Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
6 : This file is part of SLEPc.
7 : SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 : */
10 :
11 : static char help[] = "Test DSGSVD with compact storage.\n\n";
12 :
13 : #include <slepcds.h>
14 :
15 3 : int main(int argc,char **argv)
16 : {
17 3 : DS ds;
18 3 : Mat X;
19 3 : Vec x0;
20 3 : SlepcSC sc;
21 3 : PetscReal *T,*D,sigma,rnorm,aux,cond;
22 3 : PetscScalar *U,*V,*w,d;
23 3 : PetscInt i,n=10,l=0,k=0,ld;
24 3 : PetscViewer viewer;
25 3 : PetscBool verbose,test_dsview,extrarow;
26 :
27 3 : PetscFunctionBeginUser;
28 3 : PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
29 3 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
30 3 : 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 3 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-l",&l,NULL));
32 3 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL));
33 3 : PetscCheck(l<=n && k<=n && l<=k,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"Wrong value of dimensions");
34 3 : PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
35 3 : PetscCall(PetscOptionsHasName(NULL,NULL,"-test_dsview",&test_dsview));
36 3 : PetscCall(PetscOptionsHasName(NULL,NULL,"-extrarow",&extrarow));
37 :
38 : /* Create DS object */
39 3 : PetscCall(DSCreate(PETSC_COMM_WORLD,&ds));
40 3 : PetscCall(DSSetType(ds,DSGSVD));
41 3 : PetscCall(DSSetFromOptions(ds));
42 3 : ld = n+2; /* test leading dimension larger than n */
43 3 : PetscCall(DSAllocate(ds,ld));
44 3 : PetscCall(DSSetDimensions(ds,n,l,k));
45 3 : PetscCall(DSGSVDSetDimensions(ds,n,PETSC_DECIDE));
46 3 : PetscCall(DSSetCompact(ds,PETSC_TRUE));
47 3 : PetscCall(DSSetExtraRow(ds,extrarow));
48 :
49 : /* Set up viewer */
50 3 : PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
51 3 : PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
52 3 : PetscCall(DSView(ds,viewer));
53 3 : PetscCall(PetscViewerPopFormat(viewer));
54 :
55 3 : if (test_dsview) {
56 : /* Fill A and B with dummy values to test DSView */
57 1 : PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
58 1 : PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
59 11 : for (i=0;i<n;i++) { T[i] = i+1; D[i] = -i-1; }
60 10 : for (i=0;i<n-1;i++) { T[i+ld] = -1.0; T[i+2*ld] = 1.0; }
61 1 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
62 1 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
63 1 : PetscCall(DSView(ds,viewer));
64 : }
65 :
66 : /* Fill A and B with upper arrow-bidiagonal matrices
67 : verifying that [A;B] has orthonormal columns */
68 3 : PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
69 3 : PetscCall(DSGetArrayReal(ds,DS_MAT_D,&D));
70 33 : for (i=0;i<n;i++) T[i] = (PetscReal)(i+1)/(n+1); /* diagonal of matrix A */
71 11 : for (i=0;i<k;i++) D[i] = PetscSqrtReal(1.0-T[i]*T[i]);
72 9 : for (i=l;i<k;i++) {
73 6 : 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 6 : T[i+2*ld] = -T[i+ld]*T[i]/D[i]; /* upper diagonal of matrix B */
75 : }
76 3 : aux = 1.0-T[k]*T[k];
77 9 : for (i=l;i<k;i++) aux -= T[i+ld]*T[i+ld]+T[i+2*ld]*T[i+2*ld];
78 3 : D[k] = PetscSqrtReal(aux);
79 22 : for (i=k;i<n-1;i++) {
80 19 : 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 19 : T[i+2*ld] = -T[i+ld]*T[i]/D[i]; /* upper diagonal of matrix B */
82 19 : 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 3 : if (extrarow) { T[n-1+ld]=-1.0; T[n-1+2*ld]=1.0; }
85 : /* Fill locked eigenvalues */
86 3 : PetscCall(PetscMalloc1(n,&w));
87 5 : for (i=0;i<l;i++) w[i] = T[i]/D[i];
