Actual source code: test11.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: */
10: /*
11: Define the function
13: f(x) = (exp(x)-1)/x (the phi_1 function)
15: with the following tree:
17: f(x) f(x) (combined by division)
18: / \ p(x) = x (polynomial)
19: a(x) p(x) a(x) (combined by addition)
20: / \ e(x) = exp(x) (exponential)
21: e(x) c(x) c(x) = -1 (constant)
22: */
24: static char help[] = "Another test of a combined function.\n\n";
26: #include <slepcfn.h>
28: /*
29: Compute matrix function B = A\(exp(A)-I)
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,p,a,e,c,f1,f2;
83: FNCombineType ctype;
84: Mat A=NULL;
85: PetscInt i,j,n=10,np;
86: PetscScalar x,y,yp,*As,coeffs[10];
87: char strx[50],str[50];
88: PetscViewer viewer;
89: PetscBool verbose,inplace,matcuda;
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,"Phi1 via a combined function, n=%" PetscInt_FMT ".\n",n);
99: /* Create function */
101: /* e(x) = exp(x) */
102: FNCreate(PETSC_COMM_WORLD,&e);
103: PetscObjectSetName((PetscObject)e,"e");
104: FNSetType(e,FNEXP);
105: FNSetFromOptions(e);
106: /* c(x) = -1 */
107: FNCreate(PETSC_COMM_WORLD,&c);
108: PetscObjectSetName((PetscObject)c,"c");
109: FNSetType(c,FNRATIONAL);
110: FNSetFromOptions(c);
111: np = 1;
112: coeffs[0] = -1.0;
113: FNRationalSetNumerator(c,np,coeffs);
114: /* a(x) */
115: FNCreate(PETSC_COMM_WORLD,&a);
116: PetscObjectSetName((PetscObject)a,"a");
117: FNSetType(a,FNCOMBINE);
118: FNSetFromOptions(a);
119: FNCombineSetChildren(a,FN_COMBINE_ADD,e,c);
120: /* p(x) = x */
121: FNCreate(PETSC_COMM_WORLD,&p);
122: PetscObjectSetName((PetscObject)p,"p");
123: FNSetType(p,FNRATIONAL);
124: FNSetFromOptions(p);
125: np = 2;
126: coeffs[0] = 1.0; coeffs[1] = 0.0;
127: FNRationalSetNumerator(p,np,coeffs);
128: /* f(x) */
129: FNCreate(PETSC_COMM_WORLD,&f);
130: PetscObjectSetName((PetscObject)f,"f");
131: FNSetType(f,FNCOMBINE);
132: FNSetFromOptions(f);
133: FNCombineSetChildren(f,FN_COMBINE_DIVIDE,a,p);
135: /* Set up viewer */
136: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
137: FNCombineGetChildren(f,&ctype,&f1,&f2);
138: PetscPrintf(PETSC_COMM_WORLD,"Two functions combined with division:\n");
139: FNView(f1,viewer);
140: FNView(f2,viewer);
141: if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
143: /* Scalar evaluation */
144: x = 2.2;
145: SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
146: FNEvaluateFunction(f,x,&y);
147: FNEvaluateDerivative(f,x,&yp);
148: SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
149: PetscPrintf(PETSC_COMM_WORLD," f(%s)=%s\n",strx,str);
150: SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
151: PetscPrintf(PETSC_COMM_WORLD," f'(%s)=%s\n",strx,str);
153: /* Create matrices */
154: if (matcuda) {
155: #if defined(PETSC_HAVE_CUDA)
156: MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A);
157: #endif
158: } else MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
159: PetscObjectSetName((PetscObject)A,"A");
161: /* Fill A with 1-D Laplacian matrix */
162: MatDenseGetArray(A,&As);
163: for (i=0;i<n;i++) As[i+i*n]=2.0;
164: j=1;
165: for (i=0;i<n-j;i++) { As[i+(i+j)*n]=-1.0; As[(i+j)+i*n]=-1.0; }
166: MatDenseRestoreArray(A,&As);
167: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
168: TestMatCombine(f,A,viewer,verbose,inplace);
170: /* Repeat with same matrix as non-symmetric */
171: MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
172: TestMatCombine(f,A,viewer,verbose,inplace);
174: MatDestroy(&A);
175: FNDestroy(&f);
176: FNDestroy(&p);
177: FNDestroy(&a);
178: FNDestroy(&e);
179: FNDestroy(&c);
180: SlepcFinalize();
181: return 0;
182: }
184: /*TEST
186: testset:
187: output_file: output/test11_1.out
188: test:
189: suffix: 1
190: test:
191: suffix: 1_cuda
192: args: -matcuda
193: requires: cuda
194: test:
195: suffix: 2
196: args: -inplace
197: test:
198: suffix: 2_cuda
199: args: -inplace -matcuda
200: requires: cuda
202: TEST*/