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function [lGrid, points] = tsgMakeLocalPolynomial(sGridName, iDim, iOut, s1D, iDepth, iOrder, mTransformAB, sConformalMap, vConfromalWeights, vLimitLevels)
%
% [lGrid, points]
% tsgMakeLocalPolynomial(sGridName, iDim, iOut, s1D, iDepth, iOrder,
% mTransformAB, sConformalMap, vConfromalWeights,
% vLimitLevels)
%
% creates a new sparse grid using a sequence rule
%
% INPUT:
%
% sGridName: the name of the grid, give it a string name,
% i.e. 'myGrid' or '1' or 'pi314'
% DO NOT LEAVE THIS EMPTY
%
% iDim: (integer, positive)
% the number of inputs
%
% iOut: (integer, non-negative)
% the number of outputs
%
% s1D: (string for the underlying 1-D rule that induces the grid)
%
% 'localp' 'localp-zero' 'semi-localp' 'localp-boundary'
%
% iDepth: (integer non-negative)
% controls the density of the grid,
% i.e., the number of levels to use
%
%
% iOrder: (integer must be -1 or bigger)
% -1 indicates largest possible order
% 1 means linear, 2 means quadratic, etc.
%
% mTransformAB: (optional matrix of size iDim x 2)
% for all but gauss-laguerre and gauss-hermite grids, the
% transform specifies the lower and upper bound of the domain
% in each direction. For gauss-laguerre and gauss-hermite
% grids, the transform gives the a and b parameters that
% change the weight to
% exp(-b (x - a)) and exp(-b (x - a)^2)
%
% sConformalMap: (optional string giving the type of transform)
% conformal maps provide a non-linear domain transform,
% approximation (quadrature or interpolation) is done
% on the composition of f and the transform. A suitable
% transform could reduce the error by as much as an
% order of magnitude.
%
% 'asin': truncated MacLaurin series of arch-sin
%
% vConfromalWeights: (optional parameters for the conformal trnasform)
% 'asin': indicate the number of terms to keep after
% truncation
%
% vLimitLevels: (optional vector of integers of size iDim)
% limit the level in each direction, no points beyond the
% specified limit will be used, e.g., in 2D [1, 99] forces
% the grid to have at most 3 possible values in the first
% variable and ~2^99 (practicallyt infinite) number in the
% second direction. vLimitLevels works in conjunction with
% iDepth, for each direction, we chose the lesser of the
% vLimitLevels and iDepth
%
% OUTPUT:
%
% lGrid: list containing information about the sparse grid, can be used
% to call other functions
%
% points: (optional) the points of the grid in an array
% of dimension [num_poits, dim]
%
% [lGrid, points] =
% tsgMakeLocalPolynomial(sGridName, iDim, iOut, s1D, iDepth, iOrder,
% mTransformAB, sConformalMap, vConfromalWeights,
% vLimitLevels)
%
% create lGrid object
lGrid.sName = sGridName;
lGrid.sFilename = tsgMakeGridFilename(sGridName);
lGrid.iDim = iDim;
lGrid.iOut = iOut;
lGrid.sType = 'localpolynomial';
% check for conflict with tsgMakeQuadrature
if (strcmp(sGridName, ''))
error('sGridName cannot be empty');
end
% generate filenames
[sFiles, sTasGrid] = tsgGetPaths();
[sFileG, sFileX, sFileV, sFileO, sFileW, sFileC, sFileL] = tsgMakeFilenames(lGrid);
sCommand = [sTasGrid,' -makelocalpoly'];
sCommand = [sCommand, ' -gridfile ', sFileG];
sCommand = [sCommand, ' -dimensions ', num2str(lGrid.iDim)];
sCommand = [sCommand, ' -outputs ', num2str(lGrid.iOut)];
sCommand = [sCommand, ' -onedim ', s1D];
sCommand = [sCommand, ' -depth ', num2str(iDepth)];
sCommand = [sCommand, ' -order ', num2str(iOrder)];
% set the domain transformation
if (exist('mTransformAB') && (max(size(mTransformAB)) ~= 0))
if (size(mTransformAB, 2) ~= 2)
error(' mTransformAB must be a matrix with 2 columns');
end
if (size(mTransformAB, 1) ~= lGrid.iDim)
error(' mTransformAB must be a matrix with iDim number of rows');
end
tsgWriteMatrix(sFileV, mTransformAB);
lGlean.sFileV = 1;
sCommand = [sCommand, ' -tf ',sFileV];
end
% set conformal mapping
if (exist('sConformalMap') && (max(size(sConformalMap)) ~= 0))
if (~exist('vConfromalWeights'))
error(' sConformalMap requires vConfromalWeights')
end
sCommand = [sCommand, ' -conformaltype ', sConformalMap];
if (size(vConfromalWeights, 1) > size(vConfromalWeights, 2))
tsgWriteMatrix(sFileC, vConfromalWeights');
else
tsgWriteMatrix(sFileC, vConfromalWeights);
end
lClean.sFileC = 1;
sCommand = [sCommand, ' -conformalfile ',sFileC];
end
% set level limits
if (exist('vLimitLevels') && (max(size(vLimitLevels)) ~= 0))
if (min(size(vLimitLevels)) ~= 1)
error(' vLimitLevels must be a vector, i.e., one row or one column');
end
if (max(size(vLimitLevels)) ~= lGrid.iDim)
error(' vLimitLevels must be a vector of size iDim');
end
if (size(vLimitLevels, 1) > size(vLimitLevels, 2))
tsgWriteMatrix(sFileL, vLimitLevels');
else
tsgWriteMatrix(sFileL, vLimitLevels);
end
lClean.sFileL = 1;
sCommand = [sCommand, ' -levellimitsfile ', sFileL];
end
% read the points for the grid
if (nargout > 1)
sCommand = [sCommand, ' -of ',sFileO];
lGlean.sFileO = 1;
end
[status, cmdout] = system(sCommand);
if (max(size(strfind(cmdout, 'ERROR'))) ~= 0)
disp(cmdout);
error('The tasgrid execurable returned an error, see above');
return;
else
if (~isempty(cmdout))
fprintf(1,['WARNING: Command had non-empty output:\n']);
disp(cmdout);
end
if (nargout > 1)
points = tsgReadMatrix(sFileO);
end
end
if (exist('lClean'))
tsgCleanTempFiles(lGrid, lClean);
end
end
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