Plotting a function of numpy vector

Question

I want to plot a function of a numpy matrix

f = lambda X: X.T @ X

but I'm not sure how to proceed. I'm familiar with the method for multivariable functions, and the equivalent function with multivariable functions (along with plotting) would be

g = lambda x, y: x**2 + y**2
X, Y = np.meshgrid(
    np.linspace(start = -10, stop = 10, num = 101),
    np.linspace(start = -10, stop = 10, num = 101))
plt.plot_surface(X,Y,g(X,Y))

so f(np.matrix((x,y))) == g(x,y), but I don't know how to extend this to my vector function. So how can this be achieved?

What is X.T @ X supposed to be? It's not valid python syntax, is it? — ImportanceOfBeingErnest
– ImportanceOfBeingErnest, Commented Feb 13, 2018 at 21:35
@ImportanceOfBeingErnest that's matrix multiplication, new in Python 3. See this documentation — relay
– relay, Commented Feb 13, 2018 at 22:00

Aguy · Accepted Answer · 2018-02-14 18:32:18Z

1

The issue here is arranging dimensions. Your f seem to expect X and Y to be cast as a collection of vectors. But X and Y are two 101x101 matrices. So some rearranging and massaging is required. The good news is that using the map command below can be done to any function. The bad news - efficiency is elegance are probably not optimal.

This is what I would try:

Z = map(f, np.array([X.ravel(), Y.ravel()]).T)
Z = np.array(list(Z)).reshape(X.shape)

And then

ax.plot_surface(X,Y,Z)

answered Feb 14, 2018 at 18:32

Aguy

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Comments

ImportanceOfBeingErnest · Accepted Answer · 2018-02-14 12:49:37Z

1

Assuming that what is meant by X.T @ X is numpy.dot(X.T,X), you may directly plot the result just as with any other function.

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

f = lambda X: np.dot(X.T,X)

fig = plt.figure()
ax = plt.subplot(projection="3d")

X, Y = np.meshgrid(
    np.linspace(start = -10, stop = 10, num = 101),
    np.linspace(start = -10, stop = 10, num = 101))
ax.plot_surface(X,Y,f(X))

plt.show()

However, in order to get the desired output from the question, the function depends on both x and y, so what is wanted is probably

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

f = lambda xi,yi: np.dot(np.dot([xi,yi],np.identity(2)),[[xi],[yi]])

fig = plt.figure()
ax = plt.subplot(projection="3d")

X, Y = np.meshgrid(
    np.linspace(start = -10, stop = 10, num = 101),
    np.linspace(start = -10, stop = 10, num = 101))

Z = np.vectorize(f)(X,Y)
ax.plot_surface(X,Y,Z)

plt.show()

edited Feb 14, 2018 at 12:49

answered Feb 13, 2018 at 22:06

ImportanceOfBeingErnest

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10 Comments

Frank Vel Over a year ago

@ was added in 3.5, but is equivalent to np.dot(,). While this approach works with this particular function, I was more interested in a slightly more general approach, as this break down for f = lambda X: X.T @ A @ X, where A is a square matrix of size n≠101.

ImportanceOfBeingErnest Over a year ago

Not sure what you mean. For matrix multiplication the number of columns of the first matrix needs to match the number of rows of the second. This is rather a mathematical necessity than a question of implementation in some programming language.

Frank Vel Over a year ago

Indeed, so I believe the input to f should be a list of grid points, not a matrix of the gridlines.

ImportanceOfBeingErnest Over a year ago

What exactly is the desired outcome?

Frank Vel Over a year ago

The exact same result as your plot above when using f = lambda X: X.T @ np.identity(2) @ X, which is mathematically identical to your function.

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