sscp¶

sofia_redux.toolkit.resampling.sscp(matrix, weight=None, normalize=False)[source]¶

Calculate the sum-of-squares-and-cross-products of a matrix.

For the matrix \(A\), calculates \(A^TA\). If weights (\(W\)) are provided.

\[sscp = WA^TAW^T\]

Note that the weight should only contain the diagonal elements of \(W\), and as such should be a 1-dimensional array.

If normalize=True:

\[sscp = \frac{WA^TAW^T}{trace(W^TW)}\]

where \(W = I\), the identity matrix if weight is not supplied.

Parameters:

matrixnumpy.ndarray (M, N): Input matrix.
weightnumpy.ndarray (N,), optional: Weights to be applied during sscp.
normalizebool, optional: If True, scales result as described above. Default is False.

Returns:

numpy.ndarray of numpy.float64 (M, M): Square output array containing the sum-of-squares-and-cross-products matrix.