`i@_|dZddlmZddlmZmZddlmZmZej dddd Z d Z ej d d d e dZ ej dddd Z dZdZdZej dddeezdZej dddeezdZej dd d!eezd"Zej d#d$d%ed&Zej d'd$d(ed)Zd*Zd+Zd,Zej d-d.d/eezd0Zej d1d.d2eezd3Zej d4d.d5eezd6Zd7Zd8Zd9Zej d:d$d;eezd<Zej d=d$d>eezd?Z ej d@d$dAeezdBZ!dCZ"dDZ#ej dEd$dFee"zdGZ$ej dHd$dIee#zdJZ%dKZ&dLZ'dMZ(ej dNdOdPee&zdQZ)ej dRdSdTee'zdUZ*ej dVdWdXee(zdYZ+dZZ,d[Z-d\Z.ej d]d.d^ee,zd_Z/ej d`d.daee-zdbZ0ej dcdddeee.zdfZ1dgS)haStatistical distribution functions (Beta, Binomial, Poisson, etc.) The source code here is an adaptation with minimal changes from the following files in SciPy's bundled Cephes library: https://github.com/scipy/scipy/blob/main/scipy/special/cephes/bdtr.c https://github.com/scipy/scipy/blob/main/scipy/special/cephes/chdtr.c https://github.com/scipy/scipy/blob/main/scipy/special/cephes/fdtr.c https://github.com/scipy/scipy/blob/main/scipy/special/cephes/gdtr.c https://github.com/scipy/scipy/blob/main/scipy/special/cephes/nbdtr.c https://github.com/scipy/scipy/blob/main/scipy/special/cephes/pdtr.c Cephes Math Library, Release 2.3: March, 1995 Copyright 1984, 1995 by Stephen L. Moshier )_core)incbet_preambleincbi_preamble)_igam_preamble_igami_preamblecupyx_scipy_special_ndtr))f->fzout0 = normcdff(in0)d->dzout0 = normcdf(in0)zkCumulative distribution function of normal distribution. .. seealso:: :data:`scipy.special.ndtr` )doca #define NPY_SQRT1_2 0.707106781186547524400844362104849039 /* 1/sqrt(2) */ static __device__ double log_ndtr(double x) { double t = x * NPY_SQRT1_2; if (x < -1.0) { return log(erfcx(-t) / 2) - t * t; } else { return log1p(-erfc(t) / 2); } } static __device__ float log_ndtrf(float x) { float t = x * NPY_SQRT1_2; if (x < -1.0) { return logf(erfcxf(-t) / 2) - t * t; } else { return log1pf(-erfcf(t) / 2); } } cupyx_scipy_special_log_ndtr))r zout0 = log_ndtrf(in0)r zout0 = log_ndtr(in0)aLogarithm of Gaussian cumulative distribution function. Returns the log of the area under the standard Gaussian probability density function. Parameters ---------- x : array-like The input array Returns ------- y : cupy.ndarray The value of the log of the normal cumulative distribution function evaluated at x See Also -------- :func:`scipy.special.log_ndtr` )preambler cupyx_scipy_special_ndtri))r zout0 = normcdfinvf(in0)r zout0 = normcdfinv(in0)zInverse of the cumulative distribution function of the standard normal distribution. .. seealso:: :data:`scipy.special.ndtri` a __device__ double bdtr(double k, int n, double p) { double dk, dn; double fk = floor(k); if (isnan(p) || isnan(k)) { return CUDART_NAN; } if (p < 0.0 || p > 1.0 || fk < 0 || n < fk) { return CUDART_NAN; } if (fk == n) { return 1.0; } dn = n - fk; if (fk == 0) { dk = pow(1.0 - p, dn); } else { dk = fk + 1.; dk = incbet(dn, dk, 1.0 - p); } return dk; } __device__ double bdtr_unsafe(double k, double n, double p) { if (isnan(n) || isinf(n)) { return CUDART_NAN; } else { return bdtr(k, (int)n, p); } } a __device__ double bdtrc(double k, int n, double p) { double dk, dn; double fk = floor(k); if (isnan(p) || isnan(k)) { return CUDART_NAN; } if (p < 0.0 || p > 1.0 || n < fk) { return CUDART_NAN; } if (fk < 0) { return 1.0; } if (fk == n) { return 0.0; } dn = n - fk; if (k == 0) { if (p < .01) { dk = -expm1(dn * log1p(-p)); } else { dk = 1.0 - pow(1.0 - p, dn); } } else { dk = fk + 1; dk = incbet(dk, dn, p); } return dk; } __device__ double bdtrc_unsafe(double k, double n, double p) { if (isnan(n) || isinf(n)) { return CUDART_NAN; } else { return bdtrc(k, (int)n, p); } } a_ __device__ double bdtri(double k, int n, double y) { double p, dn, dk; double fk = floor(k); if (isnan(k)) { return CUDART_NAN; } if (y < 0.0 || y > 1.0 || fk < 0.0 || n <= fk) { return CUDART_NAN; } dn = n - fk; if (fk == n) { return 1.0; } if (fk == 0) { if (y > 0.8) { p = -expm1(log1p(y - 1.0) / dn); } else { p = 1.0 - pow(y, 1.0 / dn); } } else { dk = fk + 1; p = incbet(dn, dk, 0.5); if (p > 0.5) { p = incbi(dk, dn, 1.0 - y); } else { p = 1.0 - incbi(dn, dk, y); } } return p; } __device__ double bdtri_unsafe(double k, double n, double p) { if (isnan(n) || isinf(n)) { return CUDART_NAN; } else { return bdtri(k, (int)n, p); } } cupyx_scipy_bdtr))fff->fz-out0 = out0_type(bdtr_unsafe(in0, in1, in2));dld->d)ddd->dz"out0 = bdtr_unsafe(in0, in1, in2);z out0 = bdtr(in0, (int)in1, in2);aBinomial distribution cumulative distribution function. Parameters ---------- k : cupy.ndarray Number of successes (float), rounded down to the nearest integer. n : cupy.ndarray Number of events (int). p : cupy.ndarray Probability of success in a single event (float). Returns ------- y : cupy.ndarray Probability of floor(k) or fewer successes in n independent events with success probabilities of p. See Also -------- :func:`scipy.special.bdtr` cupyx_scipy_bdtrc))rz.out0 = out0_type(bdtrc_unsafe(in0, in1, in2));r)rz#out0 = bdtrc_unsafe(in0, in1, in2);z'out0 = out0_type(bdtrc(in0, in1, in2));aBinomial distribution survival function. Returns the complemented binomial distribution function (the integral of the density from x to infinity). Parameters ---------- k : cupy.ndarray Number of successes (float), rounded down to the nearest integer. n : cupy.ndarray Number of events (int). p : cupy.ndarray Probability of success in a single event (float). Returns ------- y : cupy.ndarray Probability of floor(k) + 1 or more successes in n independent events with success probabilities of p. See Also -------- :func:`scipy.special.bdtrc` cupyx_scipy_bdtri))rz.out0 = out0_type(bdtri_unsafe(in0, in1, in2));r)rz#out0 = bdtri_unsafe(in0, in1, in2);z'out0 = out0_type(bdtri(in0, in1, in2));aInverse function to `bdtr` with respect to `p`. Parameters ---------- k : cupy.ndarray Number of successes (float), rounded down to the nearest integer. n : cupy.ndarray Number of events (int). y : cupy.ndarray Cumulative probability (probability of k or fewer successes in n events). Returns ------- p : cupy.ndarray The event probability such that bdtr(floor(k), n, p) = y. See Also -------- :func:`scipy.special.bdtri` cupyx_scipy_btdtr)rrz(out0 = out0_type(incbet(in0, in1, in2));aCumulative distribution function of the beta distribution. Parameters ---------- a : cupy.ndarray Shape parameter (a > 0). b : cupy.ndarray Shape parameter (b > 0). x : cupy.ndarray Upper limit of integration, in [0, 1]. Returns ------- I : cupy.ndarray Cumulative distribution function of the beta distribution with parameters a and b at x. See Also -------- :func:`scipy.special.btdtr` cupyx_scipy_btdtriz'out0 = out0_type(incbi(in0, in1, in2));a)The p-th quantile of the beta distribution. This function is the inverse of the beta cumulative distribution function, `btdtr`, returning the value of `x` for which ``btdtr(a, b, x) = p``. Parameters ---------- a : cupy.ndarray Shape parameter (a > 0). b : cupy.ndarray Shape parameter (b > 0). p : cupy.ndarray Cumulative probability, in [0, 1]. Returns ------- x : cupy.ndarray The quantile corresponding to p. See Also -------- :func:`scipy.special.btdtri` z __device__ double chdtrc(double df, double x) { if (x < 0.0) { return 1.0; /* modified by T. Oliphant */ } return igamc(df / 2.0, x / 2.0); } z __device__ double chdtr(double df, double x) { if (x < 0.0) { /* || (df < 1.0) ) */ return CUDART_NAN; } return igam(df / 2.0, x / 2.0); } z __device__ double chdtri(double df, double y) { double x; if ((y < 0.0) || (y > 1.0)) { /* || (df < 1.0) ) */ return CUDART_NAN; } x = igamci(0.5 * df, y); return 2.0 * x; } cupyx_scipy_chdtrc)ff->fdd->dz#out0 = out0_type(chdtrc(in0, in1));aChi square survival function. Returns the complemented chi-squared distribution function (the integral of the density from x to infinity). Parameters ---------- v : cupy.ndarray Degrees of freedom. x : cupy.ndarray Upper bound of the integral (nonnegative float). Returns ------- y : cupy.ndarray The complemented chi-squared distribution function with parameter df at x. See Also -------- :func:`scipy.special.chdtrc` cupyx_scipy_chdtriz#out0 = out0_type(chdtri(in0, in1));aInverse to `chdtrc` with respect to `x`. Parameters ---------- v : cupy.ndarray Degrees of freedom. p : cupy.ndarray Probability. p : cupy.ndarray, optional Optional output array for the function results. Returns ------- x : cupy.ndarray Value so that the probability a Chi square random variable with `v` degrees of freedom is greater than `x` equals `p`. See Also -------- :func:`scipy.special.chdtri` cupyx_scipy_chdtrz"out0 = out0_type(chdtr(in0, in1));aChi-square cumulative distribution function. Parameters ---------- v : cupy.ndarray Degrees of freedom. x : cupy.ndarray Upper bound of the integral (nonnegative float). Returns ------- y : cupy.ndarray The CDF of the chi-squared distribution with parameter df at x. See Also -------- :func:`scipy.special.chdtr` a __device__ double fdtrc(double a, double b, double x) { double w; if ((a <= 0.0) || (b <= 0.0) || (x < 0.0)) { // sf_error("fdtrc", SF_ERROR_DOMAIN, NULL); return CUDART_NAN; } w = b / (b + a * x); return incbet(0.5 * b, 0.5 * a, w); } a __device__ double fdtr(double a, double b, double x) { double w; if ((a <= 0.0) || (b <= 0.0) || (x < 0.0)) { // sf_error("fdtr", SF_ERROR_DOMAIN, NULL); return CUDART_NAN; } w = a * x; w = w / (b + w); return incbet(0.5 * a, 0.5 * b, w); } a __device__ double fdtri(double a, double b, double y) { double w, x; if ((a <= 0.0) || (b <= 0.0) || (y <= 0.0) || (y > 1.0)) { // sf_error("fdtri", SF_ERROR_DOMAIN, NULL); return CUDART_NAN; } y = 1.0 - y; /* Compute probability for x = 0.5. */ w = incbet(0.5 * b, 0.5 * a, 0.5); /* If that is greater than y, then the solution w < .5. * Otherwise, solve at 1-y to remove cancellation in (b - b*w). */ if (w > y || y < 0.001) { w = incbi(0.5 * b, 0.5 * a, y); x = (b - b * w) / (a * w); } else { w = incbi(0.5 * a, 0.5 * b, 1.0 - y); x = b * w / (a * (1.0 - w)); } return x; } cupyx_scipy_fdtrcz'out0 = out0_type(fdtrc(in0, in1, in2));aF survival function. Returns the complemented F-distribution function (the integral of the density from x to infinity). Parameters ---------- dfn : cupy.ndarray First parameter (positive float). dfd : cupy.ndarray Second parameter (positive float). x : cupy.ndarray Argument (nonnegative float). Returns ------- y : cupy.ndarray The complemented F-distribution function with parameters dfn and dfd at x. .. seealso:: :meth:`scipy.special.fdtrc` cupyx_scipy_fdtriz'out0 = out0_type(fdtri(in0, in1, in2));aThe p-th quantile of the F-distribution. This function is the inverse of the F-distribution CDF, `fdtr`, returning the `x` such that `fdtr(dfn, dfd, x)` = `p`. Parameters ---------- dfn : cupy.ndarray First parameter (positive float). dfd : cupy.ndarray Second parameter (positive float). p : cupy.ndarray Cumulative probability, in [0, 1]. Returns ------- y : cupy.ndarray The quantile corresponding to p. .. seealso:: :meth:`scipy.special.fdtri` cupyx_scipy_fdtrz&out0 = out0_type(fdtr(in0, in1, in2));aF cumulative distribution function. Parameters ---------- dfn : cupy.ndarray First parameter (positive float). dfd : cupy.ndarray Second parameter (positive