public static void sparse_grid_cc_weights(int dim_num, int level_max, int point_num,
int[] grid_index, ref double[] grid_weight)
//****************************************************************************80
//
// Purpose:
//
// SPARSE_GRID_CC_WEIGHTS gathers the weights.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 12 March 2013
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Fabio Nobile, Raul Tempone, Clayton Webster,
// A Sparse Grid Stochastic Collocation Method for Partial Differential
// Equations with Random Input Data,
// SIAM Journal on Numerical Analysis,
// Volume 46, Number 5, 2008, pages 2309-2345.
//
// Parameters:
//
// Input, int DIM_NUM, the spatial dimension.
//
// Input, int LEVEL_MAX, the maximum value of LEVEL.
//
// Input, int POINT_NUM, the total number of points in the grids.
//
// Input, int GRID_INDEX[DIM_NUM*POINT_NUM], a list of point indices,
// representing a subset of the product grid of level LEVEL_MAX,
// representing (exactly once) each point that will show up in a
// sparse grid of level LEVEL_MAX.
//
// Output, double GRID_WEIGHT[POINT_NUM], the weights
// associated with the sparse grid points.
//
{
int level;
int point;
switch (level_max)
{
case 0:
{
for (point = 0; point < point_num; point++)
{
grid_weight[point] = Math.Pow(2.0, dim_num);
}
return;
}
}
int[] level_1d = new int[dim_num];
int[] order_1d = new int[dim_num];
for (point = 0; point < point_num; point++)
{
grid_weight[point] = 0.0;
}
int level_min = Math.Max(0, level_max + 1 - dim_num);
for (level = level_min; level <= level_max; level++)
{
//
// The middle loop generates the next partition LEVEL_1D(1:DIM_NUM)
// that adds up to LEVEL.
//
bool more = false;
int h = 0;
int t = 0;
for (;;)
{
Comp.comp_next(level, dim_num, ref level_1d, ref more, ref h, ref t);
//
// Transform each 1D level to a corresponding 1D order.
//
ClenshawCurtis.level_to_order_closed(dim_num, level_1d, ref order_1d);
//
// The product of the 1D orders gives us the number of points in this grid.
//
int order_nd = typeMethods.i4vec_product(dim_num, order_1d);
//
// Generate the indices of the points corresponding to the grid.
//
int[] grid_index2 = Multigrid.multigrid_index0(dim_num, order_1d, order_nd);
//
// Compute the weights for this grid.
//
double[] grid_weight2 = ClenshawCurtis.product_weights_cc(dim_num, order_1d, order_nd);
//
// Adjust the grid indices to reflect LEVEL_MAX.
//
Multigrid.multigrid_scale_closed(dim_num, order_nd, level_max, level_1d,
ref grid_index2);
//
// Now determine the coefficient.
//
int coeff = typeMethods.i4_mop(level_max - level)
* typeMethods.i4_choose(dim_num - 1, level_max - level);
int point2;
for (point2 = 0; point2 < order_nd; point2++)
{
bool found = false;
for (point = 0; point < point_num; point++)
{
bool all_equal = true;
int dim;
for (dim = 0; dim < dim_num; dim++)
{
if (grid_index2[dim + point2 * dim_num] == grid_index[dim + point * dim_num])
{
continue;
}
all_equal = false;
break;
}
if (!all_equal)
{
continue;
}
grid_weight[point] += coeff * grid_weight2[point2];
found = true;
break;
}
switch (found)
{
case false:
Console.WriteLine("");
Console.WriteLine("SPARSE_GRID_CC_WEIGHTS - Fatal error!");
Console.WriteLine(" Could not find a match for a point.");
return;
}
}
if (!more)
{
break;
}
}
}
}
public static int[] sparse_grid_cc_index(int dim_num, int level_max, int point_num)
//****************************************************************************80
//
// Purpose:
//
// SPARSE_GRID_CC_INDEX indexes the points forming a sparse grid.
//
// Discussion:
//
// The points forming the sparse grid are guaranteed to be a subset
// of a certain product grid. The product grid is formed by DIM_NUM
// copies of a 1D rule of fixed order. The orders of the 1D rule,
// (called ORDER_1D) and the order of the product grid, (called ORDER)
// are determined from the value LEVEL_MAX.
//
// Thus, any point in the product grid can be identified by its grid index,
// a set of DIM_NUM indices, each between 1 and ORDER_1D.
//
// This routine creates the GRID_INDEX array, listing (uniquely) the
// points of the sparse grid.
//
// An assumption has been made that the 1D rule is closed (includes
// the interval endpoints) and nested (points that are part of a rule
// of a given level will be part of every rule of higher level).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 09 November 2007
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Fabio Nobile, Raul Tempone, Clayton Webster,
// A Sparse Grid Stochastic Collocation Method for Partial Differential
// Equations with Random Input Data,
// SIAM Journal on Numerical Analysis,
// Volume 46, Number 5, 2008, pages 2309-2345.
//
// Parameters:
//
// Input, int DIM_NUM, the spatial dimension.
