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Stokhos_LegendreBasisUnitTest.cpp
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43
44#include "Teuchos_UnitTestHarness.hpp"
45#include "Teuchos_TestingHelpers.hpp"
46#include "Teuchos_UnitTestRepository.hpp"
47#include "Teuchos_GlobalMPISession.hpp"
48
49#include "Stokhos.hpp"
51#ifdef HAVE_STOKHOS_FORUQTK
52#include "Stokhos_gaussq.h"
53#endif
54
56
57 // Common setup for unit tests
58 template <typename OrdinalType, typename ValueType>
60 ValueType rtol, atol;
61 OrdinalType p;
63
64 UnitTestSetup() : rtol(1e-12), atol(1e-12), p(10), basis(p) {}
65
66 };
67
68 UnitTestSetup<int,double> setup;
69
70 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, Order ) {
71 int order = setup.basis.order();
72 TEUCHOS_TEST_EQUALITY(order, setup.p, out, success);
73 }
74
75 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, Size ) {
76 int size = setup.basis.size();
77 TEUCHOS_TEST_EQUALITY(size, setup.p+1, out, success);
78 }
79
80 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, Norm ) {
81 const Teuchos::Array<double>& n1 = setup.basis.norm_squared();
82 Teuchos::Array<double> n2(setup.p+1);
83 for (int i=0; i<=setup.p; i++)
84 n2[i] = 1.0/(2.0*i+1.0);
85 success = Stokhos::compareArrays(n1, "n1", n2, "n2", setup.rtol, setup.atol,
86 out);
87 }
88
89 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, Norm2 ) {
90 Teuchos::Array<double> n1(setup.p+1);
91 Teuchos::Array<double> n2(setup.p+1);
92 for (int i=0; i<=setup.p; i++) {
93 n1[i] = setup.basis.norm_squared(i);
94 n2[i] = 1.0/(2.0*i+1.0);
95 }
96 success = Stokhos::compareArrays(n1, "n1", n2, "n2", setup.rtol, setup.atol,
97 out);
98 }
99
100 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, QuadNorm ) {
101 const Teuchos::Array<double>& n1 = setup.basis.norm_squared();
102 Teuchos::Array<double> n2(setup.p+1);
103 Teuchos::Array<double> x, w;
104 Teuchos::Array< Teuchos::Array<double> > v;
105 setup.basis.getQuadPoints(2*setup.p, x, w, v);
106 int nqp = w.size();
107 for (int i=0; i<=setup.p; i++) {
108 n2[i] = 0;
109 for (int j=0; j<nqp; j++)
110 n2[i] += w[j]*v[j][i]*v[j][i];
111 }
112 success = Stokhos::compareArrays(n1, "n1", n2, "n2", setup.rtol, setup.atol,
113 out);
114 }
115
116 // Tests basis is orthogonal
117 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, QuadOrthog ) {
118 const Teuchos::Array<double>& norms = setup.basis.norm_squared();
119 Teuchos::Array<double> x, w;
120 Teuchos::Array< Teuchos::Array<double> > v;
121 setup.basis.getQuadPoints(2*setup.p, x, w, v);
122 int nqp = w.size();
123 Teuchos::SerialDenseMatrix<int,double> mat(setup.p+1, setup.p+1);
124 for (int i=0; i<=setup.p; i++) {
125 for (int j=0; j<=setup.p; j++) {
126 for (int k=0; k<nqp; k++)
127 mat(i,j) += w[k]*v[k][i]*v[k][j];
128 mat(i,j) /= std::sqrt(norms[i]*norms[j]);
129 }
130 mat(i,i) -= 1.0;
131 }
132 success = mat.normInf() < setup.atol;
133 if (!success) {
134 out << "\n Error, mat.normInf() < atol = " << mat.normInf()
135 << " < " << setup.atol << ": failed!\n";
136 out << "mat = " << printMat(mat) << std::endl;
137 }
138 }
139
140 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, TripleProduct ) {
141 Teuchos::RCP< Stokhos::Dense3Tensor<int, double> > Cijk =
142 setup.basis.computeTripleProductTensor();
143
