private static void sgmg_create_rule(int dim_num, int level_max,
int[] rule, int[] growth, int[] np, double[] p,
Func <int, int, double[], double[], double[]>[] gw_compute_points,
Func <int, int, double[], double[], double[]>[] gw_compute_weights,
double tol, string file_name)
//***************************************************************************80
//
// Purpose:
//
// SGMG_CREATE_RULE creates the requested rule and writes it to a file.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 July 2013
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, integer DIM_NUM, the spatial dimension.
//
// Input, integer LEVEL_MAX, the level that defines the grid.
//
// Input, int RULE[DIM_NUM], the rule in each dimension.
// 1, "CC", Clenshaw Curtis, Closed Fully Nested.
// 2, "F2", Fejer Type 2, Open Fully Nested.
// 3, "GP", Gauss Patterson, Open Fully Nested.
// 4, "GL", Gauss Legendre, Open Weakly Nested.
// 5, "GH", Gauss Hermite, Open Weakly Nested.
// 6, "GGH", Generalized Gauss Hermite, Open Weakly Nested.
// 7, "LG", Gauss Laguerre, Open Non Nested.
// 8, "GLG", Generalized Gauss Laguerre, Open Non Nested.
// 9, "GJ", Gauss Jacobi, Open Non Nested.
// 10, "HGK", Hermite Genz-Keister, Open Fully Nested.
// 11, "UO", User supplied Open, presumably Non Nested.
// 12, "UC", User supplied Closed, presumably Non Nested.
//
// Input, int GROWTH[DIM_NUM], the growth rule in each dimension.
// 0, "DF", default growth associated with this quadrature rule;
// 1, "SL", slow linear, L+1;
// 2 "SO", slow linear odd, O=1+2((L+1)/2)
// 3, "ML", moderate linear, 2L+1;
// 4, "SE", slow exponential;
// 5, "ME", moderate exponential;
// 6, "FE", full exponential.
//
// Input, int NP[RULE_NUM], the number of parameters used by each rule.
//
// Input, double P[sum(NP[*])], the parameters needed by each rule.
//
// Input, void ( *GW_COMPUTE_POINTS[] ) ( int order, int np, double p[], double x[] ),
// an array of pointers to functions which return the 1D quadrature points
// associated with each spatial dimension for which a Golub Welsch rule
// is used.
//
// Input, void ( *GW_COMPUTE_WEIGHTS[] ) ( int order, int np, double p[], double w[] ),
// an array of pointers to functions which return the 1D quadrature weights
// associated with each spatial dimension for which a Golub Welsch rule
// is used.
//
// Input, double TOL, a tolerance for point equality.
//
// Input, string FILE_NAME, the main name of the output files.
//
{
Console.WriteLine("");
Console.WriteLine("SGMG_CREATE_RULE");
Console.WriteLine(" Create the requested sparse grid rule, and write it");
Console.WriteLine(" to X, W and R files.");
//
// Compute necessary data.
//
int point_total_num = SGMG.sgmg_size_total(dim_num,
level_max, rule, growth);
int point_num = SGMG.sgmg_size(dim_num, level_max,
rule, np, p, gw_compute_points, tol, growth);
int[] sparse_unique_index = new int[point_total_num];
SGMG.sgmg_unique_index(dim_num, level_max, rule,
np, p, gw_compute_points, tol, point_num, point_total_num,
growth, ref sparse_unique_index);
int[] sparse_order = new int[dim_num * point_num];
int[] sparse_index = new int[dim_num * point_num];
SGMG.sgmg_index(dim_num, level_max, rule, point_num,
point_total_num, sparse_unique_index, growth, ref sparse_order, ref sparse_index);
//
// Compute points and weights.
//
double[] sparse_point = new double [dim_num * point_num];
SGMG.sgmg_point(dim_num, level_max, rule, np,
p, gw_compute_points, point_num, sparse_order, sparse_index,
growth, ref sparse_point);
double[] sparse_weight = new double[point_num];
SGMG.sgmg_weight(dim_num, level_max, rule, np,
p, gw_compute_weights, point_num, point_total_num, sparse_unique_index,
growth, ref sparse_weight);
//
// Write points and weights to files.
//
SGMG.sgmg_write(dim_num, rule, np, p,
point_num, sparse_weight, sparse_point, file_name);
}
private static void sgmg_unique_index_test(int dim_num, int level_max_min,
int level_max_max, int[] rule, int[] growth, int[] np, double[] p,
Func <int, int, double[], double[], double[]>[] gw_compute_points,
double tol)
//***************************************************************************80
//
// Purpose:
//
// SGMG_UNIQUE_INDEX_TEST tests SGMG_UNIQUE_INDEX.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 20 June 2010
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int DIM_NUM, the spatial dimension.
