Weighted Total Least Squares with correlated coefficients

Solving linear systems with correlated coefficients using weighted total least squares

This function solves over-determined linear systems of the form (A+dA)x = (b+db) numerically.

Individual weights for and correlations between the deviations [dA,db] are allowed.

These weights have to be given as a matrix W, which typically is the inverse of a (positive definite) covariance-matrix.

If A is a (m x n) matrix, then b has to be a (m x 1) vector and the weight matrix has to be a (m (n+1) x m (n+1)) matrix.

This is different from the so-called "general total leat squares" method, where only column or row-wise correlations are considered.

Additionally it is allowed to declare individual elements of a [A,b] to be free of errors.

The covariance matrix of the best fitting x-vector is provided.

The code has been optimized to achieve high computational speed.

"lsqnonlin" from the "optimization toolbox" is needed.

For large problems and highest performance A, b, and W should be declared as gpuArrays (which requires the "Parallel Computing Toolbox").

Partially modified code from other authors is required and included:

- "wtls_line" and "wtlsc_line" from Anton

- "multiprod" from de Leva

- "derivest", "hessdiag", "hessian", and "nderivediag" from D'Errico

- "gmtls" and "mtls" from Houtzager

- "gtls" from Rhode

(full references are given in the paper)

Best practice: Use the demo to see some examples and check the paper.