I use sympy and numpy to solve the following problem:
For the point (x0, y0) and the curve y = a * x ** 2 + b * x + c, we calculate the minimum distances (x0, y0) to (x, y).
from sympy.core.symbol import symbols
from sympy.solvers.solvers import solve
from sympy.utilities.lambdify import lambdify
x, y = symbols('x y')
a,b,c, x0, y0 = symbols('a b c x0 y0')
y = a*x**2 + b*x + c
dist2 = (x-x0)**2 + (y-y0)**2
sol = solve(dist2.diff(x), x)
dist2_diff_solve = lambdify( (x0,y0,a,b,c), solve(dist2.diff(x),x), modules='numpy')
So far, everything is fine. I can even get some results:
dist2_diff_solve(1, 1, 1, 1, 1)
[0.31718264650678707, (-0.9085913232533936-0.8665105933073626j),
(-0.9085913232533936+0.8665105933073626j)]
However, with another group of parameters, I have problems:
dist2_diff_solve(664515.9375, 3998106.0, 0.053674994761459802, -71340.561832823907, 23709057427.266102)
*** ValueError: negative number cannot be raised to a fractional power
I think this is a bug from lambdify, as I can do the following:
sol[0].evalf(subs={x0:664515.9375, y0:3998106.0, a:0.053674994761459802, b:-71340.561832823907, c:23709057427.266102})
664515.759983973 + .0e-19*I
I need lambdify because I need to calculate a large amount (~ 100K) of computation (vectorization) at a time. Can anyone confirm that this is a bug from lambdify? Any comments / suggestions are welcome.