solve_rank_deficiency¶
- sofia_redux.toolkit.splines.spline_utils.solve_rank_deficiency(amat, beta, n_coefficients, bandwidth, tolerance)[source]¶
Solve a rank-deficient row-echelon reduced form matrix.
- Parameters:
- amatnumpy.ndarray (float)
The ‘A’ in the system Ax = B of shape (>=n_coefficients, >=bandwidth).
- betanumpy.ndarray (float)
The ‘B’ in the system Ax = B of shape (>=n_coefficients,).
- n_coefficientsint
The number of coefficients to solve for.
- bandwidthint
The bandwidth of matrix A (amat).
- tolerancefloat
The value over which the zeroth element of
amatwill be considered rank deficient. Deficient rows will be rotated into a new reduced rank matrix and solved accordingly.
- Returns:
- coefficients, ssr, ranknumpy.ndarray (float), float, int
The coefficients of shape (n_coefficients.), the sum of the squared residuals (ssr), and the rank.