Actual source code: ex21.c


  2: static char help[] = "Solves a RBF kernel matrix with KSP and PCH2OPUS.\n\n";

  4: #include <petscksp.h>

  6: typedef struct {
  7:   PetscReal  sigma;
  8:   PetscReal *l;
  9:   PetscReal  lambda;
 10: } RBFCtx;

 12: static PetscScalar RBF(PetscInt sdim, PetscReal x[], PetscReal y[], void *ctx)
 13: {
 14:   RBFCtx    *rbfctx = (RBFCtx *)ctx;
 15:   PetscInt   d;
 16:   PetscReal  diff   = 0.0;
 17:   PetscReal  s      = rbfctx->sigma;
 18:   PetscReal *l      = rbfctx->l;
 19:   PetscReal  lambda = rbfctx->lambda;

 21:   for (d = 0; d < sdim; d++) diff += (x[d] - y[d]) * (x[d] - y[d]) / (l[d] * l[d]);
 22:   return s * s * PetscExpReal(-0.5 * diff) + (diff != 0.0 ? 0.0 : lambda);
 23: }

 25: int main(int argc, char **args)
 26: {
 27:   Vec         x, b, u, d;
 28:   Mat         A, Ae = NULL, Ad = NULL;
 29:   KSP         ksp;
 30:   PetscRandom r;
 31:   PC          pc;
 32:   PetscReal   norm, *coords, eta, scale = 0.5;
 33:   PetscInt    basisord, leafsize, sdim, n, its, i;
 34:   PetscMPIInt size;
 35:   RBFCtx      fctx;

 37:   PetscFunctionBeginUser;
 38:   PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
 39:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
 40:   PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
 41:   PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &r));
 42:   PetscCall(PetscRandomSetFromOptions(r));

 44:   sdim = 2;
 45:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-sdim", &sdim, NULL));
 46:   n = 32;
 47:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
 48:   eta = 0.6;
 49:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-eta", &eta, NULL));
 50:   leafsize = 32;
 51:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-leafsize", &leafsize, NULL));
 52:   basisord = 8;
 53:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-basisord", &basisord, NULL));

 55:   /* Create random points */
 56:   PetscCall(PetscMalloc1(sdim * n, &coords));
 57:   PetscCall(PetscRandomGetValuesReal(r, sdim * n, coords));

 59:   fctx.lambda = 0.01;
 60:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-lambda", &fctx.lambda, NULL));
 61:   PetscCall(PetscRandomGetValueReal(r, &fctx.sigma));
 62:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-sigma", &fctx.sigma, NULL));
 63:   PetscCall(PetscMalloc1(sdim, &fctx.l));
 64:   PetscCall(PetscRandomGetValuesReal(r, sdim, fctx.l));
 65:   PetscCall(PetscOptionsGetRealArray(NULL, NULL, "-l", fctx.l, (i = sdim, &i), NULL));
 66:   PetscCall(PetscOptionsGetReal(NULL, NULL, "-scale", &scale, NULL));

 68:   /* Populate dense matrix for comparisons */
 69:   {
 70:     PetscInt i, j;

 72:     PetscCall(MatCreateDense(PETSC_COMM_WORLD, n, n, PETSC_DECIDE, PETSC_DECIDE, NULL, &Ad));
 73:     for (i = 0; i < n; i++) {
 74:       for (j = 0; j < n; j++) PetscCall(MatSetValue(Ad, i, j, RBF(sdim, coords + i * sdim, coords + j * sdim, &fctx), INSERT_VALUES));
 75:     }
 76:     PetscCall(MatAssemblyBegin(Ad, MAT_FINAL_ASSEMBLY));
 77:     PetscCall(MatAssemblyEnd(Ad, MAT_FINAL_ASSEMBLY));
 78:   }

 80:   /* Create and assemble the matrix */
 81:   PetscCall(MatCreateH2OpusFromKernel(PETSC_COMM_WORLD, n, n, PETSC_DECIDE, PETSC_DECIDE, sdim, coords, PETSC_FALSE, RBF, &fctx, eta, leafsize, basisord, &A));
 82:   PetscCall(MatSetOption(A, MAT_SYMMETRIC, PETSC_TRUE));
 83:   PetscCall(MatSetOption(A, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
 84:   PetscCall(PetscObjectSetName((PetscObject)A, "RBF"));
 85:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 86:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
 87:   PetscCall(MatViewFromOptions(A, NULL, "-rbf_view"));

 89:   PetscCall(MatCreateVecs(A, &x, &b));
 90:   PetscCall(VecDuplicate(x, &u));
 91:   PetscCall(VecDuplicate(x, &d));

