1 static char help[] = "Test sequential USFFT interface on a uniform DMDA and compares the result to FFTW\n\n"; 2 3 /* 4 Compiling the code: 5 This code uses the complex numbers version of PETSc and the FFTW package, so configure 6 must be run to enable these. 7 8 */ 9 10 #include <petscmat.h> 11 #include <petscdm.h> 12 #include <petscdmda.h> 13 int main(int argc, char **args) { 14 typedef enum { 15 RANDOM, 16 CONSTANT, 17 TANH, 18 NUM_FUNCS 19 } FuncType; 20 const char *funcNames[NUM_FUNCS] = {"random", "constant", "tanh"}; 21 Mat A, AA; 22 PetscMPIInt size; 23 PetscInt N, i, stencil = 1, dof = 1; 24 PetscInt dim[3] = {10, 10, 10}, ndim = 3; 25 Vec coords, x, y, z, xx, yy, zz; 26 PetscReal h[3]; 27 PetscScalar s; 28 PetscRandom rdm; 29 PetscReal norm, enorm; 30 PetscInt func; 31 FuncType function = TANH; 32 DM da, coordsda; 33 PetscBool view_x = PETSC_FALSE, view_y = PETSC_FALSE, view_z = PETSC_FALSE; 34 35 PetscFunctionBeginUser; 36 PetscCall(PetscInitialize(&argc, &args, (char *)0, help)); 37 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 38 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_SUP, "This is a uniprocessor example only!"); 39 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "USFFT Options", "ex27"); 40 PetscCall(PetscOptionsEList("-function", "Function type", "ex27", funcNames, NUM_FUNCS, funcNames[function], &func, NULL)); 41 function = (FuncType)func; 42 PetscOptionsEnd(); 43 PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_x", &view_x, NULL)); 44 PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_y", &view_y, NULL)); 45 PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_z", &view_z, NULL)); 46 PetscCall(PetscOptionsGetIntArray(NULL, NULL, "-dim", dim, &ndim, NULL)); 47 48 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)); 49 PetscCall(DMSetFromOptions(da)); 50 PetscCall(DMSetUp(da)); 51 52 /* Coordinates */ 53 PetscCall(DMGetCoordinateDM(da, &coordsda)); 54 PetscCall(DMGetGlobalVector(coordsda, &coords)); 55 PetscCall(PetscObjectSetName((PetscObject)coords, "Grid coordinates")); 56 for (i = 0, N = 1; i < 3; i++) { 57 h[i] = 1.0 / dim[i]; 58 PetscScalar *a; 59 PetscCall(VecGetArray(coords, &a)); 60 PetscInt j, k, n = 0; 61 for (i = 0; i < 3; ++i) { 62 for (j = 0; j < dim[i]; ++j) { 63 for (k = 0; k < 3; ++k) { 64 a[n] = j * h[i]; /* coordinate along the j-th point in the i-th dimension */ 65 ++n; 66 } 67 } 68 } 69 PetscCall(VecRestoreArray(coords, &a)); 70 } 71 PetscCall(DMSetCoordinates(da, coords)); 72 73 /* Work vectors */ 74 PetscCall(DMGetGlobalVector(da, &x)); 75 PetscCall(PetscObjectSetName((PetscObject)x, "Real space vector")); 76 PetscCall(DMGetGlobalVector(da, &xx)); 77 PetscCall(PetscObjectSetName((PetscObject)xx, "Real space vector")); 78 PetscCall(DMGetGlobalVector(da, &y)); 79 PetscCall(PetscObjectSetName((PetscObject)y, "USFFT frequency space vector")); 80 PetscCall(DMGetGlobalVector(da, &yy)); 81 PetscCall(PetscObjectSetName((PetscObject)yy, "FFTW frequency space vector")); 82 PetscCall(DMGetGlobalVector(da, &z)); 83 PetscCall(PetscObjectSetName((PetscObject)z, "USFFT reconstructed vector")); 84 PetscCall(DMGetGlobalVector(da, &zz)); 85 PetscCall(PetscObjectSetName((PetscObject)zz, "FFTW reconstructed vector")); 86 87 PetscCall(PetscPrintf(PETSC_COMM_SELF, "%3-" PetscInt_FMT ": USFFT on vector of ")); 88 for (i = 0, N = 1; i < 3; i++) { 89 PetscCall(PetscPrintf(PETSC_COMM_SELF, "dim[%d] = %d ", i, dim[i])); 90 N *= dim[i]; 91 } 92 PetscCall(PetscPrintf(PETSC_COMM_SELF, "; total size %d \n", N)); 93 94 if (function == RANDOM) { 