Actual source code: test22.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.\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;
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,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,"-test_dsview",&test_dsview);
36: PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow);
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,n,l,k);
45: DSGSVDSetDimensions(ds,n,PETSC_DECIDE);
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: if (test_dsview) {
56: /* Fill A and B with dummy values to test DSView */
57: DSGetArrayReal(ds,DS_MAT_T,&T);
58: 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: DSRestoreArrayReal(ds,DS_MAT_T,&T);
62: DSRestoreArrayReal(ds,DS_MAT_D,&D);
63: DSView(ds,viewer);
64: }
66: /* Fill A and B with upper arrow-bidiagonal matrices
67: verifying that [A;B] has orthonormal columns */
68: DSGetArrayReal(ds,DS_MAT_T,&T);
69: 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: PetscMalloc1(n,&w);
87: for (i=0;i<l;i++) w[i] = T[i]/D[i];
88: DSRestoreArrayReal(ds,DS_MAT_T,&T);
89: DSRestoreArrayReal(ds,DS_MAT_D,&D);
90: if (l==0 && k==0) DSSetState(ds,DS_STATE_INTERMEDIATE);
91: else DSSetState(ds,DS_STATE_RAW);
92: if (verbose) {
93: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
94: PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
95: DSView(ds,viewer);
96: }
98: /* Condition number */
99: DSCond(ds,&cond);
100: PetscPrintf(PETSC_COMM_WORLD,"Condition number = %.3f\n",(double)cond);
102: /* Solve */
103: DSGetSlepcSC(ds,&sc);
104: sc->comparison = SlepcCompareLargestReal;
105: sc->comparisonctx = NULL;
106: sc->map = NULL;
107: sc->mapobj = NULL;
108: DSSolve(ds,w,NULL);
109: DSSort(ds,w,NULL,NULL,NULL,NULL);
110: if (extrarow) DSUpdateExtraRow(ds);
111: DSSynchronize(ds,w,NULL);
112: if (verbose) {
113: PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");
114: DSView(ds,viewer);
115: }
117: /* Print singular values */
118: PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n");
119: for (i=0;i<n;i++) {
120: sigma = PetscRealPart(w[i]);
121: PetscViewerASCIIPrintf(viewer," %.5f\n",(double)sigma);
122: }
124: if (extrarow) {
125: /* Check that extra row is correct */
126: DSGetArrayReal(ds,DS_MAT_T,&T);
127: DSGetArray(ds,DS_MAT_U,&U);
128: 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) 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) PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in B's extra row of %g\n",(double)PetscAbsScalar(d));
135: DSRestoreArrayReal(ds,DS_MAT_T,&T);
136: DSRestoreArray(ds,DS_MAT_U,&U);
137: DSRestoreArray(ds,DS_MAT_V,&V);
138: }
140: /* Singular vectors */
141: DSVectors(ds,DS_MAT_X,NULL,NULL); /* all singular vectors */
142: DSGetMat(ds,DS_MAT_X,&X);
143: MatCreateVecs(X,NULL,&x0);
144: MatGetColumnVector(X,x0,0);
145: VecNorm(x0,NORM_2,&rnorm);
146: DSRestoreMat(ds,DS_MAT_X,&X);
147: VecDestroy(&x0);
148: PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st X vector = %.3f\n",(double)rnorm);
150: DSGetMat(ds,DS_MAT_U,&X);
151: MatCreateVecs(X,NULL,&x0);
152: MatGetColumnVector(X,x0,0);
153: VecNorm(x0,NORM_2,&rnorm);
154: DSRestoreMat(ds,DS_MAT_U,&X);
155: VecDestroy(&x0);
156: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st U vector has norm %g\n",(double)rnorm);
158: DSGetMat(ds,DS_MAT_V,&X);
159: MatCreateVecs(X,NULL,&x0);
160: MatGetColumnVector(X,x0,0);
161: VecNorm(x0,NORM_2,&rnorm);
162: DSRestoreMat(ds,DS_MAT_V,&X);
163: VecDestroy(&x0);
164: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st V vector has norm %g\n",(double)rnorm);
166: PetscFree(w);
167: DSDestroy(&ds);
168: 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*/