Intrepid
test_05.cpp
Go to the documentation of this file.
1// @HEADER
2// ************************************************************************
3//
4// Intrepid Package
5// Copyright (2007) Sandia Corporation
6//
7// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
8// license for use of this work by or on behalf of the U.S. Government.
9//
10// Redistribution and use in source and binary forms, with or without
11// modification, are permitted provided that the following conditions are
12// met:
13//
14// 1. Redistributions of source code must retain the above copyright
15// notice, this list of conditions and the following disclaimer.
16//
17// 2. Redistributions in binary form must reproduce the above copyright
18// notice, this list of conditions and the following disclaimer in the
19// documentation and/or other materials provided with the distribution.
20//
21// 3. Neither the name of the Corporation nor the names of the
22// contributors may be used to endorse or promote products derived from
23// this software without specific prior written permission.
24//
25// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
26// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
28// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
29// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
30// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
31// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
32// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
33// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
34// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
35// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
36//
37// Questions? Contact Pavel Bochev (pbboche@sandia.gov)
38// Denis Ridzal (dridzal@sandia.gov), or
39// Kara Peterson (kjpeter@sandia.gov)
40//
41// ************************************************************************
42// @HEADER
43
44
52#include "Intrepid_Utils.hpp"
53#include "Teuchos_oblackholestream.hpp"
54#include "Teuchos_RCP.hpp"
55#include "Teuchos_BLAS.hpp"
56#include "Teuchos_GlobalMPISession.hpp"
57
58using namespace Intrepid;
59
60/*
61 Monomial evaluation.
62 in 1D, for point p(x) : x^xDeg
63 in 2D, for point p(x,y) : x^xDeg * y^yDeg
64 in 3D, for point p(x,y,z): x^xDeg * y^yDeg * z^zDeg
65*/
66double computeMonomial(FieldContainer<double> & p, int xDeg, int yDeg=0, int zDeg=0) {
67 double val = 1.0;
68 int polydeg[3];
69 polydeg[0] = xDeg; polydeg[1] = yDeg; polydeg[2] = zDeg;
70 for (int i=0; i<p.dimension(0); i++) {
71 val *= std::pow(p(i),polydeg[i]);
72 }
73 return val;
74}
75
76
77/*
78 Computes integrals of monomials over a given reference cell.
79*/
80double computeIntegral(shards::CellTopology & cellTopology, int cubDegree, int xDeg, int yDeg, int zDeg) {
81
82 DefaultCubatureFactory<double> cubFactory; // create factory
83 Teuchos::RCP<Cubature<double> > myCub = cubFactory.create(cellTopology, cubDegree); // create default cubature
84
85 double val = 0.0;
86 int cubDim = myCub->getDimension();
87 int numCubPoints = myCub->getNumPoints();
88
89 FieldContainer<double> point(cubDim);
90 FieldContainer<double> cubPoints(numCubPoints, cubDim);
91 FieldContainer<double> cubWeights(numCubPoints);
92 FieldContainer<double> functValues(numCubPoints);
93
94 myCub->getCubature(cubPoints, cubWeights);
95
96 for (int i=0; i<numCubPoints; i++) {
97 for (int j=0; j<cubDim; j++) {
98 point(j) = cubPoints(i,j);
99 }
100 functValues(i) = computeMonomial(point, xDeg, yDeg, zDeg);
101 }
102
103 Teuchos::BLAS<int, double> myblas;
104 int inc = 1;
105 val = myblas.DOT(numCubPoints, &functValues[0], inc, &cubWeights[0], inc);
106
107 return val;
108}
109
110
111
112int main(int argc, char *argv[]) {
113
114 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
115
116 // This little trick lets us print to std::cout only if
117 // a (dummy) command-line argument is provided.
118 int iprint = argc - 1;
119 Teuchos::RCP<std::ostream> outStream;
120 Teuchos::oblackholestream bhs; // outputs nothing
121 if (iprint > 0)
122 outStream = Teuchos::rcp(&std::cout, false);
123 else
124 outStream = Teuchos::rcp(&bhs, false);
125
126 // Save the format state of the original std::cout.
