Python regression with matrices

Question

I have about 100 7x7 matrices of dependent variables (so 49 dependent variables). My independent variable is time. I am doing a physics project in which I am supposed to get a matrix function (every element of the matrix is a function of time) by solving an ODE. I used numpy's ODE solver which goves me numerical answers of my matrix function evaluated at different times. Now with these matrices and times I want to find a time-dependent expression for each element matrix to get the time-dependent matrix. I have heard that what I should do is find a hat matrix and I guess that the predicted or fitted values would be my 7x7 matrices and the response values would be the array of times. So how can I find this hat matrix in Python?

I was originally thinking of doing polynomial regression in scikit-learn using their LinearRegression model. Will that work? Is there a possible way in StatsModel, or better, in scipy or numpy?

Basically I want to go from:

enter image description here

to:

enter image description here

Clearly, I will use more test cases, but this is the overall idea. So I will have univariate X (X will be an array of the different times) and multivariate Y (Y will be the matrices evaluated at different times)

In the above example, t=1 would be included in the X array and the Y array would have the first matrix

Moritz · Accepted Answer · 2015-06-21 08:14:04Z

6

Given that the task you would like to do is the classical linear regression:

Using the matrix notation in numpy (you would have to manually account for an intercept by adding a row of ones to X) :

import numpy as np
a = np.linalg.inv(np.dot(X.T,X))
c = np.dot(X.T,Y)
b = np.dot(a,c)

Using numpy

np.polyfit(X,Y,1)

Using scipy:

scipy.linalg.solve(X,Y)

scipy.stats.linregr(X,Y)

and many more

edited Jun 21, 2015 at 8:14

answered Jun 21, 2015 at 7:57

Moritz

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11 Comments

TanMath Over a year ago

now this would give me a single time dependent matrix? or like a matrix function?

TanMath Over a year ago

and why do you define variables a, b, and c?

Moritz Over a year ago

a,b,c: just for the readability. This would give you the coefficients of the linear fit.

TanMath Over a year ago

I want a 'matrix function' does this give one? Or will it give the elements of this 'matrix' function?

Moritz Over a year ago

So you would like to do a linear regression of the for Y = b*X ? And try to find the coefficients, stored in b ?

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