//! Initialisation des zones de calibration
void CalibrationUtils::initTriangles(){
int base = 1, node_dim, node_num, triangle_num, triangle_order;
int *triangle_neighbor, *triangle_node;
double *node_xy;
//Copie de la liste de points dans un vecteur
std::vector<calibrationPoint*> *list = new std::vector<calibrationPoint*>();
for(int i=0; i < GRID_POINTS; i++) { list->push_back(&screenPoints[i]); }
//Lecture de la liste de points
r8mat_header_read (list, &node_dim, &node_num );
node_xy = r8mat_data_read (list, node_dim, node_num);
//Application de l'algorithme de Delaunay
triangle_order = 3;
triangle_node = new int[triangle_order*3*node_num];
triangle_neighbor = new int[triangle_order*3*node_num];
dtris2( node_num, base, node_xy, &triangle_num, triangle_node, triangle_neighbor );
//On affecte les points formant les trianges aux triangles
i4mat_tomat (triangle_order, triangle_num, triangle_node, list, triangles);
delete [] node_xy;
delete [] triangle_node;
delete [] triangle_neighbor;
}
//! Initialisation des zones de calibration
void CalibrationUtils::initTriangles(){
int base = 1, node_dim, node_num, triangle_num, triangle_order;
int *triangle_neighbor, *triangle_node;
double *node_xy;
//Lecture de la liste de points
r8mat_header_read (cameraPoints, &node_dim, &node_num );
node_xy = r8mat_data_read (cameraPoints, node_dim, node_num);
//Application de l'algorithme de Delaunay
triangle_order = 3;
triangle_node = new int[triangle_order*3*node_num];
triangle_neighbor = new int[triangle_order*3*node_num];
dtris2( node_num, base, node_xy, &triangle_num, triangle_node, triangle_neighbor );
//On affecte les points formant les trianges aux triangles
i4mat_tomat (triangle_order, triangle_num, triangle_node, cameraPoints, triangles);
delete [] node_xy;
delete [] triangle_node;
delete [] triangle_neighbor;
}
void test01 ( char *input_filename )
/******************************************************************************/
/*
Purpose:
TEST01 latinizes a given file.
Discussion:
The dataset is presumed to be an M by N array of real numbers,
where M is the spatial dimension, and N is the number of sample points.
The dataset is presumed to be stored in a file, with N records,
one per each sample point. (Comment records may be included,
which begin with '#'.)
The program reads the data file, "latinizes" the data, and writes
the latinized data to a new file.
Modified:
08 October 2004
Author:
John Burkardt
*/
{
int m;
int n;
FILE *output;
char *output_filename;
double *table;
/*
Need to create the output file name from the input filename.
*/
output_filename = file_name_ext_swap ( input_filename, "latin.txt" );
r8mat_header_read ( input_filename, &m, &n );
printf ( "\n" );
printf ( " Read the header of \"%s\".\n", input_filename );
printf ( "\n" );
printf ( " Spatial dimension M = %d\n", m );
printf ( " Number of points N = %d\n", n );
table = r8mat_data_read ( input_filename, m, n );
printf ( "\n" );
printf ( " Read the data in \"%s\".\n", input_filename );
r8mat_transpose_print_some ( m, n, table, 1, 1, 5, 5,
" Small portion of data read from file:" );
r8mat_latinize ( m, n, table );
printf ( "\n" );
printf ( " Latinized the data.\n" );
r8mat_transpose_print_some ( m, n, table, 1, 1, 5, 5,
" Small portion of Latinized data:" );
/*
Write the data to a file.
*/
r8mat_write ( output_filename, m, n, table );
printf ( "\n" );
printf ( " Wrote the latinized data to \"%s\".\n", output_filename );
free ( table );
return;
}
int main ( int argc, char *argv[] )
/******************************************************************************/
/*
Purpose:
MAIN is the main program for FEM_TO_MEDIT.
Discussion:
FEM_TO_MEDIT converts mesh data from FEM format to MEDIT format.
The FEM format defines "node", "element", and "boundary_node_mask",
files for a mesh. A typical set of such files might have the names
"suv_nodes.txt", "suv_elements.txt" and "suv_boundary_node_mask.txt".
This program reads these files and creates a MEDIT mesh file, whose
name might be "suv.mesh".
