Actual source code: ex3.c
1: static char help[] = "Tests quadrature.\n\n";
3: #include <petscdt.h>
5: static void func1(const PetscReal a[], void *dummy, PetscReal *val)
6: {
7: const PetscReal x = a[0];
8: *val = x * PetscLogReal(1 + x);
9: }
11: static void func2(const PetscReal a[], void *dummy, PetscReal *val)
12: {
13: const PetscReal x = a[0];
14: *val = x * x * PetscAtanReal(x);
15: }
17: static void func3(const PetscReal a[], void *dummy, PetscReal *val)
18: {
19: const PetscReal x = a[0];
20: *val = PetscExpReal(x) * PetscCosReal(x);
21: }
23: static void func4(const PetscReal a[], void *dummy, PetscReal *val)
24: {
25: const PetscReal x = a[0];
26: const PetscReal u = PetscSqrtReal(2.0 + x * x);
27: *val = PetscAtanReal(u) / ((1.0 + x * x) * u);
28: }
30: static void func5(const PetscReal a[], void *dummy, PetscReal *val)
31: {
32: const PetscReal x = a[0];
33: if (x == 0.0) *val = 0.0;
34: else *val = PetscSqrtReal(x) * PetscLogReal(x);
35: }
37: static void func6(const PetscReal a[], void *dummy, PetscReal *val)
38: {
39: const PetscReal x = a[0];
40: *val = PetscSqrtReal(1 - x * x);
41: }
43: static void func7(const PetscReal a[], void *dummy, PetscReal *val)
44: {
45: const PetscReal x = a[0];
46: if (x == 1.0) *val = PETSC_INFINITY;
47: else *val = PetscSqrtReal(x) / PetscSqrtReal(1 - x * x);
48: }
50: static void func8(const PetscReal a[], void *dummy, PetscReal *val)
51: {
52: const PetscReal x = a[0];
53: if (x == 0.0) *val = PETSC_INFINITY;
54: else *val = PetscLogReal(x) * PetscLogReal(x);
55: }
57: static void func9(const PetscReal x[], void *dummy, PetscReal *val)
58: {
59: *val = PetscLogReal(PetscCosReal(x[0]));
60: }
62: static void func10(const PetscReal a[], void *dummy, PetscReal *val)
63: {
64: const PetscReal x = a[0];
65: if (x == 0.0) *val = 0.0;
66: else if (x == 1.0) *val = PETSC_INFINITY;
67: *val = PetscSqrtReal(PetscTanReal(x));
68: }
70: static void func11(const PetscReal a[], void *dummy, PetscReal *val)
71: {
72: const PetscReal x = a[0];
73: *val = 1 / (1 - 2 * x + 2 * x * x);
74: }
76: static void func12(const PetscReal a[], void *dummy, PetscReal *val)
77: {
78: const PetscReal x = a[0];
79: if (x == 0.0) *val = 0.0;
80: else if (x == 1.0) *val = PETSC_INFINITY;
81: else *val = PetscExpReal(1 - 1 / x) / PetscSqrtReal(x * x * x - x * x * x * x);
82: }
84: static void func13(const PetscReal a[], void *dummy, PetscReal *val)
85: {
86: const PetscReal x = a[0];
87: if (x == 0.0) *val = 0.0;
88: else if (x == 1.0) *val = 1.0;
89: else *val = PetscExpReal(-(1 / x - 1) * (1 / x - 1) / 2) / (x * x);
90: }
92: static void func14(const PetscReal a[], void *dummy, PetscReal *val)
93: {
94: const PetscReal x = a[0];
95: if (x == 0.0) *val = 0.0;
96: else if (x == 1.0) *val = 1.0;
97: else *val = PetscExpReal(1 - 1 / x) * PetscCosReal(1 / x - 1) / (x * x);
98: }
100: int main(int argc, char **argv)
101: {
102: #if PETSC_SCALAR_SIZE == 32
103: PetscInt digits = 7;
104: #elif PETSC_SCALAR_SIZE == 64
105: PetscInt digits = 14;
106: #else
107: PetscInt digits = 14;
108: #endif
