Date: 2017-05-17T08:25:25+00:00

Actual source code: test12.c
slepc-3.7.4 2017-05-17
Report Typos and Errors

      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: }