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:   PetscFunctionBeginUser;
 27:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
 28:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 29:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL));
 30:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
 31:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Test BV block orthogonalization (length %" PetscInt_FMT ", k=%" PetscInt_FMT ").\n",n,k));
 32:   PetscCheck(k>5,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"k must be at least 6");

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

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

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

 49:   /* Fill X entries (first half) */
 50:   for (j=0;j<k/2;j++) {
 51:     PetscCall(BVGetColumn(X,j,&v));
 52:     PetscCall(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:         PetscCall(VecSetValue(v,i+j,alpha,INSERT_VALUES));
 57:       }
 58:     }
 59:     PetscCall(VecAssemblyBegin(v));
 60:     PetscCall(VecAssemblyEnd(v));
 61:     PetscCall(BVRestoreColumn(X,j,&v));
 62:   }

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

 73:   /* Fill X entries (second half) */
 74:   for (;j<k-1;j++) {
 75:     PetscCall(BVGetColumn(X,j,&v));
 76:     PetscCall(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:         PetscCall(VecSetValue(v,i+j,alpha,INSERT_VALUES));
 81:       }
 82:     }
 83:     PetscCall(VecAssemblyBegin(v));
 84:     PetscCall(VecAssemblyEnd(v));
 85:     PetscCall(BVRestoreColumn(X,j,&v));
 86:   }

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

 96:   if (verbose) PetscCall(BVView(X,view));

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

103:   /* Test BVOrthogonalize */
104:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&R));
105:   PetscCall(PetscObjectSetName((PetscObject)R,"R"));
106:   PetscCall(BVOrthogonalize(X,R));
107:   if (verbose) {
108:     PetscCall(BVView(X,view));
109:     PetscCall(MatView(R,view));
110:   }

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

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

127:   PetscCall(MatDestroy(&R));
128:   PetscCall(MatDestroy(&M));
129:   PetscCall(BVDestroy(&X));
130:   PetscCall(BVDestroy(&Z));
131:   PetscCall(VecDestroy(&t));
132:   PetscCall(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*/