solve_observation

sofia_redux.toolkit.splines.spline_utils.solve_observation(amat, beta, n_coefficients, bandwidth, eps)

Solve a row-echelon reduced linear system of equations Ax=B.

Returns the results of back_substitute() if A is full rank, or the results of solve_rank_deficiency() otherwise.

Parameters:

amatnumpy.ndarray (float)

The array A in row-echelon form. Should be of shape (>=n_coefficients, >=bandwidth).

betanumpy.ndarray (float)

The array B accounting for row-echelon form. Should be of shape (>=n_coefficients,).

n_coefficientsint

The number of coefficients to solve for.

bandwidthint

The bandwidth of the observation matrix A (amat).

epsfloat

The precision to determine singular values of A. If any row of amat[:,0] < (eps * max(amat[:,0])) it will be considered singular.

Returns:

coefficients, rank, ssrnumpy.ndarray (float), int, float

The derived coefficients, the rank of A, and the sum of the squared residuals.