Actual source code: ex15.c
slepc-3.18.3 2023-03-24
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;
28: SlepcInitialize(&argc,&argv,(char*)0,help);
30: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
31: PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL);
32: 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: MatCreate(PETSC_COMM_WORLD,&A);
39: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n);
40: MatSetFromOptions(A);
41: MatSetUp(A);
43: MatGetOwnershipRange(A,&Istart,&Iend);
44: for (i=Istart;i<Iend;i++) {
45: if (i == 0) {
46: for (j=0;j<n;j++) MatSetValue(A,0,j,1.0,INSERT_VALUES);
47: } else MatSetValue(A,i,i-1,mu,INSERT_VALUES);
48: }
50: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
51: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
52: 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: SVDCreate(PETSC_COMM_WORLD,&svd);
63: /*
64: Set operators and problem type
65: */
66: SVDSetOperators(svd,A,NULL);
67: SVDSetProblemType(svd,SVD_STANDARD);
69: /*
70: Use thick-restart Lanczos as default solver
71: */
72: SVDSetType(svd,SVDTRLANCZOS);
74: /*
75: Set solver parameters at runtime
76: */
77: SVDSetFromOptions(svd);
79: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
80: Solve the singular value system
81: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
83: SVDSolve(svd);
84: SVDGetIterationNumber(svd,&its);
85: 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: SVDGetType(svd,&type);
91: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
92: SVDGetDimensions(svd,&nsv,NULL,NULL);
93: PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %" PetscInt_FMT "\n",nsv);
94: SVDGetTolerances(svd,&tol,&maxit);
95: 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: SVDGetConverged(svd,&nconv);
105: 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: SVDGetSingularTriplet(svd,i,&sigma,u,v);
120: /*
121: Compute the error associated to each singular triplet
122: */
123: SVDComputeError(svd,i,SVD_ERROR_RELATIVE,&error);
125: PetscPrintf(PETSC_COMM_WORLD," % 6f ",(double)sigma);
126: PetscPrintf(PETSC_COMM_WORLD," % 12g\n",(double)error);
127: }
128: PetscPrintf(PETSC_COMM_WORLD,"\n");
129: }
131: /*
132: Free work space
133: */
134: SVDDestroy(&svd);
135: MatDestroy(&A);
136: VecDestroy(&u);
137: VecDestroy(&v);
138: 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*/