# verde.base.least_squares¶

verde.base.least_squares(jacobian, data, weights, damping=None)[source]

Solve a weighted least-squares problem with optional damping regularization

Scales the Jacobian matrix so that each column has unit variance. This helps keep the regularization parameter in a sensible range. The scaling is undone before returning the estimated parameters so that scaling isn’t required for predictions. Doesn’t normalize the column means because that operation can’t be undone.

Parameters
• jacobian (2d-array) – The Jacobian/sensitivity/feature matrix.

• data (1d-array) – The data array. Must be a single 1D array. If fitting multiple data components, stack the arrays and the Jacobian matrices.

• weights (None or 1d-array) – The data weights. Like the data, this must also be a 1D array. Stack the weights in the same order as the data. Use weights=None to fit without weights.

• damping (None or float) – The positive damping (Tikhonov 0th order) regularization parameter. If damping=None, will use a regular least-squares fit.

Returns

parameters (1d-array) – The estimated 1D array of parameters that fit the data.