Actual source code: test7.c
slepc-3.7.1 2016-05-27
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
8: SLEPc is free software: you can redistribute it and/or modify it under the
9: terms of version 3 of the GNU Lesser General Public License as published by
10: the Free Software Foundation.
12: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
13: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
14: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
15: more details.
17: You should have received a copy of the GNU Lesser General Public License
18: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
19: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
20: */
22: static char help[] = "Test matrix square root.\n\n";
24: #include <slepcfn.h>
28: /*
29: Compute matrix square root B = sqrtm(A)
30: Check result as norm(B*B-A)
31: */
32: PetscErrorCode TestMatSqrt(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
33: {
35: PetscScalar tau,eta;
36: PetscReal nrm;
37: PetscBool set,flg;
38: PetscInt n;
39: Mat S,R;
40: Vec v,f0;
43: MatGetSize(A,&n,NULL);
44: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&S);
45: PetscObjectSetName((PetscObject)S,"S");
46: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&R);
47: PetscObjectSetName((PetscObject)R,"R");
48: FNGetScale(fn,&tau,&eta);
49: /* compute square root */
50: if (inplace) {
51: MatCopy(A,S,SAME_NONZERO_PATTERN);
52: MatIsHermitianKnown(A,&set,&flg);
53: if (set && flg) { MatSetOption(S,MAT_HERMITIAN,PETSC_TRUE); }
54: FNEvaluateFunctionMat(fn,S,NULL);
55: } else {
56: FNEvaluateFunctionMat(fn,A,S);
57: }
58: if (verbose) {
59: PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
60: MatView(A,viewer);
61: PetscPrintf(PETSC_COMM_WORLD,"Computed sqrtm(A) - - - - - - -\n");
62: MatView(S,viewer);
63: }
64: /* check error ||S*S-A||_F */
65: MatMatMult(S,S,MAT_REUSE_MATRIX,PETSC_DEFAULT,&R);
66: if (eta!=1.0) {
67: MatScale(R,1.0/(eta*eta));
68: }
69: MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN);
70: MatNorm(R,NORM_FROBENIUS,&nrm);
71: if (nrm<100*PETSC_MACHINE_EPSILON) {
72: PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F < 100*eps\n");
73: } else {
74: PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F = %g\n",(double)nrm);
75: }
76: /* check FNEvaluateFunctionMatVec() */
77: MatCreateVecs(A,&v,&f0);
78: MatGetColumnVector(S,f0,0);
79: FNEvaluateFunctionMatVec(fn,A,v);
80: VecAXPY(v,-1.0,f0);
81: VecNorm(v,NORM_2,&nrm);
82: if (nrm>100*PETSC_MACHINE_EPSILON) {
83: PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
84: }
85: MatDestroy(&S);
86: MatDestroy(&R);
87: VecDestroy(&v);
88: VecDestroy(&f0);
89: return(0);
90: }
94: int main(int argc,char **argv)
95: {
97: FN fn;
98: Mat A;
99: PetscInt i,j,n=10;
100: PetscScalar *As,tau=1.0,eta=1.0;
101: PetscViewer viewer;
102: PetscBool verbose,inplace;
103: PetscRandom myrand;
104: PetscReal v;
106: SlepcInitialize(&argc,&argv,(char*)0,help);
107: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
108: PetscOptionsGetScalar(NULL,NULL,"-tau",&tau,NULL);
109: PetscOptionsGetScalar(NULL,NULL,"-eta",&eta,NULL);
110: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
111: PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
112: PetscPrintf(PETSC_COMM_WORLD,"Matrix square root, n=%D.\n",n);
114: /* Create function eta*sqrt(tau*x) */
115: FNCreate(PETSC_COMM_WORLD,&fn);
116: FNSetType(fn,FNSQRT);
117: FNSetScale(fn,tau,eta);
119: /* Set up viewer */
120: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
121: FNView(fn,viewer);
122: if (verbose) {
123: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
124: }
126: /* Create matrix */
127: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
128: PetscObjectSetName((PetscObject)A,"A");
130: /* Compute square root of a symmetric matrix A */
131: MatDenseGetArray(A,&As);
132: for (i=0;i<n;i++) As[i+i*n]=2.5;
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: MatDenseRestoreArray(A,&As);
137: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
138: TestMatSqrt(fn,A,viewer,verbose,inplace);
140: /* Repeat with upper triangular A */
141: MatDenseGetArray(A,&As);
142: for (j=1;j<3;j++) {
143: for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
144: }
145: MatDenseRestoreArray(A,&As);
146: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
147: TestMatSqrt(fn,A,viewer,verbose,inplace);
149: /* Repeat with non-symmetic A */
150: PetscRandomCreate(PETSC_COMM_WORLD,&myrand);
151: PetscRandomSetFromOptions(myrand);
152: PetscRandomSetInterval(myrand,0.0,1.0);
153: MatDenseGetArray(A,&As);
154: for (j=1;j<3;j++) {
155: for (i=0;i<n-j;i++) {
156: PetscRandomGetValueReal(myrand,&v);
157: As[(i+j)+i*n]=v;
158: }
159: }
160: MatDenseRestoreArray(A,&As);
161: PetscRandomDestroy(&myrand);
162: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
163: TestMatSqrt(fn,A,viewer,verbose,inplace);
165: MatDestroy(&A);
166: FNDestroy(&fn);
167: SlepcFinalize();
168: return ierr;
169: }