Actual source code: ex14.c

  1: const char help[] = "Tests properties of probability distributions";

  3: #include <petscdt.h>

  5: /* Checks that
  6:    - the PDF integrates to 1
  7:    - the incomplete integral of the PDF is the CDF at many points
  8: */
  9: static PetscErrorCode VerifyDistribution(const char name[], PetscBool pos, PetscProbFunc pdf, PetscProbFunc cdf)
 10: {
 11:   const PetscInt digits = 14;
 12:   PetscReal      lower = pos ? 0. : -10., upper = 10.;
 13:   PetscReal      integral, integral2;
 14:   PetscInt       i;

 16:   PetscFunctionBeginUser;
 17:   PetscCall(PetscDTTanhSinhIntegrate((void (*)(const PetscReal[], void *, PetscReal *))pdf, lower, upper, digits, NULL, &integral));
 18:   PetscCheck(PetscAbsReal(integral - 1) < 100 * PETSC_MACHINE_EPSILON, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PDF %s must integrate to 1, not %g", name, (double)integral);
 19:   for (i = 0; i <= 10; ++i) {
 20:     const PetscReal x = i;

 22:     PetscCall(PetscDTTanhSinhIntegrate((void (*)(const PetscReal[], void *, PetscReal *))pdf, lower, x, digits, NULL, &integral));
 23:     PetscCall(cdf(&x, NULL, &integral2));
 24:     PetscCheck(PetscAbsReal(integral - integral2) < PETSC_SQRT_MACHINE_EPSILON, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Integral of PDF %s %g != %g CDF at x = %g", name, (double)integral, (double)integral2, (double)x);
 25:   }
 26:   PetscFunctionReturn(PETSC_SUCCESS);
 27: }

 29: static PetscErrorCode TestDistributions()
 30: {
 31:   PetscProbFunc pdf[]  = {PetscPDFMaxwellBoltzmann1D, PetscPDFMaxwellBoltzmann2D, PetscPDFMaxwellBoltzmann3D, PetscPDFGaussian1D};
 32:   PetscProbFunc cdf[]  = {PetscCDFMaxwellBoltzmann1D, PetscCDFMaxwellBoltzmann2D, PetscCDFMaxwellBoltzmann3D, PetscCDFGaussian1D};
 33:   PetscBool     pos[]  = {PETSC_TRUE, PETSC_TRUE, PETSC_TRUE, PETSC_FALSE};
 34:   const char   *name[] = {"Maxwell-Boltzmann 1D", "Maxwell-Boltzmann 2D", "Maxwell-Boltzmann 3D", "Gaussian"};

 36:   PetscFunctionBeginUser;
 37:   for (PetscInt i = 0; i < (PetscInt)(sizeof(pdf) / sizeof(PetscProbFunc)); ++i) PetscCall(VerifyDistribution(name[i], pos[i], pdf[i], cdf[i]));
 38:   PetscFunctionReturn(PETSC_SUCCESS);
 39: }

 41: static PetscErrorCode TestSampling()
 42: {
 43:   PetscProbFunc cdf[2]     = {PetscCDFMaxwellBoltzmann1D, PetscCDFMaxwellBoltzmann2D};
 44:   PetscProbFunc sampler[2] = {PetscPDFSampleGaussian1D, PetscPDFSampleGaussian2D};
 45:   PetscInt      dim[2]     = {1, 2};
 46:   PetscRandom   rnd;
 47:   Vec           v;
 48:   PetscScalar  *a;
 49:   PetscReal     alpha, confidenceLevel = 0.05;
 50:   PetscInt      n = 1000, s, i, d;

 52:   PetscFunctionBeginUser;
 53:   PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rnd));
 54:   PetscCall(PetscRandomSetInterval(rnd, 0, 1.));
 55:   PetscCall(PetscRandomSetFromOptions(rnd));

 57:   for (s = 0; s < 2; ++s) {
 58:     PetscCall(VecCreateSeq(PETSC_COMM_SELF, n * dim[s], &v));
 59:     PetscCall(VecSetBlockSize(v, dim[s]));
 60:     PetscCall(VecGetArray(v, &a));
 61:     for (i = 0; i < n; ++i) {
 62:       PetscReal r[3], o[3];

 64:       for (d = 0; d < dim[s]; ++d) PetscCall(PetscRandomGetValueReal(rnd, &r[d]));
 65:       PetscCall(sampler[s](r, NULL, o));
 66:       for (d = 0; d < dim[s]; ++d) a[i * dim[s] + d] = o[d];
 67:     }
 68:     PetscCall(VecRestoreArray(v, &a));
 69:     PetscCall(PetscProbComputeKSStatistic(v, cdf[s], &alpha));
 70:     PetscCheck(alpha < confidenceLevel, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "KS finds sampling does not match the distribution at confidence level %.2g", (double)confidenceLevel);
 71:     PetscCall(VecDestroy(&v));
 72:   }
 73:   PetscCall(PetscRandomDestroy(&rnd));
 74:   PetscFunctionReturn(PETSC_SUCCESS);
 75: }

 77: int main(int argc, char **argv)
 78: {
 79:   PetscFunctionBeginUser;
 80:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
 81:   PetscCall(TestDistributions());
 82:   PetscCall(TestSampling());
 83:   PetscCall(PetscFinalize());
 84:   return 0;
 85: }

 87: /*TEST

 89:   test:
 90:     suffix: 0
 91:     requires: ks
 92:     args:

 94: TEST*/