float). x : cupy.ndarray Argument (nonnegative float). Returns ------- y : cupy.ndarray The CDF of the F-distribution with parameters dfn and dfd at x. .. seealso:: :meth:`scipy.special.fdtr` z __device__ double gdtr(double a, double b, double x) { if (x < 0.0) { return CUDART_NAN; } return igam(b, a * x); } z __device__ double gdtrc(double a, double b, double x) { if (x < 0.0) { return CUDART_NAN; } return (igamc(b, a * x)); } cupyx_scipy_gdtrz&out0 = out0_type(gdtr(in0, in1, in2));aGamma distribution cumulative distribution function. Parameters ---------- a : cupy.ndarray The rate parameter of the gamma distribution, sometimes denoted beta (float). It is also the reciprocal of the scale parameter theta. b : cupy.ndarray The shape parameter of the gamma distribution, sometimes denoted alpha (float). x : cupy.ndarray The quantile (upper limit of integration; float). Returns ------- F : cupy.ndarray The CDF of the gamma distribution with parameters `a` and `b` evaluated at `x`. See Also -------- :func:`scipy.special.gdtr` cupyx_scipy_gdtrcz'out0 = out0_type(gdtrc(in0, in1, in2));aGamma distribution survival function. Parameters ---------- a : cupy.ndarray The rate parameter of the gamma distribution, sometimes denoted beta (float). It is also the reciprocal of the scale parameter theta. b : cupy.ndarray The shape parameter of the gamma distribution, sometimes denoted alpha (float). x : cupy.ndarray The quantile (lower limit of integration; float). Returns ------- I : cupy.ndarray The survival function of the gamma distribution with parameters `a` and `b` at `x`. See Also -------- :func:`scipy.special.gdtrc` a __device__ double nbdtr(int k, int n, double p) { double dk, dn; if (((p < 0.0) || (p > 1.0)) || (k < 0)) { return CUDART_NAN; } dk = k + 1; dn = n; return (incbet(dn, dk, p)); } __device__ double nbdtr_unsafe(double k, double n, double p) { if (isnan(k) || isnan(n)) { return CUDART_NAN; } return nbdtr((int)k, (int)n, p); } a __device__ double nbdtrc(int k, int n, double p) { double dk, dn; if (((p < 0.0) || (p > 1.0)) || k < 0) { return CUDART_NAN; } dk = k + 1; dn = n; return (incbet(dk, dn, 1.0 - p)); } __device__ double nbdtrc_unsafe(double k, double n, double p) { if (isnan(k) || isnan(n)) { return CUDART_NAN; } return nbdtrc((int)k, (int)n, p); } a __device__ double nbdtri(int k, int n, double y) { double dk, dn, w; if (((y < 0.0) || (y > 1.0)) || (k < 0)) { return CUDART_NAN; } dk = k + 1; dn = n; w = incbi(dn, dk, y); return (w); } __device__ double nbdtri_unsafe(double k, double n, double y) { if (isnan(k) || isnan(n)) { return CUDART_NAN; } return nbdtri((int)k, (int)n, y); } cupyx_scipy_nbdtr)lld->d)rz.out0 = out0_type(nbdtr_unsafe(in0, in1, in2));)rz#out0 = nbdtr_unsafe(in0, in1, in2);zout0 = nbdtr(in0, in1, in2);aONegative binomial distribution cumulative distribution function. Parameters ---------- k : cupy.ndarray The maximum number of allowed failures (nonnegative int). n : cupy.ndarray The target number of successes (positive int). p : cupy.ndarray Probability of success in a single event (float). Returns ------- F : cupy.ndarray The probability of `k` or fewer failures before `n` successes in a sequence of events with individual success probability `p`. See Also -------- :func:`scipy.special.nbdtr` cupyx_scipy_nbdtrc)r")rz/out0 = out0_type(nbdtrc_unsafe(in0, in1, in2));)rz$out0 = nbdtrc_unsafe(in0, in1, in2);zout0 = nbdtrc(in0, in1, in2);aFNegative binomial distribution survival function. Parameters ---------- k : cupy.ndarray The maximum number of allowed failures (nonnegative int). n : cupy.ndarray The target number of successes (positive int). p : cupy.ndarray Probability of success