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 matrix logarithm.\n\n";

 13: #include <slepcfn.h>

 15: /*
 16:    Compute matrix logarithm B = logm(A)
 17:  */
 18: PetscErrorCode TestMatLog(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
 19: {
 20:   PetscBool      set,flg;
 21:   PetscScalar    tau,eta;
 22:   PetscInt       n;
 23:   Mat            F,R;
 24:   Vec            v,f0;
 25:   FN             fnexp;
 26:   PetscReal      nrm;

 28:   PetscFunctionBeginUser;
 29:   PetscCall(MatGetSize(A,&n,NULL));
 30:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F));
 31:   PetscCall(PetscObjectSetName((PetscObject)F,"F"));
 32:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&R));
 33:   PetscCall(PetscObjectSetName((PetscObject)R,"R"));
 34:   PetscCall(FNGetScale(fn,&tau,&eta));
 35:   /* compute matrix logarithm */
 36:   if (inplace) {
 37:     PetscCall(MatCopy(A,F,SAME_NONZERO_PATTERN));
 38:     PetscCall(MatIsHermitianKnown(A,&set,&flg));
 39:     if (set && flg) PetscCall(MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE));
 40:     PetscCall(FNEvaluateFunctionMat(fn,F,NULL));
 41:   } else PetscCall(FNEvaluateFunctionMat(fn,A,F));
 42:   if (verbose) {
 43:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n"));
 44:     PetscCall(MatView(A,viewer));
 45:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed logm(A) - - - - - - -\n"));
 46:     PetscCall(MatView(F,viewer));
 47:   }
 48:   /* check error ||expm(F)-A||_F */
 49:   PetscCall(FNCreate(PETSC_COMM_WORLD,&fnexp));
 50:   PetscCall(FNSetType(fnexp,FNEXP));
 51:   PetscCall(MatCopy(F,R,SAME_NONZERO_PATTERN));
 52:   if (eta!=1.0) PetscCall(MatScale(R,1.0/eta));
 53:   PetscCall(FNEvaluateFunctionMat(fnexp,R,NULL));
 54:   PetscCall(FNDestroy(&fnexp));
 55:   PetscCall(MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN));
 56:   PetscCall(MatNorm(R,NORM_FROBENIUS,&nrm));
 57:   if (nrm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F < 100*eps\n"));
 58:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F = %g\n",(double)nrm));
 59:   /* check FNEvaluateFunctionMatVec() */
 60:   PetscCall(MatCreateVecs(A,&v,&f0));
 61:   PetscCall(MatGetColumnVector(F,f0,0));
 62:   PetscCall(FNEvaluateFunctionMatVec(fn,A,v));
 63:   PetscCall(VecAXPY(v,-1.0,f0));
 64:   PetscCall(VecNorm(v,NORM_2,&nrm));
 65:   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));
 66:   PetscCall(MatDestroy(&F));
 67:   PetscCall(MatDestroy(&R));
 68:   PetscCall(VecDestroy(&v));
 69:   PetscCall(VecDestroy(&f0));
 70:   PetscFunctionReturn(PETSC_SUCCESS);
 71: }

 73: int main(int argc,char **argv)
 74: {
 75:   FN             fn;
 76:   Mat            A;
 77:   PetscInt       i,j,n=10;
 78:   PetscScalar    *As;
 79:   PetscViewer    viewer;
 80:   PetscBool      verbose,inplace,random,triang;

 82:   PetscFunctionBeginUser;
 83:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
 84:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 85:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
 86:   PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace));
 87:   PetscCall(PetscOptionsHasName(NULL,NULL,"-random",&random));
 88:   PetscCall(PetscOptionsHasName(NULL,NULL,"-triang",&triang));
 89:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix logarithm, n=%" PetscInt_FMT ".\n",n));

 91:   /* Create logarithm function object */
 92:   PetscCall(FNCreate(PETSC_COMM_WORLD,&fn));
 93:   PetscCall(FNSetType(fn,FNLOG));
 94:   PetscCall(FNSetFromOptions(fn));

 96:   /* Set up viewer */
 97:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
 98:   PetscCall(FNView(fn,viewer));
 99:   if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));

101:   /* Create matrices */
102:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A));
103:   PetscCall(PetscObjectSetName((PetscObject)A,"A"));

105:   if (random) PetscCall(MatSetRandom(A,NULL));
106:   else {
107:     /* Fill A with a non-symmetric Toeplitz matrix */
108:     PetscCall(MatDenseGetArray(A,&As));
109:     for (i=0;i<n;i++) As[i+i*n]=2.0;
110:     for (j=1;j<3;j++) {
111:       for (i=0;i<n-j;i++) {
112:         As[i+(i+j)*n]=1.0;
113:         if (!triang) As[(i+j)+i*n]=-1.0;
114:       }
115:     }
116:     As[(n-1)*n] = -5.0;
117:     As[0] = 2.01;
118:     PetscCall(MatDenseRestoreArray(A,&As));
119:   }
120:   PetscCall(TestMatLog(fn,A,viewer,verbose,inplace));

122:   PetscCall(MatDestroy(&A));
123:   PetscCall(FNDestroy(&fn));
124:   PetscCall(SlepcFinalize());
125:   return 0;
126: }

128: /*TEST

130:    testset:
131:       filter: grep -v "computing matrix functions"
132:       output_file: output/test13_1.out
133:       test:
134:          suffix: 1
135:          args: -fn_scale .04,2 -n 75
136:          requires: c99_complex !__float128
137:       test:
138:          suffix: 1_triang
139:          args: -fn_scale .04,2 -n 75 -triang
140:          requires: c99_complex !__float128
141:       test:
142:          suffix: 1_random
143:          args: -fn_scale .02,2 -n 75 -random
144:          requires: complex !__float128
145:          filter_output: sed -e 's/04/02/'

147: TEST*/