Function naming issue. Rename boys to gamma_inc.

Author: sunqm

code-examples/chap12/analytical_integrals/v1/coulomb_1e_MD.py

@@ -3,19 +3,19 @@
 import numpy as np
 from scipy.special import roots_hermite
 from basis import CGTO, n_cart
-from rys_roots import boys as _boys
+from rys_roots import gamma_inc as _gamma_inc
 from overlap_MD import get_E_tensor
 
 
 @lru_cache(100)
-def boys(n, x):
-    return _boys(n, x)[n]
+def gamma_inc(n, x):
+    return _gamma_inc(n, x)[n]
 
 def get_R_tensor(l, a, rpq):
     @lru_cache(4000)
     def get_R(n, t, u, v):
         if t == u == v == 0:
-            return (-2*a)**n * boys(n, a*np.array(rpq).dot(rpq))
+            return (-2*a)**n * gamma_inc(n, a*np.array(rpq).dot(rpq))
         elif t < 0 or u < 0 or v < 0:
             return 0.
         elif t > 0:

code-examples/chap12/analytical_integrals/v1/eri_OS.py

@@ -2,7 +2,7 @@
 from typing import List
 import numpy as np
 from basis import CGTO, n_cart, iter_cart_xyz
-from rys_roots import boys as _boys
+from rys_roots import gamma_inc as _gamma_inc
 
 
 def contracted_ERI(bas_i, bas_j, bas_k, bas_l) -> np.ndarray:
@@ -29,8 +29,8 @@ def contracted_ERI(bas_i, bas_j, bas_k, bas_l) -> np.ndarray:
     return V
 
 @lru_cache(100)
-def boys(n, x):
-    return _boys(n, x)[n]
+def gamma_inc(n, x):
+    return _gamma_inc(n, x)[n]
 
 def primitive_ERI(li, lj, lk, ll, ai, aj, ak, al, Ra, Rb, Rc, Rd) -> np.ndarray:
     aij = ai + aj
@@ -78,7 +78,7 @@ def vrr(n, ix, iy, iz):
                 val += (ix-1)*.5/aij * (vrr(n, ix-2, iy, iz) - theta/aij*vrr(n+1, ix-2, iy, iz))
             return val
 
-        return Kabcd * boys(n, theta_r2)
+        return Kabcd * gamma_inc(n, theta_r2)
 
     @lru_cache()
     def trr(ix, iy, iz, kx, ky, kz):
@@ -193,7 +193,7 @@ def vrr(n, ix, iy, iz):
                 val += (ix-1)*.5/aij * (vrr(n, ix-2, iy, iz) - theta/aij*vrr(n+1, ix-2, iy, iz))
             return val
 
-        return Kabcd * boys(n, theta_r2)
+        return Kabcd * gamma_inc(n, theta_r2)
 
     @lru_cache()
     def trr(n, ix, iy, iz, kx, ky, kz):

code-examples/chap12/analytical_integrals/v1/rys_roots.py

@@ -1,7 +1,7 @@
 import numpy as np
 import scipy.special
 
-def boys(m, t):
+def gamma_inc(m, t):
 #             _ 1           2
 #            /     2 m  -t u
 # F (t)  =   |    u    e      du,
@@ -73,7 +73,7 @@ def schmidt_orth(moments, nroots):
     return np.linalg.inv(np.linalg.cholesky(s))
 
 def rys_roots_weights(nroots, x):
-    moments = boys(nroots*2, x)
+    moments = gamma_inc(nroots*2, x)
     if moments[0] < 1e-16:
         return np.zeros(nroots), np.zeros(nroots)
 

code-examples/chap12/analytical_integrals/v2/coulomb_1e_MD.py

@@ -1,7 +1,7 @@
 from typing import List
 import numpy as np
 from basis import CGTO, n_cart
-from rys_roots import boys
+from rys_roots import gamma_inc
 from overlap_MD import get_E_tensor
 