88 3 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
89 3 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_D,&D));
90 3 : if (l==0 && k==0) PetscCall(DSSetState(ds,DS_STATE_INTERMEDIATE));
91 2 : else PetscCall(DSSetState(ds,DS_STATE_RAW));
92 3 : if (verbose) {
93 0 : PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));
94 0 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n"));
95 0 : PetscCall(DSView(ds,viewer));
96 : }
97 :
98 : /* Condition number */
99 3 : PetscCall(DSCond(ds,&cond));
100 3 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Condition number = %.3f\n",(double)cond));
101 :
102 : /* Solve */
103 3 : PetscCall(DSGetSlepcSC(ds,&sc));
104 3 : sc->comparison = SlepcCompareLargestReal;
105 3 : sc->comparisonctx = NULL;
106 3 : sc->map = NULL;
107 3 : sc->mapobj = NULL;
108 3 : PetscCall(DSSolve(ds,w,NULL));
109 3 : PetscCall(DSSort(ds,w,NULL,NULL,NULL,NULL));
110 3 : if (extrarow) PetscCall(DSUpdateExtraRow(ds));
111 3 : PetscCall(DSSynchronize(ds,w,NULL));
112 3 : if (verbose) {
113 0 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n"));
114 0 : PetscCall(DSView(ds,viewer));
115 : }
116 :
117 : /* Print singular values */
118 3 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed singular values =\n"));
119 33 : for (i=0;i<n;i++) {
120 30 : sigma = PetscRealPart(w[i]);
121 30 : PetscCall(PetscViewerASCIIPrintf(viewer," %.5f\n",(double)sigma));
122 : }
123 :
124 3 : if (extrarow) {
125 : /* Check that extra row is correct */
126 1 : PetscCall(DSGetArrayReal(ds,DS_MAT_T,&T));
127 1 : PetscCall(DSGetArray(ds,DS_MAT_U,&U));
128 1 : PetscCall(DSGetArray(ds,DS_MAT_V,&V));
129 : d = 0.0;
130 11 : for (i=0;i<n;i++) d += T[i+ld]+U[n-1+i*ld];
131 1 : 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 1 : d = 0.0;
133 11 : for (i=0;i<n;i++) d += T[i+2*ld]-V[n-1+i*ld];
134 1 : 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 1 : PetscCall(DSRestoreArrayReal(ds,DS_MAT_T,&T));
136 1 : PetscCall(DSRestoreArray(ds,DS_MAT_U,&U));
137 1 : PetscCall(DSRestoreArray(ds,DS_MAT_V,&V));
138 : }
139 :
140 : /* Singular vectors */
141 3 : PetscCall(DSVectors(ds,DS_MAT_X,NULL,NULL)); /* all singular vectors */
142 3 : PetscCall(DSGetMat(ds,DS_MAT_X,&X));
143 3 : PetscCall(MatCreateVecs(X,NULL,&x0));
144 3 : PetscCall(MatGetColumnVector(X,x0,0));
145 3 : PetscCall(VecNorm(x0,NORM_2,&rnorm));
146 3 : PetscCall(DSRestoreMat(ds,DS_MAT_X,&X));
147 3 : PetscCall(VecDestroy(&x0));
148 3 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st X vector = %.3f\n",(double)rnorm));
149 :
150 3 : PetscCall(DSGetMat(ds,DS_MAT_U,&X));
151 3 : PetscCall(MatCreateVecs(X,NULL,&x0));
152 3 : PetscCall(MatGetColumnVector(X,x0,0));
153 3 : PetscCall(VecNorm(x0,NORM_2,&rnorm));
154 3 : PetscCall(DSRestoreMat(ds,DS_MAT_U,&X));
155 3 : PetscCall(VecDestroy(&x0));
156 3 : 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));
157 :
158 3 : PetscCall(DSGetMat(ds,DS_MAT_V,&X));
159 3 : PetscCall(MatCreateVecs(X,NULL,&x0));
160 3 : PetscCall(MatGetColumnVector(X,x0,0));
161 3 : PetscCall(VecNorm(x0,NORM_2,&rnorm));
162 3 : PetscCall(DSRestoreMat(ds,DS_MAT_V,&X));
163 3 : PetscCall(VecDestroy(&x0));
164 3 : 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));
165 :
166 3 : PetscCall(PetscFree(w));
167 3 : PetscCall(DSDestroy(&ds));
168 3 : PetscCall(SlepcFinalize());
169 : return 0;
170 : }
171 :
172 : /*TEST
173 :
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
187 :
188 : TEST*/
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