◆ Dgecovs()

Unscaled covariance matrix of linear least squares problem solved by Dgelss

Purpose: This routine 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. (Note that the lower trangle is computed different from Dgecov and Dgecovy) = 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,out]	A()	Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= 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 - 1) (LS >= N) Singular values computed by Dgelss.
[out]	Ci()	Array Ci(LCi - 1) (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]	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 A() is invalid. = -4: The argument S() is invalid. = -5: The argument Ci() is invalid.