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 BV bi-orthogonalization functions.\n\n";

 13: #include <slepcbv.h>

 15: int main(int argc,char **argv)
 16: {
 17:   BV             X,Y;
 18:   Mat            M;
 19:   Vec            v,t;
 20:   PetscInt       i,j,n=20,k=7;
 21:   PetscViewer    view;
 22:   PetscBool      verbose;
 23:   PetscReal      norm,condn=1.0;
 24:   PetscScalar    alpha;

 26:   PetscFunctionBeginUser;
 27:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
 28:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 29:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL));
 30:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-condn",&condn,NULL));
 31:   PetscCheck(condn>=1.0,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"The condition number must be > 1");
 32:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
 33:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Test BV bi-orthogonalization with %" PetscInt_FMT " columns of length %" PetscInt_FMT ".\n",k,n));
 34:   if (condn>1.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," - Using random BVs with condition number = %g\n",(double)condn));

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

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

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

 51:   /* Fill X entries */
 52:   if (condn==1.0) {
 53:     for (j=0;j<k;j++) {
 54:       PetscCall(BVGetColumn(X,j,&v));
 55:       PetscCall(VecSet(v,0.0));
 56:       for (i=0;i<=n/2;i++) {
 57:         if (i+j<n) {
 58:           alpha = (3.0*i+j-2)/(2*(i+j+1));
 59: #if defined(PETSC_USE_COMPLEX)
 60:           alpha += (1.2*i+j-2)/(0.1*(i+j+1))*PETSC_i;
 61: #endif
 62:           PetscCall(VecSetValue(v,i+j,alpha,INSERT_VALUES));
 63:         }
 64:       }
 65:       PetscCall(VecAssemblyBegin(v));
 66:       PetscCall(VecAssemblyEnd(v));
 67:       PetscCall(BVRestoreColumn(X,j,&v));
 68:     }
 69:   } else PetscCall(BVSetRandomCond(X,condn));
 70:   if (verbose) PetscCall(BVView(X,view));

 72:   /* Create Y and fill its entries */
 73:   PetscCall(BVDuplicate(X,&Y));
 74:   PetscCall(PetscObjectSetName((PetscObject)Y,"Y"));
 75:   if (condn==1.0) {
 76:     for (j=0;j<k;j++) {
 77:       PetscCall(BVGetColumn(Y,j,&v));
 78:       PetscCall(VecSet(v,0.0));
 79:       for (i=PetscMin(n,2+(2*j)%6);i<PetscMin(n,6+(3*j)%9);i++) {
 80:         if (i%5 && i!=j) {
 81:           alpha = (1.5*i+j)/(2.2*(i-j));
 82:           PetscCall(VecSetValue(v,i+j,alpha,INSERT_VALUES));
 83:         }
 84:       }
 85:       PetscCall(VecAssemblyBegin(v));
 86:       PetscCall(VecAssemblyEnd(v));
 87:       PetscCall(BVRestoreColumn(Y,j,&v));
 88:     }
 89:   } else PetscCall(BVSetRandomCond(Y,condn));
 90:   if (verbose) PetscCall(BVView(Y,view));

 92:   /* Test BVBiorthonormalizeColumn */
 93:   for (j=0;j<k;j++) PetscCall(BVBiorthonormalizeColumn(X,Y,j,NULL));
 94:   if (verbose) {
 95:     PetscCall(BVView(X,view));
 96:     PetscCall(BVView(Y,view));
 97:   }

 99:   /* Check orthogonality */
100:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M));
101:   PetscCall(PetscObjectSetName((PetscObject)M,"M"));
102:   PetscCall(BVDot(X,Y,M));
103:   if (verbose) PetscCall(MatView(M,view));
104:   PetscCall(MatShift(M,-1.0));
105:   PetscCall(MatNorm(M,NORM_1,&norm));
106:   if (norm<200*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of bi-orthogonality < 200*eps\n"));
107:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of bi-orthogonality: %g\n",(double)norm));

109:   PetscCall(MatDestroy(&M));
110:   PetscCall(BVDestroy(&X));
111:   PetscCall(BVDestroy(&Y));
112:   PetscCall(VecDestroy(&t));
113:   PetscCall(SlepcFinalize());
114:   return 0;
115: }

117: /*TEST

119:    testset:
120:       output_file: output/test17_1.out
121:       test:
122:          suffix: 1
123:          args: -bv_type {{vecs contiguous svec mat}} -bv_orthog_type cgs
124:          requires: double
125:       test:
126:          suffix: 1_cuda
127:          args: -bv_type {{svec mat}} -vec_type cuda -bv_orthog_type cgs
128:          requires: cuda
129:       test:
130:          suffix: 2
131:          args: -bv_type {{vecs contiguous svec mat}} -bv_orthog_type mgs
132:       test:
133:          suffix: 2_cuda
134:          args: -bv_type {{svec mat}} -vec_type cuda -bv_orthog_type mgs
135:          requires: cuda

137: TEST*/