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env-llmeval/lib/python3.10/site-packages/scipy/special/_lambertw.py

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+from ._ufuncs import _lambertw
+
+import numpy as np
+
+
+def lambertw(z, k=0, tol=1e-8):
+    r"""
+    lambertw(z, k=0, tol=1e-8)
+
+    Lambert W function.
+
+    The Lambert W function `W(z)` is defined as the inverse function
+    of ``w * exp(w)``. In other words, the value of ``W(z)`` is
+    such that ``z = W(z) * exp(W(z))`` for any complex number
+    ``z``.
+
+    The Lambert W function is a multivalued function with infinitely
+    many branches. Each branch gives a separate solution of the
+    equation ``z = w exp(w)``. Here, the branches are indexed by the
+    integer `k`.
+
+    Parameters
+    ----------
+    z : array_like
+        Input argument.
+    k : int, optional
+        Branch index.
+    tol : float, optional
+        Evaluation tolerance.
+
+    Returns
+    -------
+    w : array
+        `w` will have the same shape as `z`.
+
+    See Also
+    --------
+    wrightomega : the Wright Omega function
+
+    Notes
+    -----
+    All branches are supported by `lambertw`:
+
+    * ``lambertw(z)`` gives the principal solution (branch 0)
+    * ``lambertw(z, k)`` gives the solution on branch `k`
+
+    The Lambert W function has two partially real branches: the
+    principal branch (`k = 0`) is real for real ``z > -1/e``, and the
+    ``k = -1`` branch is real for ``-1/e < z < 0``. All branches except
+    ``k = 0`` have a logarithmic singularity at ``z = 0``.
+
+    **Possible issues**
+
+    The evaluation can become inaccurate very close to the branch point
+    at ``-1/e``. In some corner cases, `lambertw` might currently
+    fail to converge, or can end up on the wrong branch.
+
+    **Algorithm**
+
+    Halley's iteration is used to invert ``w * exp(w)``, using a first-order
+    asymptotic approximation (O(log(w)) or `O(w)`) as the initial estimate.
+
+    The definition, implementation and choice of branches is based on [2]_.
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Lambert_W_function
+    .. [2] Corless et al, "On the Lambert W function", Adv. Comp. Math. 5
+       (1996) 329-359.
+       https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf
+
+    Examples
+    --------
+    The Lambert W function is the inverse of ``w exp(w)``:
+
+    >>> import numpy as np
+    >>> from scipy.special import lambertw
+    >>> w = lambertw(1)
+    >>> w
+    (0.56714329040978384+0j)
+    >>> w * np.exp(w)
+    (1.0+0j)
+
+    Any branch gives a valid inverse:
+
+    >>> w = lambertw(1, k=3)
+    >>> w
+    (-2.8535817554090377+17.113535539412148j)
+    >>> w*np.exp(w)
+    (1.0000000000000002+1.609823385706477e-15j)
+
+    **Applications to equation-solving**
+
+    The Lambert W function may be used to solve various kinds of
+    equations.  We give two examples here.
+
+    First, the function can be used to solve implicit equations of the
+    form
+
+        :math:`x = a + b e^{c x}`
+
+    for :math:`x`.  We assume :math:`c` is not zero.  After a little
+    algebra, the equation may be written
+
+        :math:`z e^z = -b c e^{a c}`
+
+    where :math:`z = c (a - x)`.  :math:`z` may then be expressed using
+    the Lambert W function
+
+        :math:`z = W(-b c e^{a c})`
+
+    giving
+
+        :math:`x = a - W(-b c e^{a c})/c`
+
+    For example,
+
+    >>> a = 3
+    >>> b = 2
+    >>> c = -0.5
+
+    The solution to :math:`x = a + b e^{c x}` is:
+
+    >>> x = a - lambertw(-b*c*np.exp(a*c))/c
+    >>> x
+    (3.3707498368978794+0j)
+
+    Verify that it solves the equation:
+
+    >>> a + b*np.exp(c*x)
+    (3.37074983689788+0j)
+
+    The Lambert W function may also be used find the value of the infinite
+    power tower :math:`z^{z^{z^{\ldots}}}`:
+
+    >>> def tower(z, n):
+    ...     if n == 0:
+    ...         return z
+    ...     return z ** tower(z, n-1)
+    ...