Usage:
fem_to_medit prefix
where 'prefix' is the common filename prefix so that:
* prefix_nodes.txt contains the coordinates of the nodes;
* prefix_elements.txt contains the indices of nodes forming each element;
* prefix_boundary_node_mask.txt is 0 for interior nodes, 1 for boundary nodes;
* prefix.mesh will be the MEDIT mesh file created by the program.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
10 October 2014
Author:
John Burkardt
*/
{
int *boundary_node;
char boundary_node_mask_filename[255];
int dim;
int *edge_label;
int *edge_vertex;
int edges;
char element_filename[255];
int *element_node;
int element_num;
int element_order;
int *hexahedron_label;
int *hexahedron_vertex;
int hexahedrons;
int i;
int j;
char medit_filename[255];
double *node_coord;
int node_dim;
char node_filename[255];
int node_num;
char prefix[255];
int *quadrilateral_label;
int *quadrilateral_vertex;
int quadrilaterals;
int *tetrahedron_label;
int *tetrahedron_vertex;
int tetrahedrons;
int *triangle_label;
int *triangle_vertex;
int triangles;
double *vertex_coordinate;
int *vertex_label;
int vertices;
timestamp ( );
printf ( "\n" );
printf ( "FEM_TO_MEDIT:\n" );
printf ( " C version\n" );
printf ( " Read a set of FEM files.\n" );
printf ( " Write a corresponding MEDIT mesh file.\n" );
/*
Get the filename prefix.
*/
if ( argc <= 1 )
{
printf ( "\n" );
printf ( "MESH_TO_XML:\n" );
printf ( " Please enter the filename prefix.\n" );
scanf ( "%s", prefix );
}
else
{
strcpy ( prefix, argv[1] );
}
/*
Create the file names.
*/
strcpy ( node_filename, prefix );
strcat ( node_filename, "_nodes.txt" );
strcpy ( boundary_node_mask_filename, prefix );
strcat ( boundary_node_mask_filename, "_boundary_node_mask.txt" );
strcpy ( element_filename, prefix );
strcat ( element_filename, "_elements.txt" );
strcpy ( medit_filename, prefix );
strcat ( medit_filename, ".mesh" );
printf ( "\n" );
printf ( " Read FEM node file \"%s\"\n", node_filename );
printf ( " and FEM element file \"%s\"\n", element_filename );
printf ( " and FEM boundary node mask file \"%s\"\n", boundary_node_mask_filename );
printf ( " Create MEDIT file \"%s\"\n", medit_filename );
/*
Read the FEM node data.
*/
r8mat_header_read ( node_filename, &node_dim, &node_num );
node_coord = r8mat_data_read ( node_filename, node_dim, node_num );
printf ( "\n" );
printf ( " The node dimension is %d\n", node_dim );
printf ( " The node number is %d\n", node_num );
/*
Read the FEM boundary node data.
*/
boundary_node = i4mat_data_read ( boundary_node_mask_filename, 1, node_num );
/*
Read the FEM element data.
*/
i4mat_header_read ( element_filename, &element_order, &element_num );
element_node = i4mat_data_read ( element_filename, element_order,
element_num );
printf ( " The FEM element order is %d\n", element_order );
printf ( " The FEM element number is %d\n", element_num );
/*
Write the MEDIT mesh data.
*/
dim = node_dim;
vertices = node_num;
edges = 0;
triangles = element_num;
quadrilaterals = 0;
tetrahedrons = 0;
hexahedrons = 0;
vertex_coordinate = ( double * ) malloc ( dim * vertices * sizeof ( double ) );
for ( j = 0; j < vertices; j++ )
{
for ( i = 0; i < dim; i++ )
{
vertex_coordinate[i+j*dim] = node_coord[i+j*dim];
}
}
vertex_label = ( int * ) malloc ( vertices * sizeof ( int ) );
for ( j = 0; j < vertices; j++ )
{
vertex_label[j] = boundary_node[j];
}
edge_vertex = NULL;
edge_label = NULL;
triangle_vertex = ( int * ) malloc ( 3 * triangles * sizeof ( int ) );
for ( j = 0; j < triangles; j++ )
{
for ( i = 0; i < 3; i++ )
{
triangle_vertex[i+j*3] = element_node[i+j*3];
}
}
triangle_label = ( int * ) malloc ( triangles * sizeof ( int ) );
for ( j = 0; j < triangles; j++ )
{
triangle_label[j] = 0;
}
quadrilateral_vertex = NULL;
quadrilateral_label = NULL;
tetrahedron_vertex = NULL;
tetrahedron_label = NULL;
hexahedron_vertex = NULL;
hexahedron_label = NULL;
medit_write ( medit_filename, dim, vertices, edges, triangles, quadrilaterals,
tetrahedrons, hexahedrons, vertex_coordinate, vertex_label, edge_vertex,
edge_label, triangle_vertex, triangle_label, quadrilateral_vertex,
quadrilateral_label, tetrahedron_vertex, tetrahedron_label,
hexahedron_vertex, hexahedron_label );
/*
Free memory.
