Menu
I really can not understand what numpy.gradient function does and how to use it for computation of multivariable function gradient.
For example, I have such a function:
def func(q, chi, delta): return q * chi * delta I need to compute it's 3-dimensional gradient (in other words, I want to compute partial derivatives with respect to all variables (q, chi, delta)).
How can I calculate this gradient using NumPy?
539
The gradient is computed using second order accurate central differences in the interior points and either first or second order accurate one-sides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.
We will use numdifftools to find Gradient of a function. Examples: Input : x^4+x+1 Output :Gradient of x^4+x+1 at x=1 is 4.99 Input :(1-x)^2+(y-x^2)^2 Output :Gradient of (1-x^2)+(y-x^2)^2 at (1, 2) is [-4.
The output of numpy. gradient() function is a list of ndarrays (or a single ndarray if there is only one dimension) corresponding to the derivatives of input f with respect to each dimension. Each derivative has the same shape as input f .
gradient is the function or any Python callable object that takes a vector and returns the gradient of the function you're trying to minimize. start is the point where the algorithm starts its search, given as a sequence (tuple, list, NumPy array, and so on) or scalar (in the case of a one-dimensional problem).
The problem is, that numpy can't give you the derivatives directly and you have two options:
With NUMPY
What you essentially have to do, is to define a grid in three dimension and to evaluate the function on this grid. Afterwards you feed this table of function values to numpy.gradient to get an array with the numerical derivative for every dimension (variable).
Example from here:
from numpy import * x,y,z = mgrid[-100:101:25., -100:101:25., -100:101:25.] V = 2*x**2 + 3*y**2 - 4*z # just a random function for the potential Ex,Ey,Ez = gradient(V) Without NUMPY
You could also calculate the derivative yourself by using the centered difference quotient. 
This is essentially, what numpy.gradient is doing for every point of your predefined grid.
82
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
