CODEWITHSUNDEEP
pythonpython-2.7sympysymbolic-math
makansij
makansij

Reputation: 9875

How to take derivative in sympy with respect to a vector?

I want to know if it is possible in sympy to take derivatives of polynomials and expressions using vector notation. For example, if I have an expression as a function of two coordinates, x1 and x2, can I just make one call to diff(x), where x is a vector of x1 and x2, or do I need to make two separate diff calls to x1 and x2, and stack them in a matrix?

This illustrates what works, versus what I want to work ideally:

import sympy
from sympy.matrices import Matrix

# I understand that this is possible: 
x1 = sympy.symbol.symbols('x1')  
x2 = sympy.symbol.symbols('x2')

expr_1 = x1**2+x2
poly_1 = sympy.poly(expr_1, x1, x2)

print Matrix([[poly_1.diff(x1)],[poly_1.diff(x2)]])

# but is something like this also possible?
x1 = sympy.symbol.symbols('x1')  
x2 = sympy.symbol.symbols('x2')
x_vec = Matrix([[x1],[x2]])

expr_1 = x1**2+x2
poly_1 = sympy.poly(expr_1, x1, x2)

# taking derivative with respect to a vector
poly_1.diff(x_vec)

# should ideally return same as first example: 
'''
Matrix([
[Poly(2*x1, x1, x2, domain='ZZ')],
[   Poly(1, x1, x2, domain='ZZ')]])
'''
# but it fails :(

Is there a way to take derivatives with respect to vectors in sympy?

Thank you.

Upvotes: 5

Views: 3137

Answers (1)

smichr
smichr

Reputation: 19093

Perhaps you are thinking of the jacobian:

>>> Matrix([Poly(x**2+y,x,y)]).jacobian([x, y])
Matrix([[Poly(2*x, x, y, domain='ZZ'), Poly(1, x, y, domain='ZZ')]])

And that [x, y] argument can be Matrix([x, y]) or its transpose, too.

Upvotes: 4

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