Actual source code: test12.c
slepc-3.18.3 2023-03-24
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 block orthogonalization on a rank-deficient BV.\n\n";
13: #include <slepcbv.h>
15: int main(int argc,char **argv)
16: {
17: BV X,Z;
18: Mat M,R;
19: Vec v,w,t;
20: PetscInt i,j,n=20,k=8;
21: PetscViewer view;
22: PetscBool verbose;
23: PetscReal norm;
24: PetscScalar alpha;
27: SlepcInitialize(&argc,&argv,(char*)0,help);
28: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
29: PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
30: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
31: PetscPrintf(PETSC_COMM_WORLD,"Test BV block orthogonalization (length %" PetscInt_FMT ", k=%" PetscInt_FMT ").\n",n,k);
34: /* Create template vector */
35: VecCreate(PETSC_COMM_WORLD,&t);
36: VecSetSizes(t,PETSC_DECIDE,n);
37: VecSetFromOptions(t);
39: /* Create BV object X */
40: BVCreate(PETSC_COMM_WORLD,&X);
41: PetscObjectSetName((PetscObject)X,"X");
42: BVSetSizesFromVec(X,t,k);
43: BVSetFromOptions(X);
45: /* Set up viewer */
46: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view);
47: if (verbose) PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);
49: /* Fill X entries (first half) */
50: for (j=0;j<k/2;j++) {
51: BVGetColumn(X,j,&v);
52: VecSet(v,0.0);
53: for (i=0;i<=n/2;i++) {
54: if (i+j<n) {
55: alpha = (3.0*i+j-2)/(2*(i+j+1));
56: VecSetValue(v,i+j,alpha,INSERT_VALUES);
57: }
58: }
59: VecAssemblyBegin(v);
60: VecAssemblyEnd(v);
61: BVRestoreColumn(X,j,&v);
62: }
64: /* make middle column linearly dependent wrt columns 0 and 1 */
65: BVCopyColumn(X,0,j);
66: BVGetColumn(X,j,&v);
67: BVGetColumn(X,1,&w);
68: VecAXPY(v,0.5,w);
69: BVRestoreColumn(X,1,&w);
70: BVRestoreColumn(X,j,&v);
71: j++;
73: /* Fill X entries (second half) */
74: for (;j<k-1;j++) {
75: BVGetColumn(X,j,&v);
76: VecSet(v,0.0);
77: for (i=0;i<=n/2;i++) {
78: if (i+j<n) {
79: alpha = (3.0*i+j-2)/(2*(i+j+1));
80: VecSetValue(v,i+j,alpha,INSERT_VALUES);
81: }
82: }
83: VecAssemblyBegin(v);
84: VecAssemblyEnd(v);
85: BVRestoreColumn(X,j,&v);
86: }
88: /* make middle column linearly dependent wrt columns 1 and k/2+1 */
89: BVCopyColumn(X,1,j);
90: BVGetColumn(X,j,&v);
91: BVGetColumn(X,k/2+1,&w);
92: VecAXPY(v,-1.2,w);
93: BVRestoreColumn(X,k/2+1,&w);
94: BVRestoreColumn(X,j,&v);
96: if (verbose) BVView(X,view);
98: /* Create a copy on Z */
99: BVDuplicate(X,&Z);
100: PetscObjectSetName((PetscObject)Z,"Z");
101: BVCopy(X,Z);
103: /* Test BVOrthogonalize */
104: MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R);
105: PetscObjectSetName((PetscObject)R,"R");
106: BVOrthogonalize(X,R);
107: if (verbose) {
108: BVView(X,view);
109: MatView(R,view);
110: }
112: /* Check orthogonality */
113: MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M);
114: MatShift(M,1.0); /* set leading part to identity */
115: BVDot(X,X,M);
116: MatShift(M,-1.0);
117: MatNorm(M,NORM_1,&norm);
118: if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality < 100*eps\n");
119: else PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)norm);
121: /* Check residual */
122: BVMult(Z,-1.0,1.0,X,R);
123: BVNorm(Z,NORM_FROBENIUS,&norm);
124: if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR|| < 100*eps\n");
125: else PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR||: %g\n",(double)norm);
127: MatDestroy(&R);
128: MatDestroy(&M);
129: BVDestroy(&X);
130: BVDestroy(&Z);
131: VecDestroy(&t);
132: SlepcFinalize();
133: return 0;
134: }
136: /*TEST
138: test:
139: suffix: 1
140: nsize: 1
141: args: -bv_orthog_block gs -bv_type {{vecs contiguous svec mat}shared output}
142: output_file: output/test12_1.out
144: TEST*/