How do you replace a function argument with a float?

[Jason Moore]

I don't understand this behavior:

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In [1]: from sympy import *

In [2]: phi = symbols('phi', cls=Function)

In [3]: t = symbols('t')

In [4]: phi(t).xreplace({t: 0})
Out[4]: phi(0)

In [5]: phi(t).xreplace({t: 0.0})
Out[5]: 1.61803398874989

In [6]: phi(t).xreplace({t: 5.0})
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/core/evalf.py in evalf(x, prec, options)
   1209     try:
-> 1210         rf = evalf_table[x.func]
   1211         r = rf(x, prec, options)

KeyError: phi

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
<ipython-input-6-ec5c48b4cb2f> in <module>()
----> 1 phi(t).xreplace({t: 5.0})

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/core/basic.py in xreplace(self, rule)
   1086             args = tuple(args)
   1087             if not _aresame(args, self.args):
-> 1088                 return self.func(*args)
   1089         return self
   1090

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/core/function.py in __new__(cls, *args, **options)
    683     def __new__(cls, *args, **options):
    684         args = list(map(sympify, args))
--> 685         obj = super(AppliedUndef, cls).__new__(cls, *args, **options)
    686         return obj
    687

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/core/function.py in __new__(cls, *args, **options)
    380         pr2 = min(cls._should_evalf(a) for a in result.args)
    381         if pr2 > 0:
--> 382             return result.evalf(mlib.libmpf.prec_to_dps(pr))
    383         return result
    384

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/core/evalf.py in evalf(self, n, subs, maxn, chop, strict, quad, verbose)
   1315             options['quad'] = quad
   1316         try:
-> 1317             result = evalf(self, prec + 4, options)
   1318         except NotImplementedError:
   1319             # Fall back to the ordinary evalf

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/core/evalf.py in evalf(x, prec, options)
   1215             if 'subs' in options:
   1216                 x = x.subs(evalf_subs(prec, options['subs']))
-> 1217             re, im = x._eval_evalf(prec).as_real_imag()
   1218             if re.has(re_) or im.has(im_):
   1219                 raise NotImplementedError

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/core/function.py in _eval_evalf(self, prec)
    484
    485         with mpmath.workprec(prec):
--> 486             v = func(*args)
    487
    488         return Expr._from_mpmath(v, prec)

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/mpmath/ctx_mp_python.py in __call__(self, prec, dps, rounding)
    344         if not rounding: rounding = rounding2
    345         if dps: prec = dps_to_prec(dps)
--> 346         return self.context.make_mpf(self.func(prec, rounding))
    347
    348     @property

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/mpmath/libmp/libelefun.py in f(prec, rnd)
    114     def f(prec, rnd=round_fast):
    115         wp = prec + 20
--> 116         v = fixed(wp)
    117         if rnd in (round_up, round_ceiling):
    118             v += 1

/home/moorepants/miniconda3/lib/python3.5/site-packages/sympy/mpmath/libmp/libelefun.py in g(prec, **kwargs)
     95         memo_prec = f.memo_prec
     96         if prec <= memo_prec:
---> 97             return f.memo_val >> (memo_prec-prec)
     98         newprec = int(prec*1.05+10)
     99         f.memo_val = f(newprec, **kwargs)

TypeError: unsupported operand type(s) for >>: 'int' and 'mpf'

Can someone explain to me what is going on? I would expect "t" to be simply replaced with the number.

Jason
moorepants.info
+01 530-601-9791

[Sartaj Singh]

Apparently, this also does not work,

# leosartaj at Mothership in ~/projects/sympy on git:master o [0:09:48]

$ isympy

IPython console for SymPy 1.0.1.dev (Python 2.7.11-64-bit) (ground types: python)

These commands were executed:

>>> from __future__ import division

>>> from sympy import *

>>> x, y, z, t = symbols('x y z t')

>>> k, m, n = symbols('k m n', integer=True)

>>> f, g, h = symbols('f g h', cls=Function)

>>> init_printing()

Documentation can be found at http://docs.sympy.org/dev

In [1]: phi = symbols('phi', cls=Function)

In [2]: phi(5.0)

---------------------------------------------------------------------------

TypeError                                 Traceback (most recent call last)

<ipython-input-2-68868fcc8946> in <module>()

----> 1 phi(5.0)

/home/leosartaj/projects/sympy/sympy/core/function.pyc in __new__(cls, *args, **options)

    718     def __new__(cls, *args, **options):

    719         args = list(map(sympify, args))

--> 720         obj = super(AppliedUndef, cls).__new__(cls, *args, **options)

    721         return obj

    722 

/home/leosartaj/projects/sympy/sympy/core/cache.pyc in wrapper(*args, **kwargs)

     93                     retval = cfunc(*args, **kwargs)

     94                 except TypeError:

---> 95                     retval = func(*args, **kwargs)