+    >>> tower(0.5, 100)
+    0.641185744504986
+    >>> -lambertw(-np.log(0.5)) / np.log(0.5)
+    (0.64118574450498589+0j)
+    """
+    # TODO: special expert should inspect this
+    # interception; better place to do it?
+    k = np.asarray(k, dtype=np.dtype("long"))
+    return _lambertw(z, k, tol)

env-llmeval/lib/python3.10/site-packages/scipy/special/_test_internal.pyi

@@ -0,0 +1,9 @@
+import numpy as np
+
+def have_fenv() -> bool: ...
+def random_double(size: int) -> np.float64: ...
+def test_add_round(size: int, mode: str): ...
+
+def _dd_exp(xhi: float, xlo: float) -> tuple[float, float]: ...
+def _dd_log(xhi: float, xlo: float) -> tuple[float, float]: ...
+def _dd_expm1(xhi: float, xlo: float) -> tuple[float, float]: ...

env-llmeval/lib/python3.10/site-packages/scipy/special/_ufuncs_defs.h

@@ -0,0 +1,185 @@
+#ifndef UFUNCS_PROTO_H
+#define UFUNCS_PROTO_H 1
+#include "_cosine.h"
+npy_double cosine_cdf(npy_double);
+npy_double cosine_invcdf(npy_double);
+#include "cephes.h"
+npy_double cospi(npy_double);
+npy_double igam_fac(npy_double, npy_double);
+npy_double kolmogc(npy_double);
+npy_double kolmogci(npy_double);
+npy_double kolmogp(npy_double);
+npy_double lanczos_sum_expg_scaled(npy_double);
+npy_double lgam1p(npy_double);
+npy_double log1pmx(npy_double);
+npy_double riemann_zeta(npy_double);
+#include "scaled_exp1.h"
+npy_double scaled_exp1(npy_double);
+npy_double sinpi(npy_double);
+npy_double smirnovc(npy_int, npy_double);
+npy_double smirnovci(npy_int, npy_double);
+npy_double smirnovp(npy_int, npy_double);
+npy_double struve_asymp_large_z(npy_double, npy_double, npy_int, npy_double *);
+npy_double struve_bessel_series(npy_double, npy_double, npy_int, npy_double *);
+npy_double struve_power_series(npy_double, npy_double, npy_int, npy_double *);
+npy_double zeta(npy_double, npy_double);
+#include "amos_wrappers.h"
+npy_int airy_wrap(npy_double, npy_double *, npy_double *, npy_double *, npy_double *);
+npy_int cairy_wrap(npy_cdouble, npy_cdouble *, npy_cdouble *, npy_cdouble *, npy_cdouble *);
+npy_int cairy_wrap_e(npy_cdouble, npy_cdouble *, npy_cdouble *, npy_cdouble *, npy_cdouble *);
+npy_int cairy_wrap_e_real(npy_double, npy_double *, npy_double *, npy_double *, npy_double *);
+npy_double bdtr(npy_double, npy_int, npy_double);
+npy_double bdtrc(npy_double, npy_int, npy_double);
+npy_double bdtri(npy_double, npy_int, npy_double);
+#include "specfun_wrappers.h"
+npy_double bei_wrap(npy_double);
+npy_double beip_wrap(npy_double);
+npy_double ber_wrap(npy_double);
+npy_double berp_wrap(npy_double);
+npy_double besselpoly(npy_double, npy_double, npy_double);
+npy_double beta(npy_double, npy_double);
+npy_double lbeta(npy_double, npy_double);
+npy_double btdtr(npy_double, npy_double, npy_double);
+npy_double incbi(npy_double, npy_double, npy_double);
+npy_double cbrt(npy_double);
+npy_double chdtr(npy_double, npy_double);
+npy_double chdtrc(npy_double, npy_double);
+npy_double chdtri(npy_double, npy_double);
+npy_double cosdg(npy_double);
+npy_double cosm1(npy_double);
+npy_double cotdg(npy_double);
+npy_double ellpe(npy_double);
+npy_double ellie(npy_double, npy_double);
+npy_int ellpj(npy_double, npy_double, npy_double *, npy_double *, npy_double *, npy_double *);
+npy_double ellik(npy_double, npy_double);
+npy_double ellpk(npy_double);
+npy_double erf(npy_double);
+npy_double erfc(npy_double);
+npy_double erfcinv(npy_double);
