Actual source code: test22.c
slepc-3.22.1 2024-10-28
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.\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,l=0,k=0,ld;
24: PetscViewer viewer;
25: PetscBool verbose,test_dsview,extrarow;
27: PetscFunctionBeginUser;
28: PetscCall(SlepcInitialize(&argc,&argv,NULL,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,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,"-test_dsview",&test_dsview));
36: PetscCall(PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow));
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,n,l,k));
45: PetscCall(DSGSVDSetDimensions(ds,n,PETSC_DECIDE));
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: if (test_dsview) {
56: /* Fill A and B with dummy values to test DSView */
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] = i+1; D[i] = -i-1; }
60: for (i=0;i<n-1;i++) { T[i+ld] = -1.0; T[i+2*ld] = 1.0; }
61: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
62: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
63: PetscCall(DSView(ds,viewer));
64: }
66: /* Fill A and B with upper arrow-bidiagonal matrices
67: verifying that [A;B] has orthonormal columns */
68: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
69: PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
70: for (i=0;i<n;i++) T[i] = (PetscReal)(i+1)/(n+1); /* diagonal of matrix A */
71: for (i=0;i<k;i++) D[i] = PetscSqrtReal(1.0-T[i]*T[i]);
72: for (i=l;i<k;i++) {
73: 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 */
74: T[i+2*ld] = -T[i+ld]*T[i]/D[i]; /* upper diagonal of matrix B */
75: }
76: aux = 1.0-T[k]*T[k];
77: for (i=l;i<k;i++) aux -= T[i+ld]*T[i+ld]+T[i+2*ld]*T[i+2*ld];
78: D[k] = PetscSqrtReal(aux);
79: for (i=k;i<n-1;i++) {
80: T[i+ld] = PetscSqrtReal((1.0-T[i+1]*T[i+1])/(1.0+T[i]*T[i]/(D[i]*D[i])))*0.5; /* upper diagonal of matrix A */
81: T[i+2*ld] = -T[i+ld]*T[i]/D[i]; /* upper diagonal of matrix B */
82: D[i+1] = PetscSqrtReal(1.0-T[i+1]*T[i+1]-T[ld+i]*T[ld+i]-T[2*ld+i]*T[2*ld+i]); /* diagonal of matrix B */
83: }
84: if (extrarow) { T[n-1+ld]=-1.0; T[n-1+2*ld]=1.0; }
85: /* Fill locked eigenvalues */
86: PetscCall(PetscMalloc1(n,&w));
87: for (i=0;i<l;i++) w[i] = T[i]/D[i];
88: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
89: PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
90: if (l==0 && k==0) PetscCall(DSSetState(ds,DS_STATE_INTERMEDIATE));
91: else PetscCall(DSSetState(ds,DS_STATE_RAW));
92: if (verbose) {
93: PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));
94: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n"));
95: PetscCall(DSView(ds,viewer));
96: }
98: /* Condition number */
99: PetscCall(DSCond(ds,&cond));
100: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Condition number = %.3f\n",(double)cond));
102: /* Solve */
103: PetscCall(DSGetSlepcSC(ds,&sc));
104: sc->comparison = SlepcCompareLargestReal;
105: sc->comparisonctx = NULL;
106: sc->map = NULL;
107: sc->mapobj = NULL;
108: PetscCall(DSSolve(ds,w,NULL));
109: PetscCall(DSSort(ds,w,NULL,NULL,NULL,NULL));
110: if (extrarow) PetscCall(DSUpdateExtraRow(ds));
111: PetscCall(DSSynchronize(ds,w,NULL));
112: if (verbose) {
113: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n"));
114: PetscCall(DSView(ds,viewer));
115: }
117: /* Print singular values */
118: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n"));
119: for (i=0;i<n;i++) {
120: sigma = PetscRealPart(w[i]);
121: PetscCall(PetscViewerASCIIPrintf(viewer," %.5f\n",(double)sigma));
122: }
124: if (extrarow) {
125: /* Check that extra row is correct */
126: PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
127: PetscCall(DSGetArray(ds,DS_MAT_U,&U));
128: PetscCall(DSGetArray(ds,DS_MAT_V,&V));
129: d = 0.0;
130: for (i=0;i<n;i++) d += T[i+ld]+U[n-1+i*ld];
131: 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)));
132: d = 0.0;
133: for (i=0;i<n;i++) d += T[i+2*ld]-V[n-1+i*ld];
134: 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)));
135: PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
136: PetscCall(DSRestoreArray(ds,DS_MAT_U,&U));
137: PetscCall(DSRestoreArray(ds,DS_MAT_V,&V));
138: }
140: /* Singular vectors */
141: PetscCall(DSVectors(ds,DS_MAT_X,NULL,NULL)); /* all singular vectors */
142: PetscCall(DSGetMat(ds,DS_MAT_X,&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_X,&X));
147: PetscCall(VecDestroy(&x0));
148: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st X vector = %.3f\n",(double)rnorm));
150: PetscCall(DSGetMat(ds,DS_MAT_U,&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_U,&X));
155: PetscCall(VecDestroy(&x0));
156: 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));
158: PetscCall(DSGetMat(ds,DS_MAT_V,&X));
159: PetscCall(MatCreateVecs(X,NULL,&x0));
160: PetscCall(MatGetColumnVector(X,x0,0));
161: PetscCall(VecNorm(x0,NORM_2,&rnorm));
162: PetscCall(DSRestoreMat(ds,DS_MAT_V,&X));
163: PetscCall(VecDestroy(&x0));
164: 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));
166: PetscCall(PetscFree(w));
167: PetscCall(DSDestroy(&ds));
168: PetscCall(SlepcFinalize());
169: return 0;
170: }
172: /*TEST
174: testset:
175: requires: double
176: test:
177: suffix: 1
178: args: -test_dsview
179: test:
180: suffix: 2
181: args: -l 1 -k 4
182: test:
183: suffix: 2_extrarow
184: filter: sed -e "s/extrarow//"
185: args: -l 1 -k 4 -extrarow
186: output_file: output/test22_2.out
188: TEST*/