Add an additional line in ctx_mp_python.py line 679 to convert also numpy ndarrays of length 1

[sven0schuierer]

Hi,

I would suggest adding the line

    if isinstance(x, np.ndarray) and len(x) == 1: x = x[0]

as line 679 in ctx_mp_python.py to convert numpy ndarrays of length 1.

Justification:
The following code fails without this:

from mpmath import *
from scipy.optimize import fsolve
fsolve (lambda x: exp(x) - 5, 1)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/scipy/optimize/_minpack_py.py", line 170, in fsolve
    res = _root_hybr(_wrapped_func, x0, args, jac=fprime, **options)
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/scipy/optimize/_minpack_py.py", line 238, in _root_hybr
    shape, dtype = _check_func('fsolve', 'func', func, x0, args, n, (n,))
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/scipy/optimize/_minpack_py.py", line 23, in _check_func
    res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
                     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/scipy/optimize/_minpack_py.py", line 158, in _wrapped_func
    return func(*fargs)
           ^^^^^^^^^^^^
  File "<stdin>", line 1, in <lambda>
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/mpmath/ctx_mp_python.py", line 991, in f
    x = ctx.convert(x)
        ^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/mpmath/ctx_mp_python.py", line 650, in convert
    if type(x).__module__ == 'numpy': return ctx.npconvert(x)
                                             ^^^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/mpmath/ctx_mp_python.py", line 683, in npconvert
    raise TypeError("cannot create mpf from " + repr(x))
TypeError: cannot create mpf from array([1])

Of course, one could use findroot instead of fsolve above. But there are instances in which fsolve works and findroot does not:

n_1, n_obs_1, n_2, n_obs_2 = 62380000, 34539224.0, 62390000, 34542106.0
def f_1 (N0, N1):
    return N0 * (1 - exp (-1 * n_1 / (N0 + 2 * N1))) + N1 * (1 - exp (-2 * n_1 / (N0 + 2 * N1))) - n_obs_1,  \
           N0 * (1 - exp (-1 * n_2 / (N0 + 2 * N1))) + N1 * (1 - exp (-2 * n_2 / (N0 + 2 * N1))) - n_obs_2

findroot (f_1, (27109937, 28500053))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/mpmath/calculus/optimization.py", line 969, in findroot
    for x, error in iterations:
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/mpmath/calculus/optimization.py", line 660, in __iter__
    s = self.ctx.lu_solve(Jx, fxn)
        ^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/mpmath/matrices/linalg.py", line 224, in lu_solve
    A, p = ctx.LU_decomp(A)
           ^^^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/mpmath/matrices/linalg.py", line 149, in LU_decomp
    raise ZeroDivisionError('matrix is numerically singular')
ZeroDivisionError: matrix is numerically singular

def f_2 (param):
    N0, N1 = param
    return [N0 * (1 - exp (-1 * n_1 / (N0 + 2 * N1))) + N1 * (1 - exp (-2 * n_1 / (N0 + 2 * N1))) - n_obs_1,  \
            N0 * (1 - exp (-1 * n_2 / (N0 + 2 * N1))) + N1 * (1 - exp (-2 * n_2 / (N0 + 2 * N1))) - n_obs_2]

fsolve (f_2, [27109937, 28500053])
<stdin>:1: RuntimeWarning: The iteration is not making good progress, as measured by the 
  improvement from the last ten iterations.
array([36079713.35263181, 14271606.52089586])

Finally, there are instances in which fsolve runs into an overflow with the imports from math but not from mpmath:

from math import *
from scipy.optimize import fsolve

def f (param):
  N0, N1, N2 = param
  return [N0 * (1 - exp (-1 * n_1 / (N0 + 2 * N1 + 3 * N2))) + N1 * (1 - exp (-2 * n_1 / (N0 + 2 * N1 + 3 * N2))) + N2 * (1 - exp (-3 * n_1 / (N0 + 2 * N1 + 3 * N2))) - n_obs_1, 
          N0 * (1 - exp (-1 * n_2 / (N0 + 2 * N1 + 3 * N2))) + N1 * (1 - exp (-2 * n_2 / (N0 + 2 * N1 + 3 * N2))) + N2 * (1 - exp (-3 * n_1 / (N0 + 2 * N1 + 3 * N2))) - n_obs_2, 
          N0 * (1 - exp (-1 * n_3 / (N0 + 2 * N1 + 3 * N2))) + N1 * (1 - exp (-2 * n_3 / (N0 + 2 * N1 + 3 * N2))) + N2 * (1 - exp (-3 * n_1 / (N0 + 2 * N1 + 3 * N2))) - n_obs_3]

n_1, n_obs_1, n_2, n_obs_2, n_3, n_obs_3 = 62380000, 34539224.0, 62390000, 34542106.0, 62400000, 34544973.0
initial_estimate = [27376700.0, 18251133.333333332, 9125566.666666666]
fsolve (f, initial_estimate)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/scipy/optimize/_minpack_py.py", line 170, in fsolve
    res = _root_hybr(_wrapped_func, x0, args, jac=fprime, **options)
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/scipy/optimize/_minpack_py.py", line 249, in _root_hybr
    retval = _minpack._hybrd(func, x0, args, 1, xtol, maxfev,
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/da/cbt/GX/schuisv1/python/envs/library-complexity-test/lib/python3.12/site-packages/scipy/optimize/_minpack_py.py", line 158, in _wrapped_func
    return func(*fargs)
           ^^^^^^^^^^^^
  File "<stdin>", line 3, in f
OverflowError: math range error
from mpmath import *
>>> fsolve (f, initial_estimate)
<stdin>:3: RuntimeWarning: invalid value encountered in multiply
<stdin>:4: RuntimeWarning: invalid value encountered in multiply
<stdin>:5: RuntimeWarning: invalid value encountered in multiply
<stdin>:1: RuntimeWarning: The iteration is not making good progress, as measured by the 
  improvement from the last ten iterations.
array([27376700.        , 18251133.33333333,  9125566.66666667])

Best regards,
Sven

[skirpichev]

convert also numpy ndarrays of length 1

No, I think it's a bad idea, see e.g. numpy/numpy#10404.

Numpy has scalar arrays, and it does make sense to convert them. But in your case you should do this explicitly, e.g.:

>>> fsolve (lambda x: exp(x[0]) - 5, 1)
array([1.60943791])