Actual source code: test22.c
slepc-3.16.3 2022-04-11
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[] = "Test DSGSVD with compact storage.\n\n";
13: #include <slepcds.h>
15: int main(int argc,char **argv)
16: {
18: DS ds;
19: Mat X;
20: Vec x0;
21: SlepcSC sc;
22: PetscReal *T,*D,sigma,rnorm,aux;
23: PetscScalar *U,*V,*w,d;
24: PetscInt i,n=10,l=0,k=0,ld;
25: PetscViewer viewer;
26: PetscBool verbose,test_dsview,extrarow;
28: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
29: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
30: PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type GSVD with compact storage - dimension %Dx%D.\n",n,n);
31: PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL);
32: PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
33: if (l>n || k>n || l>k) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"Wrong value of dimensions");
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) {
91: DSSetState(ds,DS_STATE_INTERMEDIATE);
92: } else {
93: DSSetState(ds,DS_STATE_RAW);
94: }
95: if (verbose) {
96: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
97: PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
98: DSView(ds,viewer);
99: }
101: /* Solve */
102: DSGetSlepcSC(ds,&sc);
103: sc->comparison = SlepcCompareLargestReal;
104: sc->comparisonctx = NULL;
105: sc->map = NULL;
106: sc->mapobj = NULL;
107: DSSolve(ds,w,NULL);
108: DSSort(ds,w,NULL,NULL,NULL,NULL);
109: if (extrarow) { DSUpdateExtraRow(ds); }
110: DSSynchronize(ds,w,NULL);
111: if (verbose) {
112: PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");
113: DSView(ds,viewer);
114: }
116: /* Print singular values */
117: PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n");
118: for (i=0;i<n;i++) {
119: sigma = PetscRealPart(w[i]);
120: PetscViewerASCIIPrintf(viewer," %.5f\n",(double)sigma);
121: }
123: if (extrarow) {
124: /* Check that extra row is correct */
125: DSGetArrayReal(ds,DS_MAT_T,&T);
126: DSGetArray(ds,DS_MAT_U,&U);
127: DSGetArray(ds,DS_MAT_V,&V);
128: d = 0.0;
129: for (i=0;i<n;i++) d += T[i+ld]+U[n-1+i*ld];
130: if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) {
131: PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in A's extra row of %g\n",(double)PetscAbsScalar(d));
132: }
133: d = 0.0;
134: for (i=0;i<n;i++) d += T[i+2*ld]-V[n-1+i*ld];
135: if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) {
136: PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in B's extra row of %g\n",(double)PetscAbsScalar(d));
137: }
138: DSRestoreArrayReal(ds,DS_MAT_T,&T);
139: DSRestoreArray(ds,DS_MAT_U,&U);
140: DSRestoreArray(ds,DS_MAT_V,&V);
141: }
143: /* Singular vectors */
144: DSVectors(ds,DS_MAT_X,NULL,NULL); /* all singular vectors */
145: DSGetMat(ds,DS_MAT_X,&X);
146: MatCreateVecs(X,NULL,&x0);
147: MatGetColumnVector(X,x0,0);
148: VecNorm(x0,NORM_2,&rnorm);
149: MatDestroy(&X);
150: VecDestroy(&x0);
151: PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st X vector = %.3f\n",(double)rnorm);
153: DSGetMat(ds,DS_MAT_U,&X);
154: MatCreateVecs(X,NULL,&x0);
155: MatGetColumnVector(X,x0,0);
156: VecNorm(x0,NORM_2,&rnorm);
157: MatDestroy(&X);
158: VecDestroy(&x0);
159: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) {
160: PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st U vector has norm %g\n",(double)rnorm);
161: }
163: DSGetMat(ds,DS_MAT_V,&X);
164: MatCreateVecs(X,NULL,&x0);
165: MatGetColumnVector(X,x0,0);
166: VecNorm(x0,NORM_2,&rnorm);
167: MatDestroy(&X);
168: VecDestroy(&x0);
169: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) {
170: PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st V vector has norm %g\n",(double)rnorm);
171: }
173: PetscFree(w);
174: DSDestroy(&ds);
175: SlepcFinalize();
176: return ierr;
177: }
179: /*TEST
181: testset:
182: requires: double
183: test:
184: suffix: 1
185: args: -test_dsview
186: test:
187: suffix: 2
188: args: -l 1 -k 4
189: test:
190: suffix: 2_extrarow
191: filter: sed -e "s/extrarow//"
192: args: -l 1 -k 4 -extrarow
193: output_file: output/test22_2.out
195: TEST*/