+npy_cdouble cexp1_wrap(npy_cdouble);
+npy_double exp1_wrap(npy_double);
+npy_double exp10(npy_double);
+npy_double exp2(npy_double);
+npy_cdouble cexpi_wrap(npy_cdouble);
+npy_double expi_wrap(npy_double);
+npy_double expm1(npy_double);
+npy_double expn(npy_int, npy_double);
+npy_double fdtr(npy_double, npy_double, npy_double);
+npy_double fdtrc(npy_double, npy_double, npy_double);
+npy_double fdtri(npy_double, npy_double, npy_double);
+npy_int fresnl(npy_double, npy_double *, npy_double *);
+npy_int cfresnl_wrap(npy_cdouble, npy_cdouble *, npy_cdouble *);
+npy_double Gamma(npy_double);
+npy_double igam(npy_double, npy_double);
+npy_double igamc(npy_double, npy_double);
+npy_double igamci(npy_double, npy_double);
+npy_double igami(npy_double, npy_double);
+npy_double lgam(npy_double);
+npy_double gammasgn(npy_double);
+npy_double gdtr(npy_double, npy_double, npy_double);
+npy_double gdtrc(npy_double, npy_double, npy_double);
+npy_cdouble cbesh_wrap1(npy_double, npy_cdouble);
+npy_cdouble cbesh_wrap1_e(npy_double, npy_cdouble);
+npy_cdouble cbesh_wrap2(npy_double, npy_cdouble);
+npy_cdouble cbesh_wrap2_e(npy_double, npy_cdouble);
+npy_cdouble chyp1f1_wrap(npy_double, npy_double, npy_cdouble);
+npy_double hyp2f1(npy_double, npy_double, npy_double, npy_double);
+npy_double i0(npy_double);
+npy_double i0e(npy_double);
+npy_double i1(npy_double);
+npy_double i1e(npy_double);
+npy_int it2i0k0_wrap(npy_double, npy_double *, npy_double *);
+npy_int it2j0y0_wrap(npy_double, npy_double *, npy_double *);
+npy_double it2struve0_wrap(npy_double);
+npy_int itairy_wrap(npy_double, npy_double *, npy_double *, npy_double *, npy_double *);
+npy_int it1i0k0_wrap(npy_double, npy_double *, npy_double *);
+npy_int it1j0y0_wrap(npy_double, npy_double *, npy_double *);
+npy_double itmodstruve0_wrap(npy_double);
+npy_double itstruve0_wrap(npy_double);
+npy_cdouble cbesi_wrap(npy_double, npy_cdouble);
+npy_double iv(npy_double, npy_double);
+npy_cdouble cbesi_wrap_e(npy_double, npy_cdouble);
+npy_double cbesi_wrap_e_real(npy_double, npy_double);
+npy_double j0(npy_double);
+npy_double j1(npy_double);
+npy_cdouble cbesj_wrap(npy_double, npy_cdouble);
+npy_double cbesj_wrap_real(npy_double, npy_double);
+npy_cdouble cbesj_wrap_e(npy_double, npy_cdouble);
+npy_double cbesj_wrap_e_real(npy_double, npy_double);
+npy_double k0(npy_double);
+npy_double k0e(npy_double);
+npy_double k1(npy_double);
+npy_double k1e(npy_double);
+npy_double kei_wrap(npy_double);
+npy_double keip_wrap(npy_double);
+npy_int kelvin_wrap(npy_double, npy_cdouble *, npy_cdouble *, npy_cdouble *, npy_cdouble *);
+npy_double ker_wrap(npy_double);
+npy_double kerp_wrap(npy_double);
+npy_double cbesk_wrap_real_int(npy_int, npy_double);
+npy_double kolmogi(npy_double);
+npy_double kolmogorov(npy_double);
+npy_cdouble cbesk_wrap(npy_double, npy_cdouble);
+npy_double cbesk_wrap_real(npy_double, npy_double);
+npy_cdouble cbesk_wrap_e(npy_double, npy_cdouble);
+npy_double cbesk_wrap_e_real(npy_double, npy_double);
+npy_double log1p(npy_double);
+npy_double pmv_wrap(npy_double, npy_double, npy_double);
+npy_double cem_cva_wrap(npy_double, npy_double);
+npy_double sem_cva_wrap(npy_double, npy_double);
