Actual source code: test11.c

slepc-3.17.2 2022-08-09
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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: */
 10: /*
 11:    Define the function

 13:         f(x) = (exp(x)-1)/x    (the phi_1 function)

 15:    with the following tree:

 17:             f(x)                  f(x)              (combined by division)
 18:            /    \                 p(x) = x          (polynomial)
 19:         a(x)    p(x)              a(x)              (combined by addition)
 20:        /    \                     e(x) = exp(x)     (exponential)
 21:      e(x)   c(x)                  c(x) = -1         (constant)
 22: */

 24: static char help[] = "Another test of a combined function.\n\n";

 26: #include <slepcfn.h>

 28: /*
 29:    Compute matrix function B = A\(exp(A)-I)
 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;
 36:   Vec            v,f0;
 37:   PetscReal      nrm;

 40:   MatGetSize(A,&n,NULL);
 41:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
 42:   PetscObjectSetName((PetscObject)F,"F");
 43:   /* compute matrix function */
 44:   if (inplace) {
 45:     MatCopy(A,F,SAME_NONZERO_PATTERN);
 46:     MatIsHermitianKnown(A,&set,&flg);
 47:     if (set && flg) MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE);
 48:     FNEvaluateFunctionMat(fn,F,NULL);
 49:   } else FNEvaluateFunctionMat(fn,A,F);
 50:   if (verbose) {
 51:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
 52:     MatView(A,viewer);
 53:     PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");
 54:     MatView(F,viewer);
 55:   }
 56:   /* print matrix norm for checking */
 57:   MatNorm(F,NORM_1,&nrm);
 58:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %6.3f\n",(double)nrm);
 59:   /* check FNEvaluateFunctionMatVec() */
 60:   MatCreateVecs(A,&v,&f0);
 61:   MatGetColumnVector(F,f0,0);
 62:   FNEvaluateFunctionMatVec(fn,A,v);
 63:   VecAXPY(v,-1.0,f0);
 64:   VecNorm(v,NORM_2,&nrm);
 65:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
 66:   MatDestroy(&F);
 67:   VecDestroy(&v);
 68:   VecDestroy(&f0);
 69:   PetscFunctionReturn(0);
 70: }

 72: int main(int argc,char **argv)
 73: {
 74:   FN             f,p,a,e,c,f1,f2;
 75:   FNCombineType  ctype;
 76:   Mat            A;
 77:   PetscInt       i,j,n=10,np;
 78:   PetscScalar    x,y,yp,*As,coeffs[10];
 79:   char           strx[50],str[50];
 80:   PetscViewer    viewer;
 81:   PetscBool      verbose,inplace;

 83:   SlepcInitialize(&argc,&argv,(char*)0,help);
 84:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 85:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 86:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
 87:   PetscPrintf(PETSC_COMM_WORLD,"Phi1 via a combined function, n=%" PetscInt_FMT ".\n",n);

 89:   /* Create function */

 91:   /* e(x) = exp(x) */
 92:   FNCreate(PETSC_COMM_WORLD,&e);
 93:   PetscObjectSetName((PetscObject)e,"e");
 94:   FNSetType(e,FNEXP);
 95:   FNSetFromOptions(e);
 96:   /* c(x) = -1 */
 97:   FNCreate(PETSC_COMM_WORLD,&c);
 98:   PetscObjectSetName((PetscObject)c,"c");
 99:   FNSetType(c,FNRATIONAL);
100:   FNSetFromOptions(c);
101:   np = 1;
102:   coeffs[0] = -1.0;
103:   FNRationalSetNumerator(c,np,coeffs);
104:   /* a(x) */
105:   FNCreate(PETSC_COMM_WORLD,&a);
106:   PetscObjectSetName((PetscObject)a,"a");
107:   FNSetType(a,FNCOMBINE);
108:   FNSetFromOptions(a);
109:   FNCombineSetChildren(a,FN_COMBINE_ADD,e,c);
110:   /* p(x) = x */
111:   FNCreate(PETSC_COMM_WORLD,&p);
112:   PetscObjectSetName((PetscObject)p,"p");
113:   FNSetType(p,FNRATIONAL);
114:   FNSetFromOptions(p);
115:   np = 2;
116:   coeffs[0] = 1.0; coeffs[1] = 0.0;
117:   FNRationalSetNumerator(p,np,coeffs);
118:   /* f(x) */
119:   FNCreate(PETSC_COMM_WORLD,&f);
120:   PetscObjectSetName((PetscObject)f,"f");
121:   FNSetType(f,FNCOMBINE);
122:   FNSetFromOptions(f);
123:   FNCombineSetChildren(f,FN_COMBINE_DIVIDE,a,p);

125:   /* Set up viewer */
126:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
127:   FNCombineGetChildren(f,&ctype,&f1,&f2);
128:   PetscPrintf(PETSC_COMM_WORLD,"Two functions combined with division:\n");
129:   FNView(f1,viewer);
130:   FNView(f2,viewer);
131:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

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

143:   /* Create matrices */
144:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
145:   PetscObjectSetName((PetscObject)A,"A");

147:   /* Fill A with 1-D Laplacian matrix */
148:   MatDenseGetArray(A,&As);
149:   for (i=0;i<n;i++) As[i+i*n]=2.0;
150:   j=1;
151:   for (i=0;i<n-j;i++) { As[i+(i+j)*n]=-1.0; As[(i+j)+i*n]=-1.0; }
152:   MatDenseRestoreArray(A,&As);
153:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
154:   TestMatCombine(f,A,viewer,verbose,inplace);

156:   /* Repeat with same matrix as non-symmetric */
157:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
158:   TestMatCombine(f,A,viewer,verbose,inplace);

160:   MatDestroy(&A);
161:   FNDestroy(&f);
162:   FNDestroy(&p);
163:   FNDestroy(&a);
164:   FNDestroy(&e);
165:   FNDestroy(&c);
166:   SlepcFinalize();
167:   return 0;
168: }

170: /*TEST

172:    test:
173:       suffix: 1
174:       nsize: 1

176:    test:
177:       suffix: 2
178:       nsize: 1
179:       args: -inplace
180:       output_file: output/test11_1.out

182: TEST*/