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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]])