Actual source code: test6.c
slepc-3.18.2 2023-01-26
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: */
10: /*
11: Define the function
13: f(x) = (1-x^2) exp(-x/(1+x^2))
15: with the following tree:
17: f(x) f(x) (combined by product)
18: / \ g(x) = 1-x^2 (polynomial)
19: g(x) h(x) h(x) (combined by composition)
20: / \ r(x) = -x/(1+x^2) (rational)
21: r(x) e(x) e(x) = exp(x) (exponential)
22: */
24: static char help[] = "Test combined function.\n\n";
26: #include <slepcfn.h>
28: /*
29: Compute matrix function B = (I-A^2) exp(-(I+A^2)\A)
30: */
31: PetscErrorCode TestMatCombine(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
32: {
33: PetscBool set,flg;
34: PetscInt n;
35: Mat F,Acopy;
36: Vec v,f0;
37: PetscReal nrm;
40: MatGetSize(A,&n,NULL);
41: MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&F);
42: PetscObjectSetName((PetscObject)F,"F");
43: /* compute matrix function */
44: if (inplace) {
45: MatCopy(A,F,SAME_NONZERO_PATTERN);
46: MatIsHermitianKnown(A,&set,&flg);
47: if (set && flg) MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE);
48: FNEvaluateFunctionMat(fn,F,NULL);
49: } else {
50: MatDuplicate(A,MAT_COPY_VALUES,&Acopy);
51: FNEvaluateFunctionMat(fn,A,F);
52: /* check that A has not been modified */
53: MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN);
54: MatNorm(Acopy,NORM_1,&nrm);
55: if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm);
56: MatDestroy(&Acopy);
57: }
58: if (verbose) {
59: PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
60: MatView(A,viewer);
61: PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");
62: MatView(F,viewer);
63: }
64: /* print matrix norm for checking */
65: MatNorm(F,NORM_1,&nrm);
66: PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %6.3f\n",(double)nrm);
67: /* check FNEvaluateFunctionMatVec() */
68: MatCreateVecs(A,&v,&f0);
69: MatGetColumnVector(F,f0,0);
70: FNEvaluateFunctionMatVec(fn,A,v);
71: VecAXPY(v,-1.0,f0);
72: VecNorm(v,NORM_2,&nrm);
73: if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
74: MatDestroy(&F);
75: VecDestroy(&v);
76: VecDestroy(&f0);
77: return 0;
78: }
80: int main(int argc,char **argv)
81: {
82: FN f,g,h,e,r,fcopy;
83: Mat A=NULL;
84: PetscInt i,j,n=10,np,nq;
85: PetscScalar x,y,yp,*As,p[10],q[10];
86: char strx[50],str[50];
87: PetscViewer viewer;
88: PetscBool verbose,inplace,matcuda;
91: SlepcInitialize(&argc,&argv,(char*)0,help);
92: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
93: PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
94: PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
95: PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda);
96: PetscPrintf(PETSC_COMM_WORLD,"Combined function, n=%" PetscInt_FMT ".\n",n);
98: /* Create function */
100: /* e(x) = exp(x) */
101: FNCreate(PETSC_COMM_WORLD,&e);
102: FNSetType(e,FNEXP);
103: FNSetFromOptions(e);
104: /* r(x) = x/(1+x^2) */
105: FNCreate(PETSC_COMM_WORLD,&r);
106: FNSetType(r,FNRATIONAL);
107: FNSetFromOptions(r);
108: np = 2; nq = 3;
109: p[0] = -1.0; p[1] = 0.0;
110: q[0] = 1.0; q[1] = 0.0; q[2] = 1.0;
111: FNRationalSetNumerator(r,np,p);
112: FNRationalSetDenominator(r,nq,q);
113: /* h(x) */
114: FNCreate(PETSC_COMM_WORLD,&h);
115: FNSetType(h,FNCOMBINE);
116: FNSetFromOptions(h);
117: FNCombineSetChildren(h,FN_COMBINE_COMPOSE,r,e);
118: /* g(x) = 1-x^2 */
119: FNCreate(PETSC_COMM_WORLD,&g);
120: FNSetType(g,FNRATIONAL);
121: FNSetFromOptions(g);
122: np = 3;
123: p[0] = -1.0; p[1] = 0.0; p[2] = 1.0;
124: FNRationalSetNumerator(g,np,p);
125: /* f(x) */
126: FNCreate(PETSC_COMM_WORLD,&f);
127: FNSetType(f,FNCOMBINE);
128: FNSetFromOptions(f);
129: FNCombineSetChildren(f,FN_COMBINE_MULTIPLY,g,h);
131: /* Set up viewer */
132: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
133: FNView(f,viewer);
134: if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
136: /* Scalar evaluation */
137: x = 2.2;
138: SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
139: FNEvaluateFunction(f,x,&y);
140: FNEvaluateDerivative(f,x,&yp);
141: SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
142: PetscPrintf(PETSC_COMM_WORLD," f(%s)=%s\n",strx,str);
143: SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
144: PetscPrintf(PETSC_COMM_WORLD," f'(%s)=%s\n",strx,str);
146: /* Test duplication */
147: FNDuplicate(f,PetscObjectComm((PetscObject)f),&fcopy);
149: /* Create matrices */
150: if (matcuda) {
151: #if defined(PETSC_HAVE_CUDA)
152: MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A);
153: #endif
154: } else MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
155: PetscObjectSetName((PetscObject)A,"A");
157: /* Fill A with a symmetric Toeplitz matrix */
158: MatDenseGetArray(A,&As);
159: for (i=0;i<n;i++) As[i+i*n]=2.0;
160: for (j=1;j<3;j++) {
161: for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
162: }
163: MatDenseRestoreArray(A,&As);
164: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
165: TestMatCombine(fcopy,A,viewer,verbose,inplace);
167: /* Repeat with same matrix as non-symmetric */
168: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
169: TestMatCombine(fcopy,A,viewer,verbose,inplace);
171: MatDestroy(&A);
172: FNDestroy(&f);
173: FNDestroy(&fcopy);
174: FNDestroy(&g);
175: FNDestroy(&h);
176: FNDestroy(&e);
177: FNDestroy(&r);
178: SlepcFinalize();
179: return 0;
180: }
182: /*TEST
184: testset:
185: output_file: output/test6_1.out
186: test:
187: suffix: 1
188: test:
189: suffix: 1_cuda
190: args: -matcuda
191: requires: cuda
192: test:
193: suffix: 2
194: args: -inplace
195: test:
196: suffix: 2_cuda
197: args: -inplace -matcuda
198: requires: cuda
200: TEST*/