Actual source code: test7.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 square root.\n\n";
13: #include <slepcfn.h>
15: /*
16: Compute matrix square root B = sqrtm(A)
17: Check result as norm(B*B-A)
18: */
19: PetscErrorCode TestMatSqrt(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
20: {
22: PetscScalar tau,eta;
23: PetscReal nrm;
24: PetscBool set,flg;
25: PetscInt n;
26: Mat S,R;
27: Vec v,f0;
30: MatGetSize(A,&n,NULL);
31: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&S);
32: PetscObjectSetName((PetscObject)S,"S");
33: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&R);
34: PetscObjectSetName((PetscObject)R,"R");
35: FNGetScale(fn,&tau,&eta);
36: /* compute square root */
37: if (inplace) {
38: MatCopy(A,S,SAME_NONZERO_PATTERN);
39: MatIsHermitianKnown(A,&set,&flg);
40: if (set && flg) { MatSetOption(S,MAT_HERMITIAN,PETSC_TRUE); }
41: FNEvaluateFunctionMat(fn,S,NULL);
42: } else {
43: FNEvaluateFunctionMat(fn,A,S);
44: }
45: if (verbose) {
46: PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
47: MatView(A,viewer);
48: PetscPrintf(PETSC_COMM_WORLD,"Computed sqrtm(A) - - - - - - -\n");
49: MatView(S,viewer);
50: }
51: /* check error ||S*S-A||_F */
52: MatMatMult(S,S,MAT_REUSE_MATRIX,PETSC_DEFAULT,&R);
53: if (eta!=1.0) {
54: MatScale(R,1.0/(eta*eta));
55: }
56: MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN);
57: MatNorm(R,NORM_FROBENIUS,&nrm);
58: if (nrm<100*PETSC_MACHINE_EPSILON) {
59: PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F < 100*eps\n");
60: } else {
61: PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F = %g\n",(double)nrm);
62: }
63: /* check FNEvaluateFunctionMatVec() */
64: MatCreateVecs(A,&v,&f0);
65: MatGetColumnVector(S,f0,0);
66: FNEvaluateFunctionMatVec(fn,A,v);
67: VecAXPY(v,-1.0,f0);
68: VecNorm(v,NORM_2,&nrm);
69: if (nrm>100*PETSC_MACHINE_EPSILON) {
70: PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
71: }
72: MatDestroy(&S);
73: MatDestroy(&R);
74: VecDestroy(&v);
75: VecDestroy(&f0);
76: return(0);
77: }
79: int main(int argc,char **argv)
80: {
82: FN fn;
83: Mat A;
84: PetscInt i,j,n=10;
85: PetscScalar *As;
86: PetscViewer viewer;
87: PetscBool verbose,inplace;
88: PetscRandom myrand;
89: PetscReal v;
91: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
92: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
93: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
94: PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
95: PetscPrintf(PETSC_COMM_WORLD,"Matrix square root, n=%D.\n",n);
97: /* Create function object */
98: FNCreate(PETSC_COMM_WORLD,&fn);
99: FNSetType(fn,FNSQRT);
100: FNSetFromOptions(fn);
102: /* Set up viewer */
103: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
104: FNView(fn,viewer);
105: if (verbose) {
106: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
107: }
109: /* Create matrix */
110: MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
111: PetscObjectSetName((PetscObject)A,"A");
113: /* Compute square root of a symmetric matrix A */
114: MatDenseGetArray(A,&As);
115: for (i=0;i<n;i++) As[i+i*n]=2.5;
116: for (j=1;j<3;j++) {
117: for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
118: }
119: MatDenseRestoreArray(A,&As);
120: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
121: TestMatSqrt(fn,A,viewer,verbose,inplace);
123: /* Repeat with upper triangular A */
124: MatDenseGetArray(A,&As);
125: for (j=1;j<3;j++) {
126: for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
127: }
128: MatDenseRestoreArray(A,&As);
129: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
130: TestMatSqrt(fn,A,viewer,verbose,inplace);
132: /* Repeat with non-symmetic A */
133: PetscRandomCreate(PETSC_COMM_WORLD,&myrand);
134: PetscRandomSetFromOptions(myrand);
135: PetscRandomSetInterval(myrand,0.0,1.0);
136: MatDenseGetArray(A,&As);
137: for (j=1;j<3;j++) {
138: for (i=0;i<n-j;i++) {
139: PetscRandomGetValueReal(myrand,&v);
140: As[(i+j)+i*n]=v;
141: }
142: }
143: MatDenseRestoreArray(A,&As);
144: PetscRandomDestroy(&myrand);
145: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
146: TestMatSqrt(fn,A,viewer,verbose,inplace);
148: MatDestroy(&A);
149: FNDestroy(&fn);
150: SlepcFinalize();
151: return ierr;
152: }
154: /*TEST
156: test:
157: suffix: 1
158: nsize: 1
159: args: -fn_scale .05,2 -n 100 -fn_method {{0 1 2}shared output}
160: filter: grep -v "computing matrix functions"
161: output_file: output/test7_1.out
162: timeoutfactor: 2
164: test:
165: suffix: 1_sadeghi
166: nsize: 1
167: args: -fn_scale .05,2 -n 100 -fn_method 3
168: requires: !single
169: filter: grep -v "computing matrix functions"
170: output_file: output/test7_1.out
172: test:
173: suffix: 2
174: nsize: 1
175: args: -fn_scale .05,2 -n 100 -inplace -fn_method {{0 1 2}shared output}
176: filter: grep -v "computing matrix functions"
177: output_file: output/test7_1.out
178: timeoutfactor: 2
180: test:
181: suffix: 2_sadeghi
182: nsize: 1
183: args: -fn_scale .05,2 -n 100 -inplace -fn_method 3
184: requires: !single
185: filter: grep -v "computing matrix functions"
186: output_file: output/test7_1.out
188: test:
189: suffix: 3
190: nsize: 3
191: args: -fn_scale .05,2 -n 100 -fn_parallel synchronized
192: filter: grep -v "computing matrix functions" | grep -v "SYNCHRONIZED" | sed -e "s/3 MPI/1 MPI/g"
193: output_file: output/test7_1.out
195: test:
196: suffix: 4
197: nsize: 3
198: args: -fn_scale .05,2 -n 100 -inplace -fn_parallel synchronized
199: filter: grep -v "computing matrix functions" | grep -v "SYNCHRONIZED" | sed -e "s/3 MPI/1 MPI/g"
200: output_file: output/test7_1.out
202: TEST*/