*/
free ( element_node );
free ( node_coord );
free ( boundary_node );
free ( triangle_label );
free ( triangle_vertex );
/*
Terminate.
*/
printf ( "\n" );
printf ( "FEM_TO_MEDIT:\n" );
printf ( " Normal end of execution.\n" );
printf ( "\n" );
timestamp ( );
}
int main ( int argc, char *argv[] )
/******************************************************************************/
/*
Purpose:
MAIN is the main program for LEGENDRE_EXACTNESS.
Discussion:
This program investigates a standard Gauss-Legendre quadrature rule
by using it to integrate monomials over [-1,1], and comparing the
approximate result to the known exact value.
The user specifies:
* the "root" name of the R, W and X files that specify the rule;
* DEGREE_MAX, the maximum monomial degree to be checked.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
15 May 2014
Author:
John Burkardt
*/
{
int degree;
int degree_max;
int dim_num;
int dim_num2;
int i;
int order;
int point_num;
int point_num2;
double quad_error;
double quad_error2;
char quad_filename[255];
char quad_r_filename[255];
char quad_w_filename[255];
char quad_x_filename[255];
double *r;
double *w;
double *w2;
double *x;
double *x2;
timestamp ( );
printf ( "\n" );
printf ( "LEGENDRE_EXACTNESS\n" );
printf ( " C++ version\n" );
printf ( "\n" );
printf ( " Investigate the polynomial exactness of a Gauss-Legendre\n" );
printf ( " quadrature rule by integrating weighted\n" );
printf ( " monomials up to a given degree over the [-1,+1] interval.\n" );
/*
Get the quadrature file rootname.
*/
if ( 1 < argc )
{
strcpy ( quad_filename, argv[1] );
}
else
{
printf ( "\n" );
printf ( " Enter the quadrature file rootname:\n" );
scanf ( "%s", quad_filename );
}
printf ( "\n" );
printf ( " The quadrature file rootname is \"%s\".\n", quad_filename );
/*
Create the names of:
the quadrature X file;
the quadrature W file;
the quadrature R file;
*/
strcpy ( quad_w_filename, quad_filename );
strcat ( quad_w_filename, "_w.txt" );
strcpy ( quad_x_filename, quad_filename );
strcat ( quad_x_filename, "_x.txt" );
strcpy ( quad_r_filename, quad_filename );
strcat ( quad_r_filename, "_r.txt" );
/*
Get the maximum degree:
*/
if ( 2 < argc )
{
degree_max = atoi ( argv[2] );
}
else
{
printf ( "\n" );
printf ( " Enter DEGREE_MAX, the maximum monomial degree to check.\n" );
scanf ( "%d", °ree_max );
}
/*
Summarize the input.
*/
printf ( "\n" );
printf ( "LEGENDRE_EXACTNESS: User input:\n" );
printf ( " Quadrature rule X file = \"%s\".\n", quad_x_filename );
printf ( " Quadrature rule W file = \"%s\".\n", quad_w_filename );
printf ( " Quadrature rule R file = \"%s\".\n", quad_r_filename );
printf ( " Maximum degree to check = %d\n", degree_max );
/*
Read the X file.
*/
r8mat_header_read ( quad_x_filename, &dim_num, &order );
if ( dim_num != 1 )
{
printf ( "\n" );
printf ( "LEGENDRE_EXACTNESS - Fatal error!\n" );
printf ( " The spatial dimension of X should be 1.\n" );
printf ( " The implicit input dimension was DIM_NUM = %d\n", dim_num );
exit ( 1 );
}
printf ( "\n" );
printf ( " Spatial dimension = %d\n", dim_num );
printf ( " Number of points = %d\n", order );
x = r8mat_data_read ( quad_x_filename, dim_num, order );
/*
Read the W file.
