add lambertw_pvlib

Author: cwhanse

pvlib/tools.py

@@ -586,3 +586,59 @@ def _file_context_manager(filename_or_object, mode='r', encoding=None):
         # otherwise, assume a filename or path
         context = open(str(filename_or_object), mode=mode, encoding=encoding)
     return context
+
+
+def _log_lambertw(logx):
+    r'''Computes W(x) starting from log(x).
+
+    Parameters
+    ----------
+    logx : numeric
+        Log(x) of
+
+    Returns
+    -------
+    numeric
+        Lambert's W(x)
+
+    '''
+    # handles overflow cases, but results in nan for x <= 1
+    w = logx - np.log(logx)  # initial guess, w = log(x) - log(log(x))
+
+    for _ in range(0, 3):
+        # Newton's. Halley's is not substantially faster or more accurate
+        # because f''(w) = -1 / (w**2) is small for large w
+        w = w * (1. - np.log(w) + logx) / (1. + w)
+    return w
+
+
+def lambertw_pvlib(x):
+    r'''Lambert's W function.
+
+    Parameters
+    ----------
+    x : numeric
+        Must be real numbers.
+
+    Returns
+    -------
+    numeric
+        Lambert's W(x). Principal branch only.
+
+    '''
+    w = np.full_like(x, np.nan)
+    small = x <= 10
+    # for large x, solve 0 = f(w) = w + log(w) - log(x) using Newton's
+    w[~small] = _log_lambertw(np.log(x[~small]))
+
+    # w will contain nan for these numbers due to log(w) = log(log(x))
+    # for small x, solve 0 = g(w) = w * exp(w) - x using Halley's method
+    if any(small):
+        z = x[small]
+        g = np.log(x[small] + 1) - np.log(np.log(x[small] + 1) + 1)
+        for _ in range(0, 3):
+            expg = np.exp(g)
+            g = g - (g*expg - z) * (g + 1) / (expg * (g + 1)**2 - 0.5*(g + 2)*(expg*g - z))
+        w[small] = g
+
+    return w

tests/test_tools.py

@@ -283,3 +283,28 @@ def test__file_context_manager():
     buffer = StringIO("test content")
     with tools._file_context_manager(buffer) as obj:
         assert obj.read() == "test content"
+
+
+def test_lambertw_pvlib():
+    test_exp = np.arange(-10., 300, step=10)
+    test_x = 10.**test_exp
+    # known solution from scipy.special.lambertw
+    expected = np.array([
+        9.9999999989999997e-11, 5.6714329040978384e-01,
+        2.0028685413304952e+01, 4.2306755091738395e+01,
+        6.4904633770046118e+01, 8.7630277151947183e+01,
+        1.1042491882731335e+02, 1.3326278259180333e+02,
+        1.5613026581351718e+02, 1.7901931374150624e+02,
+        2.0192476320084489e+02, 2.2484310644511851e+02,
+        2.4777185185877809e+02, 2.7070916610249782e+02,
+        2.9365366103997610e+02, 3.1660426041503479e+02,
+        3.3956011295458728e+02, 3.6252053376149752e+02,
+        3.8548496362161768e+02, 4.0845294003314166e+02,
+        4.3142407612718210e+02, 4.5439804503371403e+02,
+        4.7737456808796901e+02, 5.0035340579834485e+02,
+        5.2333435083468805e+02, 5.4631722251791496e+02,
+        5.6930186244110166e+02, 5.9228813095427859e+02,
+        6.1527590431628334e+02, 6.3826507236734335e+02,
+        6.6125553661218726e+02])
+    result = tools.lambertw_pvlib(test_x)
+    assert np.allclose(result, expected, rtol=1e-14)