Actual source code: test6.c

      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: */
     10: /*
     11:    Define the function

     13:         f(x) = (1-x^2) exp(-x/(1+x^2))

     15:    with the following tree:

     17:             f(x)                  f(x)              (combined by product)
     18:            /    \                 g(x) = 1-x^2      (polynomial)
     19:         g(x)    h(x)              h(x)              (combined by composition)
     20:                /    \             r(x) = -x/(1+x^2) (rational)
     21:              r(x)   e(x)          e(x) = exp(x)     (exponential)
     22: */

     24: static char help[] = "Test combined function.\n\n";

     26: #include <slepcfn.h>

     28: /*
     29:    Compute matrix function B = (I-A^2) exp(-(I+A^2)\A)
     30:  */
     31: PetscErrorCode TestMatCombine(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
     32: {
     33:   PetscBool      set,flg;
     34:   PetscInt       n;
     35:   Mat            F,Acopy;
     36:   Vec            v,f0;
     37:   PetscReal      nrm;

     39:   PetscFunctionBeginUser;
     40:   PetscCall(MatGetSize(A,&n,NULL));
     41:   PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&F));
     42:   PetscCall(PetscObjectSetName((PetscObject)F,"F"));
     43:   /* compute matrix function */
     44:   if (inplace) {
     45:     PetscCall(MatCopy(A,F,SAME_NONZERO_PATTERN));
     46:     PetscCall(MatIsHermitianKnown(A,&set,&flg));
     47:     if (set && flg) PetscCall(MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE));
     48:     PetscCall(FNEvaluateFunctionMat(fn,F,NULL));
     49:   } else {
     50:     PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&Acopy));
     51:     PetscCall(FNEvaluateFunctionMat(fn,A,F));
     52:     /* check that A has not been modified */
     53:     PetscCall(MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN));
     54:     PetscCall(MatNorm(Acopy,NORM_1,&nrm));
     55:     if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm));
     56:     PetscCall(MatDestroy(&Acopy));
     57:   }
     58:   if (verbose) {
     59:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n"));
     60:     PetscCall(MatView(A,viewer));
     61:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n"));
     62:     PetscCall(MatView(F,viewer));
     63:   }
     64:   /* print matrix norm for checking */
     65:   PetscCall(MatNorm(F,NORM_1,&nrm));
     66:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %6.3f\n",(double)nrm));
     67:   /* check FNEvaluateFunctionMatVec() */
     68:   PetscCall(MatCreateVecs(A,&v,&f0));
     69:   PetscCall(MatGetColumnVector(F,f0,0));
     70:   PetscCall(FNEvaluateFunctionMatVec(fn,A,v));
     71:   PetscCall(VecAXPY(v,-1.0,f0));
     72:   PetscCall(VecNorm(v,NORM_2,&nrm));
     73:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm));
     74:   PetscCall(MatDestroy(&F));
     75:   PetscCall(VecDestroy(&v));
     76:   PetscCall(VecDestroy(&f0));
     77:   PetscFunctionReturn(PETSC_SUCCESS);
     78: }

     80: int main(int argc,char **argv)
     81: {
     82:   FN             f,g,h,e,r,fcopy;
     83:   Mat            A=NULL;
     84:   PetscInt       i,j,n=10,np,nq;
     85:   PetscScalar    x,y,yp,*As,p[10],q[10];
     86:   char           strx[50],str[50];
     87:   PetscViewer    viewer;
     88:   PetscBool      verbose,inplace,matcuda;

     90:   PetscFunctionBeginUser;
     91:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     92:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     93:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
     94:   PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace));
     95:   PetscCall(PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda));
     96:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Combined function, n=%" PetscInt_FMT ".\n",n));

