givens Function

public function givens(r, idf, detnth)

overdetermined linear system by accurate Givens rotations. Prior to GIVENS call m-times GIVENSA in order to build the triangle system R (C) Alex Schwarzenberg-Czerny,2000 alex@camk.edu.pl

Arguments

Type IntentOptional AttributesName
real(kind=SP), intent(inout) :: r(:,:)

r(n1,:) - unknowns (r(k,k),k=1,n) variances (r(:k,k),k=1,n) half of covariance matrix (r(k+1:,k),k=2,n) half of inverse triangle root Q r(n1,n1) - chi^2/idf (=RHS variance=std.dev^2) For idf<0: ((r(j,k),j=1,k),k=1,n) inverse triangle root Q

integer, intent(in) :: idf

idf - >0 solve normal equations for idf degrees of freedom <0 and r(n1,n1)=1: inverse triangle matrix R

real(kind=SP), intent(out) :: detnth

=Det(R)^(1/n) - n-th root of determinant

Return Value real(kind=SP)

result condition ratio (min eigenv/max eigenv), 0 signalls singular system


Contents

None