*/
r8mat_header_read ( quad_w_filename, &dim_num2, &point_num );
if ( dim_num2 != 1 )
{
printf ( "\n" );
printf ( "LEGENDRE_EXACTNESS - Fatal error!\n" );
printf ( " The quadrature weight file should have exactly\n" );
printf ( " one value on each line.\n" );
exit ( 1 );
}
if ( point_num != order )
{
printf ( "\n" );
printf ( "LEGENDRE_EXACTNESS - Fatal error!\n" );
printf ( " The quadrature weight file should have exactly\n" );
printf ( " the same number of lines as the abscissa file.\n" );
exit ( 1 );
}
w = r8mat_data_read ( quad_w_filename, dim_num, order );
/*
Read the R file.
*/
r8mat_header_read ( quad_r_filename, &dim_num2, &point_num2 );
if ( dim_num2 != dim_num )
{
printf ( "\n" );
printf ( "LEGENDRE_EXACTNESS - Fatal error!\n" );
printf ( " The quadrature region file should have the\n" );
printf ( " same number of values on each line as the\n" );
printf ( " abscissa file does.\n" );
exit ( 1 );
}
if ( point_num2 != 2 )
{
printf ( "\n" );
printf ( "LEGENDRE_EXACTNESS - Fatal error!\n" );
printf ( " The quadrature region file should have two lines.\n" );
exit ( 1 );
}
r = r8mat_data_read ( quad_r_filename, dim_num, point_num2 );
/*
Print the input quadrature rule.
*/
printf ( "\n" );
printf ( " The quadrature rule to be tested is\n" );
printf ( " a Gauss-Legendre rule\n" );
printf ( " ORDER = %d\n", order );
printf ( "\n" );
printf ( " Standard rule:\n" );
printf ( " Integral ( -1 <= x <= +1 ) f(x) dx\n" );
printf ( " is to be approximated by\n" );
printf ( " sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).\n" );
printf ( "\n" );
printf ( " Weights W:\n" );
printf ( "\n" );
for ( i = 0; i < order; i++ )
{
printf ( " w[%d] = %g\n", i, w[i] );
}
printf ( "\n" );
printf ( " Abscissas X:\n" );
printf ( "\n" );
for ( i = 0; i < order; i++ )
{
printf ( " x[%d] = %g\n", i, x[i] );
}
printf ( "\n" );
printf ( " Region R:\n" );
printf ( "\n" );
for ( i = 0; i < 2; i++ )
{
printf ( " r[%d] = %g\n", i, r[i] );
}
/*
Generate a second rule for comparison.
*/
x2 = ( double * ) malloc ( order * sizeof ( double ) );
w2 = ( double * ) malloc ( order * sizeof ( double ) );
if ( order == 1 )
{
x2[0] = 0.0;
w2[0] = 2.0;
}
else
{
for ( i = 0; i < order; i++ )
{
w2[i] = 0.0;
}
for ( i = 0; i < order - 1; i++ )
{
w2[i] = w2[i] + 1.0 / ( double ) ( order - 1 );
}
for ( i = 1; i < order; i++ )
{
w2[i] = w2[i] + 1.0 / ( double ) ( order - 1 );
}
for ( i = 0; i < order; i++ )
{
x2[i] = ( ( double ) ( order - i - 1 ) * ( -1.0 )
+ ( double ) ( i ) * ( +1.0 ) )
/ ( double ) ( order - 1 );
}
}
/*
Explore the monomials.
*/
printf ( "\n" );
printf ( " A Gauss-Legendre rule would be able to exactly\n" );
printf ( " integrate monomials up to and including degree = %d\n",
2 * order - 1 );
printf ( "\n" );
printf ( " Error Error Degree\n" );
printf ( " (This rule) (Trapezoid)\n" );
printf ( "\n" );
for ( degree = 0; degree <= degree_max; degree++ )
{
quad_error = legendre_monomial_quadrature ( degree, order, w, x );
quad_error2 = legendre_monomial_quadrature ( degree, order, w2, x2 );
printf ( " %14.16g %14.16g %2d\n", quad_error, quad_error2, degree );
}
/*
Free memory.
