Actual source code: ex15.c
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7:
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: const SVDType type;
37: PetscReal error, tol, sigma, mu=PETSC_SQRT_MACHINE_EPSILON;
39: PetscInt n=100, i, j, Istart, Iend, nsv, maxit, its, nconv;
41: SlepcInitialize(&argc,&argv,(char*)0,help);
43: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
44: PetscOptionsGetReal(PETSC_NULL,"-mu",&mu,PETSC_NULL);
45: PetscPrintf(PETSC_COMM_WORLD,"\nLauchli singular value decomposition, (%d x %d) mu=%g\n\n",n+1,n,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);
55: MatGetOwnershipRange(A,&Istart,&Iend);
56: for (i=Istart;i<Iend;i++) {
57: if (i == 0) {
58: for (j=0;j<n;j++) {
59: MatSetValue(A,0,j,1.0,INSERT_VALUES);
60: }
61: } else {
62: MatSetValue(A,i,i-1,mu,INSERT_VALUES);
63: }
64: }
65:
66: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
67: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
68: MatGetVecs(A,&v,&u);
70: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
71: Create the singular value solver and set various options
72: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
74: /*
75: Create singular value solver context
76: */
77: SVDCreate(PETSC_COMM_WORLD,&svd);
79: /*
80: Set operator
81: */
82: SVDSetOperator(svd,A);
83:
84: /*
85: Use thick-restart Lanczos as default solver
86: */
87: SVDSetType(svd,SVDTRLANCZOS);
89: /*
90: Set solver parameters at runtime
91: */
92: SVDSetFromOptions(svd);
94: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95: Solve the singular value system
96: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
98: SVDSolve(svd);
99: SVDGetIterationNumber(svd, &its);
100: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);
102: /*
103: Optional: Get some information from the solver and display it
104: */
105: SVDGetType(svd,&type);
106: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
107: SVDGetDimensions(svd,&nsv,PETSC_NULL,PETSC_NULL);
108: PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %d\n",nsv);
109: SVDGetTolerances(svd,&tol,&maxit);
110: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);
112: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113: Display solution and clean up
114: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116: /*
117: Get number of converged singular triplets
118: */
119: SVDGetConverged(svd,&nconv);
120: PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %d\n\n",nconv);
122: if (nconv>0) {
123: /*
124: Display singular values and relative errors
125: */
126: PetscPrintf(PETSC_COMM_WORLD,
127: " sigma residual norm\n"
128: " --------------------- ------------------\n" );
129: for( i=0; i<nconv; i++ ) {
130: /*
131: Get converged singular triplets: i-th singular value is stored in sigma
132: */
133: SVDGetSingularTriplet(svd,i,&sigma,u,v);
135: /*
136: Compute the error associated to each singular triplet
137: */
138: SVDComputeRelativeError(svd,i,&error);
140: PetscPrintf(PETSC_COMM_WORLD," % 6f ",sigma);
141: PetscPrintf(PETSC_COMM_WORLD," % 12g\n",error);
142: }
143: PetscPrintf(PETSC_COMM_WORLD,"\n" );
144: }
145:
146: /*
147: Free work space
148: */
149: SVDDestroy(svd);
150: MatDestroy(A);
151: VecDestroy(u);
152: VecDestroy(v);
153: SlepcFinalize();
154: return 0;
155: }