+npy_int cem_wrap(npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_int mcm1_wrap(npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_int mcm2_wrap(npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_int msm1_wrap(npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_int msm2_wrap(npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_int sem_wrap(npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_int modified_fresnel_minus_wrap(npy_double, npy_cdouble *, npy_cdouble *);
+npy_int modified_fresnel_plus_wrap(npy_double, npy_cdouble *, npy_cdouble *);
+npy_double struve_l(npy_double, npy_double);
+npy_double nbdtr(npy_int, npy_int, npy_double);
+npy_double nbdtrc(npy_int, npy_int, npy_double);
+npy_double nbdtri(npy_int, npy_int, npy_double);
+npy_double ndtr(npy_double);
+npy_double ndtri(npy_double);
+npy_double oblate_aswfa_nocv_wrap(npy_double, npy_double, npy_double, npy_double, npy_double *);
+npy_int oblate_aswfa_wrap(npy_double, npy_double, npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_double oblate_segv_wrap(npy_double, npy_double, npy_double);
+npy_double oblate_radial1_nocv_wrap(npy_double, npy_double, npy_double, npy_double, npy_double *);
+npy_int oblate_radial1_wrap(npy_double, npy_double, npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_double oblate_radial2_nocv_wrap(npy_double, npy_double, npy_double, npy_double, npy_double *);
+npy_int oblate_radial2_wrap(npy_double, npy_double, npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_double owens_t(npy_double, npy_double);
+npy_int pbdv_wrap(npy_double, npy_double, npy_double *, npy_double *);
+npy_int pbvv_wrap(npy_double, npy_double, npy_double *, npy_double *);
+npy_int pbwa_wrap(npy_double, npy_double, npy_double *, npy_double *);
+npy_double pdtr(npy_double, npy_double);
+npy_double pdtrc(npy_double, npy_double);
+npy_double pdtri(npy_int, npy_double);
+npy_double poch(npy_double, npy_double);
+npy_double prolate_aswfa_nocv_wrap(npy_double, npy_double, npy_double, npy_double, npy_double *);
+npy_int prolate_aswfa_wrap(npy_double, npy_double, npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_double prolate_segv_wrap(npy_double, npy_double, npy_double);
+npy_double prolate_radial1_nocv_wrap(npy_double, npy_double, npy_double, npy_double, npy_double *);
+npy_int prolate_radial1_wrap(npy_double, npy_double, npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_double prolate_radial2_nocv_wrap(npy_double, npy_double, npy_double, npy_double, npy_double *);
+npy_int prolate_radial2_wrap(npy_double, npy_double, npy_double, npy_double, npy_double, npy_double *, npy_double *);
+npy_double radian(npy_double, npy_double, npy_double);
+npy_double rgamma(npy_double);
+npy_double round(npy_double);
+npy_int shichi(npy_double, npy_double *, npy_double *);
+npy_int sici(npy_double, npy_double *, npy_double *);
+npy_double sindg(npy_double);
+npy_double smirnov(npy_int, npy_double);
+npy_double smirnovi(npy_int, npy_double);
+npy_double spence(npy_double);
+npy_double struve_h(npy_double, npy_double);
+npy_double tandg(npy_double);
+npy_double tukeylambdacdf(npy_double, npy_double);
+npy_double y0(npy_double);
+npy_double y1(npy_double);
+npy_double yn(npy_int, npy_double);
+npy_cdouble cbesy_wrap(npy_double, npy_cdouble);
+npy_double cbesy_wrap_real(npy_double, npy_double);
+npy_cdouble cbesy_wrap_e(npy_double, npy_cdouble);
+npy_double cbesy_wrap_e_real(npy_double, npy_double);
+npy_double zetac(npy_double);
+#endif

env-llmeval/lib/python3.10/site-packages/scipy/special/cython_special.pxd

@@ -0,0 +1,261 @@
+# This file is automatically generated by _generate_pyx.py.
+# Do not edit manually!
