`lscov`

Least-squares solution with known covariance or weights.

Syntax

x = lscov(A, b)

Ordinary least squares, the same as A\b for a full-rank A.

x = lscov(A, b, w)

Weighted least squares with the weight vector w.

x = lscov(A, b, V)

Generalized least squares for a covariance matrix V of the errors.

Description

Observations with different reliabilities should not count equally in a fit. A weight vector w is equivalent to a diagonal covariance V = diag(1./w). Giving the weight 4 to a point has the same effect as repeating that equation four times.

Input arguments

A: Design matrix with more rows than columns.
b: Observation vector.
w: Positive weights, one per observation; larger weights mean more reliable data.
V: Symmetric positive definite covariance matrix of the observation errors.

Output arguments

x: Coefficients minimizing the weighted squared residual (b - A*x)' * inv(V) * (b - A*x).

Example

Ordinary and weighted line fit

A = [1 0; 1 1; 1 2];
b = [1; 2; 2];
x = lscov(A, b)
x2 = lscov(A, b, [1; 1; 4])

Output

lscov