static char help[] = "Test sequential USFFT interface on a uniform DMDA and compares the result to FFTW\n\n"; /* Compiling the code: This code uses the complex numbers version of PETSc and the FFTW package, so configure must be run to enable these. */ #include #include #include int main(int argc, char **args) { typedef enum { RANDOM, CONSTANT, TANH, NUM_FUNCS } FuncType; const char *funcNames[NUM_FUNCS] = {"random", "constant", "tanh"}; Mat A, AA; PetscMPIInt size; PetscInt N, i, stencil = 1, dof = 1; PetscInt dim[3] = {10, 10, 10}, ndim = 3; Vec coords, x, y, z, xx, yy, zz; PetscReal h[3]; PetscScalar s; PetscRandom rdm; PetscReal norm, enorm; PetscInt func; FuncType function = TANH; DM da, coordsda; PetscBool view_x = PETSC_FALSE, view_y = PETSC_FALSE, view_z = PETSC_FALSE; PetscFunctionBeginUser; PetscCall(PetscInitialize(&argc, &args, NULL, help)); PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!"); PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "USFFT Options", "ex27"); PetscCall(PetscOptionsEList("-function", "Function type", "ex27", funcNames, NUM_FUNCS, funcNames[function], &func, NULL)); function = (FuncType)func; PetscOptionsEnd(); PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_x", &view_x, NULL)); PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_y", &view_y, NULL)); PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_z", &view_z, NULL)); PetscCall(PetscOptionsGetIntArray(NULL, NULL, "-dim", dim, &ndim, NULL)); PetscCall(DMDACreate3d(PETSC_COMM_SELF, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, dim[0], dim[1], dim[2], PETSC_DECIDE, PETSC_DECIDE, PETSC_DECIDE, dof, stencil, NULL, NULL, NULL, &da)); PetscCall(DMSetFromOptions(da)); PetscCall(DMSetUp(da)); /* Coordinates */ PetscCall(DMGetCoordinateDM(da, &coordsda)); PetscCall(DMGetGlobalVector(coordsda, &coords)); PetscCall(PetscObjectSetName((PetscObject)coords, "Grid coordinates")); for (i = 0, N = 1; i < 3; i++) { h[i] = 1.0 / dim[i]; PetscScalar *a; PetscCall(VecGetArray(coords, &a)); PetscInt j, k, n = 0; for (i = 0; i < 3; ++i) { for (j = 0; j < dim[i]; ++j) { for (k = 0; k < 3; ++k) { a[n] = j * h[i]; /* coordinate along the j-th point in the i-th dimension */ ++n; } } } PetscCall(VecRestoreArray(coords, &a)); } PetscCall(DMSetCoordinates(da, coords)); /* Work vectors */ PetscCall(DMGetGlobalVector(da, &x)); PetscCall(PetscObjectSetName((PetscObject)x, "Real space vector")); PetscCall(DMGetGlobalVector(da, &xx)); PetscCall(PetscObjectSetName((PetscObject)xx, "Real space vector")); PetscCall(DMGetGlobalVector(da, &y)); PetscCall(PetscObjectSetName((PetscObject)y, "USFFT frequency space vector")); PetscCall(DMGetGlobalVector(da, &yy)); PetscCall(PetscObjectSetName((PetscObject)yy, "FFTW frequency space vector")); PetscCall(DMGetGlobalVector(da, &z)); PetscCall(PetscObjectSetName((PetscObject)z, "USFFT reconstructed vector")); PetscCall(DMGetGlobalVector(da, &zz)); PetscCall(PetscObjectSetName((PetscObject)zz, "FFTW reconstructed vector")); PetscCall(PetscPrintf(PETSC_COMM_SELF, "%3-" PetscInt_FMT ": USFFT on vector of ")); for (i = 0, N = 1; i < 3; i++) { PetscCall(PetscPrintf(PETSC_COMM_SELF, "dim[%d] = %d ", i, dim[i])); N *= dim[i]; } PetscCall(PetscPrintf(PETSC_COMM_SELF, "; total size %d \n", N)); if (function == RANDOM) { PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm)); PetscCall(PetscRandomSetFromOptions(rdm)); PetscCall(VecSetRandom(x, rdm)); PetscCall(PetscRandomDestroy(&rdm)); } else if (function == CONSTANT) { PetscCall(VecSet(x, 1.0)); } else if (function == TANH) { PetscScalar *a; PetscCall(VecGetArray(x, &a)); PetscInt j, k = 0; for (i = 0; i < 3; ++i) { for (j = 0; j < dim[i]; ++j) { a[k] = tanh((j - dim[i] / 2.0) * (10.0 / dim[i])); ++k; } } PetscCall(VecRestoreArray(x, &a)); } if (view_x) PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD)); PetscCall(VecCopy(x, xx)); PetscCall(VecNorm(x, NORM_2, &norm)); PetscCall(PetscPrintf(PETSC_COMM_SELF, "|x|_2 = %g\n", norm)); /* create USFFT object */ PetscCall(MatCreateSeqUSFFT(coords, da, &A)); /* create FFTW object */ PetscCall(MatCreateSeqFFTW(PETSC_COMM_SELF, 3, dim, &AA)); /* apply USFFT and FFTW FORWARD "preemptively", so the fftw_plans can be reused on different vectors */ PetscCall(MatMult(A, x, z)); PetscCall(MatMult(AA, xx, zz)); /* Now apply USFFT and FFTW forward several (3) times */ for (i = 0; i < 3; ++i) { PetscCall(MatMult(A, x, y)); PetscCall(MatMult(AA, xx, yy)); PetscCall(MatMultTranspose(A, y, z)); PetscCall(MatMultTranspose(AA, yy, zz)); } if (view_y) { PetscCall(PetscPrintf(PETSC_COMM_WORLD, "y = \n")); PetscCall(VecView(y, PETSC_VIEWER_STDOUT_WORLD)); PetscCall(PetscPrintf(PETSC_COMM_WORLD, "yy = \n")); PetscCall(VecView(yy, PETSC_VIEWER_STDOUT_WORLD)); } if (view_z) { PetscCall(PetscPrintf(PETSC_COMM_WORLD, "z = \n")); PetscCall(VecView(z, PETSC_VIEWER_STDOUT_WORLD)); PetscCall(PetscPrintf(PETSC_COMM_WORLD, "zz = \n")); PetscCall(VecView(zz, PETSC_VIEWER_STDOUT_WORLD)); } /* compare x and z. USFFT computes an unnormalized DFT, thus z = N*x */ s = 1.0 / (PetscReal)N; PetscCall(VecScale(z, s)); PetscCall(VecAXPY(x, -1.0, z)); PetscCall(VecNorm(x, NORM_1, &enorm)); PetscCall(PetscPrintf(PETSC_COMM_SELF, "|x-z| = %g\n", enorm)); /* compare xx and zz. FFTW computes an unnormalized DFT, thus zz = N*x */ s = 1.0 / (PetscReal)N; PetscCall(VecScale(zz, s)); PetscCall(VecAXPY(xx, -1.0, zz)); PetscCall(VecNorm(xx, NORM_1, &enorm)); PetscCall(PetscPrintf(PETSC_COMM_SELF, "|xx-zz| = %g\n", enorm)); /* compare y and yy: USFFT and FFTW results*/ PetscCall(VecNorm(y, NORM_2, &norm)); PetscCall(VecAXPY(y, -1.0, yy)); PetscCall(VecNorm(y, NORM_1, &enorm)); PetscCall(PetscPrintf(PETSC_COMM_SELF, "|y|_2 = %g\n", norm)); PetscCall(PetscPrintf(PETSC_COMM_SELF, "|y-yy| = %g\n", enorm)); /* compare z and zz: USFFT and FFTW results*/ PetscCall(VecNorm(z, NORM_2, &norm)); PetscCall(VecAXPY(z, -1.0, zz)); PetscCall(VecNorm(z, NORM_1, &enorm)); PetscCall(PetscPrintf(PETSC_COMM_SELF, "|z|_2 = %g\n", norm)); PetscCall(PetscPrintf(PETSC_COMM_SELF, "|z-zz| = %g\n", enorm)); /* free spaces */ PetscCall(DMRestoreGlobalVector(da, &x)); PetscCall(DMRestoreGlobalVector(da, &xx)); PetscCall(DMRestoreGlobalVector(da, &y)); PetscCall(DMRestoreGlobalVector(da, &yy)); PetscCall(DMRestoreGlobalVector(da, &z)); PetscCall(DMRestoreGlobalVector(da, &zz)); PetscCall(VecDestroy(&coords)); PetscCall(DMDestroy(&da)); PetscCall(PetscFinalize()); return 0; }