Intrepid
test_01.cpp
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43
52#include "Teuchos_oblackholestream.hpp"
53#include "Teuchos_RCP.hpp"
54#include "Teuchos_ScalarTraits.hpp"
55#include "Teuchos_GlobalMPISession.hpp"
56#include "Teuchos_Array.hpp"
57
58//# include <cstdlib>
59//# include <iostream>
60//# include <cmath>
61//# include <iomanip>
62
63using namespace std;
64using namespace Intrepid;
65
66#define INTREPID_TEST_COMMAND( S ) \
67{ \
68 try { \
69 S ; \
70 } \
71 catch (const std::logic_error & err) { \
72 *outStream << "Expected Error ----------------------------------------------------------------\n"; \
73 *outStream << err.what() << '\n'; \
74 *outStream << "-------------------------------------------------------------------------------" << "\n\n"; \
75 }; \
76}
77
78template<class Scalar>
79Scalar evalQuad(int order, int power, Scalar x[], Scalar w[]) {
80
81 int mid = order/2;
82 Scalar Q = 0.0;
83 if (order%2)
84 Q = w[mid]*powl(x[mid],power);
85
86 for (int i=0; i<mid; i++) {
87 Q += w[i]*powl(x[i],power)+w[order-i-1]*powl(x[order-i-1],power);
88 }
89
90 return Q;
91 /*
92 Scalar Q = 0.0;
93 for (int i=0; i<order; i++) {
94 Q += w[i]*powl(x[i],power);
95 }
96 return Q;
97 */
98}
99
100template<class Scalar>
101Scalar factorial2 (int n) {
102 Scalar value = 1.0;
103 if (n<1)
104 return value;
105
106 int n_copy = n;
107 while (1<n_copy) {
108 value *= (Scalar)n_copy;
109 n_copy -= 2;
110 }
111 return value;
112}
113
114template<class Scalar>
115Scalar chebyshev1(int power) {
116 Scalar bot, exact, top;
117 if (!(power%2)) {
118 top = 1; bot = 1;
119 for (int i=2;i<=power;i+=2) {
120 top *= (Scalar)(i-1);
121 bot *= (Scalar)i;
122 }
123 exact = M_PI*top/bot;
124 }
125 else {
126 exact = 0.0;
127 }
128 return exact;
129}
130
131template<class Scalar>
132Scalar chebyshev2(int power) {
133 Scalar bot, exact, top;
134 if (!(power%2)) {
135 top = 1; bot = 1;
136 for (int i=2;i<=power;i+=2) {
137 top *= (Scalar)(i-1);
138 bot *= (Scalar)i;
139 }
140 bot *= (Scalar)(power+2);
141 exact = M_PI*top/bot;
142 }
143 else {
144 exact = 0.0;
145 }
146 return exact;
147}
148
149int main(int argc, char *argv[]) {
150 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
151
152 // This little trick lets us print to std::cout only if
153 // a (dummy) command-line argument is provided.
154 int iprint = argc - 1;
155 Teuchos::RCP<std::ostream> outStream;
156 Teuchos::oblackholestream bhs; // outputs nothing
157 if (iprint > 0)
158 outStream = Teuchos::rcp(&std::cout, false);
159 else
160 outStream = Teuchos::rcp(&bhs, false);
161
162 // Save the format state of the original std::cout.
