changed cython root finder to brent q, but changed from tan to cos and sin

transportEqs.py

@@ -20,24 +20,33 @@ def SolubilityLimited(beta, tau, nmax=100):
 # finite bath model functions
 from fast_bisect import cbisect
 
+from scipy.optimize import brentq
+
 def PlaneSheetFiniteBathMassC(tau, alpha, nterms):
-    Minfty = 1. / (1. + 1. / (alpha))
 
-    qn = zeros((nterms))
+    Minfty = 1. / (1. + 1. / alpha)
+
+    qn = zeros(nterms)
+
     for j in range(nterms):
-        solved = False
-        eps = 1e-8
-        f = lambda x: tan(x) + alpha * x
-        myargs = {'alpha': alpha}
-        rts = cbisect(a=pi / 2. + j * pi + eps, b=pi * (1. + j) - eps, args=myargs)
-        # print(rts)
-        solved = True
-        qn[j] = rts
+
+        a = pi / 2. + j * pi
+        b = pi * (1. + j)
+
+        def f(x):
+            return sin(x) + alpha * x * cos(x)
+
+        qn[j] = brentq(f, a, b)
 
     result = 1.
+
     for j in range(nterms):
-        result = result - (2. * alpha * (1. + alpha)) * exp(-tau * qn[j] ** 2.) / (
-                    1. + alpha + alpha ** 2. * qn[j] ** 2.)
+        result -= (
+            2. * alpha * (1. + alpha)
+            * exp(-tau * qn[j]**2.)
+            / (1. + alpha + alpha**2. * qn[j]**2.)
+        )
+
     result = Minfty * result
 
     return result