ndmath

ndmath is a Python library for N-dimensional complex step and finite step differentiation, and Newton's method.

Installation

Use the package manager pip to install ndmath.

pip install ndmath

Examples

Calculating the Jacobian at a point:

import ndmath

ndmath.complexGrad(lambda x : x[0]**2+x[1], [1,2]) # returns array([2., 1.])
ndmath.finiteGrad(lambda x : x[0]**2+x[1], [1,2], 10**-7) # returns array([2.0000001, 1.])

Using the root-finding Newton's method:

def func(x):
    return [(x[1]-3)**2+x[0]-5, 2*x[1]+x[0]**3]

def fprime(x):
    return ndmath.complexGrad(func, x)

x0 = [0,0] #initial estimate

ndmath.nDimNewton(func, x0, fprime) # returns array([-1.02890183,  0.54461778])

Dependencies

• NumPy

Contributing

Pull requests are welcome. Feel free to open an issue first to discuss what you would like to change.

License

MIT

References

• Martins, J. R. R. A., Sturdza, P., and Alonso, J. J., 2003, "The Complex-Step Derivative Approximation," ACM Trans. Math. Software, 29(3), pp. 245–262.