163 Teuchos::oblackholestream oldFormatState;
164 oldFormatState.copyfmt(std::cout);
165
166 *outStream \
167 << "===============================================================================\n" \
168 << "| |\n" \
169 << "| Unit Test (IntrepidBurkardtRules) |\n" \
170 << "| |\n" \
171 << "| 1) the Burkardt rule tests |\n" \
172 << "| |\n" \
173 << "| Questions? Contact Drew Kouri (dpkouri@sandia.gov) or |\n" \
174 << "| Denis Ridzal (dridzal@sandia.gov). |\n" \
175 << "| |\n" \
176 << "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
177 << "| Trilinos website: http://trilinos.sandia.gov |\n" \
178 << "| |\n" \
179 << "===============================================================================\n";
180
181
182 int errorFlag = 0;
183
184 int maxOrder = 30;
185 long double reltol = 1e-8;
186 long double analyticInt = 0, testInt = 0;
187 // compute and compare integrals
188 try {
189
190 *outStream << "Gauss-Legendre Cubature \n";
191 *outStream << "Integrates functions on [-1,1] weighted by w(x) = 1\n";
192 for (int i = 1; i<=maxOrder; i++) {
193 Teuchos::Array<long double> nodes(i), weights(i);
194 IntrepidBurkardtRules::legendre_compute(i,nodes.getRawPtr(),weights.getRawPtr());
195 for (int j=0; j<=2*i-1; j++) {
196 if (j%2)
197 analyticInt = 0.0;
198 else
199 analyticInt = 2.0/((long double)j+1.0);
200 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
201 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
202 long double absdiff = std::fabs(analyticInt - testInt);
203 *outStream << "Cubature order " << std::setw(2) << std::left << i << " integrating "
204 << "x^" << std::setw(2) << std::left << j << ":" << " "
205 << std::scientific << std::setprecision(16) << testInt << " "
206 << analyticInt << " " << std::setprecision(4) << absdiff << " " << "<?"
207 << " " << abstol << "\n";
208 if (absdiff > abstol) {
209 errorFlag++;
210 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
211 }
212 }
213 }
214 *outStream << "\n";
215
216 *outStream << "Clenshaw-Curtis Cubature \n";
217 *outStream << "Integrates functions on [-1,1] weighted by w(x) = 1\n";
218 for (int i = 1; i<=maxOrder; i++) {
219 Teuchos::Array<long double> nodes(i), weights(i);
220 IntrepidBurkardtRules::clenshaw_curtis_compute(i,nodes.getRawPtr(),weights.getRawPtr());
221 for (int j=0; j<i; j++) {
222 if (j%2)
223 analyticInt = 0.0;
224 else
225 analyticInt = 2.0/((long double)j+1.0);
226 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
227 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
228 long double absdiff = std::fabs(analyticInt - testInt);
229 *outStream << "Cubature order " << std::setw(2) << std::left << i << " integrating "
230 << "x^" << std::setw(2) << std::left << j << ":" << " "
231 << std::scientific << std::setprecision(16) << testInt << " "
232 << analyticInt << " " << std::setprecision(4) << absdiff << " " << "<?"
233 << " " << abstol << "\n";
234 if (absdiff > abstol) {
235 errorFlag++;
236 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
237 }
238 }
239 }
240 *outStream << "\n";
241
242 *outStream << "Fejer Type 2 Cubature \n";
243 *outStream << "Integrates functions on [-1,1] weighted by w(x) = 1\n";
244 for (int i = 1; i<=maxOrder; i++) {
245 Teuchos::Array<long double> nodes(i), weights(i);
246 IntrepidBurkardtRules::fejer2_compute(i,nodes.getRawPtr(),weights.getRawPtr());
247 for (int j=0; j<i; j++) {
248 if (j%2)
249 analyticInt = 0.0;
250 else
251 analyticInt = 2.0/((long double)j+1.0);
252 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
253 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
254 long double absdiff = std::fabs(analyticInt - testInt);
255 *outStream << "Cubature order " << std::setw(2) << std::left << i << " integrating "
256 << "x^" << std::setw(2) << std::left << j << ":" << " "
257 << std::scientific << std::setprecision(16) << testInt << " "
258 << analyticInt << " " << std::setprecision(4) << absdiff << " " << "<?"
259 << " " << abstol << "\n";
260 if (absdiff > abstol) {
261 errorFlag++;
262 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
263 }
264 }
265 }
266 *outStream << "\n";
267
268 *outStream << "Gauss-Patterson Cubature \n";
269 *outStream << "Integrates functions on [-1,1] weighted by w(x) = 1\n";
270 for (int l = 1; l<=7; l++) {
271 int i = (int)pow(2.0,(double)l+1.0)-1;
272 Teuchos::Array<long double> nodes(i), weights(i);
273 IntrepidBurkardtRules::patterson_lookup(i,nodes.getRawPtr(),weights.getRawPtr());
274 for (int j=0; j<=(1.5*i+0.5); j++) {
275 if (j%2)
276 analyticInt = 0.0;
277 else
278 analyticInt = 2.0/((long double)j+1.0);
279 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
280 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
281 long double absdiff = std::fabs(analyticInt - testInt);
282 *outStream << "Cubature order " << std::setw(2) << std::left << i << " integrating "
283 << "x^" << std::setw(2) << std::left << j << ":" << " "
284 << std::scientific << std::setprecision(16) << testInt << " "
285 << analyticInt << " " << std::setprecision(4) << absdiff << " " << "<?"