*/
free ( r );
free ( w );
free ( w2 );
free ( x );
free ( x2 );
/*
Terminate.
*/
printf ( "\n" );
printf ( "LEGENDRE_EXACTNESS:\n" );
printf ( " Normal end of execution.\n" );
printf ( "\n" );
timestamp ( );
return 0;
}
int main ( int argc, char *argv[] )
/******************************************************************************/
/*
Purpose:
MAIN is the main program for TRIANGULATION_NODE_TO_ELEMENT.
Discussion:
TRIANGULATION_NODE_TO_ELEMENT averages node values to an element value.
This program is given a triangulation, along with the values of one or
more data items associated with each node.
It produces a file containing the average of the nodal values for
each element.
Usage:
triangulation_node_to_element ( 'prefix' )
where
* 'prefix'_nodes.txt contains the node coordinates;
* 'prefix'_elements.txt contains the element definitions
(this file is optional, and if missing, the elements will be generated
by the program);
* 'prefix'_values.txt contains the nodal values.
* 'prefix'_element_values will contain the averaged element data.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
08 April 2014
Author:
John Burkardt
*/
{
int dim_num;
char element_filename[255];
int *element_node;
int element_num;
int element_order;
double *element_value;
char element_value_filename[255];
int i;
int j;
int k;
int ni;
char node_filename[255];
int node_num;
double *node_xy;
char prefix[255];
int value_dim;
char value_filename[255];
int value_num;
double *value;
timestamp ( );
printf ( "\n" );
printf ( "TRIANGULATION_NODE_TO_ELEMENT:\n" );
printf ( " C version:\n" );
printf ( " Average nodal data to create element data.\n" );
printf ( "\n" );
printf ( " This program expects three files:\n" );
printf ( " * prefix_nodes.txt, node coordinates,\n" );
printf ( " * prefix_elements.txt, indices of nodes forming elements,\n" );
printf ( " * prefix_values.txt, data values at nodes,\n" );
printf ( " and creates:\n" );
printf ( " * prefix_element_values.txt, averaged data at elements.\n" );
/*
Get the filename prefix.
*/
if ( argc <= 1 )
{
printf ( "\n" );
printf ( " Please enter the filename prefix.\n" );
scanf ( "%s", prefix );
}
else
{
strcpy ( prefix, argv[1] );
}
/*
Create the filenames.
*/
strcpy ( node_filename, prefix );
strcat ( node_filename, "_nodes.txt" );
strcpy ( element_filename, prefix );
strcat ( element_filename, "_elements.txt" );
strcpy ( value_filename, prefix );
strcat ( value_filename, "_values.txt" );
strcpy ( element_value_filename, prefix );
strcat ( element_value_filename, "_element_values.txt" );
/*
Read the node data.
*/
r8mat_header_read ( node_filename, &dim_num, &node_num );
printf ( "\n" );
printf ( " Read the header of \"%s\".\n", node_filename );
printf ( "\n" );
printf ( " Spatial dimension DIM_NUM = %d\n", dim_num );
printf ( " Number of nodes NODE_NUM = %d\n", node_num );
node_xy = r8mat_data_read ( node_filename, dim_num, node_num );
printf ( "\n" );
printf ( " Read the data in \"%s\".\n", node_filename );
r8mat_transpose_print_some ( dim_num, node_num, node_xy, 1, 1, dim_num, 5,
" Portion of coordinate data from file:" );
/*
Read the element data.
*/
i4mat_header_read ( element_filename, &element_order, &element_num );
printf ( "\n" );
printf ( " Read the header of \"%s\".\n", element_filename );
printf ( "\n" );
printf ( " Element order ELEMENT_ORDER = %d\n", element_order );
printf ( " Number of elements ELEMENT_NUM = %d\n", element_num );
element_node = i4mat_data_read ( element_filename, element_order, element_num );
printf ( "\n" );
printf ( " Read the data in \"%s\".\n", element_filename );
i4mat_transpose_print_some ( element_order, element_num, element_node, 1, 1,
element_order, 5, " Portion of data read from file:" );
/*
Read the node value data.
