Actual source code: test13.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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: {
21: PetscBool set,flg;
22: PetscScalar tau,eta;
23: PetscInt n;
24: Mat F,R;
25: Vec v,f0;
26: FN fnexp;
27: PetscReal nrm;
30: MatGetSize(A,&n,NULL);
31: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&F);
32: PetscObjectSetName((PetscObject)F,"F");
33: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&R);
34: PetscObjectSetName((PetscObject)R,"R");
35: FNGetScale(fn,&tau,&eta);
36: /* compute matrix logarithm */
37: if (inplace) {
38: MatCopy(A,F,SAME_NONZERO_PATTERN);
39: MatIsHermitianKnown(A,&set,&flg);
40: if (set && flg) { MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE); }
41: FNEvaluateFunctionMat(fn,F,NULL);
42: } else {
43: FNEvaluateFunctionMat(fn,A,F);
44: }
45: if (verbose) {
46: PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
47: MatView(A,viewer);
48: PetscPrintf(PETSC_COMM_WORLD,"Computed logm(A) - - - - - - -\n");
49: MatView(F,viewer);
50: }
51: /* check error ||expm(F)-A||_F */
52: FNCreate(PETSC_COMM_WORLD,&fnexp);
53: FNSetType(fnexp,FNEXP);
54: MatCopy(F,R,SAME_NONZERO_PATTERN);
55: if (eta!=1.0) {
56: MatScale(R,1.0/eta);
57: }
58: FNEvaluateFunctionMat(fnexp,R,NULL);
59: FNDestroy(&fnexp);
60: MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN);
61: MatNorm(R,NORM_FROBENIUS,&nrm);
62: if (nrm<100*PETSC_MACHINE_EPSILON) {
63: PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F < 100*eps\n");
64: } else {
65: PetscPrintf(PETSC_COMM_WORLD,"||expm(F)-A||_F = %g\n",(double)nrm);
66: }
67: /* check FNEvaluateFunctionMatVec() */
68: MatCreateVecs(A,&v,&f0);
69: MatGetColumnVector(F,f0,0);
70: FNEvaluateFunctionMatVec(fn,A,v);
71: VecAXPY(v,-1.0,f0);
72: VecNorm(v,NORM_2,&nrm);
73: if (nrm>100*PETSC_MACHINE_EPSILON) {
74: PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
75: }
76: MatDestroy(&F);
77: MatDestroy(&R);
78: VecDestroy(&v);
79: VecDestroy(&f0);
80: return(0);
81: }
83: int main(int argc,char **argv)
84: {
86: FN fn;
87: Mat A;
88: PetscInt i,j,n=10;
89: PetscScalar *As;
90: PetscViewer viewer;
91: PetscBool verbose,inplace,random;
93: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
94: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
95: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
96: PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
97: PetscOptionsHasName(NULL,NULL,"-random",&random);
98: PetscPrintf(PETSC_COMM_WORLD,"Matrix logarithm, n=%D.\n",n);
100: /* Create logarithm function object */
101: FNCreate(PETSC_COMM_WORLD,&fn);
102: FNSetType(fn,FNLOG);
103: FNSetFromOptions(fn);
105: /* Set up viewer */
106: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
107: FNView(fn,viewer);
108: if (verbose) {
109: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
110: }
112: /* Create matrices */
113: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
114: PetscObjectSetName((PetscObject)A,"A");
116: if (random) {
117: MatSetRandom(A,NULL);
118: } else {
119: /* Fill A with a non-symmetric Toeplitz matrix */
120: MatDenseGetArray(A,&As);
121: for (i=0;i<n;i++) As[i+i*n]=2.0;
122: for (j=1;j<3;j++) {
123: for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=-1.0; }
124: }
125: As[(n-1)*n] = -5.0;
126: MatDenseRestoreArray(A,&As);
127: }
128: TestMatLog(fn,A,viewer,verbose,inplace);
130: MatDestroy(&A);
131: FNDestroy(&fn);
132: SlepcFinalize();
133: return ierr;
134: }
136: /*TEST
138: testset:
139: filter: grep -v "computing matrix functions"
140: output_file: output/test13_1.out
141: test:
142: suffix: 1
143: args: -fn_scale .04,2 -n 75
144: requires: c99_complex !__float128
145: test:
146: suffix: 1_random
147: args: -fn_scale .04,2 -n 75 -random
148: requires: complex
150: TEST*/