144 Teuchos::Array<double> x, w;
145 Teuchos::Array< Teuchos::Array<double> > v;
146 setup.basis.getQuadPoints(3*setup.p, x, w, v);
147
148 success = true;
149 for (int i=0; i<=setup.p; i++) {
150 for (int j=0; j<=setup.p; j++) {
151 for (int k=0; k<=setup.p; k++) {
152 double c = 0.0;
153 int nqp = w.size();
154 for (int qp=0; qp<nqp; qp++)
155 c += w[qp]*v[qp][i]*v[qp][j]*v[qp][k];
156 std::stringstream ss;
157 ss << "Cijk(" << i << "," << j << "," << k << ")";
158 success = success &&
159 Stokhos::compareValues((*Cijk)(i,j,k), ss.str(), c, "c",
160 setup.rtol, setup.atol, out);
161 }
162 }
163 }
164 }
165
166 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, DerivDoubleProduct ) {
167 Teuchos::RCP< Teuchos::SerialDenseMatrix<int, double> > Bij =
168 setup.basis.computeDerivDoubleProductTensor();
169
170 Teuchos::Array<double> x, w;
171 Teuchos::Array< Teuchos::Array<double> > v, val, deriv;
172 setup.basis.getQuadPoints(3*setup.p, x, w, v);
173 int nqp = w.size();
174 val.resize(nqp);
175 deriv.resize(nqp);
176 for (int i=0; i<nqp; i++) {
177 val[i].resize(setup.p+1);
178 deriv[i].resize(setup.p+1);
179 setup.basis.evaluateBasesAndDerivatives(x[i], val[i], deriv[i]);
180 }
181
182 success = true;
183 for (int i=0; i<=setup.p; i++) {
184 for (int j=0; j<=setup.p; j++) {
185 double b = 0.0;
186 for (int qp=0; qp<nqp; qp++)
187 b += w[qp]*deriv[qp][i]*val[qp][j];
188 std::stringstream ss;
189 ss << "Bij(" << i << "," << j << ")";
190 success = success &&
191 Stokhos::compareValues((*Bij)(i,j), ss.str(), b, "b",
192 setup.rtol, setup.atol, out);
193 }
194 }
195 }
196
197 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, DerivDoubleProduct2 ) {
198 Teuchos::RCP< Teuchos::SerialDenseMatrix<int, double> > Bij =
199 setup.basis.computeDerivDoubleProductTensor();
200 const Teuchos::Array<double>& n = setup.basis.norm_squared();
201
202 Teuchos::Array< Teuchos::Array<double> > deriv_coeffs(setup.p+1);
203 deriv_coeffs[0].resize(setup.p+1,0.0);
204 if (setup.p >= 1) {
205 deriv_coeffs[1].resize(setup.p+1,0.0);
206 deriv_coeffs[1][0] = 1.0;
207 }
208 if (setup.p >= 2) {
209 deriv_coeffs[2].resize(setup.p+1,0.0);
210 deriv_coeffs[2][1] = 3.0;
211 }
212 for (int k=3; k<=setup.p; k++) {
213 deriv_coeffs[k].resize(setup.p+1,0.0);
214 deriv_coeffs[k][0] = 1.0/3.0*deriv_coeffs[k-1][1];
215 for (int i=1; i<=k-3; i++)
216 deriv_coeffs[k][i] = i/(2.0*i - 1.0)*deriv_coeffs[k-1][i-1] +
217 (i+1.0)/(2.0*i + 3.0)*deriv_coeffs[k-1][i+1];
218 deriv_coeffs[k][k-2] = (k-2.0)/(2.0*k-5.0)*deriv_coeffs[k-1][k-3];
219 deriv_coeffs[k][k-1] = (k-1.0)/(2.0*k-3.0)*deriv_coeffs[k-1][k-2] + k;
220 }
221
222 success = true;
223 for (int i=0; i<=setup.p; i++) {
224 for (int j=0; j<=setup.p; j++) {
225 double b = deriv_coeffs[i][j]*n[j];
226 std::stringstream ss;
227 ss << "Bij(" << i << "," << j << ")";
228 success = success &&
229 Stokhos::compareValues((*Bij)(i,j), ss.str(), b, "b",
230 setup.rtol, setup.atol, out);
231 }
232 }
233 }
234
235 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, EvaluateBases ) {
236 double x = 0.1234;
237 Teuchos::Array<double> v1(setup.p+1), v2(setup.p+1);
238 setup.basis.evaluateBases(x, v1);
239
240 // evaluate bases using formula
241 // P_0(x) = 1
242 // P_1(x) = x
243 // P_i(x) = (2*i-1)/i*x*P_{i-1}(x) - (i-1)/i*P_{i-2}(x), i=2,3,...