//
// Input, int LEVEL_MAX_MIN, LEVEL_MAX_MAX, the minimum and
// maximum values of LEVEL_MAX.
//
// Input, int RULE[DIM_NUM], the rule in each dimension.
// 1, "CC", Clenshaw Curtis, Closed Fully Nested.
// 2, "F2", Fejer Type 2, Open Fully Nested.
// 3, "GP", Gauss Patterson, Open Fully Nested.
// 4, "GL", Gauss Legendre, Open Weakly Nested.
// 5, "GH", Gauss Hermite, Open Weakly Nested.
// 6, "GGH", Generalized Gauss Hermite, Open Weakly Nested.
// 7, "LG", Gauss Laguerre, Open Non Nested.
// 8, "GLG", Generalized Gauss Laguerre, Open Non Nested.
// 9, "GJ", Gauss Jacobi, Open Non Nested.
// 10, "HGK", Hermite Genz-Keister, Open Fully Nested.
// 11, "UO", User supplied Open, presumably Non Nested.
// 12, "UC", User supplied Closed, presumably Non Nested.
//
// Input, int GROWTH[DIM_NUM], the growth rule in each dimension.
// 0, "DF", default growth associated with this quadrature rule;
// 1, "SL", slow linear, L+1;
// 2 "SO", slow linear odd, O=1+2((L+1)/2)
// 3, "ML", moderate linear, 2L+1;
// 4, "SE", slow exponential;
// 5, "ME", moderate exponential;
// 6, "FE", full exponential.
//
// Input, int NP[RULE_NUM], the number of parameters used by each rule.
//
// Input, double P[sum(NP[*])], the parameters needed by each rule.
//
// Input, void ( *GW_COMPUTE_POINTS[] ) ( int order, int np, double p[], double x[] ),
// an array of pointers to functions which return the 1D quadrature points
// associated with each spatial dimension for which a Golub Welsch rule
// is used.
//
// Input, double TOL, a tolerance for point equality.
//
{
int dim;
int level_max;
Console.WriteLine("");
Console.WriteLine("SGMG_UNIQUE_INDEX_TEST");
Console.WriteLine(" SGMG_UNIQUE_INDEX returns a mapping between");
Console.WriteLine(" the nonunique and unique points in a sparse grid.");
Console.WriteLine("");
Console.WriteLine(" Dimension Rule Growth rate Parameters");
Console.WriteLine("");
int p_index = 0;
for (dim = 0; dim < dim_num; dim++)
{
double alpha;
int i;
switch (rule[dim])
{
case 1:
case 2:
case 3:
case 4:
case 5:
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8) + "");
break;
case 6:
alpha = p[p_index];
p_index += 1;
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8)
+ " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
break;
case 7:
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8) + "");
break;
case 8:
alpha = p[p_index];
p_index += 1;
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8)
+ " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
break;
case 9:
alpha = p[p_index];
p_index += 1;
double beta = p[p_index];
p_index += 1;
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8)
+ " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + beta.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
break;
case 10:
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8) + "");
break;
case 11:
{
string cout = " " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8);
for (i = 0; i < np[dim]; i++)
{
alpha = p[p_index];
p_index += 1;
cout += " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
break;
}
case 12:
{
string cout = " " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8);
for (i = 0; i < np[dim]; i++)
{
alpha = p[p_index];
p_index += 1;
cout += " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
break;
}
default:
Console.WriteLine("");
Console.WriteLine("SGMG_UNIQUE_INDEX_TEST - Fatal error!");
Console.WriteLine(" Unexpected value of RULE = " + rule[dim] + "");
return;
}
}
for (level_max = level_max_min; level_max <= level_max_max; level_max++)
{
int point_total_num = SGMG.sgmg_size_total(dim_num,
level_max, rule, growth);
int point_num = SGMG.sgmg_size(dim_num, level_max,
rule, np, p, gw_compute_points, tol, growth);
Console.WriteLine("");
Console.WriteLine(" LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM");
Console.WriteLine(" Unique Total");
int level_min = Math.Max(0, level_max + 1 - dim_num);
Console.WriteLine("");
Console.WriteLine(" " + level_min.ToString().PadLeft(8)
+ " " + level_max.ToString().PadLeft(8)
+ " " + point_num.ToString().PadLeft(8)
+ " " + point_total_num.ToString().PadLeft(8) + "");
int[] sparse_unique_index = new int[point_total_num];
SGMG.sgmg_unique_index(dim_num, level_max, rule,
np, p, gw_compute_points, tol, point_num, point_total_num,
growth, ref sparse_unique_index);
Console.WriteLine("");
Console.WriteLine(" POINT UNIQUE");
Console.WriteLine("");
int point;
for (point = 0; point < point_total_num; point++)
{
Console.WriteLine(" " + point.ToString().PadLeft(8)
+ " " + sparse_unique_index[point].ToString().PadLeft(8) + "");
}
}
}
private static void sgmg_weight_test(int dim_num, int level_max_min,
int level_max_max, int[] rule, int[] growth, int[] np, double[] p,
Func <int, int, double[], double[], double[]>[] gw_compute_points,
Func <int, int, double[], double[], double[]>[] gw_compute_weights,
double tol)
//***************************************************************************80
//
// Purpose:
//
// SGMG_WEIGHT_TEST checks the sum of the quadrature weights.