+
+ctypedef fused number_t:
+    double complex
+    double
+
+cpdef number_t spherical_jn(long n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_yn(long n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_in(long n, number_t z, bint derivative=*) noexcept nogil
+cpdef number_t spherical_kn(long n, number_t z, bint derivative=*) noexcept nogil
+
+ctypedef fused Dd_number_t:
+    double complex
+    double
+
+ctypedef fused df_number_t:
+    double
+    float
+
+ctypedef fused dfg_number_t:
+    double
+    float
+    long double
+
+ctypedef fused dl_number_t:
+    double
+    long
+
+cpdef double voigt_profile(double x0, double x1, double x2) noexcept nogil
+cpdef double agm(double x0, double x1) noexcept nogil
+cdef void airy(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1, Dd_number_t *y2, Dd_number_t *y3) noexcept nogil
+cdef void airye(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1, Dd_number_t *y2, Dd_number_t *y3) noexcept nogil
+cpdef double bdtr(double x0, dl_number_t x1, double x2) noexcept nogil
+cpdef double bdtrc(double x0, dl_number_t x1, double x2) noexcept nogil
+cpdef double bdtri(double x0, dl_number_t x1, double x2) noexcept nogil
+cpdef double bdtrik(double x0, double x1, double x2) noexcept nogil
+cpdef double bdtrin(double x0, double x1, double x2) noexcept nogil
+cpdef double bei(double x0) noexcept nogil
+cpdef double beip(double x0) noexcept nogil
+cpdef double ber(double x0) noexcept nogil
+cpdef double berp(double x0) noexcept nogil
+cpdef double besselpoly(double x0, double x1, double x2) noexcept nogil
+cpdef double beta(double x0, double x1) noexcept nogil
+cpdef df_number_t betainc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betaincc(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betaincinv(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef df_number_t betainccinv(df_number_t x0, df_number_t x1, df_number_t x2) noexcept nogil
+cpdef double betaln(double x0, double x1) noexcept nogil
+cpdef double binom(double x0, double x1) noexcept nogil
+cpdef double boxcox(double x0, double x1) noexcept nogil
+cpdef double boxcox1p(double x0, double x1) noexcept nogil
+cpdef double btdtr(double x0, double x1, double x2) noexcept nogil
+cpdef double btdtri(double x0, double x1, double x2) noexcept nogil
+cpdef double btdtria(double x0, double x1, double x2) noexcept nogil
+cpdef double btdtrib(double x0, double x1, double x2) noexcept nogil
+cpdef double cbrt(double x0) noexcept nogil
+cpdef double chdtr(double x0, double x1) noexcept nogil
+cpdef double chdtrc(double x0, double x1) noexcept nogil
+cpdef double chdtri(double x0, double x1) noexcept nogil
+cpdef double chdtriv(double x0, double x1) noexcept nogil
+cpdef double chndtr(double x0, double x1, double x2) noexcept nogil
+cpdef double chndtridf(double x0, double x1, double x2) noexcept nogil
+cpdef double chndtrinc(double x0, double x1, double x2) noexcept nogil
+cpdef double chndtrix(double x0, double x1, double x2) noexcept nogil
+cpdef double cosdg(double x0) noexcept nogil
+cpdef double cosm1(double x0) noexcept nogil
+cpdef double cotdg(double x0) noexcept nogil
+cpdef Dd_number_t dawsn(Dd_number_t x0) noexcept nogil
+cpdef double ellipe(double x0) noexcept nogil
+cpdef double ellipeinc(double x0, double x1) noexcept nogil
+cdef void ellipj(double x0, double x1, double *y0, double *y1, double *y2, double *y3) noexcept nogil
+cpdef double ellipkinc(double x0, double x1) noexcept nogil
+cpdef double ellipkm1(double x0) noexcept nogil
+cpdef double ellipk(double x0) noexcept nogil
+cpdef Dd_number_t elliprc(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t elliprd(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprf(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprg(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t elliprj(Dd_number_t x0, Dd_number_t x1, Dd_number_t x2, Dd_number_t x3) noexcept nogil
+cpdef double entr(double x0) noexcept nogil
+cpdef Dd_number_t erf(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfc(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfcx(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t erfi(Dd_number_t x0) noexcept nogil
+cpdef df_number_t erfinv(df_number_t x0) noexcept nogil
+cpdef double erfcinv(double x0) noexcept nogil