 93:   {
 94:     PetscReal norm;
 95:     PetscCall(MatComputeOperator(A, MATDENSE, &Ae));
 96:     PetscCall(MatAXPY(Ae, -1.0, Ad, SAME_NONZERO_PATTERN));
 97:     PetscCall(MatGetDiagonal(Ae, d));
 98:     PetscCall(MatViewFromOptions(Ae, NULL, "-A_view"));
 99:     PetscCall(MatViewFromOptions(Ae, NULL, "-D_view"));
100:     PetscCall(MatNorm(Ae, NORM_FROBENIUS, &norm));
101:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Approx err %g\n", norm));
102:     PetscCall(VecNorm(d, NORM_2, &norm));
103:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Approx err (diag) %g\n", norm));
104:     PetscCall(MatDestroy(&Ae));
105:   }

107:   PetscCall(VecSet(u, 1.0));
108:   PetscCall(MatMult(Ad, u, b));
109:   PetscCall(MatViewFromOptions(Ad, NULL, "-Ad_view"));
110:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
111:   PetscCall(KSPSetOperators(ksp, Ad, A));
112:   PetscCall(KSPGetPC(ksp, &pc));
113:   PetscCall(PCSetType(pc, PCH2OPUS));
114:   PetscCall(KSPSetFromOptions(ksp));
115:   /* we can also pass the points coordinates
116:      In this case it is not needed, since the preconditioning
117:      matrix is of type H2OPUS */
118:   PetscCall(PCSetCoordinates(pc, sdim, n, coords));

120:   PetscCall(KSPSolve(ksp, b, x));
121:   PetscCall(VecAXPY(x, -1.0, u));
122:   PetscCall(VecNorm(x, NORM_2, &norm));
123:   PetscCall(KSPGetIterationNumber(ksp, &its));
124:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));

126:   /* change lambda and reassemble */
127:   PetscCall(VecSet(x, (scale - 1.) * fctx.lambda));
128:   PetscCall(MatDiagonalSet(Ad, x, ADD_VALUES));
129:   fctx.lambda *= scale;
130:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
131:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
132:   {
133:     PetscReal norm;
134:     PetscCall(MatComputeOperator(A, MATDENSE, &Ae));
135:     PetscCall(MatAXPY(Ae, -1.0, Ad, SAME_NONZERO_PATTERN));
136:     PetscCall(MatGetDiagonal(Ae, d));
137:     PetscCall(MatViewFromOptions(Ae, NULL, "-A_view"));
138:     PetscCall(MatViewFromOptions(Ae, NULL, "-D_view"));
139:     PetscCall(MatNorm(Ae, NORM_FROBENIUS, &norm));
140:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Approx err %g\n", norm));
141:     PetscCall(VecNorm(d, NORM_2, &norm));
142:     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Approx err (diag) %g\n", norm));
143:     PetscCall(MatDestroy(&Ae));
144:   }
145:   PetscCall(KSPSetOperators(ksp, Ad, A));
146:   PetscCall(MatMult(Ad, u, b));
147:   PetscCall(KSPSolve(ksp, b, x));
148:   PetscCall(MatMult(Ad, x, u));
149:   PetscCall(VecAXPY(u, -1.0, b));
150:   PetscCall(VecNorm(u, NORM_2, &norm));
151:   PetscCall(KSPGetIterationNumber(ksp, &its));
152:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Residual norm error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));

154:   PetscCall(PetscFree(coords));
155:   PetscCall(PetscFree(fctx.l));
156:   PetscCall(PetscRandomDestroy(&r));
157:   PetscCall(VecDestroy(&x));
158:   PetscCall(VecDestroy(&u));
159:   PetscCall(VecDestroy(&d));
160:   PetscCall(VecDestroy(&b));
161:   PetscCall(MatDestroy(&A));
162:   PetscCall(MatDestroy(&Ad));
163:   PetscCall(KSPDestroy(&ksp));
164:   PetscCall(PetscFinalize());
165:   return 0;
166: }

168: /*TEST

170:   build:
171:     requires: h2opus

173:   test:
174:     requires: h2opus !single
175:     suffix: 1
176:     args: -ksp_error_if_not_converged -pc_h2opus_monitor

178:   test:
179:     requires: h2opus !single
180:     suffix: 1_ns
181:     output_file: output/ex21_1.out
182:     args: -ksp_error_if_not_converged -pc_h2opus_monitor -pc_h2opus_hyperorder 2

184:   test:
185:     requires: h2opus !single
186:     suffix: 2
187:     args: -ksp_error_if_not_converged -pc_h2opus_monitor -pc_h2opus_hyperorder 4

189: TEST*/