Problem converting MATLAB code to Python with NumPy-CodePudding

can anyone help me with this?

Matlab Code

test = 300
f = @(u) 2 3*u-2*u.^3 u.^6-4*u.^8;
rng(12354)
u_test = unifrnd(-1,1,[test,1]);
y_test = f(u_test);
xt0 = 1*ones(test, 1);
xt1 = u_test;
xt2 = u_test.^2;
xt3 = u_test.^3;
xt4 = u_test.^4;
xt5 = u_test.^5;
xt6 = u_test.^6;
xt7 = u_test.^7;
xt8 = u_test.^8;
xt9 = u_test.^9;
x_test = [xt0 xt1 xt2 xt3 xt4 xt5 xt6 xt7 xt8 xt9];

theta_test = (x_test'*x_test)^-1*x_test'*y_test;

Python Code

import numpy as np
test = 3
min_test = -1
max_test = 1
f = lambda u: 2 3*u-2*u**3 u**6-4*u**8
np.random.seed(12345)
u_test = np.random.uniform(min_test, max_test, [test, 1])

y_test = f(u_test)

xt0 = np.ones([test, 1])
xt1 = u_test
xt2 = u_test ** 2
xt3 = u_test ** 3
xt4 = u_test ** 4
xt5 = u_test ** 5
xt6 = u_test ** 6
xt7 = u_test ** 7
xt8 = u_test ** 8
xt9 = u_test ** 9
x_test = np.array([xt0, xt1, xt2, xt3, xt4, xt5, xt6, xt7, xt8, xt9])

theta_test = (x_test.T * x_test) ** -1 * x_test.T * y_test

The final answer of theta in MATLAB code, which is also the correct answer, is a 10 * 1 matrix. It has 10 numbers in total, but the theta answer in the Python code is a 10 * 30 matrix. We have 300 numbers in the output.

How to do this multiplication with Numpy so that the final answer is the same as the MATLAB code answer?

CodePudding user response：

As the comment on your question has said, it's better to write this code using an array rather than a list of variables.

That said, the issue is that you are using * which, in Python, denotes entrywise multiplication rather than matrix multiplication. What you should try instead is

theta_test = (x_test.T @ x_test) ** -1 * x_test.T @ y_test

CodePudding user response：

Your numpy code produces:

In [3]: x_test.shape
Out[3]: (10, 3, 1)
In [4]: y_test.shape
Out[4]: (3, 1)

Stripping off the last x_test dimension:

In [11]: x1 = x_test[:,:,0]
In [12]: (x1.T@x1).shape
Out[12]: (3, 3)
In [13]: np.linalg.inv(x1.T@x1)
Out[13]: 
array([[ 0.34307216, -0.63513713,  0.36347551],
       [-0.63513713,  8.44935183, -6.36062978],
       [ 0.36347551, -6.36062978,  5.43319377]])

Switching the transpose produces a (10,10) array, but it's singular

In [14]: np.linalg.inv([email protected])
Traceback (most recent call last):
  ...
LinAlgError: Singular matrix

The (10,3) can multiply the (3,1) to produce a (10,1)

In [18]: (x1@y_test).shape
Out[18]: (10, 1)

I'm having troubles running your MATLAB code in Octave, so can't generate its equivalent to see what you are trying to reproduce.