+cpdef Dd_number_t eval_chebyc(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebys(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebyt(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_chebyu(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_gegenbauer(dl_number_t x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t eval_genlaguerre(dl_number_t x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef double eval_hermite(long x0, double x1) noexcept nogil
+cpdef double eval_hermitenorm(long x0, double x1) noexcept nogil
+cpdef Dd_number_t eval_jacobi(dl_number_t x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef Dd_number_t eval_laguerre(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_legendre(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_chebyt(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_chebyu(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t eval_sh_jacobi(dl_number_t x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef Dd_number_t eval_sh_legendre(dl_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t exp1(Dd_number_t x0) noexcept nogil
+cpdef double exp10(double x0) noexcept nogil
+cpdef double exp2(double x0) noexcept nogil
+cpdef Dd_number_t expi(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t expit(dfg_number_t x0) noexcept nogil
+cpdef Dd_number_t expm1(Dd_number_t x0) noexcept nogil
+cpdef double expn(dl_number_t x0, double x1) noexcept nogil
+cpdef double exprel(double x0) noexcept nogil
+cpdef double fdtr(double x0, double x1, double x2) noexcept nogil
+cpdef double fdtrc(double x0, double x1, double x2) noexcept nogil
+cpdef double fdtri(double x0, double x1, double x2) noexcept nogil
+cpdef double fdtridfd(double x0, double x1, double x2) noexcept nogil
+cdef void fresnel(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cpdef Dd_number_t gamma(Dd_number_t x0) noexcept nogil
+cpdef double gammainc(double x0, double x1) noexcept nogil
+cpdef double gammaincc(double x0, double x1) noexcept nogil
+cpdef double gammainccinv(double x0, double x1) noexcept nogil
+cpdef double gammaincinv(double x0, double x1) noexcept nogil
+cpdef double gammaln(double x0) noexcept nogil
+cpdef double gammasgn(double x0) noexcept nogil
+cpdef double gdtr(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrc(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtria(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrib(double x0, double x1, double x2) noexcept nogil
+cpdef double gdtrix(double x0, double x1, double x2) noexcept nogil
+cpdef double complex hankel1(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel1e(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel2(double x0, double complex x1) noexcept nogil
+cpdef double complex hankel2e(double x0, double complex x1) noexcept nogil
+cpdef double huber(double x0, double x1) noexcept nogil
+cpdef Dd_number_t hyp0f1(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t hyp1f1(double x0, double x1, Dd_number_t x2) noexcept nogil
+cpdef Dd_number_t hyp2f1(double x0, double x1, double x2, Dd_number_t x3) noexcept nogil
+cpdef double hyperu(double x0, double x1, double x2) noexcept nogil
+cpdef double i0(double x0) noexcept nogil
+cpdef double i0e(double x0) noexcept nogil
+cpdef double i1(double x0) noexcept nogil
+cpdef double i1e(double x0) noexcept nogil
+cpdef double inv_boxcox(double x0, double x1) noexcept nogil
+cpdef double inv_boxcox1p(double x0, double x1) noexcept nogil
+cdef void it2i0k0(double x0, double *y0, double *y1) noexcept nogil
+cdef void it2j0y0(double x0, double *y0, double *y1) noexcept nogil
+cpdef double it2struve0(double x0) noexcept nogil
+cdef void itairy(double x0, double *y0, double *y1, double *y2, double *y3) noexcept nogil
+cdef void iti0k0(double x0, double *y0, double *y1) noexcept nogil
+cdef void itj0y0(double x0, double *y0, double *y1) noexcept nogil
+cpdef double itmodstruve0(double x0) noexcept nogil
+cpdef double itstruve0(double x0) noexcept nogil
+cpdef Dd_number_t iv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t ive(double x0, Dd_number_t x1) noexcept nogil
+cpdef double j0(double x0) noexcept nogil
+cpdef double j1(double x0) noexcept nogil
+cpdef Dd_number_t jv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t jve(double x0, Dd_number_t x1) noexcept nogil
