xref: /petsc/src/dm/dt/tests/ex14.c (revision b122ec5aa1bd4469eb4e0673542fb7de3f411254)

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

#include <petscdt.h>

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

  PetscFunctionBeginUser;
  CHKERRQ(PetscDTTanhSinhIntegrate((void (*)(const PetscReal[], void *, PetscReal *)) pdf, lower, upper, digits, NULL, &integral));
  PetscCheck(PetscAbsReal(integral - 1.0) < 100*PETSC_MACHINE_EPSILON, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PDF %s must integrate to 1, not %g", name, integral);
  for (i = 0; i <= 10; ++i) {
    const PetscReal x = i;

    CHKERRQ(PetscDTTanhSinhIntegrate((void (*)(const PetscReal[], void *, PetscReal *)) pdf, lower, x, digits, NULL, &integral));
    CHKERRQ(cdf(&x, NULL, &integral2));
    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, integral, integral2, x);
  }
  PetscFunctionReturn(0);
}

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

  PetscFunctionBeginUser;
  for (PetscInt i = 0; i < (PetscInt) (sizeof(pdf)/sizeof(PetscProbFunc)); ++i) {
    CHKERRQ(VerifyDistribution(name[i], pos[i], pdf[i], cdf[i]));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode TestSampling()
{
  PetscProbFunc  cdf[2]     = {PetscCDFMaxwellBoltzmann1D, PetscCDFMaxwellBoltzmann2D};
  PetscProbFunc  sampler[2] = {PetscPDFSampleGaussian1D,   PetscPDFSampleGaussian2D};
  PetscInt       dim[2]     = {1, 2};
  PetscRandom    rnd;
  Vec            v;
  PetscScalar   *a;
  PetscReal      alpha, confidenceLevel = 0.05;
  PetscInt       n = 1000, s, i, d;

  PetscFunctionBeginUser;
  CHKERRQ(PetscRandomCreate(PETSC_COMM_SELF, &rnd));
  CHKERRQ(PetscRandomSetInterval(rnd, 0, 1.));
  CHKERRQ(PetscRandomSetFromOptions(rnd));

  for (s = 0; s < 2; ++s) {
    CHKERRQ(VecCreateSeq(PETSC_COMM_SELF, n*dim[s], &v));
    CHKERRQ(VecSetBlockSize(v, dim[s]));
    CHKERRQ(VecGetArray(v, &a));
    for (i = 0; i < n; ++i) {
      PetscReal r[3], o[3];

      for (d = 0; d < dim[s]; ++d) CHKERRQ(PetscRandomGetValueReal(rnd, &r[d]));
      CHKERRQ(sampler[s](r, NULL, o));
      for (d = 0; d < dim[s]; ++d) a[i*dim[s]+d] = o[d];
    }
    CHKERRQ(VecRestoreArray(v, &a));
    CHKERRQ(PetscProbComputeKSStatistic(v, cdf[s], &alpha));
    PetscCheck(alpha < confidenceLevel, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "KS finds sampling does not match the distribution at confidence level %.2g", confidenceLevel);
    CHKERRQ(VecDestroy(&v));
  }
  CHKERRQ(PetscRandomDestroy(&rnd));
  PetscFunctionReturn(0);
}

int main(int argc, char **argv)
{

  CHKERRQ(PetscInitialize(&argc, &argv, NULL, help));
  CHKERRQ(TestDistributions());
  CHKERRQ(TestSampling());
  CHKERRQ(PetscFinalize());
  return 0;
}

/*TEST

  test:
    suffix: 0
    requires: ks
    args:

TEST*/