Actual source code: test24.c
slepc-3.21.1 2024-04-26
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;
27: PetscFunctionBeginUser;
28: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
29: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
30: PetscCall(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: PetscCall(PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL));
32: PetscCall(PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL));
33: PetscCheck(l<=n && k<=n && l<=k,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"Wrong value of dimensions");
34: PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
35: PetscCall(PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow));
36: m = n+1;
38: /* Create DS object */
39: PetscCall(DSCreate(PETSC_COMM_WORLD,&ds));
40: PetscCall(DSSetType(ds,DSGSVD));
41: PetscCall(DSSetFromOptions(ds));
42: ld = n+2; /* test leading dimension larger than n */
43: PetscCall(DSAllocate(ds,ld));
44: PetscCall(DSSetDimensions(ds,m,l,k));
45: PetscCall(DSGSVDSetDimensions(ds,n,n));
46: PetscCall(DSSetCompact(ds,PETSC_TRUE));
47: PetscCall(DSSetExtraRow(ds,extrarow));
49: /* Set up viewer */
50: PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
51: PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
52: PetscCall(DSView(ds,viewer));
53: PetscCall(PetscViewerPopFormat(viewer));
55: /* Fill A and B with lower/upper arrow-bidiagonal matrices
56: verifying that [A;B] has orthonormal columns */
57: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
58: PetscCall(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: PetscCall(PetscMalloc1(n,&w));
79: for (i=0;i<l;i++) w[i] = T[i]/D[i];
80: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
81: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
82: if (l==0 && k==0) PetscCall(DSSetState(ds,DS_STATE_INTERMEDIATE));
83: else PetscCall(DSSetState(ds,DS_STATE_RAW));
84: if (verbose) {
85: PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));
86: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n"));
87: PetscCall(DSView(ds,viewer));
88: }
90: /* Condition number */
91: PetscCall(DSCond(ds,&cond));
92: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Condition number = %.3f\n",(double)cond));
94: /* Solve */
95: PetscCall(DSGetSlepcSC(ds,&sc));
96: sc->comparison = SlepcCompareLargestReal;
97: sc->comparisonctx = NULL;
98: sc->map = NULL;
99: sc->mapobj = NULL;
100: PetscCall(DSSolve(ds,w,NULL));
101: PetscCall(DSSort(ds,w,NULL,NULL,NULL,NULL));
102: if (extrarow) PetscCall(DSUpdateExtraRow(ds));
103: PetscCall(DSSynchronize(ds,w,NULL));
104: if (verbose) {
105: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n"));
106: PetscCall(DSView(ds,viewer));
107: }
109: /* Print singular values */
110: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n"));
111: for (i=0;i<n;i++) {
112: sigma = PetscRealPart(w[i]);
113: PetscCall(PetscViewerASCIIPrintf(viewer," %.5f\n",(double)sigma));
114: }
116: if (extrarow) {
117: /* Check that extra row is correct */
118: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
119: PetscCall(DSGetArray(ds,DS_MAT_U,&U));
120: PetscCall(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) PetscCall(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) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in B's extra row of %g\n",(double)PetscAbsScalar(d)));
127: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
128: PetscCall(DSRestoreArray(ds,DS_MAT_U,&U));
129: PetscCall(DSRestoreArray(ds,DS_MAT_V,&V));
130: }
132: /* Singular vectors */
133: PetscCall(DSVectors(ds,DS_MAT_X,NULL,NULL)); /* all singular vectors */
134: PetscCall(DSGetMat(ds,DS_MAT_X,&X));
135: PetscCall(MatCreateVecs(X,NULL,&x0));
136: PetscCall(MatGetColumnVector(X,x0,0));
137: PetscCall(VecNorm(x0,NORM_2,&rnorm));
138: PetscCall(DSRestoreMat(ds,DS_MAT_X,&X));
139: PetscCall(VecDestroy(&x0));
140: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st X vector = %.3f\n",(double)rnorm));
142: PetscCall(DSGetMat(ds,DS_MAT_U,&X));
143: PetscCall(MatCreateVecs(X,NULL,&x0));
144: PetscCall(MatGetColumnVector(X,x0,0));
145: PetscCall(VecNorm(x0,NORM_2,&rnorm));
146: PetscCall(DSRestoreMat(ds,DS_MAT_U,&X));
147: PetscCall(VecDestroy(&x0));
148: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st U vector has norm %g\n",(double)rnorm));
150: PetscCall(DSGetMat(ds,DS_MAT_V,&X));
151: PetscCall(MatCreateVecs(X,NULL,&x0));
152: PetscCall(MatGetColumnVector(X,x0,0));
153: PetscCall(VecNorm(x0,NORM_2,&rnorm));
154: PetscCall(DSRestoreMat(ds,DS_MAT_V,&X));
155: PetscCall(VecDestroy(&x0));
156: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st V vector has norm %g\n",(double)rnorm));
158: PetscCall(PetscFree(w));
159: PetscCall(DSDestroy(&ds));
160: PetscCall(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*/