+cpdef double k0(double x0) noexcept nogil
+cpdef double k0e(double x0) noexcept nogil
+cpdef double k1(double x0) noexcept nogil
+cpdef double k1e(double x0) noexcept nogil
+cpdef double kei(double x0) noexcept nogil
+cpdef double keip(double x0) noexcept nogil
+cdef void kelvin(double x0, double complex *y0, double complex *y1, double complex *y2, double complex *y3) noexcept nogil
+cpdef double ker(double x0) noexcept nogil
+cpdef double kerp(double x0) noexcept nogil
+cpdef double kl_div(double x0, double x1) noexcept nogil
+cpdef double kn(dl_number_t x0, double x1) noexcept nogil
+cpdef double kolmogi(double x0) noexcept nogil
+cpdef double kolmogorov(double x0) noexcept nogil
+cpdef Dd_number_t kv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t kve(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t log1p(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t log_expit(dfg_number_t x0) noexcept nogil
+cpdef Dd_number_t log_ndtr(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t loggamma(Dd_number_t x0) noexcept nogil
+cpdef dfg_number_t logit(dfg_number_t x0) noexcept nogil
+cpdef double lpmv(double x0, double x1, double x2) noexcept nogil
+cpdef double mathieu_a(double x0, double x1) noexcept nogil
+cpdef double mathieu_b(double x0, double x1) noexcept nogil
+cdef void mathieu_cem(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modcem1(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modcem2(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modsem1(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_modsem2(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void mathieu_sem(double x0, double x1, double x2, double *y0, double *y1) noexcept nogil
+cdef void modfresnelm(double x0, double complex *y0, double complex *y1) noexcept nogil
+cdef void modfresnelp(double x0, double complex *y0, double complex *y1) noexcept nogil
+cpdef double modstruve(double x0, double x1) noexcept nogil
+cpdef double nbdtr(dl_number_t x0, dl_number_t x1, double x2) noexcept nogil
+cpdef double nbdtrc(dl_number_t x0, dl_number_t x1, double x2) noexcept nogil
+cpdef double nbdtri(dl_number_t x0, dl_number_t x1, double x2) noexcept nogil
+cpdef double nbdtrik(double x0, double x1, double x2) noexcept nogil
+cpdef double nbdtrin(double x0, double x1, double x2) noexcept nogil
+cpdef double ncfdtr(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double ncfdtri(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double ncfdtridfd(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double ncfdtridfn(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double ncfdtrinc(double x0, double x1, double x2, double x3) noexcept nogil
+cpdef double nctdtr(double x0, double x1, double x2) noexcept nogil
+cpdef double nctdtridf(double x0, double x1, double x2) noexcept nogil
+cpdef double nctdtrinc(double x0, double x1, double x2) noexcept nogil
+cpdef double nctdtrit(double x0, double x1, double x2) noexcept nogil
+cpdef Dd_number_t ndtr(Dd_number_t x0) noexcept nogil
+cpdef double ndtri(double x0) noexcept nogil
+cpdef double nrdtrimn(double x0, double x1, double x2) noexcept nogil
+cpdef double nrdtrisd(double x0, double x1, double x2) noexcept nogil
+cdef void obl_ang1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_ang1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double obl_cv(double x0, double x1, double x2) noexcept nogil
+cdef void obl_rad1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_rad1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cdef void obl_rad2(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void obl_rad2_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double owens_t(double x0, double x1) noexcept nogil
+cdef void pbdv(double x0, double x1, double *y0, double *y1) noexcept nogil
+cdef void pbvv(double x0, double x1, double *y0, double *y1) noexcept nogil
+cdef void pbwa(double x0, double x1, double *y0, double *y1) noexcept nogil
+cpdef double pdtr(double x0, double x1) noexcept nogil
+cpdef double pdtrc(double x0, double x1) noexcept nogil
+cpdef double pdtri(dl_number_t x0, double x1) noexcept nogil
+cpdef double pdtrik(double x0, double x1) noexcept nogil
+cpdef double poch(double x0, double x1) noexcept nogil