 
@@ -23,7 +23,7 @@ def get_R_tensor(l, a, rpq):
                 elif v == 1:
                     Rt[:-1,t,u,1] = rpq[2] * Rt[1:,t,u,0]
                 else: # t == u == v == 0
-                    Rt[:,0,0,0] = (-2*a)**np.arange(l*3+1) * boys(l*3, a*np.array(rpq).dot(rpq))
+                    Rt[:,0,0,0] = (-2*a)**np.arange(l*3+1) * gamma_inc(l*3, a*np.array(rpq).dot(rpq))
     return Rt[0]
 
 def get_matrix(gtos: List[CGTO], Rc) -> np.ndarray:

code-examples/chap12/analytical_integrals/v2/eri_OS.py

@@ -2,7 +2,7 @@
 from typing import List
 import numpy as np
 from basis import CGTO, n_cart, iter_cart_xyz
-from rys_roots import boys
+from rys_roots import gamma_inc
 
 
 def contracted_ERI(bas_i, bas_j, bas_k, bas_l) -> np.ndarray:
@@ -49,15 +49,15 @@ def primitive_ERI(li, lj, lk, ll, ai, aj, ak, al, Ra, Rb, Rc, Rd) -> np.ndarray:
     lij = li + lj
     lkl = lk + ll
     n = lij + lkl
-    _boys = boys(n, theta_r2)
+    _gamma_inc = gamma_inc(n, theta_r2)
 
     Xab, Yab, Zab = Rab
     Xcd, Ycd, Zcd = Rcd
     Xpq, Ypq, Zpq = Rpq
     Xpa, Ypa, Zpa = Rp - Ra
 
     vrr = np.empty((n+1, n+1,n+1,n+1))
-    vrr[:,0,0,0] = Kabcd * _boys
+    vrr[:,0,0,0] = Kabcd * _gamma_inc
     for ix in range(n+1):
         for iy in range(n+1):
             for iz in range(n+1):

code-examples/chap12/analytical_integrals/v2/rys_roots.py

@@ -1,7 +1,7 @@
 import math
 import numpy as np
 
-def boys(m, t):
+def gamma_inc(m, t):
 #             _ 1           2
 #            /     2 m  -t u
 # F (t)  =   |    u    e      du,
@@ -73,7 +73,7 @@ def schmidt_orth(moments, nroots):
     return np.linalg.inv(np.linalg.cholesky(s))
 
 def rys_roots_weights(nroots, x):
-    moments = boys(nroots*2, x)
+    moments = gamma_inc(nroots*2, x)
     if moments[0] < 1e-16:
         return np.zeros(nroots), np.zeros(nroots)
 

code-examples/chap12/analytical_integrals/v3/coulomb_1e_MD.py

@@ -1,7 +1,7 @@
 from typing import List
 import numpy as np
 from basis import CGTO, n_cart
-from rys_roots import boys
+from rys_roots import gamma_inc
 from overlap_MD import get_E_tensor, reduced_cart_iter
 
 
@@ -10,7 +10,7 @@ def get_R_tensor(l, a, rpq):
     Rt = np.zeros((l+1, l+1, l+1, l+1))
     r2 = rx*rx + ry*ry + rz*rz
 
-    Rt[:,0,0,0] = (-2*a)**np.arange(l+1) * boys(l, a*r2)
+    Rt[:,0,0,0] = (-2*a)**np.arange(l+1) * gamma_inc(l, a*r2)
     if l == 0:
         return Rt[0]
 

code-examples/chap12/analytical_integrals/v3/eri_MD.py

@@ -2,7 +2,7 @@
 import numpy as np
 from basis import CGTO, n_cart, gto_offsets
 from coulomb_1e_MD import get_R_tensor, get_E_tensor, reduced_cart_iter
-from rys_roots import boys
+from rys_roots import gamma_inc
 
 def contracted_ERI(bas_i: CGTO, bas_j: CGTO, bas_k: CGTO, bas_l: CGTO) -> np.ndarray:
     li, lj = bas_i.angular_momentum, bas_j.angular_momentum
@@ -46,8 +46,8 @@ def primitive_ERI(li, lj, lk, ll, ai, aj, ak, al, Ra, Rb, Rc, Rd) -> np.ndarray:
         theta_r2 = theta * Rpq.dot(Rpq)
         Kabcd = 2*np.pi**2.5/(aij*akl*(aij+akl)**.5)
         Kabcd *= np.exp(-theta_ij*Rab.dot(Rab) - theta_kl*Rcd.dot(Rcd))
-        _boys = boys(0, theta_r2)
-        return Kabcd * _boys.reshape(1,1,1,1)
+        _gamma_inc = gamma_inc(0, theta_r2)
+        return Kabcd * _gamma_inc.reshape(1,1,1,1)
 
