Actual source code: test8.c
slepc-3.7.2 2016-07-19
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 inverse square root.\n\n";
24: #include <slepcfn.h>
28: /*
29: Compute matrix inverse square root B = inv(sqrtm(A))
30: Check result as norm(B*B*A-I)
31: */
32: PetscErrorCode TestMatInvSqrt(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 inverse 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 inv(sqrtm(A)) - - - - - - -\n");
62: MatView(S,viewer);
63: }
64: /* check error ||S*S*A-I||_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: MatCreateVecs(A,&v,&f0);
70: MatGetColumnVector(S,f0,0);
71: MatCopy(R,S,SAME_NONZERO_PATTERN);
72: if (tau!=1.0) {
73: MatScale(S,tau);
74: }
75: MatMatMult(S,A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&R);
76: MatShift(R,-1.0);
77: MatNorm(R,NORM_FROBENIUS,&nrm);
78: if (nrm<100*PETSC_MACHINE_EPSILON) {
79: PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F < 100*eps\n");
80: } else {
81: PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F = %g\n",(double)nrm);
82: }
83: /* check FNEvaluateFunctionMatVec() */
84: FNEvaluateFunctionMatVec(fn,A,v);
85: VecAXPY(v,-1.0,f0);
86: VecNorm(v,NORM_2,&nrm);
87: if (nrm>100*PETSC_MACHINE_EPSILON) {
88: PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
89: }
90: MatDestroy(&S);
91: MatDestroy(&R);
92: VecDestroy(&v);
93: VecDestroy(&f0);
94: return(0);
95: }
99: int main(int argc,char **argv)
100: {
102: FN fn;
103: Mat A;
104: PetscInt i,j,n=10;
105: PetscScalar *As,tau=1.0,eta=1.0;
106: PetscViewer viewer;
107: PetscBool verbose,inplace;
108: PetscRandom myrand;
109: PetscReal v;
111: SlepcInitialize(&argc,&argv,(char*)0,help);
112: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
113: PetscOptionsGetScalar(NULL,NULL,"-tau",&tau,NULL);
114: PetscOptionsGetScalar(NULL,NULL,"-eta",&eta,NULL);
115: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
116: PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
117: PetscPrintf(PETSC_COMM_WORLD,"Matrix inverse square root, n=%D.\n",n);
119: /* Create function eta*inv(sqrt(tau*x)) */
120: FNCreate(PETSC_COMM_WORLD,&fn);
121: FNSetType(fn,FNINVSQRT);
122: FNSetScale(fn,tau,eta);
124: /* Set up viewer */
125: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
126: FNView(fn,viewer);
127: if (verbose) {
128: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
129: }
131: /* Create matrix */
132: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
133: PetscObjectSetName((PetscObject)A,"A");
135: /* Compute square root of a symmetric matrix A */
136: MatDenseGetArray(A,&As);
137: for (i=0;i<n;i++) As[i+i*n]=2.5;
138: for (j=1;j<3;j++) {
139: for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
140: }
141: MatDenseRestoreArray(A,&As);
142: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
143: TestMatInvSqrt(fn,A,viewer,verbose,inplace);
145: /* Repeat with upper triangular A */
146: MatDenseGetArray(A,&As);
147: for (j=1;j<3;j++) {
148: for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
149: }
150: MatDenseRestoreArray(A,&As);
151: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
152: TestMatInvSqrt(fn,A,viewer,verbose,inplace);
154: /* Repeat with non-symmetic A */
155: PetscRandomCreate(PETSC_COMM_WORLD,&myrand);
156: PetscRandomSetFromOptions(myrand);
157: PetscRandomSetInterval(myrand,0.0,1.0);
158: MatDenseGetArray(A,&As);
159: for (j=1;j<3;j++) {
160: for (i=0;i<n-j;i++) {
161: PetscRandomGetValueReal(myrand,&v);
162: As[(i+j)+i*n]=v;
163: }
164: }
165: MatDenseRestoreArray(A,&As);
166: PetscRandomDestroy(&myrand);
167: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
168: TestMatInvSqrt(fn,A,viewer,verbose,inplace);
170: MatDestroy(&A);
171: FNDestroy(&fn);
172: SlepcFinalize();
173: return ierr;
174: }