Actual source code: test11.c
slepc-3.15.0 2021-03-31
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
11: static char help[] = "Tests a user-defined convergence test (based on ex8.c).\n\n"
12: "The command line options are:\n"
13: " -n <n>, where <n> = matrix dimension.\n\n";
15: #include <slepcsvd.h>
17: /*
18: This example computes the singular values of an nxn Grcar matrix,
19: which is a nonsymmetric Toeplitz matrix:
21: | 1 1 1 1 |
22: | -1 1 1 1 1 |
23: | -1 1 1 1 1 |
24: | . . . . . |
25: A = | . . . . . |
26: | -1 1 1 1 1 |
27: | -1 1 1 1 |
28: | -1 1 1 |
29: | -1 1 |
31: */
33: /*
34: MyConvergedRel - Convergence test relative to the norm of A (given in ctx).
35: */
36: PetscErrorCode MyConvergedRel(SVD svd,PetscReal sigma,PetscReal res,PetscReal *errest,void *ctx)
37: {
38: PetscReal norm = *(PetscReal*)ctx;
41: *errest = res/norm;
42: return(0);
43: }
45: int main(int argc,char **argv)
46: {
47: Mat A; /* Grcar matrix */
48: SVD svd; /* singular value solver context */
49: PetscInt N=30,Istart,Iend,i,col[5],nconv1,nconv2;
50: PetscScalar value[] = { -1, 1, 1, 1, 1 };
51: PetscReal sigma_1,sigma_n;
54: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
56: PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
57: PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%D\n\n",N);
59: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: Generate the matrix
61: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63: MatCreate(PETSC_COMM_WORLD,&A);
64: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
65: MatSetFromOptions(A);
66: MatSetUp(A);
67: MatGetOwnershipRange(A,&Istart,&Iend);
68: for (i=Istart;i<Iend;i++) {
69: col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
70: if (i==0) {
71: MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES);
72: } else {
73: MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
74: }
75: }
76: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
77: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
79: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
80: Create the SVD solver and set the solution method
81: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
83: SVDCreate(PETSC_COMM_WORLD,&svd);
84: SVDSetOperators(svd,A,NULL);
85: SVDSetType(svd,SVDTRLANCZOS);
86: SVDSetFromOptions(svd);
88: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
89: Solve the singular value problem
90: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
92: SVDSetWhichSingularTriplets(svd,SVD_LARGEST);
93: SVDSolve(svd);
94: SVDGetConverged(svd,&nconv1);
95: if (nconv1 > 0) {
96: SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL);
97: } else {
98: PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");
99: }
101: /* compute smallest singular value relative to the matrix norm */
102: SVDSetConvergenceTestFunction(svd,MyConvergedRel,&sigma_1,NULL);
103: SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);
104: SVDSolve(svd);
105: SVDGetConverged(svd,&nconv2);
106: if (nconv2 > 0) {
107: SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL);
108: } else {
109: PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");
110: }
112: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113: Display solution and clean up
114: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
115: if (nconv1 > 0 && nconv2 > 0) {
116: PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n);
117: PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n));
118: }
120: SVDDestroy(&svd);
121: MatDestroy(&A);
122: SlepcFinalize();
123: return ierr;
124: }
126: /*TEST
128: test:
129: suffix: 1
131: TEST*/