Actual source code: test11.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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: {
 34:   PetscBool      set,flg;
 35:   PetscInt       n;
 36:   Mat            F;
 37:   Vec            v,f0;
 38:   PetscReal      nrm;

 41:   MatGetSize(A,&n,NULL);
 42:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
 43:   PetscObjectSetName((PetscObject)F,"F");
 44:   /* compute matrix function */
 45:   if (inplace) {
 46:     MatCopy(A,F,SAME_NONZERO_PATTERN);
 47:     MatIsHermitianKnown(A,&set,&flg);
 48:     if (set && flg) { MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE); }
 49:     FNEvaluateFunctionMat(fn,F,NULL);
 50:   } else {
 51:     FNEvaluateFunctionMat(fn,A,F);
 52:   }
 53:   if (verbose) {
 54:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
 55:     MatView(A,viewer);
 56:     PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");
 57:     MatView(F,viewer);
 58:   }
 59:   /* print matrix norm for checking */
 60:   MatNorm(F,NORM_1,&nrm);
 61:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %6.3f\n",(double)nrm);
 62:   /* check FNEvaluateFunctionMatVec() */
 63:   MatCreateVecs(A,&v,&f0);
 64:   MatGetColumnVector(F,f0,0);
 65:   FNEvaluateFunctionMatVec(fn,A,v);
 66:   VecAXPY(v,-1.0,f0);
 67:   VecNorm(v,NORM_2,&nrm);
 68:   if (nrm>100*PETSC_MACHINE_EPSILON) {
 69:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
 70:   }
 71:   MatDestroy(&F);
 72:   VecDestroy(&v);
 73:   VecDestroy(&f0);
 74:   return(0);
 75: }

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

 89:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 90:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 91:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 92:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
 93:   PetscPrintf(PETSC_COMM_WORLD,"Phi1 via a combined function, n=%D.\n",n);

 95:   /* Create function */

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

131:   /* Set up viewer */
132:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
133:   FNCombineGetChildren(f,&ctype,&f1,&f2);
134:   PetscPrintf(PETSC_COMM_WORLD,"Two functions combined with division:\n");
135:   FNView(f1,viewer);
136:   FNView(f2,viewer);
137:   if (verbose) {
138:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
139:   }

141:   /* Scalar evaluation */
142:   x = 2.2;
143:   SlepcSNPrintfScalar(strx,50,x,PETSC_FALSE);
144:   FNEvaluateFunction(f,x,&y);
145:   FNEvaluateDerivative(f,x,&yp);
146:   SlepcSNPrintfScalar(str,50,y,PETSC_FALSE);
147:   PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str);
148:   SlepcSNPrintfScalar(str,50,yp,PETSC_FALSE);
149:   PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str);

151:   /* Create matrices */
152:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
153:   PetscObjectSetName((PetscObject)A,"A");

155:   /* Fill A with 1-D Laplacian matrix */
156:   MatDenseGetArray(A,&As);
157:   for (i=0;i<n;i++) As[i+i*n]=2.0;
158:   j=1;
159:   for (i=0;i<n-j;i++) { As[i+(i+j)*n]=-1.0; As[(i+j)+i*n]=-1.0; }
160:   MatDenseRestoreArray(A,&As);
161:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
162:   TestMatCombine(f,A,viewer,verbose,inplace);

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

168:   MatDestroy(&A);
169:   FNDestroy(&f);
170:   FNDestroy(&p);
171:   FNDestroy(&a);
172:   FNDestroy(&e);
173:   FNDestroy(&c);
174:   SlepcFinalize();
175:   return ierr;
176: }

178: /*TEST

180:    test:
181:       suffix: 1
182:       nsize: 1

184:    test:
185:       suffix: 2
186:       nsize: 1
187:       args: -inplace
188:       output_file: output/test11_1.out

190: TEST*/