speclib Module Reference

LIBRARY ROUTINES FOR SPECTRAL METHODS. More...

Functions/Subroutines
subroutine	zwgl (Z, W, NP)
	Generate NP Gauss Legendre points Z and weights W associated with Jacobi polynomial \( P(N)(\alpha=0, \beta=0) \). The polynomial degree N = NP-1. More...
subroutine	zwgll (Z, W, NP)
subroutine	zwgj (Z, W, NP, ALPHA, BETA)
subroutine	zwgjd (Z, W, NP, ALPHA, BETA)
subroutine	zwglj (Z, W, NP, ALPHA, BETA)
subroutine	zwgljd (Z, W, NP, ALPHA, BETA)
real(kind=xp) function	endw1 (N, ALPHA, BETA)
real(kind=xp) function	endw2 (N, ALPHA, BETA)
real(kind=xp) function	gammaf (X)
real(kind=xp) function	pnormj (N, ALPHA, BETA)
subroutine	jacg (XJAC, NP, ALPHA, BETA)
subroutine	jacobf (POLY, PDER, POLYM1, PDERM1, POLYM2, PDERM2, N, ALP, BET, X)
real(kind=xp) function	hgj (II, Z, ZGJ, NP, ALPHA, BETA)
real(kind=xp) function	hgjd (II, Z, ZGJ, NP, ALPHA, BETA)
real(kind=xp) function	hglj (II, Z, ZGLJ, NP, ALPHA, BETA)
real(kind=xp) function	hgljd (I, Z, ZGLJ, NP, ALPHA, BETA)
subroutine	dgj (D, DT, Z, NZ, NZD, ALPHA, BETA)
subroutine	dgjd (D, DT, Z, NZ, NZD, ALPHA, BETA)
subroutine	dglj (D, DT, Z, NZ, NZD, ALPHA, BETA)
subroutine	dgljd (D, DT, Z, NZ, NZD, ALPHA, BETA)
subroutine	dgll (D, DT, Z, NZ, NZD)
real(kind=xp) function	hgll (I, Z, ZGLL, NZ)
real(kind=xp) function	hgl (I, Z, ZGL, NZ)
real(kind=xp) function	pnleg (Z, N)
subroutine	legendre_poly (L, x, N)
	Evaluate Legendre polynomials of degrees 0-N at point x and store in array L. More...
real(kind=xp) function	pndleg (Z, N)
subroutine	dgllgl (D, DT, ZM1, ZM2, IM12, NZM1, NZM2, ND1, ND2)
subroutine	dgljgj (D, DT, ZGL, ZG, IGLG, NPGL, NPG, ND1, ND2, ALPHA, BETA)
subroutine	dgljgjd (D, DT, ZGL, ZG, IGLG, NPGL, NPG, ND1, ND2, ALPHA, BETA)
subroutine	iglm (I12, IT12, Z1, Z2, NZ1, NZ2, ND1, ND2)
subroutine	igllm (I12, IT12, Z1, Z2, NZ1, NZ2, ND1, ND2)
subroutine	igjm (I12, IT12, Z1, Z2, NZ1, NZ2, ND1, ND2, ALPHA, BETA)
subroutine	igljm (I12, IT12, Z1, Z2, NZ1, NZ2, ND1, ND2, ALPHA, BETA)

Detailed Description

March 1989

For questions, comments or suggestions, please contact:

Einar Malvin Ronquist Room 3-243 Department of Mechanical Engineering Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 0299 U.S.A.

Function/Subroutine Documentation

dgj()

subroutine speclib::dgj	(	real(kind=xp), dimension(nzd,nzd)	D,
		real(kind=xp), dimension(nzd,nzd)	DT,
		real(kind=xp), dimension(1)	Z,
			NZ,
			NZD,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 690 of file speclib.f90.

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dgjd()

subroutine speclib::dgjd	(	real(kind=xp), dimension(nzd,nzd)	D,
		real(kind=xp), dimension(nzd,nzd)	DT,
		real(kind=xp), dimension(1)	Z,
			NZ,
			NZD,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 734 of file speclib.f90.

