Actual source code: test3.c

slepc-3.16.1 2021-11-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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,Acopy;
 25:   Vec            v,f0;
 26:   FN             finv;
 27:   PetscReal      nrm,nrmf;

 30:   MatGetSize(A,&n,NULL);
 31:   MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&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:     MatDuplicate(A,MAT_COPY_VALUES,&Acopy);
 41:     FNEvaluateFunctionMat(fn,A,F);
 42:     /* check that A has not been modified */
 43:     MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN);
 44:     MatNorm(Acopy,NORM_1,&nrm);
 45:     if (nrm>100*PETSC_MACHINE_EPSILON) {
 46:       PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm);
 47:     }
 48:     MatDestroy(&Acopy);
 49:   }
 50:   if (verbose) {
 51:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
 52:     MatView(A,viewer);
 53:     PetscPrintf(PETSC_COMM_WORLD,"Computed expm(A) - - - - - - -\n");
 54:     MatView(F,viewer);
 55:   }
 56:   /* print matrix norm for checking */
 57:   MatNorm(F,NORM_1,&nrmf);
 58:   PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %g\n",(double)nrmf);
 59:   if (checkerror) {
 60:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Finv);
 61:     PetscObjectSetName((PetscObject)Finv,"Finv");
 62:     FNGetScale(fn,&tau,&eta);
 63:     /* compute inverse exp(-tau*A)/eta */
 64:     FNCreate(PETSC_COMM_WORLD,&finv);
 65:     FNSetType(finv,FNEXP);
 66:     FNSetFromOptions(finv);
 67:     FNSetScale(finv,-tau,1.0/eta);
 68:     if (inplace) {
 69:       MatCopy(A,Finv,SAME_NONZERO_PATTERN);
 70:       MatIsHermitianKnown(A,&set,&flg);
 71:       if (set && flg) { MatSetOption(Finv,MAT_HERMITIAN,PETSC_TRUE); }
 72:       FNEvaluateFunctionMat(finv,Finv,NULL);
 73:     } else {
 74:       FNEvaluateFunctionMat(finv,A,Finv);
 75:     }
 76:     FNDestroy(&finv);
 77:     /* check error ||F*Finv-I||_F */
 78:     MatMatMult(F,Finv,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
 79:     MatShift(R,-1.0);
 80:     MatNorm(R,NORM_FROBENIUS,&nrm);
 81:     if (nrm<100*PETSC_MACHINE_EPSILON) {
 82:       PetscPrintf(PETSC_COMM_WORLD,"||exp(A)*exp(-A)-I||_F < 100*eps\n");
 83:     } else {
 84:       PetscPrintf(PETSC_COMM_WORLD,"||exp(A)*exp(-A)-I||_F = %g\n",(double)nrm);
 85:     }
 86:     MatDestroy(&R);
 87:     MatDestroy(&Finv);
 88:   }
 89:   /* check FNEvaluateFunctionMatVec() */
 90:   MatCreateVecs(A,&v,&f0);
 91:   MatGetColumnVector(F,f0,0);
 92:   FNEvaluateFunctionMatVec(fn,A,v);
 93:   VecAXPY(v,-1.0,f0);
 94:   VecNorm(v,NORM_2,&nrm);
 95:   if (nrm/nrmf>100*PETSC_MACHINE_EPSILON) {
 96:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
 97:   }
 98:   MatDestroy(&F);
 99:   VecDestroy(&v);
100:   VecDestroy(&f0);
101:   return(0);
102: }

104: int main(int argc,char **argv)
105: {
107:   FN             fn;
108:   Mat            A;
109:   PetscInt       i,j,n=10;
110:   PetscScalar    *As;
111:   PetscViewer    viewer;
112:   PetscBool      verbose,inplace,checkerror;

114:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
115:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
116:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
117:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
118:   PetscOptionsHasName(NULL,NULL,"-checkerror",&checkerror);
119:   PetscPrintf(PETSC_COMM_WORLD,"Matrix exponential, n=%D.\n",n);

121:   /* Create exponential function object */
122:   FNCreate(PETSC_COMM_WORLD,&fn);
123:   FNSetType(fn,FNEXP);
124:   FNSetFromOptions(fn);

126:   /* Set up viewer */
127:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
128:   FNView(fn,viewer);
129:   if (verbose) {
130:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
131:   }

133:   /* Create matrices */
134:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
135:   PetscObjectSetName((PetscObject)A,"A");

137:   /* Fill A with a symmetric Toeplitz matrix */
138:   MatDenseGetArray(A,&As);
139:   for (i=0;i<n;i++) As[i+i*n]=2.0;
140:   for (j=1;j<3;j++) {
141:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
142:   }
143:   MatDenseRestoreArray(A,&As);
144:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
145:   TestMatExp(fn,A,viewer,verbose,inplace,checkerror);

147:   /* Repeat with non-symmetric A */
148:   MatDenseGetArray(A,&As);
149:   for (j=1;j<3;j++) {
150:     for (i=0;i<n-j;i++) { As[(i+j)+i*n]=-1.0; }
151:   }
152:   MatDenseRestoreArray(A,&As);
153:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
154:   TestMatExp(fn,A,viewer,verbose,inplace,checkerror);

156:   MatDestroy(&A);
157:   FNDestroy(&fn);
158:   SlepcFinalize();
159:   return ierr;
160: }

162: /*TEST

164:    testset:
165:       filter: grep -v "computing matrix functions"
166:       output_file: output/test3_1.out
167:       test:
168:          suffix: 1
169:          args: -fn_method {{0 1}}
170:       test:
171:          suffix: 1_subdiagonalpade
172:          args: -fn_method {{2 3}}
173:          requires: c99_complex !single
174:       test:
175:          suffix: 1_cuda
176:          args: -fn_method 4
177:          requires: cuda
178:       test:
179:          suffix: 1_magma
180:          args: -fn_method {{5 6 7 8}}
181:          requires: cuda magma
182:       test:
183:          suffix: 2
184:          args: -inplace -fn_method{{0 1}}
185:       test:
186:          suffix: 2_subdiagonalpade
187:          args: -inplace -fn_method{{2 3}}
188:          requires: c99_complex !single
189:       test:
190:          suffix: 2_cuda
191:          args: -inplace -fn_method 4
192:          requires: cuda
193:       test:
194:          suffix: 2_magma
195:          args: -inplace -fn_method {{5 6 7 8}}
196:          requires: cuda magma

198:    testset:
199:       args: -fn_scale 0.1
200:       filter: grep -v "computing matrix functions"
201:       output_file: output/test3_3.out
202:       test:
203:          suffix: 3
204:          args: -fn_method {{0 1}}
205:       test:
206:         suffix: 3_subdiagonalpade
207:         args: -fn_method {{2 3}}
208:         requires: c99_complex !single

210:    testset:
211:       args: -n 120 -fn_scale 0.6,1.5
212:       filter: grep -v "computing matrix functions"
213:       output_file: output/test3_4.out
214:       test:
215:          suffix: 4
216:          args: -fn_method {{0 1}}
217:          requires: !single
218:       test:
219:         suffix: 4_subdiagonalpade
220:         args: -fn_method {{2 3}}
221:         requires: c99_complex !single

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

230:    test:
231:       suffix: 6
232:       args: -fn_scale 1e-9 -fn_method {{2 3}}
233:       filter: grep -v "computing matrix functions"
234:       requires: c99_complex !single
235:       output_file: output/test3_6.out

237: TEST*/