Actual source code: test11.c
slepc-3.18.1 2022-11-02
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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;
40: *errest = res/norm;
41: return 0;
42: }
44: int main(int argc,char **argv)
45: {
46: Mat A; /* Grcar matrix */
47: SVD svd; /* singular value solver context */
48: PetscInt N=30,Istart,Iend,i,col[5],nconv1,nconv2;
49: PetscScalar value[] = { -1, 1, 1, 1, 1 };
50: PetscReal sigma_1,sigma_n;
53: SlepcInitialize(&argc,&argv,(char*)0,help);
55: PetscOptionsGetInt(NULL,NULL,"-n",&N,NULL);
56: PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%" PetscInt_FMT "\n\n",N);
58: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
59: Generate the matrix
60: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62: MatCreate(PETSC_COMM_WORLD,&A);
63: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
64: MatSetFromOptions(A);
65: MatSetUp(A);
66: MatGetOwnershipRange(A,&Istart,&Iend);
67: for (i=Istart;i<Iend;i++) {
68: col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
69: if (i==0) MatSetValues(A,1,&i,PetscMin(4,N-i),col+1,value+1,INSERT_VALUES);
70: else MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);
71: }
72: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
73: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
75: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76: Create the SVD solver and set the solution method
77: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: SVDCreate(PETSC_COMM_WORLD,&svd);
80: SVDSetOperators(svd,A,NULL);
81: SVDSetType(svd,SVDTRLANCZOS);
82: SVDSetFromOptions(svd);
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Solve the singular value problem
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
88: SVDSetWhichSingularTriplets(svd,SVD_LARGEST);
89: SVDSolve(svd);
90: SVDGetConverged(svd,&nconv1);
91: if (nconv1 > 0) SVDGetSingularTriplet(svd,0,&sigma_1,NULL,NULL);
92: else PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");
94: /* compute smallest singular value relative to the matrix norm */
95: SVDSetConvergenceTestFunction(svd,MyConvergedRel,&sigma_1,NULL);
96: SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);
97: SVDSolve(svd);
98: SVDGetConverged(svd,&nconv2);
99: if (nconv2 > 0) SVDGetSingularTriplet(svd,0,&sigma_n,NULL,NULL);
100: else PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");
102: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
103: Display solution and clean up
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105: if (nconv1 > 0 && nconv2 > 0) {
106: PetscPrintf(PETSC_COMM_WORLD," Computed singular values: sigma_1=%.4f, sigma_n=%.4f\n",(double)sigma_1,(double)sigma_n);
107: PetscPrintf(PETSC_COMM_WORLD," Estimated condition number: sigma_1/sigma_n=%.4f\n\n",(double)(sigma_1/sigma_n));
108: }
110: SVDDestroy(&svd);
111: MatDestroy(&A);
112: SlepcFinalize();
113: return 0;
114: }
116: /*TEST
118: test:
119: suffix: 1
121: TEST*/