152 lines
4.8 KiB
C
152 lines
4.8 KiB
C
/* statistics accelerator C extension: _statistics module. */
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#include "Python.h"
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#include "clinic/_statisticsmodule.c.h"
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/*[clinic input]
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module _statistics
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[clinic start generated code]*/
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/*[clinic end generated code: output=da39a3ee5e6b4b0d input=864a6f59b76123b2]*/
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/*
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* There is no closed-form solution to the inverse CDF for the normal
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* distribution, so we use a rational approximation instead:
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* Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
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* Normal Distribution". Applied Statistics. Blackwell Publishing. 37
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* (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
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*/
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/*[clinic input]
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_statistics._normal_dist_inv_cdf -> double
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p: double
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mu: double
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sigma: double
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/
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[clinic start generated code]*/
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static double
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_statistics__normal_dist_inv_cdf_impl(PyObject *module, double p, double mu,
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double sigma)
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/*[clinic end generated code: output=02fd19ddaab36602 input=24715a74be15296a]*/
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{
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double q, num, den, r, x;
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if (p <= 0.0 || p >= 1.0 || sigma <= 0.0) {
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goto error;
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}
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q = p - 0.5;
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if(fabs(q) <= 0.425) {
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r = 0.180625 - q * q;
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// Hash sum-55.8831928806149014439
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num = (((((((2.5090809287301226727e+3 * r +
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3.3430575583588128105e+4) * r +
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6.7265770927008700853e+4) * r +
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4.5921953931549871457e+4) * r +
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1.3731693765509461125e+4) * r +
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1.9715909503065514427e+3) * r +
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1.3314166789178437745e+2) * r +
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3.3871328727963666080e+0) * q;
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den = (((((((5.2264952788528545610e+3 * r +
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2.8729085735721942674e+4) * r +
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3.9307895800092710610e+4) * r +
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2.1213794301586595867e+4) * r +
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5.3941960214247511077e+3) * r +
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6.8718700749205790830e+2) * r +
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4.2313330701600911252e+1) * r +
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1.0);
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if (den == 0.0) {
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goto error;
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}
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x = num / den;
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return mu + (x * sigma);
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}
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r = (q <= 0.0) ? p : (1.0 - p);
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if (r <= 0.0 || r >= 1.0) {
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goto error;
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}
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r = sqrt(-log(r));
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if (r <= 5.0) {
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r = r - 1.6;
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// Hash sum-49.33206503301610289036
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num = (((((((7.74545014278341407640e-4 * r +
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2.27238449892691845833e-2) * r +
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2.41780725177450611770e-1) * r +
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1.27045825245236838258e+0) * r +
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3.64784832476320460504e+0) * r +
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5.76949722146069140550e+0) * r +
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4.63033784615654529590e+0) * r +
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1.42343711074968357734e+0);
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den = (((((((1.05075007164441684324e-9 * r +
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5.47593808499534494600e-4) * r +
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1.51986665636164571966e-2) * r +
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1.48103976427480074590e-1) * r +
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6.89767334985100004550e-1) * r +
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1.67638483018380384940e+0) * r +
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2.05319162663775882187e+0) * r +
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1.0);
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} else {
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r -= 5.0;
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// Hash sum-47.52583317549289671629
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num = (((((((2.01033439929228813265e-7 * r +
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2.71155556874348757815e-5) * r +
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1.24266094738807843860e-3) * r +
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2.65321895265761230930e-2) * r +
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2.96560571828504891230e-1) * r +
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1.78482653991729133580e+0) * r +
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5.46378491116411436990e+0) * r +
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6.65790464350110377720e+0);
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den = (((((((2.04426310338993978564e-15 * r +
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1.42151175831644588870e-7) * r +
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1.84631831751005468180e-5) * r +
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7.86869131145613259100e-4) * r +
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1.48753612908506148525e-2) * r +
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1.36929880922735805310e-1) * r +
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5.99832206555887937690e-1) * r +
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1.0);
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}
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if (den == 0.0) {
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goto error;
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}
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x = num / den;
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if (q < 0.0) {
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x = -x;
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}
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return mu + (x * sigma);
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error:
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PyErr_SetString(PyExc_ValueError, "inv_cdf undefined for these parameters");
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return -1.0;
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}
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static PyMethodDef statistics_methods[] = {
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_STATISTICS__NORMAL_DIST_INV_CDF_METHODDEF
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{NULL, NULL, 0, NULL}
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};
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PyDoc_STRVAR(statistics_doc,
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"Accelerators for the statistics module.\n");
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static struct PyModuleDef_Slot _statisticsmodule_slots[] = {
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{0, NULL}
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};
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static struct PyModuleDef statisticsmodule = {
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PyModuleDef_HEAD_INIT,
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"_statistics",
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statistics_doc,
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0,
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statistics_methods,
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_statisticsmodule_slots,
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NULL,
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NULL,
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NULL
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};
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PyMODINIT_FUNC
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PyInit__statistics(void)
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{
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return PyModuleDef_Init(&statisticsmodule);
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}
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