SUGAW Subroutine

public subroutine SUGAW(KDGL, KM, KN, PL, PW, PANM, PFN)

*** *SUGAW * - Routine to initialize the Gaussian abcissa and the associated weights

• Interface. ---------- CALL *SUGAW(KN,PFN,PL,PW) *

  1. Initialization + root + weight computation ------------------------------------------

  1.1 Find the roots of the ordinary Legendre polynomial of degree KN using an analytical first guess and then refine to machine precision via Newton's method in double precision following Swarztrauber (2002)

  1.2 Find the roots of the associated Legendre polynomial of degree KN and the associated Gaussian weights using a Runge-Kutta 4 integration of the Pruefer transformed Sturm-Liouville problem (Tygert (J. Comput. Phys. 2008) and Glaser et al., SIAM J. SCI. COMPUT. Vol. 29 (4) 1420-1438)

  1. Diagnostics. ------------

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=JPIM),	intent(in)			::	KDGL
integer(kind=JPIM),	intent(in)			::	KM
integer(kind=JPIM),	intent(in)			::	KN
real(kind=JPRD),	intent(out)			::	PL(KDGL)
real(kind=JPRD),	intent(out)			::	PW(KDGL)
real(kind=JPRD),	intent(in)			::	PANM
real(kind=JPRD),	intent(in),	optional		::	PFN(0:KDGL,0:KDGL)