Actual source code: test3.c
slepc-3.21.1 2024-04-26
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;
28: PetscFunctionBeginUser;
29: PetscCall(MatGetSize(A,&n,NULL));
30: PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&F));
31: PetscCall(PetscObjectSetName((PetscObject)F,"F"));
32: /* compute matrix exponential */
33: if (inplace) {
34: PetscCall(MatCopy(A,F,SAME_NONZERO_PATTERN));
35: PetscCall(MatIsHermitianKnown(A,&set,&flg));
36: if (set && flg) PetscCall(MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE));
37: PetscCall(FNEvaluateFunctionMat(fn,F,NULL));
38: } else {
39: PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&Acopy));
40: PetscCall(FNEvaluateFunctionMat(fn,A,F));
41: /* check that A has not been modified */
42: PetscCall(MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN));
43: PetscCall(MatNorm(Acopy,NORM_1,&nrm));
44: if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm));
45: PetscCall(MatDestroy(&Acopy));
46: }
47: if (verbose) {
48: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n"));
49: PetscCall(MatView(A,viewer));
50: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed expm(A) - - - - - - -\n"));
51: PetscCall(MatView(F,viewer));
52: }
53: /* print matrix norm for checking */
54: PetscCall(MatNorm(F,NORM_1,&nrmf));
55: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %g\n",(double)nrmf));
56: if (checkerror) {
57: PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Finv));
58: PetscCall(PetscObjectSetName((PetscObject)Finv,"Finv"));
59: PetscCall(FNGetScale(fn,&tau,&eta));
60: /* compute inverse exp(-tau*A)/eta */
61: PetscCall(FNCreate(PETSC_COMM_WORLD,&finv));
62: PetscCall(FNSetType(finv,FNEXP));
63: PetscCall(FNSetFromOptions(finv));
64: PetscCall(FNSetScale(finv,-tau,1.0/eta));
65: if (inplace) {
66: PetscCall(MatCopy(A,Finv,SAME_NONZERO_PATTERN));
67: PetscCall(MatIsHermitianKnown(A,&set,&flg));
68: if (set && flg) PetscCall(MatSetOption(Finv,MAT_HERMITIAN,PETSC_TRUE));
69: PetscCall(FNEvaluateFunctionMat(finv,Finv,NULL));
70: } else PetscCall(FNEvaluateFunctionMat(finv,A,Finv));
71: PetscCall(FNDestroy(&finv));
72: /* check error ||F*Finv-I||_F */
73: PetscCall(MatMatMult(F,Finv,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R));
74: PetscCall(MatShift(R,-1.0));
75: PetscCall(MatNorm(R,NORM_FROBENIUS,&nrm));
76: if (nrm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||exp(A)*exp(-A)-I||_F < 100*eps\n"));
77: else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||exp(A)*exp(-A)-I||_F = %g\n",(double)nrm));
78: PetscCall(MatDestroy(&R));
79: PetscCall(MatDestroy(&Finv));
80: }
81: /* check FNEvaluateFunctionMatVec() */
82: PetscCall(MatCreateVecs(A,&v,&f0));
83: PetscCall(MatGetColumnVector(F,f0,0));
84: PetscCall(FNEvaluateFunctionMatVec(fn,A,v));
85: PetscCall(VecAXPY(v,-1.0,f0));
86: PetscCall(VecNorm(v,NORM_2,&nrm));
87: if (nrm/nrmf>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm));
88: PetscCall(MatDestroy(&F));
89: PetscCall(VecDestroy(&v));
90: PetscCall(VecDestroy(&f0));
91: PetscFunctionReturn(PETSC_SUCCESS);
92: }
94: int main(int argc,char **argv)
95: {
96: FN fn;
97: Mat A=NULL;
98: PetscInt i,j,n=10;
99: PetscScalar *As;
100: PetscViewer viewer;
101: PetscBool verbose,inplace,checkerror,matcuda;
103: PetscFunctionBeginUser;
104: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
105: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
106: PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
107: PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace));
108: PetscCall(PetscOptionsHasName(NULL,NULL,"-checkerror",&checkerror));