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dglj()

subroutine speclib::dglj	(	real(kind=xp), dimension(nzd,nzd)	D,
		real(kind=xp), dimension(nzd,nzd)	DT,
		real(kind=xp), dimension(1)	Z,
			NZ,
			NZD,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 773 of file speclib.f90.

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dgljd()

subroutine speclib::dgljd	(	real(kind=xp), dimension(nzd,nzd)	D,
		real(kind=xp), dimension(nzd,nzd)	DT,
		real(kind=xp), dimension(1)	Z,
			NZ,
			NZD,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 817 of file speclib.f90.

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dgljgj()

subroutine speclib::dgljgj	(	real(kind=xp), dimension(nd2,nd1)	D,
		real(kind=xp), dimension(nd1,nd2)	DT,
		real(kind=xp), dimension(nd1)	ZGL,
		real(kind=xp), dimension(nd2)	ZG,
		real(kind=xp), dimension(nd2,nd1)	IGLG,
			NPGL,
			NPG,
			ND1,
			ND2,
			ALPHA,
			BETA
	)

Definition at line 1060 of file speclib.f90.

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dgljgjd()

subroutine speclib::dgljgjd	(	real(kind=xp), dimension(nd2,nd1)	D,
		real(kind=xp), dimension(nd1,nd2)	DT,
		real(kind=xp), dimension(nd1)	ZGL,
		real(kind=xp), dimension(nd2)	ZG,
		real(kind=xp), dimension(nd2,nd1)	IGLG,
			NPGL,
			NPG,
			ND1,
			ND2,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 1116 of file speclib.f90.

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dgll()

subroutine speclib::dgll	(	real(kind=rp), dimension(nzd,nzd)	D,
		real(kind=rp), dimension(nzd,nzd)	DT,
		real(kind=rp), dimension(1)	Z,
			NZ,
			NZD
	)

Definition at line 864 of file speclib.f90.

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dgllgl()

subroutine speclib::dgllgl	(	real(kind=xp), dimension(nd2,nd1)	D,
		real(kind=xp), dimension(nd1,nd2)	DT,
		real(kind=xp), dimension(nd1)	ZM1,
		real(kind=xp), dimension(nd2)	ZM2,
		real(kind=xp), dimension(nd2,nd1)	IM12,
			NZM1,
			NZM2,
			ND1,
			ND2
	)

Definition at line 1023 of file speclib.f90.

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endw1()

real(kind=xp) function speclib::endw1	(		N,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 344 of file speclib.f90.

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endw2()

real(kind=xp) function speclib::endw2	(		N,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 388 of file speclib.f90.

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gammaf()

real(kind=xp) function speclib::gammaf

(

real(kind=xp)

X

)

Definition at line 432 of file speclib.f90.

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hgj()

real(kind=xp) function speclib::hgj	(		II,
		real(kind=xp)	Z,
		real(kind=xp), dimension(1)	ZGJ,
			NP,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 580 of file speclib.f90.

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hgjd()

real(kind=xp) function speclib::hgjd	(		II,
		real(kind=xp)	Z,
		real(kind=xp), dimension(1)	ZGJ,
			NP,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 609 of file speclib.f90.

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hgl()

real(kind=xp) function speclib::hgl	(		I,
		real(kind=xp)	Z,
		real(kind=xp), dimension(1)	ZGL,
			NZ
	)

Definition at line 923 of file speclib.f90.

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hglj()

real(kind=xp) function speclib::hglj	(		II,
		real(kind=xp)	Z,
		real(kind=xp), dimension(1)	ZGLJ,
			NP,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 633 of file speclib.f90.

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hgljd()

real(kind=xp) function speclib::hgljd	(		I,
		real(kind=xp)	Z,
		real(kind=xp), dimension(1)	ZGLJ,
			NP,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 662 of file speclib.f90.

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hgll()

real(kind=xp) function speclib::hgll	(		I,
		real(kind=xp)	Z,
		real(kind=xp), dimension(1)	ZGLL,
			NZ
	)

Definition at line 901 of file speclib.f90.

