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This solves min! a*x  y^2 + regstr*(xregtgt)^2, and returns (x, the_fit, rank, s). Normally, a.shape==(m,n) and y.shape==(m,q), where m is the number of data to be fit, n is the number of parameters to use in a fit (equivalently, the number of basis functions), and q is the number of separate sets of equations that you are fitting. Then, x has shape (n,q) and the_fit has shape (m,q). The regularization target, regtgt is the same shape as x, that is (n,q). (It must be a vector if and only if y is a vector.) Regstr, the strength of the regularization is normally an (n,n) matrix, though (*,n) will work, as will a scalar. Y may be a 1D matrix (a vector), in which case the fit is a vector. This is the normal case where you are fitting one equation. If y is a 2D matrix, each column (second index) in y is a separate fit, and each column in the solution is a separate result.

Returns something like the rank of the solution, but rather than counting how many dimensions can be solved at all, it reports how many dimensions can be solved with a relatively good accuracy.

Hat Matrix Diagonal Data points that are far from the centroid of the Xspace are potentially influential. A measure of the distance between a data point, xi, and the centroid of the Xspace is the data point's associated diagonal element hi in the hat matrix. Belsley, Kuh, and Welsch (1980) propose a cutoff of 2 p/n for the diagonal elements of the hat matrix, where n is the number of observations used to fit the model, and p is the number of parameters in the model. Observations with hi values above this cutoff should be investigated. For linear models, the hat matrix
can be used as a projection matrix. The hat matrix diagonal variable contains the diagonal elements of the hat matrix

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