109: PetscCall(PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda));
110: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix exponential, n=%" PetscInt_FMT ".\n",n));
112: /* Create exponential function object */
113: PetscCall(FNCreate(PETSC_COMM_WORLD,&fn));
114: PetscCall(FNSetType(fn,FNEXP));
115: PetscCall(FNSetFromOptions(fn));
117: /* Set up viewer */
118: PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
119: PetscCall(FNView(fn,viewer));
120: if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));
122: /* Create matrices */
123: if (matcuda) {
124: #if defined(PETSC_HAVE_CUDA)
125: PetscCall(MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A));
126: #endif
127: } else PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A));
128: PetscCall(PetscObjectSetName((PetscObject)A,"A"));
130: /* Fill A with a symmetric Toeplitz matrix */
131: PetscCall(MatDenseGetArray(A,&As));
132: for (i=0;i<n;i++) As[i+i*n]=2.0;
133: for (j=1;j<3;j++) {
134: for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
135: }
136: PetscCall(MatDenseRestoreArray(A,&As));
137: PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
138: PetscCall(TestMatExp(fn,A,viewer,verbose,inplace,checkerror));
140: /* Repeat with non-symmetric A */
141: PetscCall(MatDenseGetArray(A,&As));
142: for (j=1;j<3;j++) {
143: for (i=0;i<n-j;i++) { As[(i+j)+i*n]=-1.0; }
144: }
145: PetscCall(MatDenseRestoreArray(A,&As));
146: PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE));
147: PetscCall(TestMatExp(fn,A,viewer,verbose,inplace,checkerror));
149: PetscCall(MatDestroy(&A));
150: PetscCall(FNDestroy(&fn));
151: PetscCall(SlepcFinalize());
152: return 0;
153: }
155: /*TEST
157: testset:
158: filter: grep -v "computing matrix functions"
159: output_file: output/test3_1.out
160: test:
161: suffix: 1
162: args: -fn_method {{0 1}}
163: test:
164: suffix: 1_subdiagonalpade
165: args: -fn_method {{2 3}}
166: requires: c99_complex !single
167: test:
168: suffix: 1_cuda
169: args: -fn_method 1 -matcuda
170: requires: cuda !magma
171: test:
172: suffix: 1_magma
173: args: -fn_method {{0 1 2 3}} -matcuda
174: requires: cuda magma
175: test:
176: suffix: 2
177: args: -inplace -fn_method{{0 1}}
178: test:
179: suffix: 2_subdiagonalpade
180: args: -inplace -fn_method{{2 3}}
181: requires: c99_complex !single
182: test:
183: suffix: 2_cuda
184: args: -inplace -fn_method 1 -matcuda
185: requires: cuda !magma
186: test:
187: suffix: 2_magma
188: args: -inplace -fn_method {{0 1 2 3}} -matcuda
189: requires: cuda magma
191: testset:
192: args: -fn_scale 0.1
193: filter: grep -v "computing matrix functions"
194: output_file: output/test3_3.out
195: test:
196: suffix: 3
197: args: -fn_method {{0 1}}
198: test:
199: suffix: 3_subdiagonalpade
200: args: -fn_method {{2 3}}
201: requires: c99_complex !single
203: testset:
204: args: -n 120 -fn_scale 0.6,1.5
205: filter: grep -v "computing matrix functions"
206: output_file: output/test3_4.out
207: test:
208: suffix: 4
209: args: -fn_method {{0 1}}
210: requires: !single
211: test:
212: suffix: 4_subdiagonalpade
213: args: -fn_method {{2 3}}
214: requires: c99_complex !single
216: test:
217: suffix: 5
218: args: -fn_scale 30 -fn_method {{2 3}}
219: filter: grep -v "computing matrix functions"
220: requires: c99_complex !single
221: output_file: output/test3_5.out
223: test:
224: suffix: 6
225: args: -fn_scale 1e-9 -fn_method {{2 3}}
226: filter: grep -v "computing matrix functions"
227: requires: c99_complex !single
228: output_file: output/test3_6.out
230: TEST*/