How to find Gradient of a Function using Python?
The gradient of a function simply means the rate of change of a function. 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. 2.]
Approach:
- For Single variable function: For single variable function we can define directly using “lambda” as stated below:-
g=lambda x:(x**4)+x+1
- For Multi-Variable Function: We will define a function using “def” and pass an array “x” and it will return multivariate function as described below:-
def rosen(x):
return (1-x[0])**2 +(x[1]-x[0]**2)**2
where ‘rosen’ is name of function and ‘x’ is passed as array. x[0]
and x[1]
are array elements in the same order as defined in array.i.e Function defined above is (1-x^2)+(y-x^2)^2
.
Similarly, We can define function of more than 2-variables also in same manner as stated above.
Method used: Gradient()
Syntax:
nd.Gradient(func_name)
Example:
import numdifftools as nd
g = lambda x:(x * * 4 ) + x + 1
grad1 = nd.Gradient(g)([ 1 ])
print ( "Gradient of x ^ 4 + x+1 at x = 1 is " , grad1)
def rosen(x):
return ( 1 - x[ 0 ]) * * 2 + (x[ 1 ] - x[ 0 ] * * 2 ) * * 2
grad2 = nd.Gradient(rosen)([ 1 , 2 ])
print ( "Gradient of (1-x ^ 2)+(y-x ^ 2)^2 at (1, 2) is " , grad2)
|
Output:
Gradient of x^4+x+1 at x=1 is 4.999999999999998
Gradient of (1-x^2)+(y-x^2)^2 at (1, 2) is [-4. 2.]
Last Updated :
28 Jul, 2020
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