Actual source code: ex15.c
slepc-3.7.0 2016-05-16
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
8: SLEPc is free software: you can redistribute it and/or modify it under the
9: terms of version 3 of the GNU Lesser General Public License as published by
10: the Free Software Foundation.
12: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
13: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
14: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
15: more details.
17: You should have received a copy of the GNU Lesser General Public License
18: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
19: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
20: */
22: static char help[] = "Singular value decomposition of the Lauchli matrix.\n"
23: "The command line options are:\n"
24: " -n <n>, where <n> = matrix dimension.\n"
25: " -mu <mu>, where <mu> = subdiagonal value.\n\n";
27: #include <slepcsvd.h>
31: int main(int argc,char **argv)
32: {
33: Mat A; /* operator matrix */
34: Vec u,v; /* left and right singular vectors */
35: SVD svd; /* singular value problem solver context */
36: SVDType type;
37: PetscReal error,tol,sigma,mu=PETSC_SQRT_MACHINE_EPSILON;
38: PetscInt n=100,i,j,Istart,Iend,nsv,maxit,its,nconv;
41: SlepcInitialize(&argc,&argv,(char*)0,help);
43: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
44: PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL);
45: PetscPrintf(PETSC_COMM_WORLD,"\nLauchli singular value decomposition, (%D x %D) mu=%g\n\n",n+1,n,(double)mu);
47: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
48: Build the Lauchli matrix
49: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
51: MatCreate(PETSC_COMM_WORLD,&A);
52: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n+1,n);
53: MatSetFromOptions(A);
54: MatSetUp(A);
56: MatGetOwnershipRange(A,&Istart,&Iend);
57: for (i=Istart;i<Iend;i++) {
58: if (i == 0) {
59: for (j=0;j<n;j++) {
60: MatSetValue(A,0,j,1.0,INSERT_VALUES);
61: }
62: } else {
63: MatSetValue(A,i,i-1,mu,INSERT_VALUES);
64: }
65: }
67: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
68: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
69: MatCreateVecs(A,&v,&u);
71: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
72: Create the singular value solver and set various options
73: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
75: /*
76: Create singular value solver context
77: */
78: SVDCreate(PETSC_COMM_WORLD,&svd);
80: /*
81: Set operator
82: */
83: SVDSetOperator(svd,A);
85: /*
86: Use thick-restart Lanczos as default solver
87: */
88: SVDSetType(svd,SVDTRLANCZOS);
90: /*
91: Set solver parameters at runtime
92: */
93: SVDSetFromOptions(svd);
95: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
96: Solve the singular value system
97: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
99: SVDSolve(svd);
100: SVDGetIterationNumber(svd,&its);
101: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
103: /*
104: Optional: Get some information from the solver and display it
105: */
106: SVDGetType(svd,&type);
107: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
108: SVDGetDimensions(svd,&nsv,NULL,NULL);
109: PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %D\n",nsv);
110: SVDGetTolerances(svd,&tol,&maxit);
111: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);
113: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: Display solution and clean up
115: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
117: /*
118: Get number of converged singular triplets
119: */
120: SVDGetConverged(svd,&nconv);
121: PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %D\n\n",nconv);
123: if (nconv>0) {
124: /*
125: Display singular values and relative errors
126: */
127: PetscPrintf(PETSC_COMM_WORLD,
128: " sigma relative error\n"
129: " --------------------- ------------------\n");
130: for (i=0;i<nconv;i++) {
131: /*
132: Get converged singular triplets: i-th singular value is stored in sigma
133: */
134: SVDGetSingularTriplet(svd,i,&sigma,u,v);
136: /*
137: Compute the error associated to each singular triplet
138: */
139: SVDComputeError(svd,i,SVD_ERROR_RELATIVE,&error);
141: PetscPrintf(PETSC_COMM_WORLD," % 6f ",(double)sigma);
142: PetscPrintf(PETSC_COMM_WORLD," % 12g\n",(double)error);
143: }
144: PetscPrintf(PETSC_COMM_WORLD,"\n");
145: }
147: /*
148: Free work space
149: */
150: SVDDestroy(&svd);
151: MatDestroy(&A);
152: VecDestroy(&u);
153: VecDestroy(&v);
154: SlepcFinalize();
155: return ierr;
156: }