Actual source code: ex121.c
1: static char help[] = "Test sequential FFTW convolution\n\n";
3: /*
4: Compiling the code:
5: This code uses the complex numbers, so configure must be given --with-scalar-type=complex to enable this
6: */
8: #include <petscmat.h>
10: int main(int argc, char **args)
11: {
12: typedef enum {
13: RANDOM,
14: CONSTANT,
15: TANH,
16: NUM_FUNCS
17: } FuncType;
18: const char *funcNames[NUM_FUNCS] = {"random", "constant", "tanh"};
19: Mat A;
20: PetscMPIInt size;
21: PetscInt n = 10, N, ndim = 4, dim[4], DIM, i, j;
22: Vec w, x, y1, y2, z1, z2;
23: PetscScalar *a, *a2, *a3;
24: PetscScalar s;
25: PetscRandom rdm;
26: PetscReal enorm;
27: PetscInt func = 0;
28: FuncType function = RANDOM;
29: PetscBool view = PETSC_FALSE;
31: PetscFunctionBeginUser;
32: PetscCall(PetscInitialize(&argc, &args, NULL, help));
33: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
34: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
35: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "FFTW Options", "ex112");
36: PetscCall(PetscOptionsEList("-function", "Function type", "ex121", funcNames, NUM_FUNCS, funcNames[function], &func, NULL));
37: PetscCall(PetscOptionsBool("-vec_view draw", "View the functions", "ex112", view, &view, NULL));
38: function = (FuncType)func;
39: PetscOptionsEnd();
41: for (DIM = 0; DIM < ndim; DIM++) { dim[DIM] = n; /* size of transformation in DIM-dimension */ }
42: PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm));
43: PetscCall(PetscRandomSetFromOptions(rdm));
45: for (DIM = 1; DIM < 5; DIM++) {
46: /* create vectors of length N=n^DIM */
47: for (i = 0, N = 1; i < DIM; i++) N *= dim[i];
48: PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n %d-D: FFTW on vector of size %d \n", DIM, N));
49: PetscCall(VecCreateSeq(PETSC_COMM_SELF, N, &x));
50: PetscCall(PetscObjectSetName((PetscObject)x, "Real space vector"));
51: PetscCall(VecDuplicate(x, &w));
52: PetscCall(PetscObjectSetName((PetscObject)w, "Window vector"));
53: PetscCall(VecDuplicate(x, &y1));
54: PetscCall(PetscObjectSetName((PetscObject)y1, "Frequency space vector"));
55: PetscCall(VecDuplicate(x, &y2));
56: PetscCall(PetscObjectSetName((PetscObject)y2, "Frequency space window vector"));
57: PetscCall(VecDuplicate(x, &z1));
58: PetscCall(PetscObjectSetName((PetscObject)z1, "Reconstructed convolution"));
59: PetscCall(VecDuplicate(x, &z2));
60: PetscCall(PetscObjectSetName((PetscObject)z2, "Real space convolution"));
62: if (function == RANDOM) {
63: PetscCall(VecSetRandom(x, rdm));
64: } else if (function == CONSTANT) {
65: PetscCall(VecSet(x, 1.0));
66: } else if (function == TANH) {
67: PetscCall(VecGetArray(x, &a));
68: for (i = 0; i < N; ++i) a[i] = tanh((i - N / 2.0) * (10.0 / N));
69: PetscCall(VecRestoreArray(x, &a));
70: }
71: if (view) PetscCall(VecView(x, PETSC_VIEWER_DRAW_WORLD));
73: /* Create window function */
74: PetscCall(VecGetArray(w, &a));
75: for (i = 0; i < N; ++i) {
76: /* Step Function */
77: a[i] = (i > N / 4 && i < 3 * N / 4) ? 1.0 : 0.0;
78: /* Delta Function */
79: /*a[i] = (i == N/2)? 1.0: 0.0; */
80: }
81: PetscCall(VecRestoreArray(w, &a));
82: if (view) PetscCall(VecView(w, PETSC_VIEWER_DRAW_WORLD));
84: /* create FFTW object */
85: PetscCall(MatCreateFFT(PETSC_COMM_SELF, DIM, dim, MATFFTW, &A));
87: /* Convolve x with w*/
88: PetscCall(MatMult(A, x, y1));
89: PetscCall(MatMult(A, w, y2));
90: PetscCall(VecPointwiseMult(y1, y1, y2));
91: if (view && i == 0) PetscCall(VecView(y1, PETSC_VIEWER_DRAW_WORLD));
92: PetscCall(MatMultTranspose(A, y1, z1));
94: /* Compute the real space convolution */
95: PetscCall(VecGetArray(x, &a));
96: PetscCall(VecGetArray(w, &a2));
97: PetscCall(VecGetArray(z2, &a3));
98: for (i = 0; i < N; ++i) {
99: /* PetscInt checkInd = (i > N/2-1)? i-N/2: i+N/2;*/
101: a3[i] = 0.0;
102: for (j = -N / 2 + 1; j < N / 2; ++j) {
103: PetscInt xpInd = (j < 0) ? N + j : j;
104: PetscInt diffInd = (i - j < 0) ? N - (j - i) : (i - j > N - 1) ? i - j - N : i - j;
106: a3[i] += a[xpInd] * a2[diffInd];
107: }
108: }
109: PetscCall(VecRestoreArray(x, &a));
110: PetscCall(VecRestoreArray(w, &a2));
111: PetscCall(VecRestoreArray(z2, &a3));
113: /* compare z1 and z2. FFTW computes an unnormalized DFT, thus z1 = N*z2 */
114: s = 1.0 / (PetscReal)N;
115: PetscCall(VecScale(z1, s));
116: if (view) PetscCall(VecView(z1, PETSC_VIEWER_DRAW_WORLD));
117: if (view) PetscCall(VecView(z2, PETSC_VIEWER_DRAW_WORLD));
118: PetscCall(VecAXPY(z1, -1.0, z2));
119: PetscCall(VecNorm(z1, NORM_1, &enorm));
120: if (enorm > 1.e-11) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Error norm of |z1 - z2| %g\n", (double)enorm));
122: /* free spaces */
123: PetscCall(VecDestroy(&x));
124: PetscCall(VecDestroy(&y1));
125: PetscCall(VecDestroy(&y2));
126: PetscCall(VecDestroy(&z1));
127: PetscCall(VecDestroy(&z2));
128: PetscCall(VecDestroy(&w));
129: PetscCall(MatDestroy(&A));
130: }
131: PetscCall(PetscRandomDestroy(&rdm));
132: PetscCall(PetscFinalize());
133: return 0;
134: }
136: /*TEST
138: build:
139: requires: fftw complex
141: test:
142: output_file: output/ex121.out
143: TODO: Example or FFTW interface is broken
145: TEST*/