Actual source code: test12.c

slepc-3.7.1 2016-05-27
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.

  8:    SLEPc is free software: you can redistribute it and/or modify it under  the
  9:    terms of version 3 of the GNU Lesser General Public License as published by
 10:    the Free Software Foundation.

 12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 15:    more details.

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */

 22: static char help[] = "Test block orthogonalization on a rank-deficient BV.\n\n";

 24: #include <slepcbv.h>

 28: int main(int argc,char **argv)
 29: {
 31:   BV             X,Z;
 32:   Mat            M,R;
 33:   Vec            v,w,t;
 34:   PetscInt       i,j,n=20,k=8;
 35:   PetscViewer    view;
 36:   PetscBool      verbose;
 37:   PetscReal      norm;
 38:   PetscScalar    alpha;

 40:   SlepcInitialize(&argc,&argv,(char*)0,help);
 41:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 42:   PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
 43:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 44:   PetscPrintf(PETSC_COMM_WORLD,"Test BV block orthogonalization (length %D, k=%D).\n",n,k);
 45:   if (k<6) SETERRQ(PETSC_COMM_SELF,1,"k must be at least 6");

 47:   /* Create template vector */
 48:   VecCreate(PETSC_COMM_WORLD,&t);
 49:   VecSetSizes(t,PETSC_DECIDE,n);
 50:   VecSetFromOptions(t);

 52:   /* Create BV object X */
 53:   BVCreate(PETSC_COMM_WORLD,&X);
 54:   PetscObjectSetName((PetscObject)X,"X");
 55:   BVSetSizesFromVec(X,t,k);
 56:   BVSetFromOptions(X);

 58:   /* Set up viewer */
 59:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view);
 60:   if (verbose) {
 61:     PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);
 62:   }

 64:   /* Fill X entries (first half) */
 65:   for (j=0;j<k/2;j++) {
 66:     BVGetColumn(X,j,&v);
 67:     VecSet(v,0.0);
 68:     for (i=0;i<=n/2;i++) {
 69:       if (i+j<n) {
 70:         alpha = (3.0*i+j-2)/(2*(i+j+1));
 71:         VecSetValue(v,i+j,alpha,INSERT_VALUES);
 72:       }
 73:     }
 74:     VecAssemblyBegin(v);
 75:     VecAssemblyEnd(v);
 76:     BVRestoreColumn(X,j,&v);
 77:   }

 79:   /* make middle column linearly dependent wrt columns 0 and 1 */
 80:   BVCopyColumn(X,0,j);
 81:   BVGetColumn(X,j,&v);
 82:   BVGetColumn(X,1,&w);
 83:   VecAXPY(v,0.5,w);
 84:   BVRestoreColumn(X,1,&w);
 85:   BVRestoreColumn(X,j,&v);
 86:   j++;

 88:   /* Fill X entries (second half) */
 89:   for (;j<k-1;j++) {
 90:     BVGetColumn(X,j,&v);
 91:     VecSet(v,0.0);
 92:     for (i=0;i<=n/2;i++) {
 93:       if (i+j<n) {
 94:         alpha = (3.0*i+j-2)/(2*(i+j+1));
 95:         VecSetValue(v,i+j,alpha,INSERT_VALUES);
 96:       }
 97:     }
 98:     VecAssemblyBegin(v);
 99:     VecAssemblyEnd(v);
100:     BVRestoreColumn(X,j,&v);
101:   }

103:   /* make middle column linearly dependent wrt columns 1 and k/2+1 */
104:   BVCopyColumn(X,1,j);
105:   BVGetColumn(X,j,&v);
106:   BVGetColumn(X,k/2+1,&w);
107:   VecAXPY(v,-1.2,w);
108:   BVRestoreColumn(X,k/2+1,&w);
109:   BVRestoreColumn(X,j,&v);

111:   if (verbose) {
112:     BVView(X,view);
113:   }

115:   /* Create a copy on Z */
116:   BVDuplicate(X,&Z);
117:   PetscObjectSetName((PetscObject)Z,"Z");
118:   BVCopy(X,Z);

120:   /* Test BVOrthogonalize */
121:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R);
122:   PetscObjectSetName((PetscObject)R,"R");
123:   BVOrthogonalize(X,R);
124:   if (verbose) {
125:     BVView(X,view);
126:     MatView(R,view);
127:   }

129:   /* Check orthogonality */
130:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M);
131:   MatShift(M,1.0);   /* set leading part to identity */
132:   BVDot(X,X,M);
133:   MatShift(M,-1.0);
134:   MatNorm(M,NORM_1,&norm);
135:   if (norm<100*PETSC_MACHINE_EPSILON) {
136:     PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality < 100*eps\n");
137:   } else {
138:     PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)norm);
139:   }

141:   /* Check residual */
142:   BVMult(Z,-1.0,1.0,X,R);
143:   BVNorm(Z,NORM_FROBENIUS,&norm);
144:   if (norm<100*PETSC_MACHINE_EPSILON) {
145:     PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR|| < 100*eps\n");
146:   } else {
147:     PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR||: %g\n",(double)norm);
148:   }

150:   MatDestroy(&R);
151:   MatDestroy(&M);
152:   BVDestroy(&X);
153:   BVDestroy(&Z);
154:   VecDestroy(&t);
155:   SlepcFinalize();
156:   return ierr;
157: }