Actual source code: test8.c
slepc-3.18.0 2022-10-01
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;
29: MatGetSize(A,&n,NULL);
30: MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&S);
31: PetscObjectSetName((PetscObject)S,"S");
32: FNGetScale(fn,&tau,&eta);
33: /* compute inverse square root */
34: if (inplace) {
35: MatCopy(A,S,SAME_NONZERO_PATTERN);
36: MatIsHermitianKnown(A,&set,&flg);
37: if (set && flg) MatSetOption(S,MAT_HERMITIAN,PETSC_TRUE);
38: FNEvaluateFunctionMat(fn,S,NULL);
39: } else {
40: MatDuplicate(A,MAT_COPY_VALUES,&Acopy);
41: FNEvaluateFunctionMat(fn,A,S);
42: /* check that A has not been modified */
43: MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN);
44: MatNorm(Acopy,NORM_1,&nrm);
45: if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm);
46: MatDestroy(&Acopy);
47: }
48: if (verbose) {
49: PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
50: MatView(A,viewer);
51: PetscPrintf(PETSC_COMM_WORLD,"Computed inv(sqrtm(A)) - - - - - - -\n");
52: MatView(S,viewer);
53: }
54: /* check error ||S*S*A-I||_F */
55: MatMatMult(S,S,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
56: if (eta!=1.0) MatScale(R,1.0/(eta*eta));
57: MatCreateVecs(A,&v,&f0);
58: MatGetColumnVector(S,f0,0);
59: MatCopy(R,S,SAME_NONZERO_PATTERN);
60: MatDestroy(&R);
61: if (tau!=1.0) MatScale(S,tau);
62: MatMatMult(S,A,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
63: MatShift(R,-1.0);
64: MatNorm(R,NORM_FROBENIUS,&nrm);
65: MatDestroy(&R);
66: if (nrm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F < 100*eps\n");
67: else PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F = %g\n",(double)nrm);
68: /* check FNEvaluateFunctionMatVec() */
69: FNEvaluateFunctionMatVec(fn,A,v);
70: VecAXPY(v,-1.0,f0);
71: VecNorm(v,NORM_2,&nrm);
72: if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
73: MatDestroy(&S);
74: VecDestroy(&v);
75: VecDestroy(&f0);
76: return 0;
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];
92: SlepcInitialize(&argc,&argv,(char*)0,help);
93: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
94: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
95: PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
96: PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda);
97: PetscPrintf(PETSC_COMM_WORLD,"Matrix inverse square root, n=%" PetscInt_FMT ".\n",n);
99: /* Create function object */
100: FNCreate(PETSC_COMM_WORLD,&fn);
101: FNSetType(fn,FNINVSQRT);
102: FNSetFromOptions(fn);
104: /* Set up viewer */
105: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
106: FNView(fn,viewer);
107: if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
109: /* Scalar evaluation */
110: x = 2.2;
111: SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
112: FNEvaluateFunction(fn,x,&y);
113: FNEvaluateDerivative(fn,x,&yp);
114: SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
115: PetscPrintf(PETSC_COMM_WORLD," f(%s)=%s\n",strx,str);
116: SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
117: PetscPrintf(PETSC_COMM_WORLD," f'(%s)=%s\n",strx,str);
119: /* Create matrix */
120: if (matcuda) {
121: #if defined(PETSC_HAVE_CUDA)
122: MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A);
123: #endif
124: } else MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
125: PetscObjectSetName((PetscObject)A,"A");
127: /* Compute square root of a symmetric matrix A */
128: 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: MatDenseRestoreArray(A,&As);
134: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
135: TestMatInvSqrt(fn,A,viewer,verbose,inplace);
137: /* Repeat with upper triangular A */
138: 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: MatDenseRestoreArray(A,&As);
143: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
144: TestMatInvSqrt(fn,A,viewer,verbose,inplace);
146: /* Repeat with non-symmetic A */
147: PetscRandomCreate(PETSC_COMM_WORLD,&myrand);
148: PetscRandomSetFromOptions(myrand);
149: PetscRandomSetInterval(myrand,0.0,1.0);
150: MatDenseGetArray(A,&As);
151: for (j=1;j<3;j++) {
152: for (i=0;i<n-j;i++) {
153: PetscRandomGetValueReal(myrand,&v);
154: As[(i+j)+i*n]=v;
155: }
156: }
157: MatDenseRestoreArray(A,&As);
158: PetscRandomDestroy(&myrand);
159: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
160: TestMatInvSqrt(fn,A,viewer,verbose,inplace);
162: MatDestroy(&A);
163: FNDestroy(&fn);
164: 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*/