Added missing file.

GPy/util/ln_diff_erfs.py

@@ -0,0 +1,71 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+#Only works for scipy 0.12+
+try:
+    from scipy.special import erfcx, erf
+except ImportError:
+    from scipy.special import erf
+    from erfcx import erfcx
+
+import numpy as np
+
+def ln_diff_erfs(x1, x2, return_sign=False):
+    """Function for stably computing the log of difference of two erfs in a numerically stable manner.
+    :param x1 : argument of the positive erf
+    :type x1: ndarray
+    :param x2 : argument of the negative erf
+    :type x2: ndarray
+    :return: tuple containing (log(abs(erf(x1) - erf(x2))), sign(erf(x1) - erf(x2)))
+    
+    Based on MATLAB code that was written by Antti Honkela and modified by David Luengo, originally derived from code by Neil Lawrence.
+    """
+    x1 = np.require(x1).real
+    x2 = np.require(x2).real
+
+    v = np.zeros(np.max((x1.size, x2.size)))
+    
+    # if numel(x1) == 1:
+    #     x1 = x1 * ones(size(x2))
+
+    # if numel(x2) == 1:
+    #     x2 = x2 * ones(size(x1))
+
+    sign = np.sign(x1 - x2)
+    I = sign == -1
+    swap = x1[I]
+    x1[I] = x2[I]
+    x2[I] = swap
+
+    # TODO: switch off log of zero warnings.
+    # Case 1: arguments of different sign, no problems with loss of accuracy
+    I1 = np.logical_or(np.logical_and(x1>0, x2<0), np.logical_and(x2>0, x1<0)) # I1=(x1*x2)<0
+    v[I1] = np.log( erf(x1[I1]) - erf(x2[I1]) )
+
+    # Case 2: x1 = x2 so we have log of zero.
+    I2 = (x1 == x2)
+    v[I2] = -np.inf
+
+    # Case 3: Both arguments are non-negative
+    I3 = np.logical_and(x1 > 0, np.logical_and(np.logical_not(I1),
+                                               np.logical_not(I2)))
+    v[I3] = np.log(erfcx(x2[I3])
+                   -erfcx(x1[I3])*np.exp(x2[I3]**2
+                                         -x1[I3]**2)) - x2[I3]**2
+    
+    # Case 4: Both arguments are non-positive
+    I4 = np.logical_and(np.logical_and(np.logical_not(I1),
+                                       np.logical_not(I2)),
+                        np.logical_not(I3))
+    v[I4] = np.log(erfcx(-x1[I4])
+                   -erfcx(-x2[I4])*np.exp(x1[I4]**2
+                                          -x2[I4]**2))-x1[I4]**2
+    
+    # TODO: switch back on log of zero warnings.
+
+    if return_sign:
+        return v, sign
+    else:
+        # Need to add in a complex part because argument is negative.
+        v[I] += np.pi*1j
+