Difference between eye and Identity in SymPy

问题

In SymPy, what is the difference between eye(5) and Identity(5)?

If I have a matrix X, I see that X + eye(5) and X + Identity(5) give different results (the latter is not a matrix).

回答1:

SymPy distinguishes between

explicit matrices, which have certain size, like 3 by 3, and explicit (possibly symbolic) entries;
matrix expressions, which may have symbolic size, like n by n.

eye creates a matrix, Identity creates a matrix expression. For example:

n = Symbol("n")
A = Identity(n)  # works
A = eye(n)       # throws an error

One can do some computations with this object, such as

t = trace(A)     # n
B = BlockMatrix([[A, -A], [-A, A]])

When possible, a matrix expression can be turned into an explicit matrix with as_explicit method:

A = Identity(3)
print(A.as_explicit())

prints

Matrix([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])

One can use Matrix(A) to the same effect.

回答2:

Identity is more about being able to use the symbol I to stand for the identity. If you want the matrix using that, you have to do Matrix(Identity)

See:

from random import randint
from sympy import *

X = Matrix(list([randint(1, 10) for _ in range(5)] for _ in range(5)))

print(X + eye(5))

Output: Matrix([[7, 10, 5, 5, 4], [3, 7, 9, 5, 4], [1, 9, 6, 3, 4], [4, 8, 5, 2, 9], [9, 3, 6, 6, 4]])

print(X + Matrix(Identity(5)))

Same output: Matrix([[7, 10, 5, 5, 4], [3, 7, 9, 5, 4], [1, 9, 6, 3, 4], [4, 8, 5, 2, 9], [9, 3, 6, 6, 4]])

print(X + Identity(5))

'''different output more about the symbol: I + Matrix([
[6, 10, 5, 5, 4],
[3,  6, 9, 5, 4],
[1,  9, 5, 3, 4],
[4,  8, 5, 1, 9],
[9,  3, 6, 6, 3]])'''

Not too much is said about it in the docs.

来源：https://stackoverflow.com/questions/50854803/difference-between-eye-and-identity-in-sympy

标签

python

matrix

sympy

identity