verde.base.least_squares(jacobian, data, weights, damping=None, copy_jacobian=False)[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.


Setting copy_jacobian to True will copy the Jacobian matrix, doubling the memory required. Use it only if the Jacobian matrix is needed afterwards.

  • 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.

  • copy_jacobian (bool) – If False, the Jacobian matrix will be scaled inplace. If True, the Jacobian matrix will be copied before scaling. Default False.


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