#!/usr/bin/env python
# coding: utf-8

# <script async src="https://www.googletagmanager.com/gtag/js?id=UA-59152712-8"></script>
# <script>
#   window.dataLayer = window.dataLayer || [];
#   function gtag(){dataLayer.push(arguments);}
#   gtag('js', new Date());
# 
#   gtag('config', 'UA-59152712-8');
# </script>
# 
# # Creating the Finite-Difference Table for Centered First and Second  Derivatives, from 2nd through 10th-Order Accuracy
# 
# <!-- abstract? -->
# 
# ## *Courtesy Brandon Clark*

# In[1]:


print("Installing astropy, needed for creating the output table. Please wait a few seconds...")
get_ipython().system('pip install -U pip astropy > /dev/null')
print("astropy installed.")
# Step 0: Import needed modules
import numpy as np
import finite_difference as fin
from astropy.table import Table

# Step 1: Set the maximum finite-difference accuracy order computed in the table
max_fdorder = 10

# Step 2: Set up table parameters
#    One column for deriv order, one for deriv accuracy, and max_fdorder+1
numcols = 2 + max_fdorder + 1
#    8 rows: max_fdorder accuracy orders per derivative order, times 2 derivative orders (first & second derivative)
numrows = int(max_fdorder/2 * 2)
#    Center column index of table will be at 2 + max_fdorder/2  (zero-offset indexing)
column_corresponding_to_zero_fd_point = 2 + int(max_fdorder/2)
#    The table is initialized as a matrix of zeroes in numpy...
numpy_matrix = np.zeros((numrows, numcols), dtype=object)
#    Then we replace all elements with the empty string to match the Wikipedia article.
for row in range(numrows):
    for col in range(numcols):
        numpy_matrix[row,col] = ""

# Step 3: Construct the first-order derivative finite difference coefficients
rowcount = 0
for fdorder in range(2, max_fdorder+1, 2): # loop runs from 2 to max_fdorder inclusive, skipping odd orders.
    numpy_matrix[rowcount, 0] = "1st"
    numpy_matrix[rowcount, 1] = fdorder
    fdcoeffs, fdstencl = fin.compute_fdcoeffs_fdstencl("D0", fdorder)
    for i in range(fdorder):
        numpy_matrix[rowcount, column_corresponding_to_zero_fd_point + fdstencl[i][0]] = fdcoeffs[i]
    rowcount += 1

# Step 4: Construct the second-order derivative finite difference coefficients
for fdorder in range(2, max_fdorder+1, 2): # loop runs from 2 to max_fdorder inclusive, skipping odd orders.
    numpy_matrix[rowcount, 0] = "2nd"
    numpy_matrix[rowcount, 1] = fdorder
    fdcoeffs, fdstencl = fin.compute_fdcoeffs_fdstencl("DD00", fdorder)
    for i in range(fdorder+1):
        numpy_matrix[rowcount, column_corresponding_to_zero_fd_point + fdstencl[i][0]] = fdcoeffs[i]
    rowcount += 1

# Step 5: Construct an astropy table from the numpy matrix with the following header info, and then print it:
colnames = ['Derivative','Accuracy']
for i in range(-int(max_fdorder/2),int(max_fdorder/2)+1):
    colnames.append(str(i))
table = Table(numpy_matrix, names=colnames)
table.pprint(max_width=-1)