Documentation
Functions
cookies_statistics.backsub
- cookies_statistics.backsub(A, b)
Solves Ax=b using back substitution.
- Parameters:
A (np.array) – An upper triangular square matrix.
B (np.array) – A vector.
- Return type:
np.array
cookies_statistics.upper_triangularize
- cookies_statistics.upper_triangularize(X)
This function repeatedly applies Householder transformations to A nxm matrix X (n >= m) until it becomes an upper triangular matrix, and then returns it.
- Parameters:
X (np.array) – A nxm matrix (n >= m).
- Return type:
np.array
cookies_statistics.lsq_householder
- cookies_statistics.lsq_householder(Z, y)
Solve the least squares problem using Householder transformations. This function returns a tuple of the coefficient vector and the sum of squared errors.
- Parameters:
Z (np.array) – A Nxm data matrix (N >= m).
y (np.array) – A vector of length N.
- Return type:
np.array, float
Example
import numpy as np
import cookies_statistics as cs
Z = np.array([[3., -2.], [0., 3.], [4., 4.]])
y = np.array([3., 5., 4.])
print(cs.lsq_householder(Z, y))
# --> (array([0.76, 0.6 ]), 4.0)