//
// Discussion:
//
// If any component rule is of Golub-Welsch type, we cannot compute
// the exact weight sum, which we set, instead, to zero.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 20 June 2010
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int DIM_NUM, the spatial dimension.
//
// Input, int LEVEL_MAX_MIN, LEVEL_MAX_MAX, the minimum and
// maximum values of LEVEL_MAX.
//
// Input, int RULE[DIM_NUM], the rule in each dimension.
// 1, "CC", Clenshaw Curtis, Closed Fully Nested.
// 2, "F2", Fejer Type 2, Open Fully Nested.
// 3, "GP", Gauss Patterson, Open Fully Nested.
// 4, "GL", Gauss Legendre, Open Weakly Nested.
// 5, "GH", Gauss Hermite, Open Weakly Nested.
// 6, "GGH", Generalized Gauss Hermite, Open Weakly Nested.
// 7, "LG", Gauss Laguerre, Open Non Nested.
// 8, "GLG", Generalized Gauss Laguerre, Open Non Nested.
// 9, "GJ", Gauss Jacobi, Open Non Nested.
// 10, "HGK", Hermite Genz-Keister, Open Fully Nested.
// 11, "UO", User supplied Open, presumably Non Nested.
// 12, "UC", User supplied Closed, presumably Non Nested.
//
// Input, int GROWTH[DIM_NUM], the growth rule in each dimension.
// 0, "DF", default growth associated with this quadrature rule;
// 1, "SL", slow linear, L+1;
// 2 "SO", slow linear odd, O=1+2((L+1)/2)
// 3, "ML", moderate linear, 2L+1;
// 4, "SE", slow exponential;
// 5, "ME", moderate exponential;
// 6, "FE", full exponential.
//
// Input, int NP[RULE_NUM], the number of parameters used by each rule.
//
// Input, double P[sum(NP[*])], the parameters needed by each rule.
//
// Input, void ( *GW_COMPUTE_POINTS[] ) ( int order, int np, double p[], double x[] ),
// an array of pointers to functions which return the 1D quadrature points
// associated with each spatial dimension for which a Golub Welsch rule
// is used.
//
// Input, void ( *GW_COMPUTE_WEIGHTS[] ) ( int order, int np, double p[], double w[] ),
// an array of pointers to functions which return the 1D quadrature weights
// associated with each spatial dimension for which a Golub Welsch rule
// is used.
//
// Input, double TOL, a tolerance for point equality.