     98:   /* Create function */

    100:   /* e(x) = exp(x) */
    101:   PetscCall(FNCreate(PETSC_COMM_WORLD,&e));
    102:   PetscCall(FNSetType(e,FNEXP));
    103:   PetscCall(FNSetFromOptions(e));
    104:   /* r(x) = x/(1+x^2) */
    105:   PetscCall(FNCreate(PETSC_COMM_WORLD,&r));
    106:   PetscCall(FNSetType(r,FNRATIONAL));
    107:   PetscCall(FNSetFromOptions(r));
    108:   np = 2; nq = 3;
    109:   p[0] = -1.0; p[1] = 0.0;
    110:   q[0] = 1.0; q[1] = 0.0; q[2] = 1.0;
    111:   PetscCall(FNRationalSetNumerator(r,np,p));
    112:   PetscCall(FNRationalSetDenominator(r,nq,q));
    113:   /* h(x) */
    114:   PetscCall(FNCreate(PETSC_COMM_WORLD,&h));
    115:   PetscCall(FNSetType(h,FNCOMBINE));
    116:   PetscCall(FNSetFromOptions(h));
    117:   PetscCall(FNCombineSetChildren(h,FN_COMBINE_COMPOSE,r,e));
    118:   /* g(x) = 1-x^2 */
    119:   PetscCall(FNCreate(PETSC_COMM_WORLD,&g));
    120:   PetscCall(FNSetType(g,FNRATIONAL));
    121:   PetscCall(FNSetFromOptions(g));
    122:   np = 3;
    123:   p[0] = -1.0; p[1] = 0.0; p[2] = 1.0;
    124:   PetscCall(FNRationalSetNumerator(g,np,p));
    125:   /* f(x) */
    126:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f));
    127:   PetscCall(FNSetType(f,FNCOMBINE));
    128:   PetscCall(FNSetFromOptions(f));
    129:   PetscCall(FNCombineSetChildren(f,FN_COMBINE_MULTIPLY,g,h));

    131:   /* Set up viewer */
    132:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
    133:   PetscCall(FNView(f,viewer));
    134:   if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));

    136:   /* Scalar evaluation */
    137:   x = 2.2;
    138:   PetscCall(SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE));
    139:   PetscCall(FNEvaluateFunction(f,x,&y));
    140:   PetscCall(FNEvaluateDerivative(f,x,&yp));
    141:   PetscCall(SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE));
    142:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str));
    143:   PetscCall(SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE));
    144:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str));

    146:   /* Test duplication */
    147:   PetscCall(FNDuplicate(f,PetscObjectComm((PetscObject)f),&fcopy));

    149:   /* Create matrices */
    150:   if (matcuda) {
    151: #if defined(PETSC_HAVE_CUDA)
    152:     PetscCall(MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A));
    153: #endif
    154:   } else PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A));
    155:   PetscCall(PetscObjectSetName((PetscObject)A,"A"));

    157:   /* Fill A with a symmetric Toeplitz matrix */
    158:   PetscCall(MatDenseGetArray(A,&As));
    159:   for (i=0;i<n;i++) As[i+i*n]=2.0;
    160:   for (j=1;j<3;j++) {
    161:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
    162:   }
    163:   PetscCall(MatDenseRestoreArray(A,&As));
    164:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
    165:   PetscCall(TestMatCombine(fcopy,A,viewer,verbose,inplace));

    167:   /* Repeat with same matrix as non-symmetric */
    168:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE));
    169:   PetscCall(TestMatCombine(fcopy,A,viewer,verbose,inplace));

    171:   PetscCall(MatDestroy(&A));
    172:   PetscCall(FNDestroy(&f));
    173:   PetscCall(FNDestroy(&fcopy));
    174:   PetscCall(FNDestroy(&g));
    175:   PetscCall(FNDestroy(&h));
    176:   PetscCall(FNDestroy(&e));
    177:   PetscCall(FNDestroy(&r));
    178:   PetscCall(SlepcFinalize());
    179:   return 0;
    180: }

    182: /*TEST

    184:    testset:
    185:       output_file: output/test6_1.out
    186:       test:
    187:          suffix: 1
    188:       test:
    189:          suffix: 1_cuda
    190:          args: -matcuda
    191:          requires: cuda
    192:       test:
    193:          suffix: 2
    194:          args: -inplace
    195:       test:
    196:          suffix: 2_cuda
    197:          args: -inplace -matcuda
    198:          requires: cuda

    200: TEST*/