIM_NUM 2
double *center;
int i;
int ntest = 4;
double t[DIM_NUM*3];
printf ( "\n" );
printf ( "TEST06\n" );
printf ( " For a triangle in 2D:\n" );
printf ( " TRIANGLE_CIRCUMCENTER_2D computes the circumcenter.\n" );
for ( i = 1; i <= ntest; i++ )
{
if ( i == 1 )
{
t[0+0*2] = 0.0;
t[1+0*2] = 0.0;
t[0+1*2] = 1.0;
t[1+1*2] = 0.0;
t[0+2*2] = 0.0;
t[1+2*2] = 1.0;
}
else if ( i == 2 )
{
t[0+0*2] = 0.0;
t[1+0*2] = 0.0;
t[0+1*2] = 1.0;
t[1+1*2] = 0.0;
t[0+2*2] = 0.5;
t[1+2*2] = sqrt ( 3.0 ) / 2.0;
}
else if ( i == 3 )
{
t[0+0*2] = 0.0;
t[1+0*2] = 0.0;
t[0+1*2] = 1.0;
t[1+1*2] = 0.0;
t[0+2*2] = 0.5;
t[1+2*2] = 10.0;
}
else if ( i == 4 )
{
t[0+0*2] = 0.0;
t[1+0*2] = 0.0;
t[0+1*2] = 1.0;
t[1+1*2] = 0.0;
t[0+2*2] = 10.0;
t[1+2*2] = 2.0;
}
r8mat_transpose_print ( DIM_NUM, 3, t, " The triangle" );
center = triangle_circumcenter_2d ( t );
r8vec_print ( DIM_NUM, center, " Circumcenter" );
free ( center );
}
return;
# undef DIM_NUM
}
void test03 ( )
/******************************************************************************/
/*
Purpose:
TEST03 tests R82VEC_SORT_QUICK_A.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
23 October 2012
Author:
John Burkardt
*/
{
# define N 12
# define DIM_NUM 2
double *a;
double b = 0.0;
double c = 10.0;
int i;
int j;
int seed = 123456789;
printf ( "\n" );
printf ( "TEST03\n" );
printf ( " R82VEC_SORT_QUICK_A sorts a vector\n" );
printf ( " as part of a quick sort.\n" );
printf ( " Using initial random number seed = %d", seed );
a = r8mat_uniform_01_new ( DIM_NUM, N, &seed );
for ( j = 0; j < N; j++ )
{
for ( i = 0; i < DIM_NUM; i++ )
{
a[i+j*DIM_NUM] = 10.0 * a[i+j*DIM_NUM];
}
}
/*
For better testing, give a few elements the same first component.
*/
a[0+2*(3-1)] = a[0+2*(5-1)];
a[0+2*(4-1)] = a[0+2*(12-1)];
/*
Make two entries equal.
*/
a[0+2*(7-1)] = a[0+2*(11-1)];
a[1+2*(7-1)] = a[1+2*(11-1)];
r8mat_transpose_print ( DIM_NUM, N, a, " Before sorting:" );
r82vec_sort_quick_a ( N, a );
r8mat_transpose_print ( DIM_NUM, N, a, " Sorted array:" );
free ( a );
return;
# undef N
# undef DIM_NUM
}
void test02 ( )
/******************************************************************************/
/*
Purpose:
TEST02 tests R82VEC_PART_QUICK_A.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
23 October 2012
Author:
John Burkardt
*/
{
# define N 12
# define DIM_NUM 2
double *a;
int i;
int j;
int l;
int r;
int seed = 123456789;
printf ( "\n" );
printf ( "TEST02\n" );
printf ( " D2VEC_PART_QUICK_A reorders a D2 vector\n" );
printf ( " as part of a quick sort.\n" );
printf ( " Using initial random number seed = %d\n", seed );
a = r8mat_uniform_01_new ( DIM_NUM, N, &seed );
for ( j = 0; j < N; j++ )
{
for ( i = 0; i < DIM_NUM; i++ )
{
a[i+j*DIM_NUM] = 10.0 * a[i+j*DIM_NUM];
}
}
r8mat_transpose_print ( DIM_NUM, N, a, " Before rearrangment:" );
r82vec_part_quick_a ( N, a, &l, &r );
printf ( "\n" );
printf ( " Rearranged array\n" );
printf ( " Left index = %d\n", l );
printf ( " Key index = %d\n", l + 1 );
printf ( " Right index = %d\n", r );
r8mat_transpose_print ( DIM_NUM, l, a, " Left half:" );
r8mat_transpose_print ( DIM_NUM, 1, a+2*l, " Key:" );
r8mat_transpose_print ( DIM_NUM, N-l-1, a+2*(l+1), " Right half:" );
free ( a );
return;
# undef N
# undef DIM_NUM
}
void test01 ( )
/******************************************************************************/
/*
Purpose:
TEST01 tests POINTS_DELAUNAY_NAIVE_2D.
Diagram:
!....3&11....
!............
!............
X..9.........
!.....5......
!...........6
!.4.2...10...
!.....8...12.
V............
!..7.........
!......1.....
!............
!............
!----V----X--
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
23 October 2012
Author:
John Burkardt
*/
# define N 12
# define DIM_NUM 2
{
int i;
int ntri;
int *tri;
double p[DIM_NUM*N] = {
7.0, 3.0,
4.0, 7.0,
5.0, 13.0,
2.0, 7.0,
6.0, 9.0,
12.0, 10.0,
3.0, 4.0,
6.0, 6.0,
3.0, 10.0,
8.0, 7.0,
5.0, 13.0,
10.0, 6.0 };
printf ( "\n" );
printf ( "TEST01\n" );
printf ( " POINTS_DELAUNAY_NAIVE_2D computes the Delaunay\n" );
printf ( " triangulation of a set of points.\n" );
r8mat_transpose_print ( DIM_NUM, N, p, " The points:" );
tri = points_delaunay_naive_2d ( N, p, &ntri );
printf ( "\n" );
printf ( " Number of triangles is NTRI = %d\n", ntri );
i4mat_transpose_print ( 3, ntri, tri, " The Delaunay triangles:" );
free ( tri );
return;
# undef N
# undef DIM_NUM
}