Actual source code: test6.c

slepc-3.7.0 2016-05-16
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.

  8:    SLEPc is free software: you can redistribute it and/or modify it under  the
  9:    terms of version 3 of the GNU Lesser General Public License as published by
 10:    the Free Software Foundation.

 12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 15:    more details.

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */
 21: /*
 22:    Define the function

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

 26:    with the following tree:

 28:             f(x)                  f(x)              (combined by product)
 29:            /    \                 g(x) = 1-x^2      (polynomial)
 30:         g(x)    h(x)              h(x)              (combined by composition)
 31:                /    \             r(x) = -x/(1+x^2) (rational)
 32:              r(x)   e(x)          e(x) = exp(x)     (exponential)
 33: */

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

 37: #include <slepcfn.h>

 41: /*
 42:    Compute matrix function B = (I-A^2) exp( -(I+A^2)\A )
 43:  */
 44: PetscErrorCode TestMatCombine(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
 45: {
 47:   PetscBool      set,flg;
 48:   PetscInt       n;
 49:   Mat            F;
 50:   Vec            v,f0;
 51:   PetscReal      nrm;

 54:   MatGetSize(A,&n,NULL);
 55:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
 56:   PetscObjectSetName((PetscObject)F,"F");
 57:   /* compute square root */
 58:   if (inplace) {
 59:     MatCopy(A,F,SAME_NONZERO_PATTERN);
 60:     MatIsHermitianKnown(A,&set,&flg);
 61:     if (set && flg) { MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE); }
 62:     FNEvaluateFunctionMat(fn,F,NULL);
 63:   } else {
 64:     FNEvaluateFunctionMat(fn,A,F);
 65:   }
 66:   if (verbose) {
 67:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
 68:     MatView(A,viewer);
 69:     PetscPrintf(PETSC_COMM_WORLD,"Computed expm(A) - - - - - - -\n");
 70:     MatView(F,viewer);
 71:   }
 72:   /* print matrix norm for checking */
 73:   MatNorm(F,NORM_1,&nrm);
 74:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %g\n",(double)nrm);
 75:   /* check FNEvaluateFunctionMatVec() */
 76:   MatCreateVecs(A,&v,&f0);
 77:   MatGetColumnVector(F,f0,0);
 78:   FNEvaluateFunctionMatVec(fn,A,v);
 79:   VecAXPY(v,-1.0,f0);
 80:   VecNorm(v,NORM_2,&nrm);
 81:   if (nrm>100*PETSC_MACHINE_EPSILON) {
 82:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
 83:   }
 84:   MatDestroy(&F);
 85:   VecDestroy(&v);
 86:   VecDestroy(&f0);
 87:   return(0);
 88: }

 92: int main(int argc,char **argv)
 93: {
 95:   FN             f,g,h,e,r;
 96:   Mat            A;
 97:   PetscInt       i,j,n=10,np,nq;
 98:   PetscScalar    x,y,yp,*As,p[10],q[10];
 99:   char           strx[50],str[50];
100:   PetscViewer    viewer;
101:   PetscBool      verbose,inplace;

103:   SlepcInitialize(&argc,&argv,(char*)0,help);
104:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
105:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
106:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
107:   PetscPrintf(PETSC_COMM_WORLD,"Combined function, n=%D.\n",n);

109:   /* Create function */

111:   /* e(x) = exp(x) */
112:   FNCreate(PETSC_COMM_WORLD,&e);
113:   FNSetType(e,FNEXP);
114:   /* r(x) = x/(1+x^2) */
115:   FNCreate(PETSC_COMM_WORLD,&r);
116:   FNSetType(r,FNRATIONAL);
117:   np = 2; nq = 3;
118:   p[0] = -1.0; p[1] = 0.0;
119:   q[0] = 1.0; q[1] = 0.0; q[2] = 1.0;
120:   FNRationalSetNumerator(r,np,p);
121:   FNRationalSetDenominator(r,nq,q);
122:   /* h(x) */
123:   FNCreate(PETSC_COMM_WORLD,&h);
124:   FNSetType(h,FNCOMBINE);
125:   FNCombineSetChildren(h,FN_COMBINE_COMPOSE,r,e);
126:   /* g(x) = 1-x^2 */
127:   FNCreate(PETSC_COMM_WORLD,&g);
128:   FNSetType(g,FNRATIONAL);
129:   np = 3;
130:   p[0] = -1.0; p[1] = 0.0; p[2] = 1.0;
131:   FNRationalSetNumerator(g,np,p);
132:   /* f(x) */
133:   FNCreate(PETSC_COMM_WORLD,&f);
134:   FNSetType(f,FNCOMBINE);
135:   FNCombineSetChildren(f,FN_COMBINE_MULTIPLY,g,h);

137:   /* Set up viewer */
138:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
139:   FNView(f,viewer);
140:   if (verbose) {
141:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
142:   }

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

154:   /* Create matrices */
155:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
156:   PetscObjectSetName((PetscObject)A,"A");

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

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

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