     Rt = get_R_tensor(l4, theta, Rpq)
     nfi = n_cart(li)

code-examples/chap12/analytical_integrals/v3/eri_OS.py

@@ -1,7 +1,7 @@
 from functools import lru_cache
 import numpy as np
 from basis import CGTO, n_cart, iter_cart_xyz
-from rys_roots import boys
+from rys_roots import gamma_inc
 
 def contracted_ERI(bas_i, bas_j, bas_k, bas_l) -> np.ndarray:
     li, lj = bas_i.angular_momentum, bas_j.angular_momentum
@@ -47,17 +47,17 @@ def primitive_ERI(li, lj, lk, ll, ai, aj, ak, al, Ra, Rb, Rc, Rd) -> np.ndarray:
     lij = li + lj
     lkl = lk + ll
     n = lij + lkl
-    _boys = boys(n, theta_r2)
+    _gamma_inc = gamma_inc(n, theta_r2)
     if n == 0:
-        return Kabcd * _boys.reshape(1,1,1,1)
+        return Kabcd * _gamma_inc.reshape(1,1,1,1)
 
     Xab, Yab, Zab = Rab
     Xcd, Ycd, Zcd = Rcd
     Xpq, Ypq, Zpq = Rpq
     Xpa, Ypa, Zpa = Rp - Ra
 
     vrr = np.empty((n+1, n+1,n+1,n+1))
-    vrr[:,0,0,0] = Kabcd * _boys
+    vrr[:,0,0,0] = Kabcd * _gamma_inc
     ix = 0
     iy = 0
     if n > 0:

code-examples/chap12/analytical_integrals/v3/rys_roots.py

@@ -1,7 +1,7 @@
 import math
 import numpy as np
 
-def boys(m, t):
+def gamma_inc(m, t):
 #             _ 1           2
 #            /     2 m  -t u
 # F (t)  =   |    u    e      du,
@@ -82,7 +82,7 @@ def schmidt_orth(moments, nroots):
     return cs
 
 def rys_roots_weights(nroots, x):
-    moments = boys(nroots*2, x)
+    moments = gamma_inc(nroots*2, x)
     if moments[0] < 1e-16:
         return np.zeros(nroots), np.zeros(nroots)
 

code-examples/chap12/analytical_integrals/v4_cython/_tensors.pyx

@@ -47,7 +47,7 @@ cdef double[::1] upward(int m, double t):
         out[i+1] = f
     return out
 
-cdef double[::1] boys(int m, double t):
+cdef double[::1] gamma_inc(int m, double t):
     assert m >= 0
     assert t >= 0
     if (t < m + 1.5):
@@ -109,7 +109,7 @@ cdef find_roots(double[:,::1] cs, int nroots):
     return roots
 
 cdef rys_roots_weights(int nroots, double x):
-    cdef double[::1] moments = boys(nroots*2, x)
+    cdef double[::1] moments = gamma_inc(nroots*2, x)
     if moments[0] < 1e-16:
         return np.zeros(nroots), np.zeros(nroots)
 
@@ -229,10 +229,10 @@ def get_R_tensor(int l, double a, double[:] rpq):
     Rt = np.zeros((l+1, l+1, l+1, l+1))
     cdef double [:,:,:,::1] _Rt = Rt
     cdef int t, u, v, m
-    cdef double[::1] _boys = boys(l, a*r2)
+    cdef double[::1] _gamma_inc = gamma_inc(l, a*r2)
 
     for m in range(l+1):
-        _Rt[m,0,0,0] = (-2*a)**m * _boys[m]
+        _Rt[m,0,0,0] = (-2*a)**m * _gamma_inc[m]
 
     if l == 0:
         return Rt[0]
@@ -299,7 +299,7 @@ def primitive_ERI_MD(int li, int lj, int lk, int ll,
         Kabcd = 2*M_PI**2.5/(aij*akl*(aij+akl)**.5)
         Kabcd *= exp(-theta_ij * square(Rab) - theta_kl * square(Rcd))
         eri = np.empty((1,1,1,1))
-        eri[0,0,0,0] = Kabcd * boys(l4, theta_r2)[0]
+        eri[0,0,0,0] = Kabcd * gamma_inc(l4, theta_r2)[0]
         return eri
 
     cdef double[:,:,::1] Rt = get_R_tensor(l4, theta, Rpq)
@@ -358,11 +358,11 @@ def primitive_ERI_OS(int li, int lj, int lk, int ll,
     cdef int lij = li + lj
     cdef int lkl = lk + ll
     cdef int n = lij + lkl
-    cdef double[::1] _boys = boys(n, theta_r2)
+    cdef double[::1] _gamma_inc = gamma_inc(n, theta_r2)
 
     if n == 0:
         out = np.empty((1,1,1,1))
-        out[0,0,0,0] = Kabcd * _boys[0]
+        out[0,0,0,0] = Kabcd * _gamma_inc[0]
         return out
 