//
{
double alpha;
double beta;
int dim;
int i;
int level_max;
Console.WriteLine("");
Console.WriteLine("SGMG_WEIGHT_TEST");
Console.WriteLine(" Compute the weights of a sparse grid.");
Console.WriteLine("");
Console.WriteLine(" Each sparse grid is of spatial dimension DIM_NUM,");
Console.WriteLine(" and is made up of product grids of levels up to LEVEL_MAX.");
Console.WriteLine("");
Console.WriteLine(" Dimension Rule Growth rate Parameters");
Console.WriteLine("");
int p_index = 0;
for (dim = 0; dim < dim_num; dim++)
{
switch (rule[dim])
{
case 1:
case 2:
case 3:
case 4:
case 5:
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8) + "");
break;
case 6:
alpha = p[p_index];
p_index += 1;
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8)
+ " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
break;
case 7:
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8) + "");
break;
case 8:
alpha = p[p_index];
p_index += 1;
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8)
+ " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
break;
case 9:
alpha = p[p_index];
p_index += 1;
beta = p[p_index];
p_index += 1;
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8)
+ " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + beta.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
break;
case 10:
Console.WriteLine(" " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8) + "");
break;
case 11:
{
string cout = " " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8);
for (i = 0; i < np[dim]; i++)
{
alpha = p[p_index];
p_index += 1;
cout += " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
break;
}
case 12:
{
string cout = " " + dim.ToString().PadLeft(8)
+ " " + rule[dim].ToString().PadLeft(8)
+ " " + growth[dim].ToString().PadLeft(8);
for (i = 0; i < np[dim]; i++)
{
alpha = p[p_index];
p_index += 1;
cout += " " + alpha.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
break;
}
default:
Console.WriteLine("");
Console.WriteLine("SPARSE_GRID_MIXED_WEIGHT_TEST - Fatal error!");
Console.WriteLine(" Unexpected value of RULE = " + rule[dim] + "");
return;
}
}
double weight_sum_exact = 1.0;
p_index = 0;
for (dim = 0; dim < dim_num; dim++)
{
switch (rule[dim])
{
case 1:
case 2:
case 3:
case 4:
weight_sum_exact *= 2.0;
break;
case 5:
weight_sum_exact *= Math.Sqrt(Math.PI);
break;
case 6:
alpha = p[p_index];
p_index += 1;
weight_sum_exact *= typeMethods.r8_gamma(0.5 * (alpha + 1.0));
break;
case 7:
weight_sum_exact *= 1.0;
break;
case 8:
alpha = p[p_index];
p_index += 1;
weight_sum_exact *= typeMethods.r8_gamma(alpha + 1.0);
break;
case 9:
alpha = p[p_index];
p_index += 1;
beta = p[p_index];
p_index += 1;
double arg1 = -alpha;
double arg2 = 1.0;
double arg3 = beta + 2.0;
double arg4 = -1.0;
double value1 = typeMethods.r8_hyper_2f1(arg1, arg2, arg3, arg4);
arg1 = -beta;
arg2 = 1.0;
arg3 = alpha + 2.0;
arg4 = -1.0;
double value2 = typeMethods.r8_hyper_2f1(arg1, arg2, arg3, arg4);
weight_sum_exact *= value1 / (beta + 1.0) + value2 / (alpha + 1.0);
break;
case 10:
weight_sum_exact *= Math.Sqrt(Math.PI);
break;
case 11:
{
for (i = 0; i < np[dim]; i++)
{
alpha = p[p_index];
p_index += 1;
}
weight_sum_exact = 0.0;
break;
}
case 12:
{
for (i = 0; i < np[dim]; i++)
{
alpha = p[p_index];
p_index += 1;
}
weight_sum_exact = 0.0;
break;
}
default:
Console.WriteLine("");
Console.WriteLine("SPARSE_GRID_MIXED_WEIGHT_TEST - Fatal error!");
Console.WriteLine(" Unexpected value of RULE[" + dim + "] = "
+ rule[dim] + ".");
return;
}
}
switch (weight_sum_exact)
{
case 0.0:
Console.WriteLine("");
Console.WriteLine(" Because this rule includes Golub-Welsch components,");
Console.WriteLine(" we do not try to compute the exact weight sum.");
break;
default:
Console.WriteLine("");
Console.WriteLine(" As a simple test, sum these weights.");
Console.WriteLine(" They should sum to exactly " + weight_sum_exact + "");
break;
}
Console.WriteLine("");
Console.WriteLine(" Level Weight sum Expected sum Difference");
Console.WriteLine("");
for (level_max = level_max_min; level_max <= level_max_max; level_max++)
{
int point_total_num = SGMG.sgmg_size_total(dim_num,
level_max, rule, growth);
int point_num = SGMG.sgmg_size(dim_num, level_max,
rule, np, p, gw_compute_points, tol, growth);
int[] sparse_unique_index = new int[point_total_num];
SGMG.sgmg_unique_index(dim_num, level_max, rule,
np, p, gw_compute_points, tol, point_num, point_total_num,
growth, ref sparse_unique_index);
double[] sparse_weight = new double[point_num];
SGMG.sgmg_weight(dim_num, level_max, rule, np,
p, gw_compute_weights, point_num, point_total_num, sparse_unique_index,
growth, ref sparse_weight);
double weight_sum = typeMethods.r8vec_sum(point_num, sparse_weight);
double weight_sum_error = typeMethods.r8_abs(weight_sum - weight_sum_exact);
Console.WriteLine(" " + level_max.ToString().PadLeft(8)
+ " " + weight_sum.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + weight_sum_exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + weight_sum_error.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
