◆ dgecovs()

Unscaled covariance matrix of linear least squares problem solved by dgelss

Purpose: dgecovs computes the unscaled covariance matrix of linear least squares problem solved by dgelss.

The following least squares problem with m x n matrix A can be solved by dgelss.
minimize ||A*x - b||

The n x n symmetric positive definite matrix C, the unscaled covariance matrix of the estimated parameters, is defined as below.
C = (A^T*A)^(-1), rank(A) = n

The scalar multiple (sigma^2)*C has a statiscal interpretation of being an estimate of the variance-covariance matrix for the solution vector of the least squares problem. The scalar factor sigma^2 is expressed as follows.
sigma^2 = ||A*x - b||^2 / (m - n)

where x is the least squares solution. The diagonal elements of (sigma^2)*C give the variance of each component of x.

Parameters

[in]	job	= -1: The lower triangle of C is computed. = 0: The diagonal elements of C are computed. = i > 0: i-th column of C is computed. (i <= n)
[in]	n	The order of the matrix A = rank of A (should not be rank deficient). (n >= 0) (If n = 0, returns without computation)
[in]	lda	Leading dimension of the two dimensional array a[][]. (lda >= max(1, n))
[in,out]	a[][]	Array a[la][lda] (la >= n) [in] The right singular vectors returned by dgelss. [out] job = -1: a[][] is overwritten by the lower triangule of C. The strictly upper triangle part of a[][] is destroyed.
[in]	s[]	Array s[ls] (ls >= n) Singular values computed by dgelss.
[out]	ci[]	Array ci[lci] (lci >= n) job = -1: Not referenced. job = 0: The diagonal elements of C are returned. job = i > 0: The i-th column of C is returned.
[out]	work[]	Array work[lwork] (lwork >= n) Work array.
[out]	info	= 0: Successful exit = -1: The argument job had an illegal value (job < -1 or job > n) = -2: The argument n had an illegal value (n < 0) = -3: The argument lda had an illegal value (lda < max(1, n))