127 Teuchos::oblackholestream oldFormatState;
128 oldFormatState.copyfmt(std::cout);
129
130 *outStream \
131 << "===============================================================================\n" \
132 << "| |\n" \
133 << "| Unit Test (CubatureDirect,CubatureTensor,DefaultCubatureFactory) |\n" \
134 << "| |\n" \
135 << "| 1) Computing integrals of monomials on reference cells in 3D |\n" \
136 << "| - using Level 1 BLAS - |\n" \
137 << "| |\n" \
138 << "| Questions? Contact Pavel Bochev (pbboche@sandia.gov) or |\n" \
139 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
140 << "| |\n" \
141 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
142 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
143 << "| |\n" \
144 << "===============================================================================\n"\
145 << "| TEST 1: integrals of monomials in 3D (Level 1 BLAS version) |\n"\
146 << "===============================================================================\n";
147
148 // internal variables:
149 int errorFlag = 0;
150 int polyCt = 0;
151 int offset = 0;
152 Teuchos::Array< Teuchos::Array<double> > testInt;
153 Teuchos::Array< Teuchos::Array<double> > analyticInt;
154 Teuchos::Array<double> tmparray(1);
155 double reltol = 1.0e+04 * INTREPID_TOL;
156 int maxDeg[4];
157 int maxOffset[4];
158 int numPoly[4];
159 int numAnalytic[4];
160 // max polynomial degree tested, per cell type:
162 maxDeg[1] = 20; // can be as large as INTREPID_CUBATURE_LINE_GAUSS_MAX, but runtime is excessive
165 // max polynomial degree recorded in analytic comparison files, per cell type:
170 for (int i=0; i<4; i++) {
171 numPoly[i] = (maxDeg[i]+1)*(maxDeg[i]+2)*(maxDeg[i]+3)/6;
172 }
173 for (int i=0; i<4; i++) {
174 numAnalytic[i] = (maxOffset[i]+1)*(maxOffset[i]+2)*(maxOffset[i]+3)/6;
175 }
176
177 // get names of files with analytic values
178 std::string basedir = "./data";
179 std::stringstream namestream[4];
180 std::string filename[4];
181 namestream[0] << basedir << "/TET_integrals" << ".dat";
182 namestream[0] >> filename[0];
183 namestream[1] << basedir << "/HEX_integrals" << ".dat";
184 namestream[1] >> filename[1];
185 namestream[2] << basedir << "/TRIPRISM_integrals" << ".dat";
186 namestream[2] >> filename[2];
187 namestream[3] << basedir << "/PYR_integrals" << ".dat";
188 namestream[3] >> filename[3];
189
190 // reference cells tested
191 shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Tetrahedron<> >(),
192 shards::getCellTopologyData< shards::Hexahedron<> >(),
193 shards::getCellTopologyData< shards::Wedge<> >(),
194 shards::getCellTopologyData< shards::Pyramid<> >() };
195 // format of data files with analytic values
196 TypeOfExactData dataFormat[] = {INTREPID_UTILS_SCALAR, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION};
197
198 // compute and compare integrals
199 try {
200 for (int cellCt=0; cellCt < 4; cellCt++) {
201 testInt.assign(numPoly[cellCt], tmparray);
202 analyticInt.assign(numAnalytic[cellCt], tmparray);
203
204 *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseCellTopologyData()->name << ":\n";
205 std::ifstream filecompare(&filename[cellCt][0]);
206 // compute integrals
207 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
208 polyCt = 0;
209 testInt[cubDeg].resize((cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6);
210 for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
211 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
212 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
213 testInt[cubDeg][polyCt] = computeIntegral(cellType[cellCt], cubDeg, xDeg, yDeg, zDeg);
214 polyCt++;
215 }
216 }
217 }
218 }
219 // get analytic values
220 if (filecompare.is_open()) {
221 getAnalytic(analyticInt, filecompare, dataFormat[cellCt]);
222 // close file
223 filecompare.close();
224 }
225 // perform comparison
226 for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
227 polyCt = 0;
228 offset = 0;
229 int oldErrorFlag = errorFlag;
230 for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
231 for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
232 for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
233 double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
234 double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
235
236 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
237 << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg
238 << " * z^" << std::setw(2) << zDeg << ":" << " "
239 << std::scientific << std::setprecision(16)
240 << testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " "
241 << std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
242 if (absdiff > abstol) {
243 errorFlag++;
244 *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n";
245 }
246 polyCt++;
247 }
248 offset = offset + maxOffset[cellCt] - cubDeg;
249 }
250 offset = offset + (maxOffset[cellCt] - cubDeg)*(maxOffset[cellCt] - cubDeg + 1)/2;
251 }
252 *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg;
253 if (errorFlag == oldErrorFlag)
254 *outStream << " passed.\n";
255 else
256 *outStream << " failed.\n";
257 }
258 *outStream << "\n";
259 } // end for cellCt
260 }
261 catch (const std::logic_error & err) {
262 *outStream << err.what() << "\n";
263 errorFlag = -1;
264 };
265
266
267 if (errorFlag != 0)
268 std::cout << "End Result: TEST FAILED\n";
269 else
270 std::cout << "End Result: TEST PASSED\n";
271
272 // reset format state of std::cout
273 std::cout.copyfmt(oldFormatState);
274
275 return errorFlag;
276}
#define INTREPID_CUBATURE_LINE_GAUSSJACOBI20_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct line rule of the Gaus...
#define INTREPID_CUBATURE_LINE_GAUSS_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct line rule of the Gaus...
#define INTREPID_CUBATURE_TET_DEFAULT_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct tetrahedron rule of t...
#define INTREPID_CUBATURE_TRI_DEFAULT_MAX
The maximum degree of the polynomial that can be integrated exactly by a direct triangle rule of the ...
Header file for the abstract base class Intrepid::DefaultCubatureFactory.
Intrepid utilities.
void getAnalytic(Teuchos::Array< Teuchos::Array< Scalar > > &testMat, std::ifstream &inputFile, TypeOfExactData analyticDataType=INTREPID_UTILS_FRACTION)
Loads analytic values stored in a file into the matrix testMat, where the output matrix is an array o...
A factory class that generates specific instances of cubatures.
Teuchos::RCP< Cubature< Scalar, ArrayPoint, ArrayWeight > > create(const shards::CellTopology &cellTopology, const std::vector< int > &degree)
Factory method.
Implementation of a templated lexicographical container for a multi-indexed scalar quantity....
int dimension(const int whichDim) const
Returns the specified dimension.