Actual source code: ex45.c
slepc-3.15.2 2021-09-20
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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[] = "Computes a partial generalized singular value decomposition (GSVD).\n"
12: "The command line options are:\n"
13: " -m <m>, where <m> = number of rows of A.\n"
14: " -n <n>, where <n> = number of columns of A.\n"
15: " -p <p>, where <p> = number of rows of B.\n\n";
17: #include <slepcsvd.h>
19: int main(int argc,char **argv)
20: {
21: Mat A,B; /* operator matrices */
22: Vec u,v,x; /* singular vectors */
23: SVD svd; /* singular value problem solver context */
24: SVDType type;
25: Vec uv,aux[2];
26: PetscReal error,tol,sigma;
27: PetscInt m=100,n,p=14,i,j,Istart,Iend,nsv,maxit,its,nconv;
28: PetscBool flg;
31: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
33: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
34: PetscOptionsGetInt(NULL,NULL,"-n",&n,&flg);
35: if (!flg) n = m;
36: PetscOptionsGetInt(NULL,NULL,"-p",&p,&flg);
37: PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized singular value decomposition, (%D+%D)x%D\n\n",m,p,n);
39: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
40: Build the matrices
41: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
43: MatCreate(PETSC_COMM_WORLD,&A);
44: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,n);
45: MatSetFromOptions(A);
46: MatSetUp(A);
48: MatGetOwnershipRange(A,&Istart,&Iend);
49: for (i=Istart;i<Iend;i++) {
50: if (i>0 && i-1<n) { MatSetValue(A,i,i-1,-1.0,INSERT_VALUES); }
51: if (i+1<n) { MatSetValue(A,i,i+1,-1.0,INSERT_VALUES); }
52: if (i<n) { MatSetValue(A,i,i,2.0,INSERT_VALUES); }
53: if (i>n) { MatSetValue(A,i,n-1,1.0,INSERT_VALUES); }
54: }
55: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
56: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
58: MatCreate(PETSC_COMM_WORLD,&B);
59: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,p,n);
60: MatSetFromOptions(B);
61: MatSetUp(B);
63: MatGetOwnershipRange(B,&Istart,&Iend);
64: for (i=Istart;i<Iend;i++) {
65: for (j=0;j<=PetscMin(i,n-1);j++) {
66: MatSetValue(B,i,j,1.0,INSERT_VALUES);
67: }
68: }
69: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
70: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
72: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
73: Create the singular value solver and set various options
74: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
76: /*
77: Create singular value solver context
78: */
79: SVDCreate(PETSC_COMM_WORLD,&svd);
81: /*
82: Set operators and problem type
83: */
84: SVDSetOperators(svd,A,B);
85: SVDSetProblemType(svd,SVD_GENERALIZED);
87: /*
88: Set solver parameters at runtime
89: */
90: SVDSetFromOptions(svd);
92: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
93: Solve the singular value system
94: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
96: SVDSolve(svd);
97: SVDGetIterationNumber(svd,&its);
98: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
100: /*
101: Optional: Get some information from the solver and display it
102: */
103: SVDGetType(svd,&type);
104: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
105: SVDGetDimensions(svd,&nsv,NULL,NULL);
106: PetscPrintf(PETSC_COMM_WORLD," Number of requested singular values: %D\n",nsv);
107: SVDGetTolerances(svd,&tol,&maxit);
108: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);
110: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111: Display solution and clean up
112: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
114: /*
115: Get number of converged singular triplets
116: */
117: SVDGetConverged(svd,&nconv);
118: PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate singular triplets: %D\n\n",nconv);
120: if (nconv>0) {
121: /*
122: Create vectors. The interface returns u and v as stacked on top of each other
123: [u;v] so need to create a special vector (VecNest) to extract them
124: */
125: MatCreateVecs(A,&x,&u);
126: MatCreateVecs(B,NULL,&v);
127: aux[0] = u;
128: aux[1] = v;
129: VecCreateNest(PETSC_COMM_WORLD,2,NULL,aux,&uv);
131: /*
132: Display singular values and relative errors
133: */
134: PetscPrintf(PETSC_COMM_WORLD,
135: " sigma relative error\n"
136: " --------------------- ------------------\n");
137: for (i=0;i<nconv;i++) {
138: /*
139: Get converged singular triplets: i-th singular value is stored in sigma
140: */
141: SVDGetSingularTriplet(svd,i,&sigma,uv,x);
142: /* at this point, u and v can be used normally as individual vectors */
144: /*
145: Compute the error associated to each singular triplet
146: */
147: SVDComputeError(svd,i,SVD_ERROR_RELATIVE,&error);
149: PetscPrintf(PETSC_COMM_WORLD," % 6f ",(double)sigma);
150: PetscPrintf(PETSC_COMM_WORLD," % 12g\n",(double)error);
151: }
152: PetscPrintf(PETSC_COMM_WORLD,"\n");
153: VecDestroy(&x);
154: VecDestroy(&u);
155: VecDestroy(&v);
156: VecDestroy(&uv);
157: }
159: /*
160: Free work space
161: */
162: SVDDestroy(&svd);
163: MatDestroy(&A);
164: MatDestroy(&B);
165: SlepcFinalize();
166: return ierr;
167: }
169: /*TEST
171: test:
172: args: -m 20 -n 10 -p 6 -svd_type lapack
173: suffix: 1
174: filter: sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
175: requires: double
177: test:
178: args: -m 15 -n 20 -p 20 -svd_type lapack
179: suffix: 2
180: filter: sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
181: requires: double
183: TEST*/