Merge branch 'smirnovi_stability' into kolmogsmirnov

* smirnovi_stability:
  Added smirnovc/smirnovci, the CDF for the Smirnov probability distribution.
  Addresses scipy#7456, scipy#7426, scipy#7455 (scipy.special.smirnov, scipy.stats.ksone)
  scipy.special.{smirnov,smirnovi} have accuracy & convergence issues;
  incorrect values for scipy.stats.ksone.pdf()

scipy/special/__init__.py

@@ -248,7 +248,10 @@
    chndtrinc    -- Inverse to `chndtr` vs `nc`
    chndtrix     -- Inverse to `chndtr` vs `x`
    smirnov      -- Kolmogorov-Smirnov complementary cumulative distribution function
+   smirnovc     -- Kolmogorov-Smirnov cumulative distribution function
    smirnovi     -- Inverse to `smirnov`
+   smirnovic    -- Inverse to `smirnovc`
+   smirnovp     -- Derivative of `smirnov`
    kolmogorov   -- Complementary cumulative distribution function of Kolmogorov distribution
    kolmogi      -- Inverse function to kolmogorov
    tklmbda      -- Tukey-Lambda cumulative distribution function

scipy/special/_generate_pyx.py

@@ -160,7 +160,10 @@
 pdtri -- pdtri: id->d, pdtri_unsafe: dd->d                 -- cephes.h, _legacy.pxd
 yn -- yn: id->d, yn_unsafe: dd->d                          -- cephes.h, _legacy.pxd
 smirnov -- smirnov: id->d, smirnov_unsafe: dd->d           -- cephes.h, _legacy.pxd
+smirnovc -- smirnovc: id->d, smirnovc_unsafe: dd->d        -- cephes.h, _legacy.pxd
 smirnovi -- smirnovi: id->d, smirnovi_unsafe: dd->d        -- cephes.h, _legacy.pxd
+smirnovci -- smirnovci: id->d, smirnovci_unsafe: dd->d     -- cephes.h, _legacy.pxd
+smirnovp -- smirnovp: id->d, smirnovp_unsafe: dd->d        -- cephes.h, _legacy.pxd
 agm -- agm: dd->d                                          -- _agm.pxd
 airy -- airy_wrap: d*dddd->*i, cairy_wrap: D*DDDD->*i      -- amos_wrappers.h
 itairy -- itairy_wrap: d*dddd->*i                          -- specfun_wrappers.h

scipy/special/_legacy.pxd

@@ -28,7 +28,10 @@ cdef extern from "cephes.h":
     double kn(int n, double x) nogil
     double yn(int n, double x) nogil
     double smirnov(int n, double e) nogil
+    double smirnovc(int n, double e) nogil
     double smirnovi(int n, double p) nogil
+    double smirnovci(int n, double p) nogil
+    double smirnovp(int n, double p) nogil
 
 cdef extern from "amos_wrappers.h":
     double cbesk_wrap_real_int(int n, double z) nogil
@@ -89,9 +92,23 @@ cdef inline double kn_unsafe(double n, double x) nogil:
 cdef inline double yn_unsafe(double n, double x) nogil:
     _legacy_cast_check("yn", n, 0)
     return yn(<int>n, x)
+
 cdef inline double smirnov_unsafe(double n, double e) nogil:
     _legacy_cast_check("smirnov", n, 0)
     return smirnov(<int>n, e)
+
+cdef inline double smirnovc_unsafe(double n, double e) nogil:
+    _legacy_cast_check("smirnovc", n, 0)
+    return smirnovc(<int>n, e)
+
 cdef inline double smirnovi_unsafe(double n, double p) nogil:
     _legacy_cast_check("smirnovi", n, 0)
     return smirnovi(<int>n, p)
+
+cdef inline double smirnovci_unsafe(double n, double p) nogil:
+    _legacy_cast_check("smirnovci", n, 0)
+    return smirnovci(<int>n, p)
+
+cdef inline double smirnovp_unsafe(double n, double p) nogil:
+    _legacy_cast_check("smirnovp", n, 0)
+    return smirnovp(<int>n, p)

scipy/special/add_newdocs.py

@@ -6356,6 +6356,20 @@ def add_newdoc(place, name, doc):
     is greater than e.
     """)
 
+add_newdoc("scipy.special", "smirnovc",
+    """
+    smirnovc(n, e)
+
+    Kolmogorov-Smirnov cumulative distribution function
+
+    Returns the exact Kolmogorov-Smirnov cumulative
+    distribution function (Dn+ or Dn-) for a one-sided test of
+    equality between an empirical and a theoretical distribution. It
+    is equal to the probability that the maximum difference between a
+    theoretical distribution and an empirical one based on `n` samples
+    is less than or equal to e.
+    """)
+
 add_newdoc("scipy.special", "smirnovi",
     """
     smirnovi(n, y)
@@ -6365,6 +6379,23 @@ def add_newdoc(place, name, doc):
     Returns ``e`` such that ``smirnov(n, e) = y``.
     """)
 
+add_newdoc("scipy.special", "smirnovci",
+    """
+    smirnovci(n, y)
+
+    Inverse to `smirnovc`
+
+    Returns ``e`` such that ``smirnovc(n, e) = y``.
+    """)
+
+add_newdoc("scipy.special", "smirnovp",
+    """
+    smirnovp(n, y)
+
+    Derivative of `smirnov`
+    """)
+
+
 add_newdoc("scipy.special", "spence",
     r"""
     spence(z, out=None)

scipy/special/cephes.h

@@ -197,7 +197,10 @@ extern double zeta ( double x, double q );
 extern double zetac ( double x );
 
 extern double smirnov (int n, double e );
+extern double smirnovc (int n, double e );
+extern double smirnovp (int n, double x );
 extern double smirnovi (int n, double p );
+extern double smirnovci (int n, double p );
 extern double kolmogorov ( double x );
 extern double kolmogi ( double p );
 

scipy/special/cephes/cephes_names.h

@@ -90,7 +90,10 @@
 #define zeta cephes_zeta
 #define zetac cephes_zetac
 #define smirnov cephes_smirnov
+#define smirnovc cephes_smirnovc
 #define smirnovi cephes_smirnovi
+#define smirnovci cephes_smirnovci
+#define smirnovp cephes_smirnovp
 #define kolmogorov cephes_kolmogorov
 #define kolmogi cephes_kolmogi