Big numbers in lambdify-CodePudding

I have (automatically generated by SymPy) expression, including sqrt function with big numbers under sqrt and small multiplier in front of it. So overall result must be within float range, but value under sqrt - is not. I coonvert this expression to Python function using lambdify command. Call of this function gets exception:

from sympy import *
t = symbols("t")
k = 10
f = 2 * 10 ** (- k) * sqrt(10 ** (2 * k) * t ** 2   1)
print(f)
F = lambdify(t, f)
t0 = 10 ** 10
T = np.arange(t0, 2 * t0, t0 / 4)
print(T)
F(T)

Output:

2.0e-10*sqrt(100000000000000000000*t**2   1)
[1.00e 10 1.25e 10 1.50e 10 1.75e 10]
AttributeError: 'float' object has no attribute 'sqrt'

The above exception was the direct cause of the following exception:

TypeError                                 Traceback (most recent call last)
~\AppData\Local\Temp/ipykernel_15740/1035914544.py in <module>
      8 T = np.arange(t0, 2 * t0, t0 / 4)
      9 print(T)
---> 10 F(T)

<lambdifygenerated-11> in _lambdifygenerated(t)
      1 def _lambdifygenerated(t):
----> 2     return 2.0e-10*sqrt(100000000000000000000*t**2   1)

TypeError: loop of ufunc does not support argument 0 of type float which has no callable sqrt method

For k = 2 code works properly:

0.02*sqrt(10000*t**2   1)
[1.00e 10 1.25e 10 1.50e 10 1.75e 10]
array([2.0e 10, 2.5e 10, 3.0e 10, 3.5e 10])

Is there any way to fix this problem without manually rewriting expression?

UPD: Looks like it is a problem of NumPy:

import numpy as np
k = 10
def F1(t):
    return np.sqrt( (10 ** (- k)) ** 2 * 10 ** (2 * k) * t ** 2   1)
def F2(t):
    return 10 ** (- k) * np.sqrt(10 ** (2 * k) * t ** 2   1)
print(F1(10 ** 5))
print(F2(10 ** 5))

First call works, second call - not!

CodePudding user response：

Converting argument of np.sqrt to numpy.double solves problem:

def Sqrt(x):
  return np.sqrt(np.double(x))
F = lambdify(t, f, {'sqrt': Sqrt})

CodePudding user response：

Because of the large multiplier, the np.sqrt argument is object dtype array:

In [3]: 100000000000000000000 * T**2
Out[3]: array([1e 40, 1.5625e 40, 2.25e 40, 3.0625e 40], dtype=object)

With object dtype arrays, numpy iterates (at list comprehension speed), applying a 'method' to each element. In effect

 1e 40.sqrt() etc

Hence the no method error.

Your fix:

In [3]: np.double(100000000000000000000 * T**2)
Out[3]: array([1.0000e 40, 1.5625e 40, 2.2500e 40, 3.0625e 40])

In [4]: np.sqrt(_)
Out[4]: array([1.00e 20, 1.25e 20, 1.50e 20, 1.75e 20])

In [6]: np.sqrt((100000000000000000000 * T**2).astype(float))
Out[6]: array([1.00e 20, 1.25e 20, 1.50e 20, 1.75e 20])