Pass list of values to SciPy fsolve argument

Question

I have the following function:

def equation1(xy, d=7.62, G=8.2728, rhop=7.51, ut=399):
    ep, uc = xy     # define variables
    g = 981         # acceleration due to gravity, cm/s^2

    f1 = 2*g*d*((ep**-4.7) - 1) - 0.01*(uc/ep - ut)**2
    f2 = G - (uc/ep - ut)*rhop*(1 - ep)
    return f1, f2

where I solve for ep and uc by using fsolve in SciPy:

ep1, uc1 = fsolve(equation1, [1, 500])

Instead of defining a single value for G , I would to like solve for ep and uc for a range G values such as G = [8, 10, 12] . When I pass a list of values for G, I get an error about setting an array element with a sequence.

Is it possible to use fsolve where one of the arguments is a list or array of values?

Answer 1

you can keep G as a parameter to equation1 and pass it via fsolve (using its args parameter) as:

from scipy.optimize import fsolve

def equation1(xy, G, d=7.62, rhop=7.51, ut=399):
    ep, uc = xy     # define variables
    g = 981         # acceleration due to gravity, cm/s^2

    f1 = 2*g*d*((ep**-4.7) - 1) - 0.01*(uc/ep - ut)**2
    f2 = G - (uc/ep - ut)*rhop*(1 - ep)
    return f1, f2


for G in [8, 10, 12]:
    ep1, uc1 = fsolve(equation1, [1, 500], (G, ))
    print(G, ep1, uc1)

this gives on my machine:

8 0.994582431487 592.401268397
10 0.993718674117 607.148953105
12 0.992912345764 620.018209488

Answer 2

If I run your function with:

In [83]: ep1, uc1 = fsolve(equation1, [1, 500],args=(7.62, [8,10,12]))
...
ValueError: setting an array element with a sequence.

But look at the call stack. It's long, but this line stands out

res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))

It's making a test call to your function.

So for example:

In [121]: x0=np.array([1,500])
In [122]: numinputs=2
In [123]: args = (1,8)     # scalar G
In [124]: np.atleast_1d(equation1(*((x0[:numinputs],) + args)))
Out[124]: array([-102.01,    8.  ])

In [125]: args = (1,[8,10])    # list G
In [126]: np.atleast_1d(equation1(*((x0[:numinputs],) + args)))
....
ValueError: setting an array element with a sequence.

Looking specifically at what your function produces:

In [127]: equation1(*((x0[:numinputs],) + args))
Out[127]: (-102.01000000000001, array([  8.,  10.]))

It can't turn this tuple into a valid 1d array, hence the error message.

Note that the arguments to your function are:

In [128]: ((x0[:numinputs],) + args)
Out[128]: (array([  1, 500]), 1, [8, 10])

fsolve passes the whole args tuple to your function. It does not iterate through arrays or lists.

So you want fsolve for various G values, you have to do the iteration yourself. fsolve (and most of the other scipy functions) won't do it for you.