Actual source code: ex15.c
slepc-3.19.2 2023-09-05
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[] = "Singular value decomposition of the Lauchli matrix.\n"
12: "The command line options are:\n"
13: " -n <n>, where <n> = matrix dimension.\n"
14: " -mu <mu>, where <mu> = subdiagonal value.\n\n";
16: #include <slepcsvd.h>
18: int main(int argc,char **argv)
19: {
20: Mat A; /* operator matrix */
21: Vec u,v; /* left and right singular vectors */
22: SVD svd; /* singular value problem solver context */
23: SVDType type;
24: PetscReal error,tol,sigma,mu=PETSC_SQRT_MACHINE_EPSILON;
25: PetscInt n=100,i,j,Istart,Iend,nsv,maxit,its,nconv;
27: PetscFunctionBeginUser;
28: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
30: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
31: PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL));
32: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nLauchli singular value decomposition, (%" PetscInt_FMT " x %" PetscInt_FMT ") mu=%g\n\n",n+1,n,(double)mu));
34: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
35: Build the Lauchli matrix
36: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
38: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
39: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n));
40: PetscCall(MatSetFromOptions(A));
41: PetscCall(MatSetUp(A));
43: PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
44: for (i=Istart;i<Iend;i++) {
45: if (i == 0) {
46: for (j=0;j<n;j++) PetscCall(MatSetValue(A,0,j,1.0,INSERT_VALUES));
47: } else PetscCall(MatSetValue(A,i,i-1,mu,INSERT_VALUES));
48: }
50: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
51: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
52: PetscCall(MatCreateVecs(A,&v,&u));
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Create the singular value solver and set various options
56: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58: /*
59: Create singular value solver context
60: */
61: PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));
63: /*
64: Set operators and problem type
65: */
66: PetscCall(SVDSetOperators(svd,A,NULL));
67: PetscCall(SVDSetProblemType(svd,SVD_STANDARD));
69: /*
70: Use thick-restart Lanczos as default solver
71: */
72: PetscCall(SVDSetType(svd,SVDTRLANCZOS));
74: /*
75: Set solver parameters at runtime
76: */
77: PetscCall(SVDSetFromOptions(svd));
79: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
80: Solve the singular value system
81: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
83: PetscCall(SVDSolve(svd));
84: PetscCall(SVDGetIterationNumber(svd,&its));
85: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
87: /*
88: Optional: Get some information from the solver and display it
89: */
90: PetscCall(SVDGetType(svd,&type));
91: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
92: PetscCall(SVDGetDimensions(svd,&nsv,NULL,NULL));
93: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %" PetscInt_FMT "\n",nsv));
94: PetscCall(SVDGetTolerances(svd,&tol,&maxit));
95: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));
97: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
98: Display solution and clean up
99: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101: /*
102: Get number of converged singular triplets
103: */
104: PetscCall(SVDGetConverged(svd,&nconv));
105: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %" PetscInt_FMT "\n\n",nconv));
107: if (nconv>0) {
108: /*
109: Display singular values and relative errors
110: */
111: PetscCall(PetscPrintf(PETSC_COMM_WORLD,
112: " sigma relative error\n"
113: " --------------------- ------------------\n"));
114: for (i=0;i<nconv;i++) {
115: /*
116: Get converged singular triplets: i-th singular value is stored in sigma
117: */
118: PetscCall(SVDGetSingularTriplet(svd,i,&sigma,u,v));
120: /*
121: Compute the error associated to each singular triplet
122: */
123: PetscCall(SVDComputeError(svd,i,SVD_ERROR_RELATIVE,&error));
125: PetscCall(PetscPrintf(PETSC_COMM_WORLD," % 6f ",(double)sigma));
126: PetscCall(PetscPrintf(PETSC_COMM_WORLD," % 12g\n",(double)error));
127: }
128: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
129: }
131: /*
132: Free work space
133: */
134: PetscCall(SVDDestroy(&svd));
135: PetscCall(MatDestroy(&A));
136: PetscCall(VecDestroy(&u));
137: PetscCall(VecDestroy(&v));
138: PetscCall(SlepcFinalize());
139: return 0;
140: }
142: /*TEST
144: testset:
145: filter: sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
146: requires: double
147: test:
148: suffix: 1
149: test:
150: suffix: 1_scalapack
151: nsize: {{1 2}}
152: args: -svd_type scalapack
153: requires: scalapack
155: TEST*/