244 v2[0] = 1.0;
245 if (setup.p >= 1)
246 v2[1] = x;
247 for (int i=2; i<=setup.p; i++)
248 v2[i] = (2.0*i-1.0)/i*x*v2[i-1] - (i-1.0)/i*v2[i-2];
249 success = Stokhos::compareArrays(v1, "v1", v2, "v2", setup.rtol, setup.atol,
250 out);
251 }
252
253 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, EvaluateBasesAndDerivatives ) {
254 double x = 0.1234;
255 Teuchos::Array<double> val1(setup.p+1), deriv1(setup.p+1),
256 val2(setup.p+1), deriv2(setup.p+1);
257 setup.basis.evaluateBasesAndDerivatives(x, val1, deriv1);
258
259 // evaluate bases and derivatives using formula:
260 // P_0(x) = 1
261 // P_1(x) = x
262 // P_i(x) = (2*i-1)/i*x*P_{i-1}(x) - (i-1)/i*P_{i-2}(x), i=2,3,...
263 // P_0'(x) = 0
264 // P_1'(x) = 1
265 // P_i'(x) = i*P_{i-1}(x) + x*P_{i-1}'(x), i=2,3,...
266 val2[0] = 1.0;
267 if (setup.p >= 1)
268 val2[1] = x;
269 for (int i=2; i<=setup.p; i++)
270 val2[i] = (2.0*i-1.0)/i*x*val2[i-1] - (i-1.0)/i*val2[i-2];
271
272 deriv2[0] = 0.0;
273 if (setup.p >= 1)
274 deriv2[1] = 1.0;
275 for (int i=2; i<=setup.p; i++)
276 deriv2[i] = i*val2[i-1] + x*deriv2[i-1];
277 success = Stokhos::compareArrays(val1, "val1", val2, "val2",
278 setup.rtol, setup.atol, out);
279 success = success &&
280 Stokhos::compareArrays(deriv1, "deriv1", deriv2, "deriv2",
281 setup.rtol, setup.atol, out);
282
283
284 }
285
286 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, Evaluate ) {
287 double x = 0.1234;
288 Teuchos::Array<double> v1(setup.p+1), v2(setup.p+1);
289 for (int i=0; i<=setup.p; i++)
290 v1[i] = setup.basis.evaluate(x, i);
291
292 // evaluate bases using formula
293 // P_0(x) = 1
294 // P_1(x) = x
295 // P_i(x) = (2*i-1)/i*x*P_{i-1}(x) - (i-1)/i*P_{i-2}(x), i=2,3,...
