Actual source code: test12.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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: {
18: BV X,Z;
19: Mat M,R;
20: Vec v,w,t;
21: PetscInt i,j,n=20,k=8;
22: PetscViewer view;
23: PetscBool verbose;
24: PetscReal norm;
25: PetscScalar alpha;
27: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
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 %D, k=%D).\n",n,k);
32: if (k<6) SETERRQ(PETSC_COMM_WORLD,1,"k must be at least 6");
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) {
48: PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);
49: }
51: /* Fill X entries (first half) */
52: for (j=0;j<k/2;j++) {
53: BVGetColumn(X,j,&v);
54: VecSet(v,0.0);
55: for (i=0;i<=n/2;i++) {
56: if (i+j<n) {
57: alpha = (3.0*i+j-2)/(2*(i+j+1));
58: VecSetValue(v,i+j,alpha,INSERT_VALUES);
59: }
60: }
61: VecAssemblyBegin(v);
62: VecAssemblyEnd(v);
63: BVRestoreColumn(X,j,&v);
64: }
66: /* make middle column linearly dependent wrt columns 0 and 1 */
67: BVCopyColumn(X,0,j);
68: BVGetColumn(X,j,&v);
69: BVGetColumn(X,1,&w);
70: VecAXPY(v,0.5,w);
71: BVRestoreColumn(X,1,&w);
72: BVRestoreColumn(X,j,&v);
73: j++;
75: /* Fill X entries (second half) */
76: for (;j<k-1;j++) {
77: BVGetColumn(X,j,&v);
78: VecSet(v,0.0);
79: for (i=0;i<=n/2;i++) {
80: if (i+j<n) {
81: alpha = (3.0*i+j-2)/(2*(i+j+1));
82: VecSetValue(v,i+j,alpha,INSERT_VALUES);
83: }
84: }
85: VecAssemblyBegin(v);
86: VecAssemblyEnd(v);
87: BVRestoreColumn(X,j,&v);
88: }
90: /* make middle column linearly dependent wrt columns 1 and k/2+1 */
91: BVCopyColumn(X,1,j);
92: BVGetColumn(X,j,&v);
93: BVGetColumn(X,k/2+1,&w);
94: VecAXPY(v,-1.2,w);
95: BVRestoreColumn(X,k/2+1,&w);
96: BVRestoreColumn(X,j,&v);
98: if (verbose) {
99: BVView(X,view);
100: }
102: /* Create a copy on Z */
103: BVDuplicate(X,&Z);
104: PetscObjectSetName((PetscObject)Z,"Z");
105: BVCopy(X,Z);
107: /* Test BVOrthogonalize */
108: MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R);
109: PetscObjectSetName((PetscObject)R,"R");
110: BVOrthogonalize(X,R);
111: if (verbose) {
112: BVView(X,view);
113: MatView(R,view);
114: }
116: /* Check orthogonality */
117: MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M);
118: MatShift(M,1.0); /* set leading part to identity */
119: BVDot(X,X,M);
120: MatShift(M,-1.0);
121: MatNorm(M,NORM_1,&norm);
122: if (norm<100*PETSC_MACHINE_EPSILON) {
123: PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality < 100*eps\n");
124: } else {
125: PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)norm);
126: }
128: /* Check residual */
129: BVMult(Z,-1.0,1.0,X,R);
130: BVNorm(Z,NORM_FROBENIUS,&norm);
131: if (norm<100*PETSC_MACHINE_EPSILON) {
132: PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR|| < 100*eps\n");
133: } else {
134: PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR||: %g\n",(double)norm);
135: }
137: MatDestroy(&R);
138: MatDestroy(&M);
139: BVDestroy(&X);
140: BVDestroy(&Z);
141: VecDestroy(&t);
142: SlepcFinalize();
143: return ierr;
144: }
146: /*TEST
148: test:
149: suffix: 1
150: nsize: 1
151: args: -bv_orthog_block gs -bv_type {{vecs contiguous svec mat}shared output}
152: output_file: output/test12_1.out
154: TEST*/