109: /* for some reason in __float128 precision it cannot get more accuracy for some of the integrals */
110: #if defined(PETSC_USE_REAL___FLOAT128)
111: const PetscReal epsilon = 2.2204460492503131e-16;
112: #else
113: const PetscReal epsilon = 2500. * PETSC_MACHINE_EPSILON;
114: #endif
115: const PetscReal bounds[28] = {0.0, 1.0, 0.0, 1.0, 0.0, PETSC_PI / 2., 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, PETSC_PI / 2., 0.0, PETSC_PI / 2., 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0};
116: const PetscReal analytic[14] = {0.250000000000000, 0.210657251225806988108092302182988001695680805674, 1.905238690482675827736517833351916563195085437332, 0.514041895890070761397629739576882871630921844127, -.444444444444444444444444444444444444444444444444, 0.785398163397448309615660845819875721049292349843, 1.198140234735592207439922492280323878227212663216, 2.000000000000000000000000000000000000000000000000, -1.08879304515180106525034444911880697366929185018, 2.221441469079183123507940495030346849307310844687, 1.570796326794896619231321691639751442098584699687, 1.772453850905516027298167483341145182797549456122, 1.253314137315500251207882642405522626503493370304, 0.500000000000000000000000000000000000000000000000};
117: void (*funcs[14])(const PetscReal[], void *, PetscReal *) = {func1, func2, func3, func4, func5, func6, func7, func8, func9, func10, func11, func12, func13, func14};
118: PetscInt f;
120: PetscFunctionBeginUser;
121: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
122: PetscOptionsBegin(PETSC_COMM_WORLD, "", "Test Options", "none");
123: PetscCall(PetscOptionsBoundedInt("-digits", "The number of significant digits for the integral", "ex3.c", digits, &digits, NULL, 1));
124: PetscOptionsEnd();
126: /* Integrate each function */
127: for (f = 0; f < 14; ++f) {
128: PetscReal integral;
130: /* These can only be integrated accuractely using MPFR */
131: if ((f == 6) || (f == 7) || (f == 9) || (f == 11)) continue;
132: #if defined(PETSC_USE_REAL_SINGLE)
133: if (f == 8) continue;
134: #endif
135: PetscCall(PetscDTTanhSinhIntegrate(funcs[f], bounds[f * 2 + 0], bounds[f * 2 + 1], digits, NULL, &integral));
136: if (PetscAbsReal(integral - analytic[f]) > PetscMax(epsilon, PetscPowRealInt(10.0, -digits)) || PetscIsInfOrNanScalar(integral - analytic[f])) {
137: PetscCall(PetscPrintf(PETSC_COMM_SELF, "The integral of func%2" PetscInt_FMT " is wrong: %g (%g)\n", f + 1, (double)integral, (double)PetscAbsReal(integral - analytic[f])));
138: }
139: }
140: #if defined(PETSC_HAVE_MPFR)
141: for (f = 0; f < 14; ++f) {
142: PetscReal integral;
144: PetscCall(PetscDTTanhSinhIntegrateMPFR(funcs[f], bounds[f * 2 + 0], bounds[f * 2 + 1], digits, NULL, &integral));
145: if (PetscAbsReal(integral - analytic[f]) > PetscPowRealInt(10.0, -digits)) PetscCall(PetscPrintf(PETSC_COMM_SELF, "The integral of func%2d is wrong: %g (%g)\n", f + 1, (double)integral, (double)PetscAbsReal(integral - analytic[f])));
146: }
147: #endif
148: PetscCall(PetscFinalize());
149: return 0;
150: }
152: /*TEST
153: build:
154: requires: !complex
156: test:
157: suffix: 0
158: TEST*/