+cpdef df_number_t powm1(df_number_t x0, df_number_t x1) noexcept nogil
+cdef void pro_ang1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_ang1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double pro_cv(double x0, double x1, double x2) noexcept nogil
+cdef void pro_rad1(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_rad1_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cdef void pro_rad2(double x0, double x1, double x2, double x3, double *y0, double *y1) noexcept nogil
+cdef void pro_rad2_cv(double x0, double x1, double x2, double x3, double x4, double *y0, double *y1) noexcept nogil
+cpdef double pseudo_huber(double x0, double x1) noexcept nogil
+cpdef Dd_number_t psi(Dd_number_t x0) noexcept nogil
+cpdef double radian(double x0, double x1, double x2) noexcept nogil
+cpdef double rel_entr(double x0, double x1) noexcept nogil
+cpdef Dd_number_t rgamma(Dd_number_t x0) noexcept nogil
+cpdef double round(double x0) noexcept nogil
+cdef void shichi(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cdef void sici(Dd_number_t x0, Dd_number_t *y0, Dd_number_t *y1) noexcept nogil
+cpdef double sindg(double x0) noexcept nogil
+cpdef double smirnov(dl_number_t x0, double x1) noexcept nogil
+cpdef double smirnovi(dl_number_t x0, double x1) noexcept nogil
+cpdef Dd_number_t spence(Dd_number_t x0) noexcept nogil
+cpdef double complex sph_harm(dl_number_t x0, dl_number_t x1, double x2, double x3) noexcept nogil
+cpdef double stdtr(double x0, double x1) noexcept nogil
+cpdef double stdtridf(double x0, double x1) noexcept nogil
+cpdef double stdtrit(double x0, double x1) noexcept nogil
+cpdef double struve(double x0, double x1) noexcept nogil
+cpdef double tandg(double x0) noexcept nogil
+cpdef double tklmbda(double x0, double x1) noexcept nogil
+cpdef double complex wofz(double complex x0) noexcept nogil
+cpdef Dd_number_t wrightomega(Dd_number_t x0) noexcept nogil
+cpdef Dd_number_t xlog1py(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t xlogy(Dd_number_t x0, Dd_number_t x1) noexcept nogil
+cpdef double y0(double x0) noexcept nogil
+cpdef double y1(double x0) noexcept nogil
+cpdef double yn(dl_number_t x0, double x1) noexcept nogil
+cpdef Dd_number_t yv(double x0, Dd_number_t x1) noexcept nogil
+cpdef Dd_number_t yve(double x0, Dd_number_t x1) noexcept nogil
+cpdef double zetac(double x0) noexcept nogil
+cpdef double wright_bessel(double x0, double x1, double x2) noexcept nogil
+cpdef double ndtri_exp(double x0) noexcept nogil

env-llmeval/lib/python3.10/site-packages/scipy/special/orthogonal.py

@@ -0,0 +1,47 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.special` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+_polyfuns = ['legendre', 'chebyt', 'chebyu', 'chebyc', 'chebys',
+             'jacobi', 'laguerre', 'genlaguerre', 'hermite',
+             'hermitenorm', 'gegenbauer', 'sh_legendre', 'sh_chebyt',
+             'sh_chebyu', 'sh_jacobi']
+
+# Correspondence between new and old names of root functions
+_rootfuns_map = {'roots_legendre': 'p_roots',
+               'roots_chebyt': 't_roots',
+               'roots_chebyu': 'u_roots',
+               'roots_chebyc': 'c_roots',
+               'roots_chebys': 's_roots',
+               'roots_jacobi': 'j_roots',
+               'roots_laguerre': 'l_roots',
+               'roots_genlaguerre': 'la_roots',
+               'roots_hermite': 'h_roots',
+               'roots_hermitenorm': 'he_roots',
+               'roots_gegenbauer': 'cg_roots',
+               'roots_sh_legendre': 'ps_roots',
+               'roots_sh_chebyt': 'ts_roots',
+               'roots_sh_chebyu': 'us_roots',
+               'roots_sh_jacobi': 'js_roots'}
+
+
+__all__ = _polyfuns + list(_rootfuns_map.keys()) + [  # noqa: F822
+    'exp', 'inf', 'floor', 'around', 'hstack', 'arange',
+    'linalg', 'airy', 'orthopoly1d', 'newfun',
+    'oldfun', 'p_roots', 't_roots', 'u_roots', 'c_roots', 's_roots',
+    'j_roots', 'l_roots', 'la_roots', 'h_roots', 'he_roots', 'cg_roots',
+    'ps_roots', 'ts_roots', 'us_roots', 'js_roots'
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="special", module="orthogonal",
+                                   private_modules=["_orthogonal"], all=__all__,
+                                   attribute=name)