solve_fits

sofia_redux.toolkit.resampling.solve_fits(sample_indices, sample_coordinates, sample_phi_terms, sample_data, sample_error, sample_mask, fit_coordinates, fit_phi_terms, order, alpha, adaptive_alpha, is_covar=False, mean_fit=False, cval=nan, fit_threshold=0.0, error_weighting=True, estimate_covariance=False, order_algorithm_idx=1, order_term_indices=None, derivative_term_map=None, derivative_term_indices=None, edge_algorithm_idx=1, edge_threshold=None, minimum_points=None, get_error=True, get_counts=True, get_weights=True, get_distance_weights=True, get_rchi2=True, get_cross_derivatives=True, get_offset_variance=True)

Solve all fits within one intersection block.

This function is a wrapper for solve_fit() over all data sets and fit points. The main computations here involve:

1. Creating and populating the output arrays.

2. Selecting the correct samples within the region of each fitting window.

3. Calculating the full weighting factors for the fits.

For further details on the actual fitting, please see solve_fit().

Parameters:

sample_indicesnumba.typed.List

A list of 1-dimensional numpy.ndarray (dtype=int) of length n_fits. Each list element sample_indices[i], contains the indices of samples within the “window” region of fit_indices[i].

sample_coordinatesnumpy.ndarray (n_dimensions, n_samples)

The independent coordinates for each sample in n_dimensions

sample_phi_termsnumpy.ndarray (n_terms, n_samples)

The polynomial terms of sample_coordinates. Please see polynomial_terms() for further details.

sample_datanumpy.ndarray (n_sets, n_samples)

The dependent values of the samples for n_sets, each containing n_samples.

sample_errornumpy.ndarray (n_sets, n_samples)

The associated 1-sigma error values for each sample in each set. The user may also supply an array of shape (n_sets, 1) in which case all samples in a set will share the same associated error value. If the shape is set to (n_sets, 0), this indicates that no error values are available for the samples.

sample_masknumpy.ndarray (n_sets, n_samples)

A mask where False indicates that the associated sample should be excluded from all fits.

fit_coordinatesnumpy.ndarray (n_dimensions, n_fits)

The independent variables at each fit coordinate in d_dimensions.

fit_phi_termsnumpy.ndarray (n_terms, n_fits)

The polynomial terms of fit_coordinates. Please see polynomial_terms() for further details.

ordernumpy.ndarray

The desired order of the fit as a (1,) or (n_dimensions,) array. If only a single value is supplied, it will be applied over all dimensions.

alphanumpy.ndarray (n_dimensions,)

A distance weighting scaling factor per dimension. The weighting kernel is applied equally to all sets and samples. For further details, please see calculate_distance_weights(). Will be overridden by adaptive_alpha if adaptive_alpha.size > 0.

adaptive_alphanumpy.ndarray

Shape = (n_samples, n_sets, [1 or n_dimensions], n_dimensions). Defines a weighting kernel for each sample in each set. The function calculate_adaptive_distance_weights_scaled() will be used for kernels of shape (1, n_dimensions), and calculate_adaptive_distance_weights_shaped() will be used for kernels of shape (n_dimensions, n_dimensions). adaptive_alpha is a required parameter due to Numba constraints, and will override the alpha parameter unless it has a size of 0. Therefore, to disable, please set the size of any dimension to zero.

is_covarbool, optional

If True, indicates that sample_data contains covariance values that should be propagated through algorithm. If this is the case, polynomial fitting is disabled, and a weighted variance is calculated instead.

mean_fitbool, optional

If True, a weighted mean is performed instead of calculating a polynomial fit.

cvalfloat, optional

In a case that a fit is unable to be calculated at certain location, cval determines the fill value for the output fit array at those locations.

fit_thresholdfloat, optional

If fit_threshold is non-zero, perform a check on the goodness of the fit. When the reduced-chi statistic is greater than abs(fit_threshold), the fit is determined to be a failure, and a replacement value is used. If fit_threshold < 0, failed fit values will be set to cval. If fit_threshold > 0, failed fit values will be replaced by the weighted mean.

error_weightingbool, optional

If True, weight the samples in the fit by the inverse variance (1 / sample_error^2) in addition to distance weighting.

estimate_covariancebool, optional

If True, calculate the covariance of the fit coefficients using estimated_covariance_matrix_inverse(). Otherwise, use covariance_matrix_inverse().

order_algorithm_idxint, optional

An integer specifying which polynomial order validation algorithm to use. The default (1), will always be the more robust of all available options. For further information, please see check_edges().

order_term_indicesnumpy.ndarray (> max(order) + 1,), optional

A 1-dimensional lookup array for use in determining the correct phi terms to use for a given polynomial order. The order validation algorithm ensures a fit of the requested order is possible. If not, and the orders are equal in all dimensions, it may also optionally return a suggested order. In this case, order_term_indices is used to select the correct sample_phi_terms and fit_phi_terms for a given order (k), where terms are extracted via phi[order_term_indices[k]:order_term_indices[k + 2]].

derivative_term_mapnumpy.ndarray, optional

A mapping array for the determination of derivatives from the coefficients of the fit, and available terms in “phi”. The shape of the array is (n_dimensions, 3, n_derivative_terms). This is only required if the gradient is required as an output. For a full description of the derivative map, please see polynomial_derivative_map().

derivative_term_indicesnumpy.ndarray (max(order) + 1,), optional

If the fit order is allowed to vary, gives the indices in derivative_term_map for a given symmetrical order. The correct derivative_term_map mapping for order k is given as derivative_term_map[:, :, indices[k]:indices[k + 2]].

edge_algorithm_idxint, optional

Integer specifying the algorithm used to determine whether a fit should be attempted with respect to the sample distribution. Please see check_edges() for further information. The default (1), is always the most robust of the available algorithms.

edge_thresholdnumpy.ndarray (n_dimensions,)

A threshold parameter determining how close an edge should be to the center of the distribution during check_edges(). Higher values result in an edge closer to the sample mean. A value should be provided for each dimension. A zero value in any dimension will result in an infinite edge for that dimension.

minimum_pointsint, optional

Certain order validation algorithms check the number of available samples as a means to determine what order of fit is appropriate. If pre-calculated for the base order, it may be passed in here for a slight speed advantage.

get_errorbool, optional

If True, return the error on the fit.

get_countsbool, optional

If True, return the number of samples used when determining the fit at each fitting point.

get_weightsbool, optional

If True, return the sum of all sample weights used in determining the fit at each point.

get_distance_weightsbool, optional

If True, return the sum of only the distance weights used in determining the fit at each point.

get_rchi2bool, optional

If True, return the reduced chi-squared statistic for each of the fitted points.

get_cross_derivativesbool, optional

If True, return the derivative mean-squared-cross-products of the samples for each of the fitted points. See derivative_mscp() for further information.

get_offset_variancebool optional

If True, return the offset of the fitting point from the sample distribution. See offset_variance() for further information.

Returns:

fit_results8-tuple of numpy.ndarray

fit_results[0]: Fitted values. fit_results[1]: Error on the fit. fit_results[2]: Number of samples in each fit. fit_results[3]: Weight sums. fit_results[4]: Distance weight sums. fit_results[5]: Reduced chi-squared statistic. fit_results[6]: Derivative mean-squared-cross-products. fit_results[7]: Offset variances from the sample distribution center.

All arrays except for fit_results[6] have the shape (n_sets, n_fits) or (0, 0) depending on whether get_ is True or False respectively. The derivative MSCP is of shape (n_sets, n_fits, n_dimensions, n_dimensions) if requested, and (1, 0, 0, 0) otherwise.