scipy

Use of `scipy` in `physipy`¶

scipy is used in physipy for 2 reasons :

To define the values of the physical constants available in physipy.constants
To provide wrapped versions of usefull scipy functions and make them unit-aware, available in physipy.calculus

It could be discussed as constants' values could be hardcoded, and wrapped functions could be defined by the user on the go. This way scipy would not be a dependency of physipy

Constants¶

See the constant section of the quickstart.

Wrapped functions¶

Some functions are regularly used in the physics/engineering world, hence we provide some functions that wrapped the units around the underlying scipy functions. Those functions are :

quad
dblquad
tplquad
solve_ivp
root
brentq

Integrals `quad`¶

Those functions can be used to compute integral of functions from a to b:

from physipy import s
from physipy.calculus import quad

def toto(t):
    return 2*s + t

solution, abserr = quad(toto, 0*s, 5*s)
print(solution)

22.5 s**2

You can compute integrals of 2D and 3D functions using dblquad and tplquad respectively.

Initial Value Problem of ODE system¶

Solve an initial value problem for a system of ODEs. This function numerically integrates a system of ordinary differential equations given an initial value: dy / dt = f(t, y) y(t0) = y0

from physipy.calculus import solve_ivp
from physipy import s, units

# voltage unit
V = units['V']

def exponential_decay(t, y): return -0.5 * y

sol = solve_ivp(exponential_decay, [0, 10]*s, [2, 4, 8]*V)
print(sol.t)    # time samples
print(sol.y)    # voltage response

[ 0.          0.11487653  1.26364188  3.06061781  4.81611105  6.57445806
  8.33328988 10.        ] s
[<Quantity : [2.         1.88836035 1.06327177 0.43319312 0.18017253 0.07483045
 0.03107158 0.01350781] kg*m**2/(A*s**3)>, <Quantity : [4.         3.7767207  2.12654355 0.86638624 0.36034507 0.14966091
 0.06214316 0.02701561] kg*m**2/(A*s**3)>, <Quantity : [8.         7.5534414  4.25308709 1.73277247 0.72069014 0.29932181
 0.12428631 0.05403123] kg*m**2/(A*s**3)>]

Root solver `root`¶

A wrapper of scipy.optimize.root:

from physipy import s
from physipy.calculus import root

def toto(t):
    return -10*s + t

# Find the root for toto(t) = 0*s
print(root(toto, 0*s))

10.0 s

The wrapped function signature is the same as the original's one, so additionnal args and kwargs still works :

def tata(t, p):
    return -10*s*p + t

# Find the root for tata(t, 0.5) = 0*s
print(root(tata, 0*s, args=(0.5,)))

5.0 s

Quadratic Brent method `brentq`¶

Find a root of a function in a bracketing interval using Brent's method, a wrapper of scipy.optimize.brentq:

from physipy.calculus import brentq

# find the solutition for toto(t) = 0*s for t in [-10, 10]*s
print(brentq(toto, -10*s, 10*s))

print(brentq(tata, -10*s, 10*s, args=(0.5,)))

10.0 s
5.0 s

Note¶

If you want support for other scipy functions, you can either define it yourself (use the functions above as examples), or open an issue on the github page.

scipy

Use of scipy in physipy¶