g1 Subroutine

private subroutine g1(a, b, c, s, sig)

Compute orthogonal rotation matrix.

Compute matrix $$\left[ \begin{array}{cc} c & s \\ -s & c \end{array} \right]$$ so that

$$\left[ \begin{array}{cc} c & s \\ -s & c \end{array} \right] \left[ \begin{array}{c} a \\ b \end{array} \right] = \left[ \begin{array}{c} \sqrt{a^2+b^2} \\ 0 \end{array} \right]$$

Compute $\sigma = \sqrt{a^2+b^2}$

$\sigma$ is computed last to allow for the possibility that sig may be in the same location as a or b.

References

• C.L. Lawson, R.J. Hanson, 'Solving least squares problems' Prentice Hall, 1974. (revised 1995 edition)
• lawson-hanson from Netlib.

History

• Jacob Williams, refactored into modern Fortran, Jan. 2016.

Arguments

    subroutine g1(a,b,c,s,sig)

    implicit none

    real(wp)             :: a
    real(wp)             :: b
    real(wp)             :: sig
    real(wp),intent(out) :: c
    real(wp),intent(out) :: s

    real(wp) :: xr, yr

    if ( abs(a)>abs(b) ) then
        xr = b/a
        yr = sqrt(one+xr**2)
        c = sign(one/yr,a)
        s = c*xr
        sig = abs(a)*yr
    else
        if ( abs(b)>zero ) then
            xr = a/b
            yr = sqrt(one+xr**2)
            s = sign(one/yr,b)
            c = s*xr
            sig = abs(b)*yr
        else
            sig = zero
            c = zero
            s = one
        end if
    end if

    end subroutine g1