     cdef double Xab = Rab[0]
@@ -387,7 +387,7 @@ def primitive_ERI_OS(int li, int lj, int lk, int ll,
     cdef double val
     cdef double[:,:,:,::1] vrr = np.empty((n+1, n+1,n+1,n+1))
     for ni in range(n+1):
-        vrr[ni,0,0,0] = Kabcd * _boys[ni]
+        vrr[ni,0,0,0] = Kabcd * _gamma_inc[ni]
 
     ix = 0
     iy = 0

code-examples/chap12/analytical_integrals/v4_numba/coulomb_1e_MD.py

@@ -2,7 +2,7 @@
 import numpy as np
 import numba
 from basis import CGTO, n_cart
-from rys_roots import boys
+from rys_roots import gamma_inc
 from overlap_MD import get_E_tensor
 
 
@@ -12,7 +12,7 @@ def get_R_tensor(l, a, rpq):
     Rt = np.zeros((l+1, l+1, l+1, l+1))
     r2 = rx*rx + ry*ry + rz*rz
 
-    Rt[:,0,0,0] = (-2*a)**np.arange(l+1) * boys(l, a*r2)
+    Rt[:,0,0,0] = (-2*a)**np.arange(l+1) * gamma_inc(l, a*r2)
     if l == 0:
         return Rt[0]
 

code-examples/chap12/analytical_integrals/v4_numba/eri_MD.py

@@ -2,7 +2,7 @@
 import numba
 from basis import jitCGTO, CGTO, n_cart
 from coulomb_1e_MD import get_R_tensor, get_E_tensor
-from rys_roots import boys
+from rys_roots import gamma_inc
 
 
 @numba.njit
@@ -86,8 +86,8 @@ def primitive_ERI(li, lj, lk, ll, ai, aj, ak, al, Ra, Rb, Rc, Rd) -> np.ndarray:
         theta_r2 = theta * Rpq.dot(Rpq)
         Kabcd = 2*np.pi**2.5/(aij*akl*(aij+akl)**.5)
         Kabcd *= np.exp(-theta_ij*Rab.dot(Rab) - theta_kl*Rcd.dot(Rcd))
-        _boys = boys(0, theta_r2)
-        return Kabcd * _boys.reshape(1,1,1,1)
+        _gamma_inc = gamma_inc(0, theta_r2)
+        return Kabcd * _gamma_inc.reshape(1,1,1,1)
 
     Rt = get_R_tensor(l4, theta, Rpq)
     nfi = n_cart(li)

code-examples/chap12/analytical_integrals/v4_numba/eri_OS.py

@@ -2,7 +2,7 @@
 import numpy as np
 import numba
 from basis import CGTO, n_cart
-from rys_roots import boys
+from rys_roots import gamma_inc
 
 
 def contracted_ERI(bas_i, bas_j, bas_k, bas_l) -> np.ndarray:
@@ -49,17 +49,17 @@ def primitive_ERI(li, lj, lk, ll, ai, aj, ak, al, Ra, Rb, Rc, Rd) -> np.ndarray:
     lij = li + lj
     lkl = lk + ll
     n = lij + lkl
-    _boys = boys(n, theta_r2)
+    _gamma_inc = gamma_inc(n, theta_r2)
     if n == 0:
-        return _boys[:1].reshape(1,1,1,1) * Kabcd
+        return _gamma_inc[:1].reshape(1,1,1,1) * Kabcd
 
     Xab, Yab, Zab = Rab
     Xcd, Ycd, Zcd = Rcd
     Xpq, Ypq, Zpq = Rpq
     Xpa, Ypa, Zpa = Rp - Ra
 
     vrr = np.empty((n+1, n+1,n+1,n+1))
-    vrr[:,0,0,0] = Kabcd * _boys
+    vrr[:,0,0,0] = Kabcd * _gamma_inc
     ix = 0
     iy = 0
     if n > 0:

code-examples/chap12/analytical_integrals/v4_numba/rys_roots.py

@@ -3,7 +3,7 @@
 import numba
 
 @numba.njit(cache=True)
-def boys(m, t):
+def gamma_inc(m, t):
 #             _ 1           2
 #            /     2 m  -t u
 # F (t)  =   |    u    e      du,
@@ -96,7 +96,7 @@ def poly_value1(a, order, x):
 
 @numba.njit(cache=True)
 def rys_roots_weights(nroots, x):
-    moments = boys(nroots*2, x)
+    moments = gamma_inc(nroots*2, x)
     if moments[0] < 1e-16:
         return np.zeros(nroots), np.zeros(nroots)