*/
r8mat_header_read ( value_filename, &value_dim, &value_num );
printf ( "\n" );
printf ( " Read the header of \"%s\".\n", value_filename );
printf ( "\n" );
printf ( " Value dimension VALUE_DIM = %d\n", value_dim );
printf ( " Number of values VALUE_NUM = %d\n", value_num );
value = r8mat_data_read ( value_filename, value_dim, value_num );
printf ( "\n" );
printf ( " Read the data in \"%s\".\n", value_filename );
r8mat_transpose_print_some ( value_dim, value_num, value, 1, 1, value_dim, 5,
" First 5 node values:" );
/*
Detect and correct 1-based node indexing.
*/
mesh_base_zero ( node_num, element_order, element_num, element_node );
/*
Create the element values data.
*/
element_value = ( double * ) malloc ( value_dim * element_num * sizeof ( double ) );
for ( j = 0; j < element_num; j++ )
{
for ( i = 0; i < value_dim; i++ )
{
element_value[i+j*value_dim] = 0.0;
}
}
for ( j = 0; j < element_num; j++ )
{
for ( i = 0; i < element_order; i++ )
{
ni = element_node[i+j*element_order];
for ( k = 0; k < value_dim; k++ )
{
element_value[k+j*value_dim] = element_value[k+j*value_dim]
+ value[k+ni*value_dim];
}
}
}
for ( j = 0; j < element_num; j++ )
{
for ( k = 0; k < value_dim; k++ )
{
element_value[k+j*value_dim] = element_value[k+j*value_dim]
/ ( double ) ( element_order );
}
}
/*
Write out the file.
*/
r8mat_write ( element_value_filename, value_dim, element_num, element_value );
printf ( "\n" );
printf ( " Element values written to '%s'\n", element_value_filename );
/*
Free memory.
*/
free ( element_node );
free ( element_value );
free ( node_xy );
free ( value );
/*
Terminate.
*/
printf ( "\n" );
printf ( "TRIANGULATION_NODE_TO_ELEMENT:\n" );
printf ( " Normal end of execution.\n" );
printf ( "\n" );
timestamp ( );
return 0;
}
int main ( int argc, char *argv[] )
/******************************************************************************/
/*
Purpose:
MAIN is the main program for HYPERCUBE_EXACTNESS.
Usage:
hypercube_exactness prefix degree_max
where
* prefix is the common prefix for the files containing the abscissa,
weight and region information;
* degree_max is the maximum total monomial degree to check.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
30 August 2014
Author:
John Burkardt
*/
{
int degree;
int degree_max;
int dim;
int dim_num;
int dim_num2;
int error;
int *expon;
int h;
int last;
int more;
int point;
int point_num;
int point_num2;
char prefix[255];
double quad_error;
char quad_r_filename[255];
char quad_w_filename[255];
char quad_x_filename[255];
int t;
double volume;
double *weight;
double *x;
double *x_range;
timestamp ( );
printf ( "\n" );
printf ( "HYPERCUBE_EXACTNESS\n" );
printf ( " C version\n" );
printf ( "\n" );
printf ( " Investigate the polynomial exactness of a quadrature\n" );
printf ( " rule by integrating all monomials of a given degree\n" );
printf ( " over the [0,1] hypercube.\n" );
printf ( "\n" );
printf ( " The rule will be adjusted to the [0,1] hypercube.\n" );
/*
Get the quadrature file root name:
*/
if ( 1 < argc )
{
strcpy ( prefix, argv[1] );
}
else
{
printf ( "\n" );
printf ( "HYPERCUBE_EXACTNESS:\n" );
printf ( " Enter the \"root\" name of the quadrature files.\n" );
scanf ( "%s", prefix );
}
/*
Construct appropriate file names.
*/
strcpy ( quad_r_filename, prefix );
strcat ( quad_r_filename, "_r.txt" );
strcpy ( quad_w_filename, prefix );
strcat ( quad_w_filename, "_w.txt" );
strcpy ( quad_x_filename, prefix );
strcat ( quad_x_filename, "_x.txt" );
/*
The second command line argument is the maximum degree.
*/
if ( 2 < argc )
{
degree_max = s_to_i4 ( argv[2], &last, &error );
}
else
{
printf ( "\n" );
printf ( "HYPERCUBE_EXACTNESS:\n" );
printf ( " Please enter the maximum total degree to check.\n" );
scanf ( "%d", °ree_max );
}
/*
Summarize the input.
