Actual source code: test24.c
slepc-3.16.1 2021-11-17
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 and rectangular matrix A.\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,m,l=0,k=0,ld;
25: PetscViewer viewer;
26: PetscBool verbose,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+1,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,"-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) {
83: DSSetState(ds,DS_STATE_INTERMEDIATE);
84: } else {
85: DSSetState(ds,DS_STATE_RAW);
86: }
87: if (verbose) {
88: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
89: PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
90: DSView(ds,viewer);
91: }
93: /* Solve */
94: DSGetSlepcSC(ds,&sc);
95: sc->comparison = SlepcCompareLargestReal;
96: sc->comparisonctx = NULL;
97: sc->map = NULL;
98: sc->mapobj = NULL;
99: DSSolve(ds,w,NULL);
100: DSSort(ds,w,NULL,NULL,NULL,NULL);
101: if (extrarow) { DSUpdateExtraRow(ds); }
102: DSSynchronize(ds,w,NULL);
103: if (verbose) {
104: PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");
105: DSView(ds,viewer);
106: }
108: /* Print singular values */
109: PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n");
110: for (i=0;i<n;i++) {
111: sigma = PetscRealPart(w[i]);
112: PetscViewerASCIIPrintf(viewer," %.5f\n",(double)sigma);
113: }
115: if (extrarow) {
116: /* Check that extra row is correct */
117: DSGetArrayReal(ds,DS_MAT_T,&T);
118: DSGetArray(ds,DS_MAT_U,&U);
119: DSGetArray(ds,DS_MAT_V,&V);
120: d = 0.0;
121: for (i=0;i<n;i++) d += T[i+ld]+U[n+i*ld];
122: if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) {
123: PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in A's extra row of %g\n",(double)PetscAbsScalar(d));
124: }
125: d = 0.0;
126: for (i=0;i<n;i++) d += T[i+2*ld]-V[n-1+i*ld];
127: if (PetscAbsScalar(d)>10*PETSC_MACHINE_EPSILON) {
128: PetscPrintf(PETSC_COMM_WORLD,"Warning: there is a mismatch in B's extra row of %g\n",(double)PetscAbsScalar(d));
129: }
130: DSRestoreArrayReal(ds,DS_MAT_T,&T);
131: DSRestoreArray(ds,DS_MAT_U,&U);
132: DSRestoreArray(ds,DS_MAT_V,&V);
133: }
135: /* Singular vectors */
136: DSVectors(ds,DS_MAT_X,NULL,NULL); /* all singular vectors */
137: DSGetMat(ds,DS_MAT_X,&X);
138: MatCreateVecs(X,NULL,&x0);
139: MatGetColumnVector(X,x0,0);
140: VecNorm(x0,NORM_2,&rnorm);
141: MatDestroy(&X);
142: VecDestroy(&x0);
143: PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st X vector = %.3f\n",(double)rnorm);
145: DSGetMat(ds,DS_MAT_U,&X);
146: MatCreateVecs(X,NULL,&x0);
147: MatGetColumnVector(X,x0,0);
148: VecNorm(x0,NORM_2,&rnorm);
149: MatDestroy(&X);
150: VecDestroy(&x0);
151: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) {
152: PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st U vector has norm %g\n",(double)rnorm);
153: }
155: DSGetMat(ds,DS_MAT_V,&X);
156: MatCreateVecs(X,NULL,&x0);
157: MatGetColumnVector(X,x0,0);
158: VecNorm(x0,NORM_2,&rnorm);
159: MatDestroy(&X);
160: VecDestroy(&x0);
161: if (PetscAbs(rnorm-1.0)>10*PETSC_MACHINE_EPSILON) {
162: PetscPrintf(PETSC_COMM_WORLD,"Warning: the 1st V vector has norm %g\n",(double)rnorm);
163: }
165: PetscFree(w);
166: DSDestroy(&ds);
167: SlepcFinalize();
168: return ierr;
169: }
171: /*TEST
173: testset:
174: requires: double
175: output_file: output/test24_1.out
176: test:
177: suffix: 1
178: args: -l 1 -k 4
179: test:
180: suffix: 1_extrarow
181: filter: sed -e "s/extrarow//"
182: args: -l 1 -k 4 -extrarow
184: TEST*/