in a single event (float). Returns ------- F : cupy.ndarray The probability of ``k + 1`` or more failures before `n` successes in a sequence of events with individual success probability `p`. See Also -------- :func:`scipy.special.nbdtrc` cupyx_scipy_nbdtri)r")rz/out0 = out0_type(nbdtri_unsafe(in0, in1, in2));)rz$out0 = nbdtri_unsafe(in0, in1, in2);zout0 = nbdtri(in0, in1, in2);a)Inverse function to `nbdtr` with respect to `p`. Parameters ---------- k : cupy.ndarray The maximum number of allowed failures (nonnegative int). n : cupy.ndarray The target number of successes (positive int). y : cupy.ndarray The probability of `k` or fewer failures before `n` successes (float). Returns ------- p : cupy.ndarray Probability of success in a single event (float) such that ``nbdtr(k, n, p) = y``. See Also -------- :func:`scipy.special.nbdtri` z __device__ double pdtr(double k, double m) { double v; if ((k < 0) || (m < 0)) { return CUDART_NAN; } if (m == 0.0) { return 1.0; } v = floor(k) + 1; return igamc(v, m); } z __device__ double pdtrc(double k, double m) { double v; if ((k < 0.0) || (m < 0.0)) { return CUDART_NAN; } if (m == 0.0) { return 0.0; } v = floor(k) + 1; return igam(v, m); } aQ __device__ double pdtri(int k, double y) { double v; if ((k < 0) || (y < 0.0) || (y >= 1.0)) { return CUDART_NAN; } v = k + 1; return igamci(v, y); } __device__ double pdtri_unsafe(double k, double y) { if (isnan(k)) { return CUDART_NAN; } else { return pdtri((int)k, y); } } cupyx_scipy_pdtrz!out0 = out0_type(pdtr(in0, in1));amPoisson cumulative distribution function. Parameters ---------- k : cupy.ndarray Nonnegative real argument. m : cupy.ndarray Nonnegative real shape parameter. Returns ------- y : cupy.ndarray Values of the Poisson cumulative distribution function. See Also -------- :func:`scipy.special.pdtr` cupyx_scipy_pdtrcz"out0 = out0_type(pdtrc(in0, in1));aBinomial distribution survival function. Returns the complemented binomial distribution function (the integral of the density from x to infinity). Parameters ---------- k : cupy.ndarray Nonnegative real argument. m : cupy.ndarray Nonnegative real shape parameter. Returns ------- y : cupy.ndarray The sum of the terms from k+1 to infinity of the Poisson distribution. See Also -------- :func:`scipy.special.pdtrc` cupyx_scipy_pdtri)zld->d)rz)out0 = out0_type(pdtri_unsafe(in0, in1));)rzout0 = pdtri_unsafe(in0, in1);zout0 = pdtri((int)in0, in1);aInverse function to `pdtr` with respect to `m`. Parameters ---------- k : cupy.ndarray Nonnegative real argument. y : cupy.ndarray Cumulative probability. Returns ------- m : cupy.ndarray The Poisson variable `m` such that the sum from 0 to `k` of the Poisson density is equal to the given probability `y`. See Also -------- :func:`scipy.special.pdtri` N)2__doc__cupyrcupyx.scipy.special._betarrcupyx.scipy.special._gammaincrr create_ufuncndtrlog_ndtr_definitionlog_ndtrndtribdtr_definitionbdtrc_definitionbdtri_definitionbdtrbdtrcbdtribtdtrbtdtrichdtrc_definitionchdtr_definitionchdtri_definitionchdtrcchdtrichdtrfdtrc_definitionfdtr_definitionfdtri_definitionfdtrcfdtrifdtrgdtr_definitiongdtrc_definitiongdtrgdtrcnbdtr_definitionnbdtrc_definitionnbdtri_definitionnbdtrnbdtrcnbdtripdtr_definitionpdtrc_definitionpdtri_definitionpdtrpdtrcpdtri|/home/jaya/work/projects/VOICE-AGENT/VIET/agent-env/lib/python3.11/site-packages/cupyx/scipy/special/_stats_distributions.pyrXs/ EEEEEEEEIIIIIIII u.     6 5 "/      : 1     'T.b0hu '  . F  . / / " " " L  . . .    H .      <  -      D     ) / /     <  ) 0 0     < ( . .     :  "6 - . .     < - . .     <u, o -  <  u, o -  @ - . .     D686  # / /    D   $ 0 0    B   $ / /    H&&2u' o -  6 ( . .     > 2# / /    rV