Actual source code: ex21.c
1: static char help[] = "Solves a RBF kernel matrix with KSP and PCH2OPUS.\n\n";
3: #include <petscksp.h>
5: typedef struct {
6: PetscReal sigma;
7: PetscReal *l;
8: PetscReal lambda;
9: } RBFCtx;
11: static PetscScalar RBF(PetscInt sdim, PetscReal x[], PetscReal y[], void *ctx)
12: {
13: RBFCtx *rbfctx = (RBFCtx *)ctx;
14: PetscInt d;
15: PetscReal diff = 0.0;
16: PetscReal s = rbfctx->sigma;
17: PetscReal *l = rbfctx->l;
18: PetscReal lambda = rbfctx->lambda;
20: for (d = 0; d < sdim; d++) diff += (x[d] - y[d]) * (x[d] - y[d]) / (l[d] * l[d]);
21: return s * s * PetscExpReal(-0.5 * diff) + (diff != 0.0 ? 0.0 : lambda);
22: }
24: int main(int argc, char **args)
25: {
26: Vec x, b, u, d;
27: Mat A, Ae = NULL, Ad = NULL;
28: KSP ksp;
29: PetscRandom r;
30: PC pc;
31: PetscReal norm, *coords, eta, scale = 0.5;
32: PetscInt basisord, leafsize, sdim, n, its, i;
33: PetscMPIInt size;
34: RBFCtx fctx;
36: PetscFunctionBeginUser;
37: PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
38: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
39: PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
40: PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &r));
41: PetscCall(PetscRandomSetFromOptions(r));
43: sdim = 2;
44: PetscCall(PetscOptionsGetInt(NULL, NULL, "-sdim", &sdim, NULL));
45: n = 32;
46: PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
47: eta = 0.6;
48: PetscCall(PetscOptionsGetReal(NULL, NULL, "-eta", &eta, NULL));
49: leafsize = 32;
50: PetscCall(PetscOptionsGetInt(NULL, NULL, "-leafsize", &leafsize, NULL));
51: basisord = 8;
52: PetscCall(PetscOptionsGetInt(NULL, NULL, "-basisord", &basisord, NULL));
54: /* Create random points */
55: PetscCall(PetscMalloc1(sdim * n, &coords));
56: PetscCall(PetscRandomGetValuesReal(r, sdim * n, coords));
58: fctx.lambda = 0.01;
59: PetscCall(PetscOptionsGetReal(NULL, NULL, "-lambda", &fctx.lambda, NULL));
60: PetscCall(PetscRandomGetValueReal(r, &fctx.sigma));
61: PetscCall(PetscOptionsGetReal(NULL, NULL, "-sigma", &fctx.sigma, NULL));
62: PetscCall(PetscMalloc1(sdim, &fctx.l));
63: PetscCall(PetscRandomGetValuesReal(r, sdim, fctx.l));
64: PetscCall(PetscOptionsGetRealArray(NULL, NULL, "-l", fctx.l, (i = sdim, &i), NULL));
65: PetscCall(PetscOptionsGetReal(NULL, NULL, "-scale", &scale, NULL));
67: /* Populate dense matrix for comparisons */
68: {
69: PetscInt i, j;
71: PetscCall(MatCreateDense(PETSC_COMM_WORLD, n, n, PETSC_DECIDE, PETSC_DECIDE, NULL, &Ad));
72: for (i = 0; i < n; i++) {
73: for (j = 0; j < n; j++) PetscCall(MatSetValue(Ad, i, j, RBF(sdim, coords + i * sdim, coords + j * sdim, &fctx), INSERT_VALUES));
74: }
75: PetscCall(MatAssemblyBegin(Ad, MAT_FINAL_ASSEMBLY));
76: PetscCall(MatAssemblyEnd(Ad, MAT_FINAL_ASSEMBLY));
77: }
79: /* Create and assemble the matrix */
80: PetscCall(MatCreateH2OpusFromKernel(PETSC_COMM_WORLD, n, n, PETSC_DECIDE, PETSC_DECIDE, sdim, coords, PETSC_FALSE, RBF, &fctx, eta, leafsize, basisord, &A));
81: PetscCall(MatSetOption(A, MAT_SYMMETRIC, PETSC_TRUE));
82: PetscCall(MatSetOption(A, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
83: PetscCall(PetscObjectSetName((PetscObject)A, "RBF"));
84: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
85: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
86: PetscCall(MatViewFromOptions(A, NULL, "-rbf_view"));
88: PetscCall(MatCreateVecs(A, &x, &b));
89: PetscCall(VecDuplicate(x, &u));
90: PetscCall(VecDuplicate(x, &d));
92: {
93: PetscReal norm;
