Actual source code: test24.c
slepc-3.18.0 2022-10-01
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[] = "Test DSGSVD with compact storage and rectangular matrix A.\n\n";
13: #include <slepcds.h>
15: int main(int argc,char **argv)
16: {
17: DS ds;
18: Mat X;
19: Vec x0;
20: SlepcSC sc;
21: PetscReal *T,*D,sigma,rnorm,aux,cond;
22: PetscScalar *U,*V,*w,d;
23: PetscInt i,n=10,m,l=0,k=0,ld;
24: PetscViewer viewer;
25: PetscBool verbose,extrarow;
28: SlepcInitialize(&argc,&argv,(char*)0,help);
29: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
30: PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type GSVD with compact storage - dimension %" PetscInt_FMT "x%" PetscInt_FMT ".\n",n+1,n);
31: PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL);
32: PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
34: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
35: PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow);
36: m = n+1;
38: /* Create DS object */
39: DSCreate(PETSC_COMM_WORLD,&ds);
40: DSSetType(ds,DSGSVD);
41: DSSetFromOptions(ds);
42: ld = n+2; /* test leading dimension larger than n */
43: DSAllocate(ds,ld);
44: DSSetDimensions(ds,m,l,k);
45: DSGSVDSetDimensions(ds,n,n);
46: DSSetCompact(ds,PETSC_TRUE);
47: DSSetExtraRow(ds,extrarow);
49: /* Set up viewer */
50: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
51: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
52: DSView(ds,viewer);
53: PetscViewerPopFormat(viewer);
55: /* Fill A and B with lower/upper arrow-bidiagonal matrices
56: verifying that [A;B] has orthonormal columns */
57: DSGetArrayReal(ds,DS_MAT_T,&T);
58: DSGetArrayReal(ds,DS_MAT_D,&D);
59: for (i=0;i<n;i++) T[i] = (PetscReal)(i+1)/(n+1); /* diagonal of matrix A */
60: for (i=0;i<k;i++) D[i] = PetscSqrtReal(1.0-T[i]*T[i]);
61: for (i=l;i<k;i++) {
62: T[i+ld] = PetscSqrtReal((1.0-T[k]*T[k])/(1.0+T[i]*T[i]/(D[i]*D[i])))*0.5*(1.0/k); /* upper diagonal of matrix A */
63: T[i+2*ld] = -T[i+ld]*T[i]/D[i]; /* upper diagonal of matrix B */
64: }
65: aux = 1.0-T[k]*T[k];
66: for (i=l;i<k;i++) aux -= T[i+ld]*T[i+ld]+T[i+2*ld]*T[i+2*ld];
67: T[k+ld] = PetscSqrtReal((1.0-aux)*.1);
68: aux -= T[k+ld]*T[k+ld];
69: D[k] = PetscSqrtReal(aux);
70: for (i=k+1;i<n;i++) {
71: T[i-1+2*ld] = -T[i-1+ld]*T[i]/D[i-1]; /* upper diagonal of matrix B */
72: aux = 1.0-T[i]*T[i]-T[2*ld+i-1]*T[2*ld+i-1];
73: T[i+ld] = PetscSqrtReal(aux)*.1; /* upper diagonal of matrix A */
74: D[i] = PetscSqrtReal(aux-T[i+ld]*T[i+ld]);
75: }
76: if (extrarow) { T[n]=-1.0; T[n-1+2*ld]=1.0; }
77: /* Fill locked eigenvalues */
78: PetscMalloc1(n,&w);
79: for (i=0;i<l;i++) w[i] = T[i]/D[i];
80: DSRestoreArrayReal(ds,DS_MAT_T,&T);
81: DSRestoreArrayReal(ds,DS_MAT_D,&D);
82: if (l==0 && k==0) DSSetState(ds,DS_STATE_INTERMEDIATE);
83: else DSSetState(ds,DS_STATE_RAW);
84: if (verbose) {
85: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
86: PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
87: DSView(ds,viewer);
88: }
90: /* Condition number */
91: DSCond(ds,&cond);
92: PetscPrintf(PETSC_COMM_WORLD,"Condition number = %.3f\n",(double)cond);
94: /* Solve */
95: DSGetSlepcSC(ds,&sc);
96: sc->comparison = SlepcCompareLargestReal;
97: sc->comparisonctx = NULL;
98: sc->map = NULL;
99: sc->mapobj = NULL;
100: DSSolve(ds,w,NULL);
101: DSSort(ds,w,NULL,NULL,NULL,NULL);
102: if (extrarow) DSUpdateExtraRow(ds);
103: DSSynchronize(ds,w,NULL);
104: if (verbose) {
105: PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");
106: DSView(ds,viewer);
107: }
109: /* Print singular values */
110: PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n");
111: for (i=0;i<n;i++) {
112: sigma = PetscRealPart(w[i]);
113: PetscViewerASCIIPrintf(viewer," %.5f\n",(double)sigma);
114: }
116: if (extrarow) {
117: /* Check that extra row is correct */
118: DSGetArrayReal(ds,DS_MAT_T,&T);
119: DSGetArray(ds,DS_MAT_U,&U);
120: DSGetArray(ds,DS_MAT_V,&V);
121: d = 0.0;
122: for (i=0;i<n;i++) d += T[i+ld]+U[n+i*ld];
123: if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in A's extra row of %g\n",(double)PetscAbsScalar(d));
124: d = 0.0;
125: for (i=0;i<n;i++) d += T[i+2*ld]-V[n-1+i*ld];
126: if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in B's extra row of %g\n",(double)PetscAbsScalar(d));
127: DSRestoreArrayReal(ds,DS_MAT_T,&T);
128: DSRestoreArray(ds,DS_MAT_U,&U);
129: DSRestoreArray(ds,DS_MAT_V,&V);
130: }
132: /* Singular vectors */
133: DSVectors(ds,DS_MAT_X,NULL,NULL); /* all singular vectors */
134: DSGetMat(ds,DS_MAT_X,&X);
135: MatCreateVecs(X,NULL,&x0);
136: MatGetColumnVector(X,x0,0);
137: VecNorm(x0,NORM_2,&rnorm);
138: DSRestoreMat(ds,DS_MAT_X,&X);
139: VecDestroy(&x0);
140: PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st X vector = %.3f\n",(double)rnorm);
142: DSGetMat(ds,DS_MAT_U,&X);
143: MatCreateVecs(X,NULL,&x0);
144: MatGetColumnVector(X,x0,0);
145: VecNorm(x0,NORM_2,&rnorm);
146: DSRestoreMat(ds,DS_MAT_U,&X);
147: VecDestroy(&x0);
148: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st U vector has norm %g\n",(double)rnorm);
150: DSGetMat(ds,DS_MAT_V,&X);
151: MatCreateVecs(X,NULL,&x0);
152: MatGetColumnVector(X,x0,0);
153: VecNorm(x0,NORM_2,&rnorm);
154: DSRestoreMat(ds,DS_MAT_V,&X);
155: VecDestroy(&x0);
156: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st V vector has norm %g\n",(double)rnorm);
158: PetscFree(w);
159: DSDestroy(&ds);
160: SlepcFinalize();
161: return 0;
162: }
164: /*TEST
166: testset:
167: requires: double
168: output_file: output/test24_1.out
169: test:
170: suffix: 1
171: args: -l 1 -k 4
172: test:
173: suffix: 1_extrarow
174: filter: sed -e "s/extrarow//"
175: args: -l 1 -k 4 -extrarow
177: TEST*/