Source code for matrix_toolkit.anymatrix.groups.hadamard

"""
Hadamard matrix group - Various constructions of Hadamard matrices
"""

import numpy as np
from scipy.linalg import hadamard as scipy_hadamard


def register_hadamard_matrices(registry):
    """Register Hadamard matrix generators"""
    
    registry.register_matrix(
        group='hadamard',
        name='hadamard',
        generator=hadamard,
        properties=['orthogonal', 'binary'],
        description='Hadamard matrix of order n (n must be power of 2)'
    )
    
    registry.register_matrix(
        group='hadamard',
        name='walsh',
        generator=walsh,
        properties=['orthogonal', 'binary'],
        description='Walsh-Hadamard matrix (sequency ordered)'
    )




def hadamard(n: int) -> np.ndarray:
    """
    Hadamard matrix of order n
    
    A Hadamard matrix is a square matrix whose entries are +1 or -1
    and whose rows are mutually orthogonal.
    
    Args:
        n: Order (must be 1, 2, or a multiple of 4)
    
    Returns:
        n×n Hadamard matrix
    """
    if n == 1:
        return np.array([[1]])
    
    # Use scipy's implementation (Sylvester construction)
    H = scipy_hadamard(n)
    return H





def walsh(n: int) -> np.ndarray:
    """
    Walsh-Hadamard matrix (sequency ordered)
    
    Args:
        n: Order (must be power of 2)
    
    Returns:
        n×n Walsh matrix
    """
    # Start with standard Hadamard
    H = hadamard(n)
    
    # Reorder to sequency order (by number of sign changes)
    def sequency(row):
        """Count number of sign changes"""
        return np.sum(row[:-1] != row[1:])
    
    indices = sorted(range(n), key=lambda i: sequency(H[i]))
    W = H[indices, :]
    
    return W