`scipy.linalg._decomp_ldl:_ldl_sanitize_ipiv`

source: /scipy/linalg/_decomp_ldl.py :161

Signature

def _ldl_sanitize_ipiv ( a , lower = True )

Summary

This helper function takes the rather strangely encoded permutation array returned by the LAPACK routines ?(HE/SY)TRF and converts it into regularized permutation and diagonal pivot size format.

Extended Summary

Since FORTRAN uses 1-indexing and LAPACK uses different start points for upper and lower formats there are certain offsets in the indices used below.

Let's assume a result where the matrix is 6x6 and there are two 2x2 and two 1x1 blocks reported by the routine. To ease the coding efforts, we still populate a 6-sized array and fill zeros as the following

pivots = [2, 0, 2, 0, 1, 1]

This denotes a diagonal matrix of the form

[x x        ]
[x x        ]
[    x x    ]
[    x x    ]
[        x  ]
[          x]

In other words, we write 2 when the 2x2 block is first encountered and automatically write 0 to the next entry and skip the next spin of the loop. Thus, a separate counter or array appends to keep track of block sizes are avoided. If needed, zeros can be filtered out later without losing the block structure.

Parameters

a : ndarray: The permutation array ipiv returned by LAPACK
lower : bool, optional: The switch to select whether upper or lower triangle is chosen in the LAPACK call.

Returns

swap_ : ndarray: The array that defines the row/column swap operations. For example, if row two is swapped with row four, the result is [0, 3, 2, 3].
pivots : ndarray: The array that defines the block diagonal structure as given above.

Aliases

scipy.linalg._decomp_ldl._ldl_sanitize_ipiv