     96                 return retval

     97 

/home/leosartaj/projects/sympy/sympy/core/function.pyc in __new__(cls, *args, **options)

    390         pr2 = min(cls._should_evalf(a) for a in result.args)

    391         if pr2 > 0:

--> 392             return result.evalf(mlib.libmpf.prec_to_dps(pr))

    393         return result

    394 

/home/leosartaj/projects/sympy/sympy/core/evalf.pyc in evalf(self, n, subs, maxn, chop, strict, quad, verbose)

   1384             options['quad'] = quad

   1385         try:

-> 1386             result = evalf(self, prec + 4, options)

   1387         except NotImplementedError:

   1388             # Fall back to the ordinary evalf

/home/leosartaj/projects/sympy/sympy/core/evalf.pyc in evalf(x, prec, options)

   1282             if 'subs' in options:

   1283                 x = x.subs(evalf_subs(prec, options['subs']))

-> 1284             xe = x._eval_evalf(prec)

   1285             re, im = xe.as_real_imag()

   1286             if re.has(re_) or im.has(im_):

/home/leosartaj/projects/sympy/sympy/core/function.pyc in _eval_evalf(self, prec)

    501 

    502         with mpmath.workprec(prec):

--> 503             v = func(*args)

    504 

    505         return Expr._from_mpmath(v, prec)

/home/leosartaj/anaconda/envs/my/lib/python2.7/site-packages/mpmath/ctx_mp_python.pyc in __call__(self, prec, dps, rounding)

    344         if not rounding: rounding = rounding2

    345         if dps: prec = dps_to_prec(dps)

--> 346         return self.context.make_mpf(self.func(prec, rounding))

    347 

    348     @property

/home/leosartaj/anaconda/envs/my/lib/python2.7/site-packages/mpmath/libmp/libelefun.pyc in f(prec, rnd)

    114     def f(prec, rnd=round_fast):

    115         wp = prec + 20

--> 116         v = fixed(wp)

    117         if rnd in (round_up, round_ceiling):

    118             v += 1

/home/leosartaj/anaconda/envs/my/lib/python2.7/site-packages/mpmath/libmp/libelefun.pyc in g(prec, **kwargs)

     95         memo_prec = f.memo_prec

     96         if prec <= memo_prec:

---> 97             return f.memo_val >> (memo_prec-prec)

     98         newprec = int(prec*1.05+10)

     99         f.memo_val = f(newprec, **kwargs)

TypeError: unsupported operand type(s) for >>: 'long' and 'mpf'

This does work though,

>>> phi(5)

φ(5)

However,

>>> p = symbols('p', cls=Function)    

>>>  p(5.0)

p(5.0)

>>> p(t).xreplace({t: 5.0})  

p(5.0) # works without any problems

By My understanding, is symbols with cls=Function arg not expected to make an undefined function?

[Aaron Meurer]

Since this seems to break only when the function name is "phi", this
looks like an instance of https://github.com/sympy/sympy/issues/6938.
But I'm not quite sure what other SymPy function is named "phi". I
didn't find any in a quick grep.

Aaron Meurer

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[Aaron Meurer]

Oh maybe it's just looking up the mpmath function named phi. We do have

In [7]: import mpmath

In [8]: mpmath.phi
Out[8]: <Golden ratio phi: 1.61803~>

Aaron Meurer

[Sartaj Singh]

Also type(phi) gives sympy.core.function.UndefinedFunction. This is confusing.

To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6J93TOhZxUL2D-qq55v%3D6_GgfWK6e38rx66gtq%2BHazTQw%40mail.gmail.com.

For more options, visit https://groups.google.com/d/optout.

--

Regards

Sartaj Singh

Mathematics and Computing,

Indian Institute of Technology,

Varanasi - 221 005 INDIA

E-mail: singhs...@gmail.com, sartaj.si...@itbhu.ac.in

[Isuru Fernando]

It is looking for mpmath's phi. See https://github.com/sympy/sympy/blob/master/sympy/core/function.py#L458

Isuru Fernando

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[Aaron Meurer]

That is the issue here. The problem is that undefined functions do
evalf name lookups. For example

In [9]: Function("sin")(1.0)
Out[9]: 0.841470984807897

We should change it so that only direct subclasses of Function do
this, not UndefinedFunctions.

In the mean time, Jason, a workaround would be to use Function(u'φ').

Aaron Meurer

> https://groups.google.com/d/msgid/sympy/CAC%2BH8-GshNsi%2BRheh50aHcXsMeQS5KBsJLOG%3DtRUGqGZCkgotg%40mail.gmail.com.

[Jason Moore]

Thanks for explaining this. I'll try to look into pushing a fix for this.

Jason
moorepants.info
+01 530-601-9791

To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6LF083v9etxFe3SYcfqH2tp0%3DbEQg1coBiRayT8SGUeew%40mail.gmail.com.