How do I compute derivative using Numpy

Question

How do I calculate the derivative of a function  for example      y   x2 1    using numpy   Let s say  I want the value of derivative at x   5

User · Answer

I ll throw another method on the pile     scipy interpolate s many interpolating splines are capable of providing derivatives   So  using a linear spline  k 1   the derivative of the spline  using the derivative   method  should be equivalent to a forward difference   I m not entirely sure  but I believe using a cubic spline derivative would be similar to a centered difference derivative since it uses values from before and after to construct the cubic spline   from scipy interpolate import InterpolatedUnivariateSpline    Get a function that evaluates the linear spline at any x f   InterpolatedUnivariateSpline x  y  k 1     Get a function that evaluates the derivative of the linear spline at any x dfdx   f derivative      Evaluate the derivative dydx at each x location    dydx   dfdx x

User · Answer

Depending on the level of precision you require you can work it out yourself  using the simple proof of differentiation    gt  gt  gt     5   0 1     2   1  -   5     2   1     0 1 10 09999999999998  gt  gt  gt     5   0 01     2   1  -   5     2   1     0 01 10 009999999999764  gt  gt  gt     5   0 0000000001     2   1  -   5     2   1     0 0000000001 10 00000082740371   we can t actually take the limit of the gradient  but its kinda fun  You gotta watch out though because    gt  gt  gt     5 0 0000000000000001   2 1 -  5   2 1   0 0000000000000001 0 0

User · Answer

To calculate gradients  the machine learning community uses Autograd       Efficiently computes derivatives of numpy code     To install   pip install autograd   Here is an example   import autograd numpy as np from autograd import grad  def fct x       y   x  2 1     return y  grad fct   grad fct  print grad fct 1 0     It can also compute gradients of complex functions  e g  multivariate functions

User · Answer

NumPy does not provide general functionality to compute derivatives   It can handles the simple special case of polynomials however    gt  gt  gt  p   numpy poly1d  1  0  1    gt  gt  gt  print p    2 1 x   1  gt  gt  gt  q   p deriv    gt  gt  gt  print q 2 x  gt  gt  gt  q 5  10   If you want to compute the derivative numerically  you can get away with using central difference quotients for the vast majority of applications   For the derivative in a single point  the formula would be something like  x   5 0 eps   numpy sqrt numpy finfo float  eps     1 0   x  print  p x   eps  - p x - eps      2 0   eps   x    if you have an array x of abscissae with a corresponding array y of function values  you can comput approximations of derivatives with  numpy diff y    numpy diff x

User · Answer

Assuming you want to use numpy  you can numerically compute the derivative of a function at any point using the  Rigorous definition   def d fun x       h   1e-5  in theory h is an infinitesimal     return  fun x h -fun x   h   You can also use the Symmetric derivative for better results   def d fun x       h   1e-5     return  fun x h -fun x-h    2 h    Using your example  the full code should look something like   def fun x       return x  2   1  def d fun x       h   1e-5     return  fun x h -fun x-h    2 h    Now  you can numerically find the derivative at x 5   In  1   d fun 5  Out 1   9 999999999621423

User · Answer

You can use scipy  which is pretty straight forward  scipy misc derivative func  x0  dx 1 0  n 1  args     order 3   Find the nth derivative of a function at a point   In your case  from scipy misc import derivative  def f x       return x  2   1  derivative f  5  dx 1e-6    10 00000000139778

User · Answer

The most straight-forward way I can think of is using numpy s gradient function   x   numpy linspace 0 10 1000  dx   x 1 -x 0  y   x  2   1 dydx   numpy gradient y  dx    This way  dydx will be computed using central differences and will have the same length as y  unlike numpy diff  which uses forward differences and will return  n-1  size vector

User · Answer

You have four options   Finite Differences Automatic Derivatives  Symbolic Differentiation Compute derivatives by hand    Finite differences require no external tools but are prone to numerical error and  if you re in a multivariate situation  can take a while    Symbolic differentiation is ideal if your problem is simple enough  Symbolic methods are getting quite robust these days  SymPy is an excellent project for this that integrates well with NumPy  Look at the autowrap or lambdify functions or check out Jensen s blogpost about a similar question   Automatic derivatives are very cool  aren t prone to numeric errors  but do require some additional libraries  google for this  there are a few good options   This is the most robust but also the most sophisticated difficult to set up choice   If you re fine restricting yourself to numpy syntax then Theano might be a good choice   Here is an example using SymPy  In  1   from sympy import   In  2   import numpy as np In  3   x   Symbol  x   In  4   y   x  2   1 In  5   yprime   y diff x  In  6   yprime Out 6   2  x  In  7   f   lambdify x  yprime   numpy   In  8   f np ones 5   Out 8     2   2   2   2   2

[python] How do I compute derivative using Numpy?

Examples related to python

Examples related to math

Examples related to numpy