Actual source code: test3.c

slepc-3.14.0 2020-09-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2020, 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 exponential.\n\n";

 13: #include <slepcfn.h>

 15: /*
 16:    Compute matrix exponential B = expm(A)
 17:  */
 18: PetscErrorCode TestMatExp(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace,PetscBool checkerror)
 19: {
 21:   PetscScalar    tau,eta;
 22:   PetscBool      set,flg;
 23:   PetscInt       n;
 24:   Mat            F,R,Finv;
 25:   Vec            v,f0;
 26:   FN             finv;
 27:   PetscReal      nrm,nrmf;

 30:   MatGetSize(A,&n,NULL);
 31:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
 32:   PetscObjectSetName((PetscObject)F,"F");
 33:   /* compute matrix exponential */
 34:   if (inplace) {
 35:     MatCopy(A,F,SAME_NONZERO_PATTERN);
 36:     MatIsHermitianKnown(A,&set,&flg);
 37:     if (set && flg) { MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE); }
 38:     FNEvaluateFunctionMat(fn,F,NULL);
 39:   } else {
 40:     FNEvaluateFunctionMat(fn,A,F);
 41:   }
 42:   if (verbose) {
 43:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
 44:     MatView(A,viewer);
 45:     PetscPrintf(PETSC_COMM_WORLD,"Computed expm(A) - - - - - - -\n");
 46:     MatView(F,viewer);
 47:   }
 48:   /* print matrix norm for checking */
 49:   MatNorm(F,NORM_1,&nrmf);
 50:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %g\n",(double)nrmf);
 51:   if (checkerror) {
 52:     MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&Finv);
 53:     PetscObjectSetName((PetscObject)Finv,"Finv");
 54:     FNGetScale(fn,&tau,&eta);
 55:     /* compute inverse exp(-tau*A)/eta */
 56:     FNCreate(PETSC_COMM_WORLD,&finv);
 57:     FNSetType(finv,FNEXP);
 58:     FNSetFromOptions(finv);
 59:     FNSetScale(finv,-tau,1.0/eta);
 60:     if (inplace) {
 61:       MatCopy(A,Finv,SAME_NONZERO_PATTERN);
 62:       MatIsHermitianKnown(A,&set,&flg);
 63:       if (set && flg) { MatSetOption(Finv,MAT_HERMITIAN,PETSC_TRUE); }
 64:       FNEvaluateFunctionMat(finv,Finv,NULL);
 65:     } else {
 66:       FNEvaluateFunctionMat(finv,A,Finv);
 67:     }
 68:     FNDestroy(&finv);
 69:     /* check error ||F*Finv-I||_F */
 70:     MatMatMult(F,Finv,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
 71:     MatShift(R,-1.0);
 72:     MatNorm(R,NORM_FROBENIUS,&nrm);
 73:     if (nrm<100*PETSC_MACHINE_EPSILON) {
 74:       PetscPrintf(PETSC_COMM_WORLD,"||exp(A)*exp(-A)-I||_F < 100*eps\n");
 75:     } else {
 76:       PetscPrintf(PETSC_COMM_WORLD,"||exp(A)*exp(-A)-I||_F = %g\n",(double)nrm);
 77:     }
 78:     MatDestroy(&R);
 79:     MatDestroy(&Finv);
 80:   }
 81:   /* check FNEvaluateFunctionMatVec() */
 82:   MatCreateVecs(A,&v,&f0);
 83:   MatGetColumnVector(F,f0,0);
 84:   FNEvaluateFunctionMatVec(fn,A,v);
 85:   VecAXPY(v,-1.0,f0);
 86:   VecNorm(v,NORM_2,&nrm);
 87:   if (nrm/nrmf>100*PETSC_MACHINE_EPSILON) {
 88:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
 89:   }
 90:   MatDestroy(&F);
 91:   VecDestroy(&v);
 92:   VecDestroy(&f0);
 93:   return(0);
 94: }

 96: int main(int argc,char **argv)
 97: {
 99:   FN             fn;
100:   Mat            A;
101:   PetscInt       i,j,n=10;
102:   PetscScalar    *As;
103:   PetscViewer    viewer;
104:   PetscBool      verbose,inplace,checkerror;

106:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
107:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
108:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
109:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
110:   PetscOptionsHasName(NULL,NULL,"-checkerror",&checkerror);
111:   PetscPrintf(PETSC_COMM_WORLD,"Matrix exponential, n=%D.\n",n);

113:   /* Create exponential function object */
114:   FNCreate(PETSC_COMM_WORLD,&fn);
115:   FNSetType(fn,FNEXP);
116:   FNSetFromOptions(fn);

118:   /* Set up viewer */
119:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
120:   FNView(fn,viewer);
121:   if (verbose) {
122:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
123:   }

125:   /* Create matrices */
126:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
127:   PetscObjectSetName((PetscObject)A,"A");

129:   /* Fill A with a symmetric Toeplitz matrix */
130:   MatDenseGetArray(A,&As);
131:   for (i=0;i<n;i++) As[i+i*n]=2.0;
132:   for (j=1;j<3;j++) {
133:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
134:   }
135:   MatDenseRestoreArray(A,&As);
136:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
137:   TestMatExp(fn,A,viewer,verbose,inplace,checkerror);

139:   /* Repeat with non-symmetric A */
140:   MatDenseGetArray(A,&As);
141:   for (j=1;j<3;j++) {
142:     for (i=0;i<n-j;i++) { As[(i+j)+i*n]=-1.0; }
143:   }
144:   MatDenseRestoreArray(A,&As);
145:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
146:   TestMatExp(fn,A,viewer,verbose,inplace,checkerror);

148:   MatDestroy(&A);
149:   FNDestroy(&fn);
150:   SlepcFinalize();
151:   return ierr;
152: }

154: /*TEST

156:    test:
157:       suffix: 1
158:       nsize: 1
159:       args: -fn_method {{0 1}shared output}
160:       filter: grep -v "computing matrix functions"
161:       output_file: output/test3_1.out

163:    test:
164:       suffix: 1_subdiagonalpade
165:       nsize: 1
166:       args: -fn_method {{2 3}}
167:       requires: c99_complex !single
168:       filter: grep -v "computing matrix functions"
169:       output_file: output/test3_1.out

171:    test:
172:       suffix: 2
173:       nsize: 1
174:       args: -inplace
175:       filter: grep -v "computing matrix functions"
176:       output_file: output/test3_1.out

178:    test:
179:       suffix: 3
180:       nsize: 1
181:       args: -fn_scale 0.1 -fn_method {{0 1}shared output}
182:       filter: grep -v "computing matrix functions"
183:       output_file: output/test3_3.out

185:    testset:
186:       nsize: 1
187:       filter: grep -v "computing matrix functions"
188:       output_file: output/test3_3.out
189:       test:
190:         suffix: 3_subdiagonalpade_product
191:         args: -fn_scale 0.1 -fn_method 2
192:         requires: c99_complex !single
193:       test:
194:         suffix: 3_subdiagonalpade_partial
195:         args: -fn_scale 0.1 -fn_method 3
196:         requires: c99_complex !single

198:    test:
199:       suffix: 4
200:       nsize: 1
201:       args: -n 120 -fn_scale 0.6,1.5 -fn_method {{0 1}shared output}
202:       requires: !single
203:       filter: grep -v "computing matrix functions"
204:       output_file: output/test3_4.out

206:    testset:
207:       nsize: 1
208:       filter: grep -v "computing matrix functions"
209:       output_file: output/test3_4.out
210:       test:
211:         suffix: 4_subdiagonalpade_product
212:         args: -n 120 -fn_scale 0.6,1.5 -fn_method 2
213:         requires: c99_complex !single
214:       test:
215:         suffix: 4_subdiagonalpade_partial
216:         args: -n 120 -fn_scale 0.6,1.5 -fn_method 3
217:         requires: c99_complex !single

219:    test:
220:       suffix: 5
221:       args: -fn_scale 30 -fn_method {{2 3}}
222:       filter: grep -v "computing matrix functions"
223:       requires: c99_complex !single
224:       output_file: output/test3_5.out

226:    testset:
227:       suffix: 6
228:       args: -fn_scale 1e-9 -fn_method {{2 3}}
229:       filter: grep -v "computing matrix functions"
230:       requires: c99_complex !single
231:       output_file: output/test3_6.out

233: TEST*/