using SciPy to integrate a function that returns a matrix or array

Question

I have a symbolic array that can be expressed as:

from sympy import lambdify, Matrix

g_sympy = Matrix([[   x,  2*x,  3*x,  4*x,  5*x,  6*x,  7*x,  8*x,   9*         


        

Answer 1

I might have found some interesting way of doing this, at the expense of defining different symbols for the matrix g_symp:

import numpy as np
from scipy.integrate import quad
import sympy as sy

@np.vectorize
def vec_lambdify(var, expr, *args, **kw):
    return sy.lambdify(var, expr, *args, **kw)

@np.vectorize
def vec_quad(f, a, b, *args, **kw):
    return quad(f, a, b, *args, **kw)[0]

Y = sy.symbols("y1:11")
x = sy.symbols("x")
mul_x = [y.subs(y,x*(i+1)) for (i,y) in enumerate(Y)]
pow_x = [y.subs(y,x**(i+1)) for (i,y) in enumerate(Y)]

g_sympy = np.array(mul_x + pow_x).reshape((2,10))
X = x*np.ones_like(g_sympy)
G = vec_lambdify(X, g_sympy)
I = vec_quad(G, 0, 100)
print(I)

with results:

[[  5.00000000e+03   1.00000000e+04   1.50000000e+04   2.00000000e+04
    2.50000000e+04   3.00000000e+04   3.50000000e+04   4.00000000e+04
    4.50000000e+04   5.00000000e+04]
[  5.00000000e+03   3.33333333e+05   2.50000000e+07   2.00000000e+09
   1.66666667e+11   1.42857143e+13   1.25000000e+15   1.11111111e+17
   1.00000000e+19   9.09090909e+20]]

and using the ipython magic%timeit vec_quad(G,0,100) I got

1000 loops, best of 3: 527 µs per loop

I think this approach is somewhat more clean, despite the juggling with symbols.