Hopefully got compute_born_matrix numdiff method working. Also added two BORN_MATRIX examples.

examples/BORN_MATRIX/Numdiff/compute_born.py

@@ -0,0 +1,118 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+import sys
+import numpy as np
+
+def reduce_Born(Cf):
+    C = np.zeros((6,6), dtype=np.float64)
+    C[0,0] = Cf[0]
+    C[1,1] = Cf[1]
+    C[2,2] = Cf[2]
+    C[3,3] = Cf[3]
+    C[4,4] = Cf[4]
+    C[5,5] = Cf[5]
+    C[0,1] = Cf[6]
+    C[0,2] = Cf[7]
+    C[0,3] = Cf[8]
+    C[0,4] = Cf[9]
+    C[0,5] = Cf[10]
+    C[1,2] = Cf[11]
+    C[1,3] = Cf[12]
+    C[1,4] = Cf[13]
+    C[1,5] = Cf[14]
+    C[2,3] = Cf[15]
+    C[2,4] = Cf[16]
+    C[2,5] = Cf[17]
+    C[3,4] = Cf[18]
+    C[3,5] = Cf[19]
+    C[4,5] = Cf[20]
+    C = np.where(C,C,C.T)
+    return C
+
+def compute_delta():
+    D = np.zeros((3,3,3,3))
+    for a in range(3):
+        for b in range(3):
+            for m in range(3):
+                for n in range(3):
+                    D[a,b,m,n] = (a==m)*(b==n) + (a==n)*(b==m)
+    d = np.zeros((6,6))
+    d[0,0] = D[0,0,0,0]
+    d[1,1] = D[1,1,1,1]
+    d[2,2] = D[2,2,2,2]
+    d[3,3] = D[1,2,1,2]
+    d[4,4] = D[0,2,0,2]
+    d[5,5] = D[0,1,0,1]
+    d[0,1] = D[0,0,1,1]
+    d[0,2] = D[0,0,2,2]
+    d[0,3] = D[0,0,1,2]
+    d[0,4] = D[0,0,0,2]
+    d[0,5] = D[0,0,0,1]
+    d[1,2] = D[1,1,2,2]
+    d[1,3] = D[1,1,1,2]
+    d[1,4] = D[1,1,0,2]
+    d[1,5] = D[1,1,0,1]
+    d[2,3] = D[2,2,1,2]
+    d[2,4] = D[2,2,0,2]
+    d[2,5] = D[2,2,0,1]
+    d[3,4] = D[1,2,0,2]
+    d[3,5] = D[1,2,0,1]
+    d[4,5] = D[0,2,0,1]
+    d = np.where(d,d,d.T)
+    return d
+
+
+def write_matrix(C, filename):
+    with open(filename, 'w') as f:
+        f.write("# Cij Matrix from post process computation\n")
+        for i in C:
+            f.write("{:8.5f} {:8.5f} {:8.5f} {:8.5f} {:8.5f} {:8.5f}\n".format(
+                i[0]*10**-9, i[1]*10**-9, i[2]*10**-9, i[3]*10**-9, i[4]*10**-9, i[5]*10**-9,
+                )
+            )
+    return
+
+def main():
+
+    N = 500
+    vol = 27.047271**3 * 10**-30  # m^3
+    T = 60  # K
+    kb = 1.380649 * 10**-23  # J/K
+    kbT = T*kb  # J
+    kcalmol2J = 4183.9954/(6.022*10**23)
+
+    born = np.loadtxt('born.out')
+    stre = np.loadtxt('vir.out')
+    stre[:, 1:] = -stre[:, 1:]*101325  # -> Pa
+    try:
+        mean_born = np.mean(born[:, 1:], axis=0)
+    except IndexError:
+        mean_born = born[1:]
+
+    CB = kcalmol2J/vol*reduce_Born(mean_born)  # -> J/m^3=Pa
+    Cs = vol/kbT*np.cov(stre[:,1:].T)
+    Ct = N*kbT/vol * compute_delta()
+    C = CB - Cs + Ct
+    write_matrix(CB, 'born_matrix.out')
+    write_matrix(Cs, 'stre_matrix.out')
+    write_matrix(Ct, 'temp_matrix.out')
+    write_matrix(C, 'full_matrix.out')
+    C11 = np.mean([C[0,0], C[1,1], C[2,2]]) * 10**-9
+    C12 = np.mean([C[0,1], C[0,2], C[1,2]]) * 10**-9
+    C44 = np.mean([C[3,3], C[4,4], C[5,5]]) * 10**-9
+    eC11 = np.std([C[0,0], C[1,1], C[2,2]]) * 10**-9
+    eC12 = np.std([C[0,1], C[0,2], C[1,2]]) * 10**-9
+    eC44 = np.std([C[3,3], C[4,4], C[5,5]]) * 10**-9
+    print(C*10**-9)
+    print("C11 = {:f} ± {:f}; C12 = {:f} ± {:f}; C44 = {:f} ± {:f}".format(C11, eC11, C12, eC12, C44, eC44))
+
+    return
+
+
+if __name__ == "__main__":
+    try:
+        main()
+    except KeyboardInterrupt:
+        raise SystemExit("User interruption.")
+