added a Python scf library

src/scf.py

@@ -0,0 +1,44 @@
+from scipy.special import eval_gegenbauer, sph_harm
+import numpy as np
+
+class Scf:
+    def __init__(self, nmax, lmax, mmax=None, length_scale=1, basis='hernquist'):
+        self.nmax         = nmax
+        self.lmax         = lmax
+        self.length_scale = length_scale
+        self.basis        = basis
+        self.A            = None
+        if not mmax is None: raise NotImplemented
+        if (basis.lower()=='hernquist'): self.basis_phi = self.basis_phi_hernquist
+        else: raise RuntimeError('Unknown basis set "%s".' % basis)
+
+    def set_coefficients(self, A):
+        if len(A) != (self.nmax+1)*(self.lmax+1)*(self.lmax+2)//2: raise ValueError('Coefficient list has unexpected length.')
+        self.A = A
+
+    def calc_gravity(self, x, y, z, potential=True, force=False):
+        r     = np.sqrt(x**2 + y**2 + z**2)
+        theta = np.arccos(z/r)
+        phi   = np.arctan2(y, x)
+        if force: raise NotImplemented
+        if self.A is None: raise RuntimeError('Coefficient list must be set before gravity could be calculated.')
+        pot = 0
+        for n in range(self.nmax+1):
+            for l in range(self.lmax+1):
+                for m in range(l+1):
+                    i = n*(self.lmax+1)*(self.lmax+2)//2 + l*(l+1)//2 + m
+                    pot_ = np.real(self.A[i]*self.basis_phi(n, l, m, r*self.length_scale, theta, phi))
+                    if m == 0:
+                        pot += pot_
+                    else:
+                        pot += 2*pot_
+        pot *= self.length_scale
+        return pot
+
+    def calc_coefficients(self, x, y, z):
+        raise NotImplemented
+
+    def basis_phi_hernquist(self, n, l, m, r, theta, phi):
+        xi = (r-1)/(r+1)
+        W_nl = eval_gegenbauer(n, 2*l+1.5, xi)
+        return - r**l*(1+r)**(-2*l-1)*W_nl*2*np.sqrt(np.pi)*sph_harm(m, l, phi, theta)