Actual source code: test12.c

slepc-3.17.1 2022-04-11
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  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;

 26:   SlepcInitialize(&argc,&argv,(char*)0,help);
 27:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 28:   PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);
 29:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 30:   PetscPrintf(PETSC_COMM_WORLD,"Test BV block orthogonalization (length %" PetscInt_FMT ", k=%" PetscInt_FMT ").\n",n,k);

 33:   /* Create template vector */
 34:   VecCreate(PETSC_COMM_WORLD,&t);
 35:   VecSetSizes(t,PETSC_DECIDE,n);
 36:   VecSetFromOptions(t);

 38:   /* Create BV object X */
 39:   BVCreate(PETSC_COMM_WORLD,&X);
 40:   PetscObjectSetName((PetscObject)X,"X");
 41:   BVSetSizesFromVec(X,t,k);
 42:   BVSetFromOptions(X);

 44:   /* Set up viewer */
 45:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view);
 46:   if (verbose) PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);

 48:   /* Fill X entries (first half) */
 49:   for (j=0;j<k/2;j++) {
 50:     BVGetColumn(X,j,&v);
 51:     VecSet(v,0.0);
 52:     for (i=0;i<=n/2;i++) {
 53:       if (i+j<n) {
 54:         alpha = (3.0*i+j-2)/(2*(i+j+1));
 55:         VecSetValue(v,i+j,alpha,INSERT_VALUES);
 56:       }
 57:     }
 58:     VecAssemblyBegin(v);
 59:     VecAssemblyEnd(v);
 60:     BVRestoreColumn(X,j,&v);
 61:   }

 63:   /* make middle column linearly dependent wrt columns 0 and 1 */
 64:   BVCopyColumn(X,0,j);
 65:   BVGetColumn(X,j,&v);
 66:   BVGetColumn(X,1,&w);
 67:   VecAXPY(v,0.5,w);
 68:   BVRestoreColumn(X,1,&w);
 69:   BVRestoreColumn(X,j,&v);
 70:   j++;

 72:   /* Fill X entries (second half) */
 73:   for (;j<k-1;j++) {
 74:     BVGetColumn(X,j,&v);
 75:     VecSet(v,0.0);
 76:     for (i=0;i<=n/2;i++) {
 77:       if (i+j<n) {
 78:         alpha = (3.0*i+j-2)/(2*(i+j+1));
 79:         VecSetValue(v,i+j,alpha,INSERT_VALUES);
 80:       }
 81:     }
 82:     VecAssemblyBegin(v);
 83:     VecAssemblyEnd(v);
 84:     BVRestoreColumn(X,j,&v);
 85:   }

 87:   /* make middle column linearly dependent wrt columns 1 and k/2+1 */
 88:   BVCopyColumn(X,1,j);
 89:   BVGetColumn(X,j,&v);
 90:   BVGetColumn(X,k/2+1,&w);
 91:   VecAXPY(v,-1.2,w);
 92:   BVRestoreColumn(X,k/2+1,&w);
 93:   BVRestoreColumn(X,j,&v);

 95:   if (verbose) BVView(X,view);

 97:   /* Create a copy on Z */
 98:   BVDuplicate(X,&Z);
 99:   PetscObjectSetName((PetscObject)Z,"Z");
100:   BVCopy(X,Z);

102:   /* Test BVOrthogonalize */
103:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R);
104:   PetscObjectSetName((PetscObject)R,"R");
105:   BVOrthogonalize(X,R);
106:   if (verbose) {
107:     BVView(X,view);
108:     MatView(R,view);
109:   }

111:   /* Check orthogonality */
112:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M);
113:   MatShift(M,1.0);   /* set leading part to identity */
114:   BVDot(X,X,M);
115:   MatShift(M,-1.0);
116:   MatNorm(M,NORM_1,&norm);
117:   if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality < 100*eps\n");
118:   else PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)norm);

120:   /* Check residual */
121:   BVMult(Z,-1.0,1.0,X,R);
122:   BVNorm(Z,NORM_FROBENIUS,&norm);
123:   if (norm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR|| < 100*eps\n");
124:   else PetscPrintf(PETSC_COMM_WORLD,"Residual ||X-QR||: %g\n",(double)norm);

126:   MatDestroy(&R);
127:   MatDestroy(&M);
128:   BVDestroy(&X);
129:   BVDestroy(&Z);
130:   VecDestroy(&t);
131:   SlepcFinalize();
132:   return 0;
133: }

135: /*TEST

137:    test:
138:       suffix: 1
139:       nsize: 1
140:       args: -bv_orthog_block gs -bv_type {{vecs contiguous svec mat}shared output}
141:       output_file: output/test12_1.out

143: TEST*/