;----------------------------------------------------------------
; $Id: wv_fn_symlet.pro,v 1.3 2001/01/15 22:28:32 scottm Exp $
;
; Copyright (c) 1999-2001, Research Systems, Inc.  All rights reserved.
;	Unauthorized reproduction prohibited.
;+
; NAME:
;    WV_FN_SYMLET
;
; PURPOSE:
;    This function returns the Symlet wavelet coefficients.
;
; CALLING SEQUENCE:
;    info = WV_FN_SYMLET( Order, Scaling, Wavelet, Ioff, Joff)
;
; INPUTS:
;    Order: This is the order number for the Symlet wavelet.
;           Order=4 has 4 vanishing moments and 8 coefficients.
;
; OUTPUTS:
;    Scaling: A vector of the scaling (father) coefficients
;
;    Wavelet: A vector of the wavelet (mother) coefficients
;
;    Ioff: The offset index used to center the Scaling support
;
;    Joff: The offset index used to center the Wavelet support
;
; KEYWORD PARAMETERS:
;    INFO: On return, contains a structure with the following information:
;          (this is an example for order=2)
;       info = {family:'Symlet', $    ; name of wavelet family
;               order_name:'Order', $     ; term used for "order"
;               order_range:[4,15,4], $   ; valid range [first,last,default]
;               order:4, $                ; order number
;               discrete:1, $             ; 0=continuous, 1=discrete
;               orthogonal:1, $           ; 0=nonorthogonal, 1=orthogonal
;               symmetric:2, $            ; 0=asymmetric, 1=sym., 2=near sym.
;               support:7, $              ; support width
;               moments:4, $              ; # of vanishing moments
;               regularity:0.550}         ; # of continuous derivatives
;
; REFERENCE:
;    Daubechies, I., 1992: Ten Lectures on Wavelets, SIAM, p. 198.
;       Daubechies has orders 4-10, although note that Daubechies
;       has multiplied by Sqrt(2), and for some Orders the coefficients
;       are reversed.
;
;    Orders 11-15 are from <http://www.isds.duke.edu/~brani/filters.html>
;
; MODIFICATION HISTORY:
;    Written by: Chris Torrence, 1999
;-


