Actual source code: test13.c
slepc-3.18.3 2023-03-24
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 logarithm.\n\n";
13: #include <slepcfn.h>
15: /*
16: Compute matrix logarithm B = logm(A)
17: */
18: PetscErrorCode TestMatLog(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
19: {
20: PetscBool set,flg;
21: PetscScalar tau,eta;
22: PetscInt n;
23: Mat F,R;
24: Vec v,f0;
25: FN fnexp;
26: PetscReal nrm;
29: MatGetSize(A,&n,NULL);
30: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
31: PetscObjectSetName((PetscObject)F,"F");
32: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&R);
33: PetscObjectSetName((PetscObject)R,"R");
34: FNGetScale(fn,&tau,&eta);
35: /* compute matrix logarithm */
36: if (inplace) {
37: MatCopy(A,F,SAME_NONZERO_PATTERN);
38: MatIsHermitianKnown(A,&set,&flg);
39: if (set && flg) MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE);
40: FNEvaluateFunctionMat(fn,F,NULL);
41: } else FNEvaluateFunctionMat(fn,A,F);
42: if (verbose) {
43: PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
44: MatView(A,viewer);
45: PetscPrintf(PETSC_COMM_WORLD,"Computed logm(A) - - - - - - -\n");
46: MatView(F,viewer);
47: }
48: /* check error ||expm(F)-A||_F */
49: FNCreate(PETSC_COMM_WORLD,&fnexp);
50: FNSetType(fnexp,FNEXP);
51: MatCopy(F,R,SAME_NONZERO_PATTERN);
52: if (eta!=1.0) MatScale(R,1.0/eta);
53: FNEvaluateFunctionMat(fnexp,R,NULL);
54: FNDestroy(&fnexp);
55: MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN);
56: MatNorm(R,NORM_FROBENIUS,&nrm);
57: if (nrm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F < 100*eps\n");
58: else PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F = %g\n",(double)nrm);
59: /* check FNEvaluateFunctionMatVec() */
60: MatCreateVecs(A,&v,&f0);
61: MatGetColumnVector(F,f0,0);
62: FNEvaluateFunctionMatVec(fn,A,v);
63: VecAXPY(v,-1.0,f0);
64: VecNorm(v,NORM_2,&nrm);
65: if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
66: MatDestroy(&F);
67: MatDestroy(&R);
68: VecDestroy(&v);
69: VecDestroy(&f0);
70: return 0;
71: }
73: int main(int argc,char **argv)
74: {
75: FN fn;
76: Mat A;
77: PetscInt i,j,n=10;
78: PetscScalar *As;
79: PetscViewer viewer;
80: PetscBool verbose,inplace,random,triang;
83: SlepcInitialize(&argc,&argv,(char*)0,help);
84: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
85: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
86: PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
87: PetscOptionsHasName(NULL,NULL,"-random",&random);
88: PetscOptionsHasName(NULL,NULL,"-triang",&triang);
89: PetscPrintf(PETSC_COMM_WORLD,"Matrix logarithm, n=%" PetscInt_FMT ".\n",n);
91: /* Create logarithm function object */
92: FNCreate(PETSC_COMM_WORLD,&fn);
93: FNSetType(fn,FNLOG);
94: FNSetFromOptions(fn);
96: /* Set up viewer */
97: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
98: FNView(fn,viewer);
99: if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
101: /* Create matrices */
102: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
103: PetscObjectSetName((PetscObject)A,"A");
105: if (random) MatSetRandom(A,NULL);
106: else {
107: /* Fill A with a non-symmetric Toeplitz matrix */
108: MatDenseGetArray(A,&As);
109: for (i=0;i<n;i++) As[i+i*n]=2.0;
110: for (j=1;j<3;j++) {
111: for (i=0;i<n-j;i++) {
112: As[i+(i+j)*n]=1.0;
113: if (!triang) As[(i+j)+i*n]=-1.0;
114: }
115: }
116: As[(n-1)*n] = -5.0;
117: As[0] = 2.01;
118: MatDenseRestoreArray(A,&As);
119: }
120: TestMatLog(fn,A,viewer,verbose,inplace);
122: MatDestroy(&A);
123: FNDestroy(&fn);
124: SlepcFinalize();
125: return 0;
126: }
128: /*TEST
130: testset:
131: filter: grep -v "computing matrix functions"
132: output_file: output/test13_1.out
133: test:
134: suffix: 1
135: args: -fn_scale .04,2 -n 75
136: requires: c99_complex !__float128
137: test:
138: suffix: 1_triang
139: args: -fn_scale .04,2 -n 75 -triang
140: requires: c99_complex !__float128
141: test:
142: suffix: 1_random
143: args: -fn_scale .02,2 -n 75 -random
144: requires: complex !__float128
145: filter_output: sed -e 's/04/02/'
147: TEST*/