Varimax Step

Problem

Perform one varimax rotation step on a 2-factor loading matrix. With x_i = l1^2 - l2^2 and y_i = 2*l1*l2, the rotation angle is phi = 0.25*atan2(2*sum(x*y), sum(x^2 - y^2)); return the rotated loadings. Rows must have exactly two loadings, otherwise return [].

Hint

This single step sharpens the loading pattern toward simple structure.

Test cases

case 1

in: [[[0.8,0.6],[0.8,0.6]]]

expected: [[1,0],[1,0]]

case 2

in: [[[0.9,0.1],[0.1,0.9]]]

expected: [[0.9,0.1],[0.1,0.9]]

case 3

in: [[[0.7,0.7],[0.7,0.7]]]

expected: [[0.9899494936611665,1.1102230246251565e-16],[0.9899494936611665,1.1102230246251565e-16]]

case 4

in: [[[0.6,0.8],[0.6,0.8]]]

expected: [[0,1],[0,1]]

case 5

in: [[]]

expected: []

Starter codePython

import math
def varimax_step(loadings):
    # Your code here
    pass

5 test cases · run your code against them in the editor