;----------------------------------------------------------------
; Symlet orthogonal near-symmetric wavelet coefficients
FUNCTION wv_fn_symlet_coeff, order
	COMPILE_OPT strictarr, hidden
	CASE (order) OF    ; orders 1-3 are same as Daubechies 1-3
	1: coeff = [1d,1d]/SQRT(2d)  ; same as Haar
	2: coeff = [1d + SQRT(3d),3d + SQRT(3d), $
			3d - SQRT(3d),1d - SQRT(3d)]/(4d*SQRT(2d))
	3: BEGIN
		sq10 = SQRT(10d)
		sq5210 = SQRT(5d + 2d*SQRT(10d))
		coeff = [1d + sq10 + sq5210, 5d + sq10 + 3d*sq5210, $
			10d - 2d*sq10 + 2d*sq5210, 10d - 2d*sq10 - 2d*sq5210, $
			5d + sq10 - 3d*sq5210, 1d + sq10 - sq5210]/(16d*SQRT(2d))
		END
	4: coeff = [ $
		-0.07576571478950233d,$
		-0.02963552764600275d,$
		0.497618667632775d,$
		0.8037387518051327d,$
		0.2978577956053062d,$
		-0.09921954357663366d,$
		-0.01260396726203138d,$
		0.03222310060405147d]
	5: coeff = [ $
		0.0195388827352497d,$
		-0.02110183402468898d,$
		-0.1753280899080548d,$
		0.01660210576451275d,$
		0.6339789634567916d,$
		0.7234076904040388d,$
		0.1993975339768545d,$
		-0.03913424930231376d,$
		0.02951949092570631d,$
		0.02733306834499873d]
	6: coeff = [ $
		0.01540410932704474d,$
		0.003490712084221531d,$
		-0.1179901111485212d,$
		-0.04831174258569789d,$
		0.4910559419279768d,$
		0.7876411410286536d,$
		0.3379294217281644d,$
		-0.07263752278637825d,$
		-0.02106029251237119d,$
		0.04472490177078142d,$
		0.001767711864253766d,$
		-0.007800708325032496d]
	7: coeff = [ $
		0.01026817670846495d,$
		0.004010244871523197d,$
		-0.1078082377032895d,$
		-0.1400472404429405d,$
		0.2886296317506303d,$
		0.7677643170048699d,$
		0.5361019170905749d,$
		0.01744125508685128d,$
		-0.04955283493703385d,$
		0.06789269350122353d,$
		0.03051551316588014d,$
		-0.01263630340323927d,$
		-0.001047384888679668d,$
		0.002681814568260057d]
	8: coeff = [ $
		-0.003382415951003908d,$
		-0.000542132331797018d,$
		0.03169508781151886d,$
		0.00760748732494897d,$
		-0.1432942383512576d,$
		-0.06127335906765891d,$
		0.4813596512592537d,$
		0.7771857516996492d,$
		0.3644418948360139d,$
		-0.05194583810802026d,$
		-0.02721902991713553d,$
		0.04913717967372511d,$
		0.003808752013880463d,$
		-0.01495225833706814d,$
		-0.0003029205147226741d,$
		0.001889950332768561d]
	9: coeff = [ $
		0.001069490032908175d,$
		-0.0004731544986808867d,$
		-0.01026406402762793d,$
		0.008859267493410117d,$
		0.06207778930285313d,$
		-0.01823377077946773d,$
		-0.1915508312971598d,$
		0.03527248803579076d,$
		0.6173384491414731d,$
		0.7178970827644066d,$
		0.2387609146068536d,$
		-0.05456895843120489d,$
		0.0005834627459892242d,$
		0.03022487885821281d,$
		-0.01152821020772933d,$
		-0.01327196778183437d,$
		0.0006197808889867399d,$
		0.001400915525915921d]
	10: coeff = [ $
		0.0007701598091036597d,$
		0.00009563267068491565d,$
		-0.008641299277002591d,$
		-0.001465382581138532d,$
		0.04592723923095083d,$
		0.0116098939028464d,$
		-0.1594942788849671d,$
		-0.0708805357805798d,$
		0.4716906669415791d,$
		0.7695100370206782d,$
		0.3838267610640166d,$
		-0.03553674047551473d,$
		-0.03199005688220715d,$
		0.04999497207760673d,$
		0.005764912033412411d,$
		-0.02035493981234203d,$
		-0.0008043589319389408d,$
		0.004593173585320195d,$
		0.00005703608359777954d,$
		-0.0004593294210107238d]
	11: coeff = [ $
		0.0004892636102790465d,$
		0.00011053509770077d,$
		-0.006389603666537886d,$
		-0.002003471900538333d,$
		0.04300019068196203d,$
		0.03526675956730489d,$
		-0.1446023437042145d,$
		-0.2046547945050104d,$
		0.2376899090326669d,$
		0.7303435490812422d,$
		0.5720229780188006d,$
		0.09719839447055164d,$
		-0.02283265101793916d,$
		0.06997679961196318d,$
		0.03703741598066749d,$
		-0.0240808415947161d,$
		-0.009857934828835874d,$
		0.006512495674629366d,$
		0.0005883527354548924d,$
		-0.001734366267274675d,$
		-0.00003879565575380471d,$
		0.0001717219506928879d]
	12: coeff = [ $
		-0.0001790665869786187d,$
		-0.0000181580788773471d,$
		0.002350297614165271d,$
		0.0003076477963025531d,$
		-0.01458983644921009d,$
		-0.002604391031185636d,$
		0.05780417944546282d,$
		0.01530174062149447d,$
		-0.1703706972388913d,$
		-0.07833262231005749d,$
		0.4627410312313846d,$
		0.7634790977904264d,$
		0.3988859723844853d,$
		-0.0221623061807925d,$
		-0.03584883074255768d,$
		0.04917931829833128d,$
		0.007553780610861577d,$
		-0.02422072267559388d,$
		-0.001408909244210085d,$
		0.007414965517868044d,$
		0.0001802140900854918d,$
		-0.001349755755614803d,$
		-0.00001135392805049379d,$
		0.0001119671942470856d]
	13: coeff = [ $
		0.00007042986709788876d,$
		0.00003690537416474083d,$
		-0.0007213643852104347d,$
		0.0004132611973679777d,$
		0.00567485376954048d,$
		-0.00149244724795732d,$
		-0.02074968632748119d,$
		0.01761829684571489d,$
		0.09292603099190611d,$
		0.008819757923922775d,$
		-0.1404900930989444d,$
		0.1102302225796636d,$
		0.6445643835707201d,$
		0.6957391508420829d,$
		0.1977048192269691d,$
		-0.1243624606980946d,$
		-0.05975062792828035d,$
		0.01386249731469475d,$
		-0.01721164274779766d,$
		-0.02021676815629033d,$
		0.005296359721916584d,$
		0.007526225395916087d,$
		-0.0001709428497111897d,$
		-0.001136063437095249d,$
		-0.0000357386241733562d,$
		0.00006820325245288671d]
	14: coeff = [ $
		0.00004461898110644152d,$
		0.00001932902684197359d,$
		-0.0006057602055992672d,$
		-0.00007321430367811753d,$
		0.004532677588409982d,$
		0.001013142476182283d,$
		-0.01943931472230284d,$
		-0.002365051066227485d,$
		0.06982761641982026d,$
		0.02589859164319225d,$
		-0.1599974161449017d,$
		-0.05811184934484923d,$
		0.4753357348650867d,$
		0.7599762436030552d,$
		0.3932015487235067d,$
		-0.03531809075139569d,$
		-0.05763449302747868d,$
		0.03743308903888159d,$
		0.004280522331795536d,$
		-0.02919621738508546d,$
		-0.002753775776578359d,$
		0.01003769335863697d,$
		0.000366476770515625d,$
		-0.002579441672422145d,$
		-0.00006286548683867455d,$
		0.0003984356519092697d,$
		0.00001121086996816579d,$
		-0.00002587908845615303d]
	15: coeff = [ $
		0.00002866070677120333d,$
		0.00002171787955311147d,$
		-0.0004021685533613114d,$
		-0.0001081543887175515d,$
		0.003481028703942169d,$
		0.001526137844414152d,$
		-0.01717125372019869d,$
		-0.008744789536991206d,$
		0.06796982865464372d,$
		0.06839330637828124d,$
		-0.1340563101529709d,$
		-0.1966263778558184d,$
		0.2439626866290417d,$
		0.7218430206728932d,$
		0.5786404210564978d,$
		0.1115337122112223d,$
		-0.04108264812160452d,$
		0.04073549232451155d,$
		0.0219376493087618d,$
		-0.03887671358112607d,$
		-0.01940501010809092d,$
		0.01007997710234975d,$
		0.003423450420331992d,$
		-0.003590165587998719d,$
		-0.0002673164968523743d,$
		0.00107056717058685d,$
		0.00005512252372901569d,$
		-0.0001606618669228563d,$
		-7.359664092097746D-6,$
		9.712420309178714D-6]
	ELSE: coeff = -1
	ENDCASE
	RETURN,coeff
END


