1 | /* statistics accelerator C extension: _statistics module. */ |
2 | |
3 | #include "Python.h" |
4 | #include "clinic/_statisticsmodule.c.h" |
5 | |
6 | /*[clinic input] |
7 | module _statistics |
8 | |
9 | [clinic start generated code]*/ |
10 | /*[clinic end generated code: output=da39a3ee5e6b4b0d input=864a6f59b76123b2]*/ |
11 | |
12 | /* |
13 | * There is no closed-form solution to the inverse CDF for the normal |
14 | * distribution, so we use a rational approximation instead: |
15 | * Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the |
16 | * Normal Distribution". Applied Statistics. Blackwell Publishing. 37 |
17 | * (3): 477–484. doi:10.2307/2347330. JSTOR 2347330. |
18 | */ |
19 | |
20 | /*[clinic input] |
21 | _statistics._normal_dist_inv_cdf -> double |
22 | p: double |
23 | mu: double |
24 | sigma: double |
25 | / |
26 | [clinic start generated code]*/ |
27 | |
28 | static double |
29 | _statistics__normal_dist_inv_cdf_impl(PyObject *module, double p, double mu, |
30 | double sigma) |
31 | /*[clinic end generated code: output=02fd19ddaab36602 input=24715a74be15296a]*/ |
32 | { |
33 | double q, num, den, r, x; |
34 | if (p <= 0.0 || p >= 1.0 || sigma <= 0.0) { |
35 | goto error; |
36 | } |
37 | |
38 | q = p - 0.5; |
39 | if(fabs(q) <= 0.425) { |
40 | r = 0.180625 - q * q; |
41 | // Hash sum-55.8831928806149014439 |
42 | num = (((((((2.5090809287301226727e+3 * r + |
43 | 3.3430575583588128105e+4) * r + |
44 | 6.7265770927008700853e+4) * r + |
45 | 4.5921953931549871457e+4) * r + |
46 | 1.3731693765509461125e+4) * r + |
47 | 1.9715909503065514427e+3) * r + |
48 | 1.3314166789178437745e+2) * r + |
49 | 3.3871328727963666080e+0) * q; |
50 | den = (((((((5.2264952788528545610e+3 * r + |
51 | 2.8729085735721942674e+4) * r + |
52 | 3.9307895800092710610e+4) * r + |
53 | 2.1213794301586595867e+4) * r + |
54 | 5.3941960214247511077e+3) * r + |
55 | 6.8718700749205790830e+2) * r + |
56 | 4.2313330701600911252e+1) * r + |
57 | 1.0); |
58 | if (den == 0.0) { |
59 | goto error; |
60 | } |
61 | x = num / den; |
62 | return mu + (x * sigma); |
63 | } |
64 | r = (q <= 0.0) ? p : (1.0 - p); |
65 | if (r <= 0.0 || r >= 1.0) { |
66 | goto error; |
67 | } |
68 | r = sqrt(-log(r)); |
69 | if (r <= 5.0) { |
70 | r = r - 1.6; |
71 | // Hash sum-49.33206503301610289036 |
72 | num = (((((((7.74545014278341407640e-4 * r + |
73 | 2.27238449892691845833e-2) * r + |
74 | 2.41780725177450611770e-1) * r + |
75 | 1.27045825245236838258e+0) * r + |
76 | 3.64784832476320460504e+0) * r + |
77 | 5.76949722146069140550e+0) * r + |
78 | 4.63033784615654529590e+0) * r + |
79 | 1.42343711074968357734e+0); |
80 | den = (((((((1.05075007164441684324e-9 * r + |
81 | 5.47593808499534494600e-4) * r + |
82 | 1.51986665636164571966e-2) * r + |
83 | 1.48103976427480074590e-1) * r + |
84 | 6.89767334985100004550e-1) * r + |
85 | 1.67638483018380384940e+0) * r + |
86 | 2.05319162663775882187e+0) * r + |
87 | 1.0); |
88 | } else { |
89 | r -= 5.0; |
90 | // Hash sum-47.52583317549289671629 |
91 | num = (((((((2.01033439929228813265e-7 * r + |
92 | 2.71155556874348757815e-5) * r + |
93 | 1.24266094738807843860e-3) * r + |
94 | 2.65321895265761230930e-2) * r + |
95 | 2.96560571828504891230e-1) * r + |
96 | 1.78482653991729133580e+0) * r + |
97 | 5.46378491116411436990e+0) * r + |
98 | 6.65790464350110377720e+0); |
99 | den = (((((((2.04426310338993978564e-15 * r + |
100 | 1.42151175831644588870e-7) * r + |
101 | 1.84631831751005468180e-5) * r + |
102 | 7.86869131145613259100e-4) * r + |
103 | 1.48753612908506148525e-2) * r + |
104 | 1.36929880922735805310e-1) * r + |
105 | 5.99832206555887937690e-1) * r + |
106 | 1.0); |
107 | } |
108 | if (den == 0.0) { |
109 | goto error; |
110 | } |
111 | x = num / den; |
112 | if (q < 0.0) { |
113 | x = -x; |
114 | } |
115 | return mu + (x * sigma); |
116 | |
117 | error: |
118 | PyErr_SetString(PyExc_ValueError, "inv_cdf undefined for these parameters" ); |
119 | return -1.0; |
120 | } |
121 | |
122 | |
123 | static PyMethodDef statistics_methods[] = { |
124 | _STATISTICS__NORMAL_DIST_INV_CDF_METHODDEF |
125 | {NULL, NULL, 0, NULL} |
126 | }; |
127 | |
128 | PyDoc_STRVAR(statistics_doc, |
129 | "Accelerators for the statistics module.\n" ); |
130 | |
131 | static struct PyModuleDef_Slot _statisticsmodule_slots[] = { |
132 | {0, NULL} |
133 | }; |
134 | |
135 | static struct PyModuleDef statisticsmodule = { |
136 | PyModuleDef_HEAD_INIT, |
137 | "_statistics" , |
138 | statistics_doc, |
139 | 0, |
140 | statistics_methods, |
141 | _statisticsmodule_slots, |
142 | NULL, |
143 | NULL, |
144 | NULL |
145 | }; |
146 | |
147 | PyMODINIT_FUNC |
148 | PyInit__statistics(void) |
149 | { |
150 | return PyModuleDef_Init(&statisticsmodule); |
151 | } |
152 | |