Actual source code: test8.c
slepc-3.21.2 2024-09-25
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 inverse square root.\n\n";
13: #include <slepcfn.h>
15: /*
16: Compute matrix inverse square root B = inv(sqrtm(A))
17: Check result as norm(B*B*A-I)
18: */
19: PetscErrorCode TestMatInvSqrt(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
20: {
21: PetscScalar tau,eta;
22: PetscReal nrm;
23: PetscBool set,flg;
24: PetscInt n;
25: Mat S,R,Acopy;
26: Vec v,f0;
28: PetscFunctionBeginUser;
29: PetscCall(MatGetSize(A,&n,NULL));
30: PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&S));
31: PetscCall(PetscObjectSetName((PetscObject)S,"S"));
32: PetscCall(FNGetScale(fn,&tau,&eta));
33: /* compute inverse square root */
34: if (inplace) {
35: PetscCall(MatCopy(A,S,SAME_NONZERO_PATTERN));
36: PetscCall(MatIsHermitianKnown(A,&set,&flg));
37: if (set && flg) PetscCall(MatSetOption(S,MAT_HERMITIAN,PETSC_TRUE));
38: PetscCall(FNEvaluateFunctionMat(fn,S,NULL));
39: } else {
40: PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&Acopy));
41: PetscCall(FNEvaluateFunctionMat(fn,A,S));
42: /* check that A has not been modified */
43: PetscCall(MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN));
44: PetscCall(MatNorm(Acopy,NORM_1,&nrm));
45: if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm));
46: PetscCall(MatDestroy(&Acopy));
47: }
48: if (verbose) {
49: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n"));
50: PetscCall(MatView(A,viewer));
51: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed inv(sqrtm(A)) - - - - - - -\n"));
52: PetscCall(MatView(S,viewer));
53: }
54: /* check error ||S*S*A-I||_F */
55: PetscCall(MatMatMult(S,S,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R));
56: if (eta!=1.0) PetscCall(MatScale(R,1.0/(eta*eta)));
57: PetscCall(MatCreateVecs(A,&v,&f0));
58: PetscCall(MatGetColumnVector(S,f0,0));
59: PetscCall(MatCopy(R,S,SAME_NONZERO_PATTERN));
60: PetscCall(MatDestroy(&R));
61: if (tau!=1.0) PetscCall(MatScale(S,tau));
62: PetscCall(MatMatMult(S,A,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R));
63: PetscCall(MatShift(R,-1.0));
64: PetscCall(MatNorm(R,NORM_FROBENIUS,&nrm));
65: PetscCall(MatDestroy(&R));
66: if (nrm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F < 100*eps\n"));
67: else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F = %g\n",(double)nrm));
68: /* check FNEvaluateFunctionMatVec() */
69: PetscCall(FNEvaluateFunctionMatVec(fn,A,v));
70: PetscCall(VecAXPY(v,-1.0,f0));
71: PetscCall(VecNorm(v,NORM_2,&nrm));
72: if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm));
73: PetscCall(MatDestroy(&S));
74: PetscCall(VecDestroy(&v));
75: PetscCall(VecDestroy(&f0));
76: PetscFunctionReturn(PETSC_SUCCESS);
77: }
79: int main(int argc,char **argv)
80: {
81: FN fn;
82: Mat A=NULL;
83: PetscInt i,j,n=10;
84: PetscScalar x,y,yp,*As;
85: PetscViewer viewer;
86: PetscBool verbose,inplace,matcuda;
87: PetscRandom myrand;
88: PetscReal v;
89: char strx[50],str[50];
91: PetscFunctionBeginUser;
92: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
93: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
94: PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));
95: PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace));
96: PetscCall(PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda));
97: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix inverse square root, n=%" PetscInt_FMT ".\n",n));
99: /* Create function object */
100: PetscCall(FNCreate(PETSC_COMM_WORLD,&fn));
101: PetscCall(FNSetType(fn,FNINVSQRT));
102: PetscCall(FNSetFromOptions(fn));
104: /* Set up viewer */
105: PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
106: PetscCall(FNView(fn,viewer));
107: if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));
109: /* Scalar evaluation */
110: x = 2.2;
111: PetscCall(SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE));
112: PetscCall(FNEvaluateFunction(fn,x,&y));
113: PetscCall(FNEvaluateDerivative(fn,x,&yp));
114: PetscCall(SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE));
115: PetscCall(PetscPrintf(PETSC_COMM_WORLD," f(%s)=%s\n",strx,str));
116: PetscCall(SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE));
117: PetscCall(PetscPrintf(PETSC_COMM_WORLD," f'(%s)=%s\n",strx,str));
119: /* Create matrix */
120: if (matcuda) {
121: #if defined(PETSC_HAVE_CUDA)
122: PetscCall(MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A));
123: #endif
124: } else PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A));
125: PetscCall(PetscObjectSetName((PetscObject)A,"A"));
127: /* Compute square root of a symmetric matrix A */
128: PetscCall(MatDenseGetArray(A,&As));
129: for (i=0;i<n;i++) As[i+i*n]=2.5;
130: for (j=1;j<3;j++) {
131: for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
132: }
133: PetscCall(MatDenseRestoreArray(A,&As));
134: PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
135: PetscCall(TestMatInvSqrt(fn,A,viewer,verbose,inplace));
137: /* Repeat with upper triangular A */
138: PetscCall(MatDenseGetArray(A,&As));
139: for (j=1;j<3;j++) {
140: for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
141: }
142: PetscCall(MatDenseRestoreArray(A,&As));
143: PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE));
144: PetscCall(TestMatInvSqrt(fn,A,viewer,verbose,inplace));
146: /* Repeat with non-symmetic A */
147: PetscCall(PetscRandomCreate(PETSC_COMM_WORLD,&myrand));
148: PetscCall(PetscRandomSetFromOptions(myrand));
149: PetscCall(PetscRandomSetInterval(myrand,0.0,1.0));
150: PetscCall(MatDenseGetArray(A,&As));
151: for (j=1;j<3;j++) {
152: for (i=0;i<n-j;i++) {
153: PetscCall(PetscRandomGetValueReal(myrand,&v));
154: As[(i+j)+i*n]=v;
155: }
156: }
157: PetscCall(MatDenseRestoreArray(A,&As));
158: PetscCall(PetscRandomDestroy(&myrand));
159: PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE));
160: PetscCall(TestMatInvSqrt(fn,A,viewer,verbose,inplace));
162: PetscCall(MatDestroy(&A));
163: PetscCall(FNDestroy(&fn));
164: PetscCall(SlepcFinalize());
165: return 0;
166: }
168: /*TEST
170: testset:
171: args: -fn_scale 0.9,0.5 -n 10
172: filter: grep -v "computing matrix functions"
173: requires: !__float128
174: output_file: output/test8_1.out
175: test:
176: suffix: 1
177: args: -fn_method {{0 1 2 3}}
178: test:
179: suffix: 1_cuda
180: args: -fn_method 2 -matcuda
181: requires: cuda
182: test:
183: suffix: 1_magma
184: args: -fn_method {{1 3}} -matcuda
185: requires: cuda magma
186: test:
187: suffix: 2
188: args: -inplace -fn_method {{0 1 2 3}}
189: test:
190: suffix: 2_cuda
191: args: -inplace -fn_method 2 -matcuda
192: requires: cuda
193: test:
194: suffix: 2_magma
195: args: -inplace -fn_method {{1 3}} -matcuda
196: requires: cuda magma
198: TEST*/