286 << " " << abstol << "\n";
287 if (absdiff > abstol) {
288 errorFlag++;
289 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
290 }
291 }
292 }
293 *outStream << "\n";
294
295 *outStream << "Gauss-Chebyshev Type 1 Cubature \n";
296 *outStream << "Integrates functions on [-1,1] weighted by w(x) = 1/sqrt(1-x^2)\n";
297 for (int i = 1; i<=maxOrder; i++) {
298 Teuchos::Array<long double> nodes(i), weights(i);
299 IntrepidBurkardtRules::chebyshev1_compute(i,nodes.getRawPtr(),weights.getRawPtr());
300 for (int j=0; j<=2*i-1; j++) {
301 analyticInt = chebyshev1<long double>(j);
302 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
303 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
304 long double absdiff = std::fabs(analyticInt - testInt);
305 *outStream << "Cubature order " << std::setw(2) << std::left << i << " integrating "
306 << "x^" << std::setw(2) << std::left << j << ":" << " "
307 << std::scientific << std::setprecision(16) << testInt << " "
308 << analyticInt << " " << std::setprecision(4) << absdiff << " " << "<?"
309 << " " << abstol << "\n";
310 if (absdiff > abstol) {
311 errorFlag++;
312 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
313 }
314 }
315 }
316 *outStream << "\n";
317
318 *outStream << "Gauss-Chebyshev Type 2 Cubature \n";
319 *outStream << "Integrates functions on [-1,1] weighted by w(x) = sqrt(1-x^2)\n";
320 for (int i = 1; i<=maxOrder; i++) {
321 Teuchos::Array<long double> nodes(i), weights(i);
322 IntrepidBurkardtRules::chebyshev2_compute(i,nodes.getRawPtr(),weights.getRawPtr());
323 for (int j=0; j<=2*i-1; j++) {
324 analyticInt = chebyshev2<long double>(j);
325 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
326 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
327 long double absdiff = std::fabs(analyticInt - testInt);
328 *outStream << "Cubature order " << std::setw(2) << std::left << i << " integrating "
329 << "x^" << std::setw(2) << std::left << j << ":" << " "
330 << std::scientific << std::setprecision(16) << testInt << " "
331 << analyticInt << " " << std::setprecision(4) << absdiff << " " << "<?"
332 << " " << abstol << "\n";
333 if (absdiff > abstol) {
334 errorFlag++;
335 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
336 }
337 }
338 }
339 *outStream << "\n";
340
341 *outStream << "Gauss-Laguerre Cubature \n";
342 *outStream << "Integrates functions on [0,oo) weighted by w(x) = exp(-x)\n";
343 for (int i = 1; i<=maxOrder; i++) {
344 Teuchos::Array<long double> nodes(i), weights(i);
345 IntrepidBurkardtRules::laguerre_compute(i,nodes.getRawPtr(),weights.getRawPtr());
346 for (int j=0; j<=2*i-1; j++) {
347 analyticInt = tgammal((long double)(j+1));
348 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
349 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
350 long double absdiff = std::fabs(analyticInt - testInt);
351 *outStream << "Cubature order " << std::setw(2) << std::left << i << " integrating "
352 << "x^" << std::setw(2) << std::left << j << ":" << " "
353 << std::scientific << std::setprecision(16) << testInt << " "
354 << analyticInt << " " << std::setprecision(4) << absdiff << " " << "<?"