94: PetscCall(MatComputeOperator(A, MATDENSE, &Ae));
95: PetscCall(MatAXPY(Ae, -1.0, Ad, SAME_NONZERO_PATTERN));
96: PetscCall(MatGetDiagonal(Ae, d));
97: PetscCall(MatViewFromOptions(Ae, NULL, "-A_view"));
98: PetscCall(MatViewFromOptions(Ae, NULL, "-D_view"));
99: PetscCall(MatNorm(Ae, NORM_FROBENIUS, &norm));
100: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Approx err %g\n", norm));
101: PetscCall(VecNorm(d, NORM_2, &norm));
102: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Approx err (diag) %g\n", norm));
103: PetscCall(MatDestroy(&Ae));
104: }
106: PetscCall(VecSet(u, 1.0));
107: PetscCall(MatMult(Ad, u, b));
108: PetscCall(MatViewFromOptions(Ad, NULL, "-Ad_view"));
109: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
110: PetscCall(KSPSetOperators(ksp, Ad, A));
111: PetscCall(KSPGetPC(ksp, &pc));
112: PetscCall(PCSetType(pc, PCH2OPUS));
113: PetscCall(KSPSetFromOptions(ksp));
114: /* we can also pass the points coordinates
115: In this case it is not needed, since the preconditioning
116: matrix is of type H2OPUS */
117: PetscCall(PCSetCoordinates(pc, sdim, n, coords));
119: PetscCall(KSPSolve(ksp, b, x));
120: PetscCall(VecAXPY(x, -1.0, u));
121: PetscCall(VecNorm(x, NORM_2, &norm));
122: PetscCall(KSPGetIterationNumber(ksp, &its));
123: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));
125: /* change lambda and reassemble */
126: PetscCall(VecSet(x, (scale - 1.) * fctx.lambda));
127: PetscCall(MatDiagonalSet(Ad, x, ADD_VALUES));
128: fctx.lambda *= scale;
129: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
130: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
131: {
132: PetscReal norm;
133: PetscCall(MatComputeOperator(A, MATDENSE, &Ae));
134: PetscCall(MatAXPY(Ae, -1.0, Ad, SAME_NONZERO_PATTERN));
135: PetscCall(MatGetDiagonal(Ae, d));
136: PetscCall(MatViewFromOptions(Ae, NULL, "-A_view"));
137: PetscCall(MatViewFromOptions(Ae, NULL, "-D_view"));
138: PetscCall(MatNorm(Ae, NORM_FROBENIUS, &norm));
139: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Approx err %g\n", norm));
140: PetscCall(VecNorm(d, NORM_2, &norm));
141: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Approx err (diag) %g\n", norm));
142: PetscCall(MatDestroy(&Ae));
143: }
144: PetscCall(KSPSetOperators(ksp, Ad, A));
145: PetscCall(MatMult(Ad, u, b));
146: PetscCall(KSPSolve(ksp, b, x));
147: PetscCall(MatMult(Ad, x, u));
148: PetscCall(VecAXPY(u, -1.0, b));
149: PetscCall(VecNorm(u, NORM_2, &norm));
150: PetscCall(KSPGetIterationNumber(ksp, &its));
151: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Residual norm error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));
153: PetscCall(PetscFree(coords));
154: PetscCall(PetscFree(fctx.l));
155: PetscCall(PetscRandomDestroy(&r));
156: PetscCall(VecDestroy(&x));
157: PetscCall(VecDestroy(&u));
158: PetscCall(VecDestroy(&d));
159: PetscCall(VecDestroy(&b));
160: PetscCall(MatDestroy(&A));
161: PetscCall(MatDestroy(&Ad));
162: PetscCall(KSPDestroy(&ksp));
163: PetscCall(PetscFinalize());
164: return 0;
165: }
167: /*TEST
169: build:
170: requires: h2opus
172: test:
173: requires: h2opus !single
174: suffix: 1
175: args: -ksp_error_if_not_converged -pc_h2opus_monitor
177: test:
178: requires: h2opus !single
179: suffix: 1_ns
180: output_file: output/ex21_1.out
181: args: -ksp_error_if_not_converged -pc_h2opus_monitor -pc_h2opus_hyperorder 2
183: test:
184: requires: h2opus !single
185: suffix: 2
186: args: -ksp_error_if_not_converged -pc_h2opus_monitor -pc_h2opus_hyperorder 4
188: TEST*/