1 static char help[] = "Tests quadrature.\n\n"; 2 3 #include <petscdt.h> 4 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 } 10 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 } 16 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 } 22 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 } 29 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 } 36 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 } 42 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 } 49 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 } 56 57 static void func9(const PetscReal x[], void *dummy, PetscReal *val) 58 { 59 *val = PetscLogReal(PetscCosReal(x[0])); 60 } 61 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 } 69 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 } 75 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 } 83 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 } 91 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 } 99 100 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; 119 120 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(); 125 126 /* Integrate each function */ 127 for (f = 0; f < 14; ++f) { 128 PetscReal integral; 129 130 /* 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; 143 144 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 } 151 152 /*TEST 153 build: 154 requires: !complex 155 156 test: 157 suffix: 0 158 TEST*/ 159