scipy.linalg.helmert

scipy.linalg.helmert(n, full=False)

Create a Helmert matrix of order n.

This has applications in statistics, compositional or simplicial analysis, and in Aitchison geometry.

Parameters:

n : int

The size of the array to create.

full : bool, optional

If True the (n, n) ndarray will be returned. Otherwise the submatrix that does not include the first row will be returned. Default: False.

Returns:

M : ndarray

The Helmert matrix. The shape is (n, n) or (n-1, n) depending on the full argument.

Examples

>>> from scipy.linalg import helmert
>>> helmert(5, full=True)
array([[ 0.4472136 ,  0.4472136 ,  0.4472136 ,  0.4472136 ,  0.4472136 ],
       [ 0.70710678, -0.70710678,  0.        ,  0.        ,  0.        ],
       [ 0.40824829,  0.40824829, -0.81649658,  0.        ,  0.        ],
       [ 0.28867513,  0.28867513,  0.28867513, -0.8660254 ,  0.        ],
       [ 0.2236068 ,  0.2236068 ,  0.2236068 ,  0.2236068 , -0.89442719]])