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, (char *)0, 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*/