;----------------------------------------------------------------
FUNCTION wv_fn_symlet,order,scaling,wavelet,ioff,joff

	COMPILE_OPT strictarr
	ON_ERROR,2  ; return to caller

;defaults
	order_range = [1,15,4]  ; [first,last,default]
	IF (N_ELEMENTS(order) LT 1) THEN order = order_range[2]  ; default

; check for invalid Order
	order = FIX(order + 1E-5)
	IF ((order LT order_range[0]) OR (order GT order_range[1])) THEN BEGIN
		MESSAGE,/INFO,'Order out of range, reverting to default...'
		order = order_range[2]  ; default
	ENDIF

; Regularity = # of continuous derivatives
; orders 1-15 from Taswell (1998) p. 36 "DROLA"
	regularity = [0d,0d,0.550d,1.088d, $ ; order 0-3
		1.403d,1.776d,2.122d,2.468d, $   ; 4-7
		2.750d,3.039d,3.311d,3.579d, $   ; 8-11
		3.826d,4.072d,4.312d,4.550d]     ; 12-15
	regularity = regularity[order]

; construct Info structure
	info = {family:'Symlet', $
		order_name:'Order', $
		order_range:order_range, $
		order:order, $
		discrete:1, $
		orthogonal:1, $
		symmetric:2, $
		support:FIX(order*2-1), $
		moments:FIX(order), $
		regularity:regularity}

	IF (N_PARAMS() LT 1) THEN RETURN, info ; don't bother with rest

; choose scaling coefficients
	scaling = WV_FN_SYMLET_COEFF(order)

; construct wavelet coefficients & offsets
	n =N_ELEMENTS(scaling)
	wavelet = REVERSE(scaling)*((-1)^LINDGEN(n))
	ioff = -n/2 + 2  ; offset for scaling
	joff = ioff     ; offset for wavelet

	RETURN, info
END