Extracting polynomial coefficients from file in Python

Question

I have recently been working with text files that contain data like the following:

A = a_0 + a_1*x + ... + a_l*x^l
B = b_0 + b_1*x + ... + b_m*x^m
.
.
.
G = g_2*x^2 + g_n

where l and m are not necessarily the same, and B might not be the longest equation. Is there a way to import the coefficients into a NumPy array, inserting 0s where the coefficients are missing, such that the above example would yield

I was initially thinking of using numpy.genfromtxt where the x are filled with 1 (so that only the coefficient survives), but that has the problem that we lose which column and row the coefficient in. Any help is very much appreciated.

Asked By: notastringtheorist

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Source

Answer 1

This is very custom type of text you have to write a parser to do so:

considering the txt file is read, example here s
you probably have to read from file, with open('..') as fid ...

s  = """A =  2*x  + 3*x^5
B = 3 + 2*x  + 3*x^5
C = 8 + 20*x  + 3*x^9"""

like this:

equations = s.split('n')

def parse_lines(s):
    def foo(val):
        coef, _power,*_ = *val.split('*'), '^'  #  parse a_0*x^n 
        x, power, *_ =  *_power.split('^'), '1' #  parse x^n
        power = 0 if not power else power 
        return int(coef) , int(power)
    
    _, eq = s.split('=')
    return  [foo(item) for item in eq.split('+')]
 

indexes = [(idx, *t)  for idx, eq in enumerate(equations) for t in parse_lines(eq)]

output: (row, val, col)

[(0, 2, 1),
 (0, 3, 5),
 (1, 3, 0),
 (1, 2, 1),
 (1, 3, 5),
 (2, 8, 0),
 (2, 20, 1),
 (2, 3, 9)]

you could parse to a format that could be reconstructed to an array.
after this it is simple just build array:

m, _, n = np.array(d).max(axis=0)
m , n = m + 1, n + 1
arr = np.zeros((m,n))
for row, val, col in indexes:
    arr[row, col] = val

output:

array([[ 0.,  2.,  0.,  0.,  0.,  3.,  0.,  0.,  0.,  0.],
       [ 3.,  2.,  0.,  0.,  0.,  3.,  0.,  0.,  0.,  0.],
       [ 8., 20.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  3.]])

Answered By: amirhm

Extracting polynomial coefficients from file in Python

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