296 v2[0] = 1.0;
297 if (setup.p >= 1)
298 v2[1] = x;
299 for (int i=2; i<=setup.p; i++)
300 v2[i] = (2.0*i-1.0)/i*x*v2[i-1] - (i-1.0)/i*v2[i-2];
301 success = Stokhos::compareArrays(v1, "v1", v2, "v2", setup.rtol, setup.atol,
302 out);
303 }
304
305 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, Recurrence ) {
306 Teuchos::Array<double> a1(setup.p+1), b1(setup.p+1), c1(setup.p+1),
307 d1(setup.p+1);
308 Teuchos::Array<double> a2(setup.p+1), b2(setup.p+1), c2(setup.p+1),
309 d2(setup.p+1);
310 setup.basis.getRecurrenceCoefficients(a1, b1, c1, d1);
311
312 // compute coefficients using formula
313 a2[0] = 0.0; b2[0] = 1.0; c2[0] = 1.0; d2[0] = 1.0;
314 for (int i=1; i<=setup.p; i++) {
315 a2[i] = 0.0;
316 b2[i] = i/(i+1.0);
317 c2[i] = (2.0*i+1.0)/(i+1);
318 d2[i] = 1.0;
319 }
320 success = true;
321 success = success &&
322 Stokhos::compareArrays(a1, "a1", a2, "a2", setup.rtol, setup.atol, out);
323 success = success &&
324 Stokhos::compareArrays(b1, "b1", b2, "b2", setup.rtol, setup.atol, out);
325 success = success &&
326 Stokhos::compareArrays(c1, "c1", c2, "c2", setup.rtol, setup.atol, out);
327 success = success &&
328 Stokhos::compareArrays(d1, "d1", d2, "d2", setup.rtol, setup.atol, out);
329 }
330
331 // Tests alpha coefficients satisfy
332 // alpha_k = delta_k * (t*psi_k,psi_k)/(psi_k,psi_k)
333 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, RecurrenceAlpha ) {
334 Teuchos::Array<double> a1(setup.p+1), b1(setup.p+1), c1(setup.p+1),
335 d1(setup.p+1);
336 setup.basis.getRecurrenceCoefficients(a1, b1, c1, d1);
337
338 Teuchos::Array<double> a2(setup.p+1);
339 const Teuchos::Array<double>& n1 = setup.basis.norm_squared();
340 Teuchos::Array<double> x, w;
341 Teuchos::Array< Teuchos::Array<double> > v;
342 setup.basis.getQuadPoints(2*setup.p, x, w, v);
343 int nqp = w.size();
344 for (int i=0; i<=setup.p; i++) {
345 a2[i] = 0;
346 for (int j=0; j<nqp; j++)
347 a2[i] += w[j]*x[j]*v[j][i]*v[j][i];
348 a2[i] = a2[i]*c1[i]/n1[i];
349 }
350 success = Stokhos::compareArrays(a1, "a1", a2, "a2", setup.rtol, setup.atol,
351 out);
352 }
353
354 // Tests beta coefficients satisfy
355 // beta_k =
356 // gamma_k * delta_k/delta_{k-1} * (psi_k,psi_k)/(psi_{k-1},psi_{k-1})
357 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, RecurrenceBeta ) {
358 Teuchos::Array<double> a1(setup.p+1), b1(setup.p+1), c1(setup.p+1),
359 d1(setup.p+1);
360 setup.basis.getRecurrenceCoefficients(a1, b1, c1, d1);
361
362 Teuchos::Array<double> b2(setup.p+1);
363 const Teuchos::Array<double>& n1 = setup.basis.norm_squared();
364 b2[0] = b1[0];
365 for (int i=1; i<=setup.p; i++) {
366 b2[i] = d1[i]*(c1[i]/c1[i-1])*(n1[i]/n1[i-1]);
367 }
368 success = Stokhos::compareArrays(b1, "b1", b2, "b2", setup.rtol, setup.atol,
369 out);
370 }
371
372#ifdef HAVE_STOKHOS_DAKOTA
373 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, QuadPointsDakota ) {
374 int n = static_cast<int>(std::ceil((setup.p+1)/2.0));
375 Teuchos::Array<double> x1, w1;