95 PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm)); 96 PetscCall(PetscRandomSetFromOptions(rdm)); 97 PetscCall(VecSetRandom(x, rdm)); 98 PetscCall(PetscRandomDestroy(&rdm)); 99 } else if (function == CONSTANT) { 100 PetscCall(VecSet(x, 1.0)); 101 } else if (function == TANH) { 102 PetscScalar *a; 103 PetscCall(VecGetArray(x, &a)); 104 PetscInt j, k = 0; 105 for (i = 0; i < 3; ++i) { 106 for (j = 0; j < dim[i]; ++j) { 107 a[k] = tanh((j - dim[i] / 2.0) * (10.0 / dim[i])); 108 ++k; 109 } 110 } 111 PetscCall(VecRestoreArray(x, &a)); 112 } 113 if (view_x) PetscCall(VecView(x, PETSC_VIEWER_STDOUT_WORLD)); 114 PetscCall(VecCopy(x, xx)); 115 116 PetscCall(VecNorm(x, NORM_2, &norm)); 117 PetscCall(PetscPrintf(PETSC_COMM_SELF, "|x|_2 = %g\n", norm)); 118 119 /* create USFFT object */ 120 PetscCall(MatCreateSeqUSFFT(coords, da, &A)); 121 /* create FFTW object */ 122 PetscCall(MatCreateSeqFFTW(PETSC_COMM_SELF, 3, dim, &AA)); 123 124 /* apply USFFT and FFTW FORWARD "preemptively", so the fftw_plans can be reused on different vectors */ 125 PetscCall(MatMult(A, x, z)); 126 PetscCall(MatMult(AA, xx, zz)); 127 /* Now apply USFFT and FFTW forward several (3) times */ 128 for (i = 0; i < 3; ++i) { 129 PetscCall(MatMult(A, x, y)); 130 PetscCall(MatMult(AA, xx, yy)); 131 PetscCall(MatMultTranspose(A, y, z)); 132 PetscCall(MatMultTranspose(AA, yy, zz)); 133 } 134 135 if (view_y) { 136 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "y = \n")); 137 PetscCall(VecView(y, PETSC_VIEWER_STDOUT_WORLD)); 138 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "yy = \n")); 139 PetscCall(VecView(yy, PETSC_VIEWER_STDOUT_WORLD)); 140 } 141 142 if (view_z) { 143 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "z = \n")); 144 PetscCall(VecView(z, PETSC_VIEWER_STDOUT_WORLD)); 145 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "zz = \n")); 146 PetscCall(VecView(zz, PETSC_VIEWER_STDOUT_WORLD)); 147 } 148 149 /* compare x and z. USFFT computes an unnormalized DFT, thus z = N*x */ 150 s = 1.0 / (PetscReal)N; 151 PetscCall(VecScale(z, s)); 152 PetscCall(VecAXPY(x, -1.0, z)); 153 PetscCall(VecNorm(x, NORM_1, &enorm)); 154 PetscCall(PetscPrintf(PETSC_COMM_SELF, "|x-z| = %g\n", enorm)); 155 156 /* compare xx and zz. FFTW computes an unnormalized DFT, thus zz = N*x */ 157 s = 1.0 / (PetscReal)N; 158 PetscCall(VecScale(zz, s)); 159 PetscCall(VecAXPY(xx, -1.0, zz)); 160 PetscCall(VecNorm(xx, NORM_1, &enorm)); 161 PetscCall(PetscPrintf(PETSC_COMM_SELF, "|xx-zz| = %g\n", enorm)); 162 163 /* compare y and yy: USFFT and FFTW results*/ 164 PetscCall(VecNorm(y, NORM_2, &norm)); 165 PetscCall(VecAXPY(y, -1.0, yy)); 166 PetscCall(VecNorm(y, NORM_1, &enorm)); 167 PetscCall(PetscPrintf(PETSC_COMM_SELF, "|y|_2 = %g\n", norm)); 168 PetscCall(PetscPrintf(PETSC_COMM_SELF, "|y-yy| = %g\n", enorm)); 169 170 /* compare z and zz: USFFT and FFTW results*/ 171 PetscCall(VecNorm(z, NORM_2, &norm)); 172 PetscCall(VecAXPY(z, -1.0, zz)); 173 PetscCall(VecNorm(z, NORM_1, &enorm)); 174 PetscCall(PetscPrintf(PETSC_COMM_SELF, "|z|_2 = %g\n", norm)); 175 PetscCall(PetscPrintf(PETSC_COMM_SELF, "|z-zz| = %g\n", enorm)); 176 177 /* free spaces */ 178 PetscCall(DMRestoreGlobalVector(da, &x)); 179 PetscCall(DMRestoreGlobalVector(da, &xx)); 180 PetscCall(DMRestoreGlobalVector(da, &y)); 181 PetscCall(DMRestoreGlobalVector(da, &yy)); 182 PetscCall(DMRestoreGlobalVector(da, &z)); 183 PetscCall(DMRestoreGlobalVector(da, &zz)); 184 PetscCall(VecDestroy(&coords)); 185 PetscCall(DMDestroy(&da)); 186 PetscCall(PetscFinalize()); 187 return 0; 188 } 189