355 << " " << abstol << "\n";
356 if (absdiff > abstol) {
357 errorFlag++;
358 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
359 }
360 }
361 }
362 *outStream << "\n";
363
364 maxOrder = 10;
365
366 *outStream << "Gauss-Hermite Cubature \n";
367 *outStream << "Integrates functions on (-oo,oo) weighted by w(x) = exp(-x^2)\n";
368 for (int i = 1; i<=maxOrder; i++) {
369 Teuchos::Array<long double> nodes(i), weights(i);
370 IntrepidBurkardtRules::hermite_compute(i,nodes.getRawPtr(),
371 weights.getRawPtr());
372 for (int j=0; j<=2*i-1; j++) {
373 if (j%2)
374 analyticInt = 0.0;
375 else
376 analyticInt = factorial2<long double>(j-1)*sqrt(M_PI)/powl(2.0,(long double)j/2.0);
377 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
378 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
379 long double absdiff = std::fabs(analyticInt - testInt);
380 *outStream << "Cubature order " << std::setw(2) << std::left << i
381 << " integrating "
382 << "x^" << std::setw(2) << std::left << j << ":"
383 << " "
384 << std::scientific << std::setprecision(16) << testInt
385 << " "
386 << analyticInt << " " << std::setprecision(4)
387 << absdiff << " " << "<?"
388 << " " << abstol << "\n";
389 if (absdiff > abstol) {
390 errorFlag++;
391 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
392 }
393 }
394 }
395 *outStream << "\n";
396
397 reltol = 1e-6;
398
399 *outStream << "Hermite-Genz-Keister Cubature \n";
400 *outStream << "Integrates functions on (-oo,oo) weighted by w(x) = exp(-x^2)\n";
401 int order[4] = {1,3, 9,19};
402 int max[4] = {1,5,15,29};
403 for (int l = 0; l<4; l++) {
404 int i = order[l];
405 int m = max[l];
406 Teuchos::Array<long double> nodes(i), weights(i);
408 weights.getRawPtr());
409 for (int j=0; j<=m; j++) {
410 if (j%2)
411 analyticInt = 0.0;
412 else
413 analyticInt = factorial2<long double>(j-1)*sqrt(M_PI)/powl(2.0,(long double)j/2.0);
414 if (i>=36)
415 analyticInt /= sqrt(M_PI);
416 testInt = evalQuad(i,j,nodes.getRawPtr(),weights.getRawPtr());
417 long double abstol = (analyticInt == 0.0 ? reltol : std::fabs(reltol*analyticInt) );
418 long double absdiff = std::fabs(analyticInt - testInt);
419 *outStream << "Cubature order " << std::setw(2) << std::left << i
420 << " integrating "
421 << "x^" << std::setw(2) << std::left << j << ":" << " "
422 << std::scientific << std::setprecision(16) << testInt
423 << " "
424 << analyticInt << " " << std::setprecision(4) << absdiff
425 << " " << "<?"
426 << " " << abstol << "\n";
427 if (absdiff > abstol) {
428 errorFlag++;
429 *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
430 }
431 }
432 }
433 *outStream << "\n";
434 }
435 catch (const std::logic_error & err) {
436 *outStream << err.what() << "\n";
437 errorFlag = -1;
438 };
439
440
441 if (errorFlag != 0)
442 std::cout << "End Result: TEST FAILED\n";
443 else
444 std::cout << "End Result: TEST PASSED\n";
445
446 // reset format state of std::cout
447 std::cout.copyfmt(oldFormatState);
448
449 return errorFlag;
450}
451
Header file for integration rules provided by John Burkardt. <\A>
static void patterson_lookup(int n, Scalar x[], Scalar w[])
Gauss-Patterson; returns points and weights.
static void hermite_genz_keister_lookup(int n, Scalar x[], Scalar w[])
Hermite-Genz-Keister; returns points and weights.
static void fejer2_compute(int order, Scalar x[], Scalar w[])
Fejer type 2; returns points and weights.
static void chebyshev1_compute(int order, Scalar x[], Scalar w[])
Gauss-Chebyshev of Type 1; returns points and weights.
static void chebyshev2_compute(int order, Scalar x[], Scalar w[])
Gauss-Chebyshev of Type 2; returns points and weights.
static void hermite_compute(int order, Scalar x[], Scalar w[])
Gauss-Hermite; returns points and weights.
static void laguerre_compute(int n, Scalar x[], Scalar w[])
Gauss-Laguerre; returns points and weights.
static void legendre_compute(int n, Scalar x[], Scalar w[])
Gauss-Legendre; returns points and weights.
static void clenshaw_curtis_compute(int order, Scalar x[], Scalar w[])
Clenshaw-Curtis; returns points and weights.