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igjm()

subroutine speclib::igjm	(	real(kind=xp), dimension(nd2,nd1)	I12,
		real(kind=xp), dimension(nd1,nd2)	IT12,
		real(kind=xp), dimension(nd1)	Z1,
		real(kind=xp), dimension(nd2)	Z2,
			NZ1,
			NZ2,
			ND1,
			ND2,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 1222 of file speclib.f90.

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igljm()

subroutine speclib::igljm	(	real(kind=xp), dimension(nd2,nd1)	I12,
		real(kind=xp), dimension(nd1,nd2)	IT12,
		real(kind=xp), dimension(nd1)	Z1,
		real(kind=xp), dimension(nd2)	Z2,
			NZ1,
			NZ2,
			ND1,
			ND2,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 1249 of file speclib.f90.

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igllm()

subroutine speclib::igllm	(	real(kind=xp), dimension(nd2,nd1)	I12,
		real(kind=xp), dimension(nd1,nd2)	IT12,
		real(kind=xp), dimension(nd1)	Z1,
		real(kind=xp), dimension(nd2)	Z2,
			NZ1,
			NZ2,
			ND1,
			ND2
	)

Definition at line 1196 of file speclib.f90.

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iglm()

subroutine speclib::iglm	(	real(kind=xp), dimension(nd2,nd1)	I12,
		real(kind=xp), dimension(nd1,nd2)	IT12,
		real(kind=xp), dimension(nd1)	Z1,
		real(kind=xp), dimension(nd2)	Z2,
			NZ1,
			NZ2,
			ND1,
			ND2
	)

Definition at line 1170 of file speclib.f90.

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jacg()

subroutine speclib::jacg	(	real(kind=xp), dimension(1)	XJAC,
			NP,
			ALPHA,
			BETA
	)

Definition at line 482 of file speclib.f90.

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jacobf()

subroutine speclib::jacobf	(		POLY,
			PDER,
			POLYM1,
			PDERM1,
			POLYM2,
			PDERM2,
			N,
			ALP,
			BET,
			X
	)

Definition at line 540 of file speclib.f90.

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legendre_poly()

subroutine speclib::legendre_poly	(	real(kind=rp), dimension(0:n), intent(inout)	L,
		real(kind=rp)	x,
		integer	N
	)

Definition at line 979 of file speclib.f90.

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pndleg()

real(kind=xp) function speclib::pndleg	(	real(kind=xp)	Z,
			N
	)

Definition at line 994 of file speclib.f90.

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pnleg()

real(kind=xp) function speclib::pnleg	(	real(kind=xp)	Z,
			N
	)

Definition at line 942 of file speclib.f90.

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pnormj()

real(kind=xp) function speclib::pnormj	(		N,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 456 of file speclib.f90.

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zwgj()

subroutine speclib::zwgj	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 185 of file speclib.f90.

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zwgjd()

subroutine speclib::zwgjd	(	real(kind=xp), dimension(1)	Z,
		real(kind=xp), dimension(1)	W,
			NP,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 216 of file speclib.f90.

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zwgl()

subroutine speclib::zwgl	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP
	)

Parameters

Z	Quadrature points.
W	Quadrature weights.
NP	Number of quadrature points.

Definition at line 160 of file speclib.f90.

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zwglj()

subroutine speclib::zwglj	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP,
		real(kind=rp)	ALPHA,
		real(kind=rp)	BETA
	)

Definition at line 268 of file speclib.f90.

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zwgljd()

subroutine speclib::zwgljd	(	real(kind=xp), dimension(np)	Z,
		real(kind=xp), dimension(np)	W,
			NP,
		real(kind=xp)	ALPHA,
		real(kind=xp)	BETA
	)

Definition at line 299 of file speclib.f90.

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zwgll()

subroutine speclib::zwgll	(	real(kind=rp), dimension(1)	Z,
		real(kind=rp), dimension(1)	W,
			NP
	)

Definition at line 168 of file speclib.f90.

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