Actual source code: test3.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: */

 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: {
 20:   PetscScalar    tau,eta;
 21:   PetscBool      set,flg;
 22:   PetscInt       n;
 23:   Mat            F,R,Finv,Acopy;
 24:   Vec            v,f0;
 25:   FN             finv;
 26:   PetscReal      nrm,nrmf;

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

 94: int main(int argc,char **argv)
 95: {
 96:   FN             fn;
 97:   Mat            A;
 98:   PetscInt       i,j,n=10;
 99:   PetscScalar    *As;
100:   PetscViewer    viewer;
101:   PetscBool      verbose,inplace,checkerror;

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:   PetscOptionsHasName(NULL,NULL,"-checkerror",&checkerror);
108:   PetscPrintf(PETSC_COMM_WORLD,"Matrix exponential, n=%" PetscInt_FMT ".\n",n);

110:   /* Create exponential function object */
111:   FNCreate(PETSC_COMM_WORLD,&fn);
112:   FNSetType(fn,FNEXP);
113:   FNSetFromOptions(fn);

115:   /* Set up viewer */
116:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
117:   FNView(fn,viewer);
118:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

120:   /* Create matrices */
121:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
122:   PetscObjectSetName((PetscObject)A,"A");

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

134:   /* Repeat with non-symmetric A */
135:   MatDenseGetArray(A,&As);
136:   for (j=1;j<3;j++) {
137:     for (i=0;i<n-j;i++) { As[(i+j)+i*n]=-1.0; }
138:   }
139:   MatDenseRestoreArray(A,&As);
140:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
141:   TestMatExp(fn,A,viewer,verbose,inplace,checkerror);

143:   MatDestroy(&A);
144:   FNDestroy(&fn);
145:   SlepcFinalize();
146:   return 0;
147: }

149: /*TEST

151:    testset:
152:       filter: grep -v "computing matrix functions"
153:       output_file: output/test3_1.out
154:       test:
155:          suffix: 1
156:          args: -fn_method {{0 1}}
157:       test:
158:          suffix: 1_subdiagonalpade
159:          args: -fn_method {{2 3}}
160:          requires: c99_complex !single
161:       test:
162:          suffix: 1_cuda
163:          args: -fn_method 4
164:          requires: cuda
165:       test:
166:          suffix: 1_magma
167:          args: -fn_method {{5 6 7 8}}
168:          requires: cuda magma
169:       test:
170:          suffix: 2
171:          args: -inplace -fn_method{{0 1}}
172:       test:
173:          suffix: 2_subdiagonalpade
174:          args: -inplace -fn_method{{2 3}}
175:          requires: c99_complex !single
176:       test:
177:          suffix: 2_cuda
178:          args: -inplace -fn_method 4
179:          requires: cuda
180:       test:
181:          suffix: 2_magma
182:          args: -inplace -fn_method {{5 6 7 8}}
183:          requires: cuda magma

185:    testset:
186:       args: -fn_scale 0.1
187:       filter: grep -v "computing matrix functions"
188:       output_file: output/test3_3.out
189:       test:
190:          suffix: 3
191:          args: -fn_method {{0 1}}
192:       test:
193:         suffix: 3_subdiagonalpade
194:         args: -fn_method {{2 3}}
195:         requires: c99_complex !single

197:    testset:
198:       args: -n 120 -fn_scale 0.6,1.5
199:       filter: grep -v "computing matrix functions"
200:       output_file: output/test3_4.out
201:       test:
202:          suffix: 4
203:          args: -fn_method {{0 1}}
204:          requires: !single
205:       test:
206:         suffix: 4_subdiagonalpade
207:         args: -fn_method {{2 3}}
208:         requires: c99_complex !single

210:    test:
211:       suffix: 5
212:       args: -fn_scale 30 -fn_method {{2 3}}
213:       filter: grep -v "computing matrix functions"
214:       requires: c99_complex !single
215:       output_file: output/test3_5.out

217:    test:
218:       suffix: 6
219:       args: -fn_scale 1e-9 -fn_method {{2 3}}
220:       filter: grep -v "computing matrix functions"
221:       requires: c99_complex !single
222:       output_file: output/test3_6.out

224: TEST*/