scipy.optimize.newton does not accept Sage input anymore

[videlec]

As reported in this sage-support thread, the scipy.optimize.newton became more picky about input and broke an interact.

The problem is reproducible below with sage-9.1.beta4

sage: f(t) = t**2 - 1/2
sage: df(t) = 2*t
sage: import scipy.optimize
sage: scipy.optimize.newton(f, 0.3, df)
Traceback (most recent call last)
<ipython-input-1-3a75ef95af3d> in <module>()
      2 __tmp__=var("t"); df = symbolic_expression(Integer(2)*t).function(t)
      3 import scipy.optimize
----> 4 scipy.optimize.newton(f, RealNumber('0.3'), df, maxiter=Integer(10))

/opt/sage/local/lib/python3.7/site-packages/scipy/optimize/zeros.py in newton(func, x0, fprime, args, tol, maxiter, fprime2, x1, rtol, full_output, disp)
    297                     newton_step /= 1.0 - adj
    298             p = p0 - newton_step
--> 299             if np.isclose(p, p0, rtol=rtol, atol=tol):
    300                 return _results_select(
    301                     full_output, (p, funcalls, itr + 1, _ECONVERGED))

/opt/sage/local/lib/python3.7/site-packages/numpy/core/numeric.py in isclose(a, b, rtol, atol, equal_nan)
   2519     y = array(y, dtype=dt, copy=False, subok=True)
   2520 
-> 2521     xfin = isfinite(x)
   2522     yfin = isfinite(y)
   2523     if all(xfin) and all(yfin):

TypeError: ufunc 'isfinite' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''

The smartest way to achieve what is wanted is certainly

sage: f_fc = fast_callable(f, float)
sage: df_fc = fast_callable(df, float)
sage: scipy.optimize.newton(f_fc, 0.3r, df_fc)
0.7071067811865475

Should we just aknowledge the incompatibility or should we try something on the numpy side?

CC: @mkoeppe @dimpase

Component: interfaces

Issue created by migration from https://trac.sagemath.org/ticket/29210

[mkoeppe]

comment:3

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

[mkoeppe]

comment:5

Moving this ticket to 9.4, as it seems unlikely that it will be merged in 9.3, which is in the release candidate stage

[mkoeppe]

comment:10

I think here we have run into the changes to numpy's casting rules. Many functions now default to casting='safe'.

sage: sage: f(t) = t**2 - 1/2
sage: y = f(0.3r)
sage: type(y)
<class 'sage.symbolic.expression.Expression'>
sage: np.array([y]).astype('float', casting='safe')
TypeError: Cannot cast array data from dtype('O') to dtype('float64') according to the rule 'safe'
sage: np.array([y]).astype('float', casting='unsafe')
array([-0.41])

[kwankyu]

comment:11

I guess the problem will be solved if we introduce ConstantExpression palatable to numpy as commented in #34693.