Plotting a function with 2D vector entry in Python

Question

I have the following function to plot:

f(x) = 3 + (x - (2  6)T )T · (x - (2  6)T)

where (2 6) is a vector, T represents transpose and x is a vector of size 2. My question is how can I implement a np.linspace so that I can get a continuous 2D function?

I have written my function in the following form:

def f(x):
    a = np.array([[2],[6]])
    t = lambda x: 3 + np.dot((x - (a)).T, (x - a))
    return t(x)

x = np.array([[4],[1]]) # Some random (2,1) sized vector
y = f(x) # Returns an array sized (1,1)

For example, to plot a variation of the function f(x) = x^2 (x-squared) I can write the following code:

def f(x):
   return x**2

x = np.linspace(-5, 5, 20)
y = f(x)
plt.plot(x, y)

I want to know whether it is possible to plot a continuous function for a case where x input is two-dimensional vector. If it is not feasible, how the first function should be plotted? A 3-D plot is not possible since my function only has x as its parameter.

Edit:

Can you provide results for your function for an example vector x? — Michael Szczesny
– Michael Szczesny, Commented Dec 19, 2020 at 16:56
I have slightly updated my question. Hopefully, it is a bit clearer now — Beginn_noob
– Beginn_noob, Commented Dec 19, 2020 at 17:09

Michael Szczesny · Accepted Answer · 2020-12-19 19:21:46Z

1

@deeenizka is right that we have to plot 3 dimensions. One way to do it is to use a contour line plot.

First we have to vectorize your function to compute the values of the function with an array of 2D vectors

import numpy as np
import matplotlib.pyplot as plt

def f(x):
    a = np.array([[2],[6]])
    x = x - a
    return 3 + np.einsum('ij,ij->j',x ,x)

To get the input coordinate vectors we can use meshgrid and ravel the 2D arrays to pass them to the function f

x = np.linspace(-50, 50, 100)
y = np.linspace(-50, 50, 100)

X,Y = np.meshgrid(x, y)
data = np.vstack([X.ravel(), Y.ravel()])

We can plot the data with contourf after we reshaped the returned array of function values.

plt.figure(figsize=(8,6))
plt.contourf(X, Y, f(data).reshape(X.shape), levels=20)
plt.colorbar();

Out:

edited Dec 19, 2020 at 19:21

answered Dec 19, 2020 at 19:14

Michael Szczesny

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1 Comment

Beginn_noob Over a year ago

Thanks very much! That's what I needed

deethereal · Accepted Answer · 2020-12-19 17:56:37Z

1

Dimension of your vectors is 2. You also have value of function for this vector. In total you have 3 parametrs, so I think it can't be plotted as 2D plot and you need to use 3D plot.(Your x vector is just a tuple, so you can use x[0] and x[1] as axis)

edited Dec 19, 2020 at 17:56

answered Dec 19, 2020 at 17:38

deethereal

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4 Comments

Beginn_noob Over a year ago

I am not sure how to implement that. My function only has only a x input parameter and it should have the same size as a vector (2 6). If you can think of a way to plot a function as a 3D, can you please share that?

deethereal Over a year ago

your function gets vetctor of size 2, so there is two variables: first element of your vector and the second one. You can rename it to x and y if you want

deethereal Over a year ago

You can read about 3D surfaces here

Beginn_noob Over a year ago

Got it, Thanks for your help!

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