I'd like to change a 3D array of integers into a SymPy
matrix of rationals. I know that I should use Sympy
(Rational
and Matrix
) but I don't know how to do it.
For example,
[[[2, 1], [1, 3], [3, 2]], [[4, 3], [5, 2], [0, 1]]]
should become
2 1/3 3/2
4/3 5/2 0
A Picture of how it should look:
A convenient way is to create a matrix from a function as follows:
from sympy import Matrix, S
a = [[[2, 1], [1, 3], [3, 2]], [[4, 3], [5, 2], [0, 1]]]
m, n = len(a), len(a[0])
b = Matrix(m, n, lambda i, j: S(a[i][j][0])/a[i][j][1])
The above is assuming the array is a nested Python list. If it was a NumPy 3D array, one can do
from sympy import Matrix, S
import numpy as np
a = np.array([[[2, 1], [1, 3], [3, 2]], [[4, 3], [5, 2], [0, 1]]])
m, n, _ = a.shape
b = Matrix(m, n, lambda i, j: S(a[i, j, 0])/a[i, j, 1])
Note about S(x)/y
versus Rational(x, y)
: the former is division preceded by converting x
into a SymPy object. (See SymPy numbers.)
This makes a rational out of any kind of integer-looking inputs. Rational(x, y)
is a direct construction of a Rational object, which is fine with Python integers as inputs but has an issue with np.int64
datatype. For this reason, Rational(a[i, j, 0], a[i, j, 1])
would not work in the second snippet. (Possibly a SymPy bug.)