SciPy fixes and extensions

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Deep Learningscipyx
Overview

scipyx

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SciPy is large library used everywhere in scientific computing. That's why breaking backwards-compatibility comes as a significant cost and is almost always avoided, even if the API of some methods is arguably lacking. This package provides drop-in wrappers "fixing" those.

npx does the same for NumPy.

If you have a fix for a SciPy method that can't go upstream for some reason, feel free to PR here.

Krylov methods

import numpy as np
import scipy.sparse
import scipyx as spx

# create tridiagonal (-1, 2, -1) matrix
n = 100
data = -np.ones((3, n))
data[1] = 2.0
A = scipy.sparse.spdiags(data, [-1, 0, 1], n, n)
A = A.tocsr()
b = np.ones(n)


sol, info = spx.cg(A, b, tol=1.0e-10)
sol, info = spx.minres(A, b, tol=1.0e-10)
sol, info = spx.gmres(A, b, tol=1.0e-10)
sol, info = spx.bicg(A, b, tol=1.0e-10)
sol, info = spx.bicgstab(A, b, tol=1.0e-10)
sol, info = spx.cgs(A, b, tol=1.0e-10)
sol, info = spx.qmr(A, b, tol=1.0e-10)

sol is the solution of the linear system A @ x = b (or None if no convergence), and info contains some useful data, e.g., info.resnorms. The solution sol and all callback x have the shape of x0/b. The methods are wrappers around SciPy's iterative solvers.

Relevant issues:

Optimization

import scipyx as spx


def f(x):
    return (x ** 2 - 2) ** 2


x0 = 1.5
out = spx.minimize(f, x0)
print(out.x)

x0 = -3.2
x, _ = spx.leastsq(f, x0)
print(x)

In scipyx, all intermediate values x and the result from a minimization out.x will have the same shape as x0. (In SciPy, they always have shape (n,), no matter the input vector.)

Relevant issues:

Root-finding

import scipyx as spx


def f(x):
    return x ** 2 - 2


a, b = spx.bisect(f, 0.0, 5.0, tol=1.0e-12)
a, b = spx.regula_falsi(f, 0.0, 5.0, tol=1.0e-12)

scipyx provides some basic nonlinear root-findings algorithms: bisection and regula falsi. They're not as fast-converging as other methods, but are very robust and work with almost any function.

License

This software is published under the BSD-3-Clause license.

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Comments
  • Add ITP method?

    Add ITP method?

    I think the ITP method for root-finding would be a nice addition since it's unlikely to make it into scipy.

    Reference

    https://en.wikipedia.org/wiki/ITP_Method

    opened by zoj613 3
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Nico Schlömer
Mathematics, numerical analysis, scientific computing, Python. Always interested in new problems. Contact me!
Nico Schlömer
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