Date: 2022-03-31T15:28:48+00:00

Actual source code: test10.c
slepc-3.17.0 2022-03-31
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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 Phi functions.\n\n";

     13: #include <slepcfn.h>

     15: /*
     16:    Evaluates phi_k function on a scalar and on a matrix
     17:  */
     18: PetscErrorCode TestPhiFunction(FN fn,PetscScalar x,Mat A,PetscBool verbose)
     19: {
     20:   PetscScalar    y,yp;
     21:   char           strx[50],str[50];
     22:   Vec            v,f;
     23:   PetscReal      nrm;

     26:   PetscPrintf(PETSC_COMM_WORLD,"\n");
     27:   FNView(fn,NULL);
     28:   SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
     29:   FNEvaluateFunction(fn,x,&y);
     30:   FNEvaluateDerivative(fn,x,&yp);
     31:   SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
     32:   PetscPrintf(PETSC_COMM_WORLD,"\nf(%s)=%s\n",strx,str);
     33:   SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
     34:   PetscPrintf(PETSC_COMM_WORLD,"f'(%s)=%s\n",strx,str);
     35:   /* compute phi_k(A)*e_1 */
     36:   MatCreateVecs(A,&v,&f);
     37:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
     38:   FNEvaluateFunctionMatVec(fn,A,f);  /* reference result by diagonalization */
     39:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
     40:   FNEvaluateFunctionMatVec(fn,A,v);
     41:   VecAXPY(v,-1.0,f);
     42:   VecNorm(v,NORM_2,&nrm);
     43:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-ref is %g\n",(double)nrm);
     44:   if (verbose) {
     45:     PetscPrintf(PETSC_COMM_WORLD,"f(A)*e_1 =\n");
     46:     VecView(v,NULL);
     47:   }
     48:   VecDestroy(&v);
     49:   VecDestroy(&f);
     50:   PetscFunctionReturn(0);
     51: }

     53: int main(int argc,char **argv)
     54: {
     55:   FN             phi0,phi1,phik,phicopy;
     56:   Mat            A;
     57:   PetscInt       i,j,n=8,k;
     58:   PetscScalar    tau,eta,*As;
     59:   PetscBool      verbose;

     61:   SlepcInitialize(&argc,&argv,(char*)0,help);
     62:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     63:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
     64:   PetscPrintf(PETSC_COMM_WORLD,"Test Phi functions, n=%" PetscInt_FMT ".\n",n);

     66:   /* Create matrix, fill it with 1-D Laplacian */
     67:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
     68:   PetscObjectSetName((PetscObject)A,"A");
     69:   MatDenseGetArray(A,&As);
     70:   for (i=0;i<n;i++) As[i+i*n]=2.0;
     71:   j=1;
     72:   for (i=0;i<n-j;i++) { As[i+(i+j)*n]=-1.0; As[(i+j)+i*n]=-1.0; }
     73:   MatDenseRestoreArray(A,&As);

     75:   /* phi_0(x) = exp(x) */
     76:   FNCreate(PETSC_COMM_WORLD,&phi0);
     77:   FNSetType(phi0,FNPHI);
     78:   FNPhiSetIndex(phi0,0);
     79:   TestPhiFunction(phi0,2.2,A,verbose);

     81:   /* phi_1(x) = (exp(x)-1)/x with scaling factors eta*phi_1(tau*x) */
     82:   FNCreate(PETSC_COMM_WORLD,&phi1);
     83:   FNSetType(phi1,FNPHI);  /* default index should be 1 */
     84:   tau = 0.2;
     85:   eta = 1.3;
     86:   FNSetScale(phi1,tau,eta);
     87:   TestPhiFunction(phi1,2.2,A,verbose);

     89:   /* phi_k(x) with index set from command-line arguments */
     90:   FNCreate(PETSC_COMM_WORLD,&phik);
     91:   FNSetType(phik,FNPHI);
     92:   FNSetFromOptions(phik);

     94:   FNDuplicate(phik,PETSC_COMM_WORLD,&phicopy);
     95:   FNPhiGetIndex(phicopy,&k);
     96:   PetscPrintf(PETSC_COMM_WORLD,"Index of phi function is %" PetscInt_FMT "\n",k);
     97:   TestPhiFunction(phicopy,2.2,A,verbose);

     99:   FNDestroy(&phi0);
    100:   FNDestroy(&phi1);
    101:   FNDestroy(&phik);
    102:   FNDestroy(&phicopy);
    103:   MatDestroy(&A);
    104:   SlepcFinalize();
    105:   return 0;
    106: }

    108: /*TEST

    110:    test:
    111:       suffix: 1
    112:       nsize: 1
    113:       args: -fn_phi_index 3

    115: TEST*/