//
// Input, int LEVEL_MAX, the maximum value of LEVEL.
//
// Input, int POINT_NUM, the total number of points in the grids.
//
// Output, int SPARSE_GRID_CC_INDEX[DIM_NUM*POINT_NUM], a list of point
// indices, representing a subset of the product grid of level LEVEL_MAX,
// representing (exactly once) each point that will show up in a
// sparse grid of level LEVEL_MAX.
//
{
int level;
int[] grid_index = new int[dim_num * point_num];
//
// The outer loop generates LEVELs from 0 to LEVEL_MAX.
//
int point_num2 = 0;
int[] level_1d = new int[dim_num];
int[] order_1d = new int[dim_num];
for (level = 0; level <= level_max; level++)
{
//
// The middle loop generates the next partition LEVEL_1D(1:DIM_NUM)
// that adds up to LEVEL.
//
bool more = false;
int h = 0;
int t = 0;
for (;;)
{
Comp.comp_next(level, dim_num, ref level_1d, ref more, ref h, ref t);
//
// Transform each 1D level to a corresponding 1D order.
//
ClenshawCurtis.level_to_order_closed(dim_num, level_1d, ref order_1d);
//
// The product of the 1D orders gives us the number of points in this grid.
//
int order_nd = typeMethods.i4vec_product(dim_num, order_1d);
//
// The inner (hidden) loop generates all points corresponding to given grid.
//
int[] grid_index2 = Multigrid.multigrid_index0(dim_num, order_1d, order_nd);
//
// Adjust these grid indices to reflect LEVEL_MAX.
//
Multigrid.multigrid_scale_closed(dim_num, order_nd, level_max, level_1d,
ref grid_index2);
//
// Determine the first level of appearance of each of the points.
//
int[] grid_level = Abscissa.abscissa_level_closed_nd(level_max, dim_num, order_nd,
grid_index2);
//
// Only keep those points which first appear on this level.
//
int point;
for (point = 0; point < order_nd; point++)
{
if (grid_level[point] != level)
{
continue;
}
int dim;
for (dim = 0; dim < dim_num; dim++)
{
grid_index[dim + point_num2 * dim_num] =
grid_index2[dim + point * dim_num];
}
point_num2 += 1;
}
if (!more)
{
break;
}
}
}
return(grid_index);
}
public static int sparse_grid_cc_size_old(int dim_num, int level_max)
//****************************************************************************80
//
// Purpose:
//
// SPARSE_GRID_CC_SIZE_OLD sizes a sparse grid of Clenshaw Curtis points.
//
// Discussion:
//
// This function has been replaced by a new version which is much faster.
//
// This version is retained for historical interest.
//
// The grid is defined as the sum of the product rules whose LEVEL
// satisfies:
//
// 0 <= LEVEL <= LEVEL_MAX.
//
// This routine works on an abstract set of nested grids.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 09 November 2007
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Fabio Nobile, Raul Tempone, Clayton Webster,
// A Sparse Grid Stochastic Collocation Method for Partial Differential
// Equations with Random Input Data,
// SIAM Journal on Numerical Analysis,
// Volume 46, Number 5, 2008, pages 2309-2345.
//
// Parameters:
//
// Input, int DIM_NUM, the spatial dimension.
//
// Input, int LEVEL_MAX, the maximum value of LEVEL.
//
// Output, int SPARSE_GRID_CC_SIZE, the number of points in the grid.
//
{
int level;
int point_num;
switch (level_max)
{
//
// Special case.
//
case 0:
point_num = 1;
return(point_num);
}
//
// The outer loop generates LEVELs from 0 to LEVEL_MAX.
//
point_num = 0;
int[] level_1d = new int[dim_num];
int[] order_1d = new int[dim_num];
for (level = 0; level <= level_max; level++)
{
//
// The middle loop generates the next partition that adds up to LEVEL.
//
bool more = false;
int h = 0;
int t = 0;
for (;;)
{
Comp.comp_next(level, dim_num, ref level_1d, ref more, ref h, ref t);
//
// Transform each 1D level to a corresponding 1D order.
//
ClenshawCurtis.level_to_order_closed(dim_num, level_1d, ref order_1d);
//
// The product of the 1D orders gives us the number of points in this grid.
//
int order_nd = typeMethods.i4vec_product(dim_num, order_1d);
//
// The inner (hidden) loop generates all points corresponding to given grid.
//
int[] grid_index = Multigrid.multigrid_index0(dim_num, order_1d, order_nd);
//
// Adjust these grid indices to reflect LEVEL_MAX.
//
Multigrid.multigrid_scale_closed(dim_num, order_nd, level_max, level_1d,
ref grid_index);
//
// Determine the first level of appearance of each of the points.
//
int[] grid_level = Abscissa.abscissa_level_closed_nd(level_max, dim_num, order_nd,
grid_index);
//
// Only keep those points which first appear on this level.
//
int point;
for (point = 0; point < order_nd; point++)
{
if (grid_level[point] == level)
{
point_num += 1;
}
}
if (!more)
{
break;
}
}
}
return(point_num);
}
