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trial_plot_numericerrors.py
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'''
This program prints numerical derivative convergance
'''
import representation_ZRN as ZRNrep
from jax.config import config
config.update("jax_enable_x64", True) #increase precision from float32 to float64
import jax_representation as jrep
import numpy as np
from numpy import linalg
import jax_derivative as jder
import database_preparation as datprep
import matplotlib.pyplot as plt
import numerical_derivative as numder
#give xyz coordinates of H2O
path = "./TEST/H2O.xyz"
#read xyz file and create compound instances
Z_orig, R_orig, N, e_orig = datprep.read_xyzfile(path)
Z_orig = np.array(Z_orig, dtype = np.float64)
M, order = jrep.CM_full_sorted(Z_orig, R_orig, N)
which_derivative = 1
#reorder your initial data. otherwise numerical differentiation will fail
#needs to be performed with preordered data, otherwise sorting can change
Z = Z_orig[order.tolist()]
R = R_orig[order]
R = np.asarray(R, dtype = np.float64)
Z = np.asarray(Z, dtype = np.float64)
functionnames = ['CM_unsrt', 'CM_EV_unsrt', 'OM', 'OM_EV']
functions = [ZRNrep.Coulomb_Matrix, ZRNrep.Eigenvalue_Coulomb_Matrix, ZRNrep.Overlap_Matrix, ZRNrep.Eigenvalue_Overlap_Matrix]
def get_first_order_errors(fun, fname, hlist, d1):
if d1[0] == 0:
name = "dZ%i" % (d1[1] + 1)
dx = "Z"
exact = jder.sort_derivative(fname, Z, R, N, 1, dx)[d1[1]]
if d1[0] == 1:
xyz = ['x', 'y', 'z']
name = "d%s%i" %(xyz[d1[1]], d1[2]+1)
dx = 'R'
exact = jder.sort_derivative(fname, Z, R, N, 1, dx)[d1[1]][d1[2]]
print("\n ------------------- \n Derivative %s \n ------------------ \nAnalytical derivative" %name)
print(exact)
ylist = []
#calculate numerical derivatives for increasingly small h
for h in hlist:
derf = numder.derivative(fun, [Z,R,N], 'numerical', 1, d1, [0,0], h)
exf = exact.flatten()
print("derf")
print(derf)
print("exf")
print(exf)
error = linalg.norm(derf - exf)
ylist.append(error)
return(ylist, name)
def get_second_order_errors(fun, fname, hlist, d1, d2):
'''
fun: function from representation_ZRN.py
fname: string, 'CM', 'CM_EV', 'CM_unsrt', 'OM', 'OM_EV'
'''
#calculate exact result
if d1[0] == 0:
name1 = "dZ%i" % (d1[1] + 1)
dx1 = "Z"
if d2[0] == 0:
name = name1 + "dZ%i" % (d2[1] + 1)
dx2 = "Z"
exact = jder.sort_derivative(fname, Z, R, N, 2, dx1, dx2)[d1[1]][d2[1]]
if d1[0] == 1:
xyz = ['x', 'y', 'z']
name1 = "d%s%i" %(xyz[d1[1]], d1[2])
dx1 = 'R'
if d2[0] == 1:
name = name1 + "d%s%i" %(xyz[d2[1]], (d2[2] + 1))
dx2 = 'R'
exact = jder.sort_derivative(fname, Z, R, N, 2, dx1, dx2)[d1[1]][d1[2]][d2[1]][d2[2]]
if (d1[0] == 0 and d2[0] == 1) or (d1[0] == 1 and d2[0] == 0):
xyz = ['x', 'y', 'z']
#translate dx1 and dx2 to numbers for functions and names
dx1 = "Z"
dx2 = "R"
if d1[0] == 0:
ZR_order = True
name1 = "dZ%i" % (d1[1]+1)
name2 = "d%s%i" %(xyz[d2[1]], d2[2]+1)
else:
ZR_order = False
name1 = "dZ%i" % (d2[1]+1)
name2 = "d%s%i" %(xyz[d1[1]], d1[2]+1)
name = name1 + name2
if ZR_order:
exact = jder.sort_derivative(fname, Z, R, N, 2, dx1, dx2)[d1[1]][d2[1]][d2[2]]
else:
exact = jder.sort_derivative(fname, Z, R, N, 2, dx1, dx2)[d2[1]][d1[1]][d1[2]]
print("\n ------------------- \n Derivative %s \n ------------------ \nAnalytical derivative" %name)
print(exact)
ylist = []
#calculate numerical derivatives for increasingly small h
for h in hlist:
derf = numder.derivative(fun, [Z,R,N], 'numerical', 2, d1, d2, h)
exf = exact.flatten()
error = linalg.norm(derf - exf)
print("derf")
print(derf)
print("exf")
print(exf)
#print("h", h, "error", error)
#print(derf.reshape(3,3))
ylist.append(error)
return(ylist, name)
def plot_numeric_errors(fun, fname, do_first_order = True, do_second_order = True, show_legend = False):
'''
fun : function from representation_ZRN.py file
fname : function name: 'CM', 'CM_unsrt', 'CM_EV', 'OM' or 'OM_EV'
'''
#prepare panels for plots
fig = plt.figure(tight_layout = True, figsize=(8, 6))
#create subfigure spacing as needed
if do_first_order:
if do_second_order:
'''create 5 panel image'''
ax1 = plt.subplot2grid((2,6),(0,0), rowspan=1, colspan=3)
ax2 = plt.subplot2grid((2,6), (0,3), rowspan=1, colspan=3)
ax3 = plt.subplot2grid((2,6), (1,0), rowspan=1, colspan=2)
ax4 = plt.subplot2grid((2,6), (1,2), rowspan=1, colspan=2)
ax5 = plt.subplot2grid((2,6), (1,4), rowspan=1, colspan=2)
else:
'''create 2 panel image for dZ and dR'''
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)
elif do_second_order:
'''create 3 panel image for dZdZ, dRdR and dZdR'''
ax3 = fig.add_subplot(131)
ax4 = fig.add_subplot(132)
ax5 = fig.add_subplot(133)
#derivatives: standard parameters by which to derive.
'''
[0, ...] is dZ
[1, ...] is dR
[...,0,...] is dZ1 or dR1
for dR, [...,...,0] is dx, [...,...,1] dy and [...,...,2] dz
'''
derivative_1 = [[0,0], [0,1], [0,2],[1,0,0], [1,0,1],[1,0,2],[1,1,0], [1,1,1],[1,1,2],[1,2,0], [1,2,1], [1,2,2]]
derivative_2 = [[0,0], [0,1], [0,2], [1, 1, 2], [1,0, 1], [1,0,0], [1,2,2], [1,1,2]]
#hlist: small steps that are taken for numerical derivation
hlist = np.logspace(-1, -5, 10)
#plot 1st order if needed
if do_first_order:
for d1 in derivative_1:
ylist, name = get_first_order_errors(fun, fname, hlist, d1)
#plot errors in correct subplot
if d1[0] == 0:
ax1.loglog(hlist, ylist, 'o-', label = name)
else:
ax2.loglog(hlist, ylist, 'o-', label = name)
if show_legend:
ax1.legend()
ax2.legend()
ax1.title.set_text('dZ (nuclear charge)')
ax2.title.set_text('dR (nuclear coordinate)')
ax1.set_xlabel("dh")
ax2.set_xlabel("dh")
if do_second_order:
for d1 in derivative_1:
for d2 in derivative_2:
ylist, name = get_second_order_errors(fun, fname, hlist, d1, d2)
#plot errors in correct subplot
if d1[0] == 0:
if d2[0] == 0:
ax3.loglog(hlist, ylist, 'o-', label = name)
else:
ax5.loglog(hlist, ylist, 'o-', label = name)
if d1[0] == 1:
if d2[0] == 1:
ax4.loglog(hlist, ylist, 'o-', label = name)
else:
ax5.loglog(hlist, ylist,'o-', label = name)
if show_legend:
ax3.legend()
ax4.legend()
ax5.legend()
ax3.title.set_text("dZdZ")
ax4.title.set_text("dRdR")
ax5.title.set_text("dZdR")
ax3.set_xlabel("dh")
ax4.set_xlabel("dh")
ax5.set_xlabel("dh")
fig.suptitle('Finite Central Difference Derivative on %s of H2O Molecule' %fname, fontsize = 15)
#ad title to overall y axis
fig.text(0.5, 0.0004, '(dh is the small change introduced in numerical differentiation)', ha='center', fontsize = 13)
fig.text(0.0004, 0.5, 'Absolute Error w.r.t. Analytical Derivative [a.u.]', rotation = 'vertical', va='center', fontsize =13)
filename = "./Images/numerical_errors_%s.png" % fname
plt.savefig(filename, bbox_inches = 'tight')
return()
fun = functions[1]
fname = functionnames[1]
print("function:", fun)
print("function name:", fname)
plot_numeric_errors(fun, fname)