376 Teuchos::Array< Teuchos::Array<double> > v1;
377 setup.basis.getQuadPoints(setup.p, x1, w1, v1);
378
379 Teuchos::Array<double> x2(n), w2(n);
380 Teuchos::Array< Teuchos::Array<double> > v2(n);
381 webbur::legendre_compute(n, &x2[0], &w2[0]);
382
383 for (int i=0; i<n; i++) {
384 w2[i] *= 0.5; // measure = 1/2
385 v2[i].resize(setup.p+1);
386 setup.basis.evaluateBases(x2[i], v2[i]);
387 }
388 success = true;
389 success = success &&
390 Stokhos::compareArrays(x1, "x1", x2, "x2", setup.rtol, setup.atol, out);
391 success = success &&
392 Stokhos::compareArrays(w1, "w1", w2, "w2", setup.rtol, setup.atol, out);
393 for (int i=0; i<n; i++) {
394 std::stringstream ss1, ss2;
395 ss1 << "v1[" << i << "]";
396 ss2 << "v2[" << i << "]";
397 success = success &&
398 Stokhos::compareArrays(v1[i], ss1.str(), v2[i], ss2.str(),
399 setup.rtol, setup.atol, out);
400 }
401 }
402#endif
403
404#ifdef HAVE_STOKHOS_FORUQTK
405 TEUCHOS_UNIT_TEST( Stokhos_LegendreBasis, QuadPointsForUQTK ) {
406 int n = static_cast<int>(std::ceil((setup.p+1)/2.0));
407 Teuchos::Array<double> x1, w1;
408 Teuchos::Array< Teuchos::Array<double> > v1;
409 setup.basis.getQuadPoints(setup.p, x1, w1, v1);
410
411 Teuchos::Array<double> x2(n), w2(n);
412 Teuchos::Array< Teuchos::Array<double> > v2(n);
413 int kind = 1;
414 int kpts = 0;
415 double endpts[2] = {0.0, 0.0};
416 Teuchos::Array<double> b(n);
417 double alpha = 0.0;
418 double beta = 0.0;
419 GAUSSQ_F77(&kind, &n, &alpha, &beta, &kpts, endpts, &b[0], &x2[0], &w2[0]);
420
421 for (int i=0; i<n; i++) {
422 w2[i] *= 0.5; // measure = 1/2
423 v2[i].resize(setup.p+1);
424 setup.basis.evaluateBases(x2[i], v2[i]);
425 }
426 success = true;
427 success = success &&
428 Stokhos::compareArrays(x1, "x1", x2, "x2", setup.rtol, setup.atol, out);
429 success = success &&
430 Stokhos::compareArrays(w1, "w1", w2, "w2", setup.rtol, setup.atol, out);
431 for (int i=0; i<n; i++) {
432 std::stringstream ss1, ss2;
433 ss1 << "v1[" << i << "]";
434 ss2 << "v2[" << i << "]";
435 success = success &&
436 Stokhos::compareArrays(v1[i], ss1.str(), v2[i], ss2.str(),
437 setup.rtol, setup.atol, out);
438 }
439 }
440#endif
441
442}
443
444int main( int argc, char* argv[] ) {
445 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
446 return Teuchos::UnitTestRepository::runUnitTestsFromMain(argc, argv);
447}
expr val()
int main(int argc, char *argv[])
#define GAUSSQ_F77
Legendre polynomial basis.
UnitTestSetup< int, double > setup
TEUCHOS_UNIT_TEST(Stokhos_LegendreBasis, Order)
bool compareValues(const ValueType &a1, const std::string &a1_name, const ValueType &a2, const std::string &a2_name, const ValueType &rel_tol, const ValueType &abs_tol, Teuchos::FancyOStream &out)
bool compareArrays(const Array1 &a1, const std::string &a1_name, const Array2 &a2, const std::string &a2_name, const ValueType &rel_tol, const ValueType &abs_tol, Teuchos::FancyOStream &out)
Stokhos::LegendreBasis< OrdinalType, ValueType > basis
void printMat(const char *name, Epetra_IntSerialDenseMatrix &matrix)