*/
printf ( "\n" );
printf ( "HYPERCUBE_EXACTNESS: User input:\n" );
printf ( " Quadrature rule X file = \"%s\"\n", quad_x_filename );
printf ( " Quadrature rule W file = \"%s\"\n", quad_w_filename );
printf ( " Quadrature rule R file = \"%s\"\n", quad_r_filename );
printf ( " Maximum total degree to check = %d\n", degree_max );
/*
Read the X file.
*/
r8mat_header_read ( quad_x_filename, &dim_num, &point_num );
printf ( "\n" );
printf ( " Spatial dimension = %d\n", dim_num );
printf ( " Number of points = %d\n", point_num );
x = r8mat_data_read ( quad_x_filename, dim_num, point_num );
/*
Read the W file.
*/
r8mat_header_read ( quad_w_filename, &dim_num2, &point_num2 );
if ( dim_num2 != 1 )
{
fprintf ( stderr, "\n" );
fprintf ( stderr, "HYPERCUBE_EXACTNESS - Fatal error!\n" );
fprintf ( stderr, " The quadrature weight file should have exactly\n" );
fprintf ( stderr, " one value on each line.\n" );
exit ( 1 );
}
if ( point_num2 != point_num )
{
fprintf ( stderr, "\n" );
fprintf ( stderr, "HYPERCUBE_EXACTNESS - Fatal error!\n" );
fprintf ( stderr, " The quadrature weight file should have exactly\n" );
fprintf ( stderr, " the same number of lines as the abscissa file.\n" );
exit ( 1 );
}
weight = r8mat_data_read ( quad_w_filename, 1, point_num );
/*
Read the R file.
*/
r8mat_header_read ( quad_r_filename, &dim_num2, &point_num2 );
if ( dim_num2 != dim_num )
{
fprintf ( stderr, "\n" );
fprintf ( stderr, "HYPERCUBE_EXACTNESS - Fatal error!\n" );
fprintf ( stderr, " The quadrature region file should have the same\n" );
fprintf ( stderr, " number of values on each line as the abscissa file\n" );
fprintf ( stderr, " does.\n" );
exit ( 1 );
}
if ( point_num2 != 2 )
{
fprintf ( stderr, "\n" );
fprintf ( stderr, "HYPERCUBE_EXACTNESS - Fatal error!\n" );
fprintf ( stderr, " The quadrature region file should have two lines.\n" );
exit ( 1 );
}
x_range = r8mat_data_read ( quad_r_filename, dim_num, 2 );
/*
Rescale the weights, and translate the abscissas.
*/
volume = 1.0;
for ( dim = 0; dim < dim_num; dim++ )
{
volume = volume * ( x_range[dim+1*dim_num] - x_range[dim+0*dim_num] );
}
volume = fabs ( volume );
for ( point = 0; point < point_num; point++ )
{
weight[point] = weight[point] / volume;
}
for ( dim = 0; dim < dim_num; dim++ )
{
for ( point = 0; point < point_num; point++ )
{
x[dim+point*dim_num] =
( x[dim+point*dim_num] - x_range[dim+0*dim_num] )
/ ( x_range[dim+1*dim_num] - x_range[dim+0*dim_num] );
}
}
/*
Explore the monomials.
*/
expon = ( int * ) malloc ( dim_num * sizeof ( int ) );
printf ( "\n" );
printf ( " Error Degree Exponents\n" );
printf ( "\n" );
for ( degree = 0; degree <= degree_max; degree++ )
{
more = 0;
h = 0;
t = 0;
for ( ; ; )
{
comp_next ( degree, dim_num, expon, &more, &h, &t );
quad_error = monomial_quadrature ( dim_num, expon, point_num, weight, x );
printf ( " %12g %2d ", quad_error, degree );
for ( dim = 0; dim < dim_num; dim++ )
{
printf ( "%3d", expon[dim] );
}
printf ( "\n" );
if ( !more )
{
break;
}
}
printf ( "\n" );
}
/*
Free memory.
*/
free ( expon );
free ( weight );
free ( x );
free ( x_range );
/*
Terminate.
*/
printf ( "\n" );
printf ( "HYPERCUBE_EXACTNESS:\n" );
printf ( " Normal end of execution.\n" );
printf ( "\n" );
timestamp ( );
return 0;
}