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fan_trans_old.pro
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fan_trans_old.pro
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PRO FAN_TRANS, image, arrdim, reso, wt, tab_k, S1a, image2=image2, S11=S11, S22=S22, S12=S12, S21=S21, apodize=radius, header=header
;------------------------------------------------------------------------------
;+
; NAME: FAN_TRANS
;
; PURPOSE: this routine computes the wavelet transform of a map
; with the Fan wavelet described in Kirby, J. F. 2005
; Computers and Geosciences, 31(7), 846–864.
;
; CALLING SEQUENCE: FAN_TRANSFORM, image, arrdim, reso, wt, tab_k, spec_k,
; apodize=radius
;
; INPUTS:
; image (2D fltarr): the input map
; arrdim (1D fltarr): array of new map dimensions to pad with zeros [x,y]
; reso (float): the physical resolution (X/pixel where X is
; degree, or arcmin or ...)
;
; OUTPUTS:
; wt (3D complexarr): Fan wavelet transform of the map. Each channel represents the
; wavelet coefficients at a particular scale averaged over angles.
; tab_k (1D fltarr): contains k in unit of X^(-1)
; S1a (1D fltarr): contains power spectrum [if image2 is set, S1a returns the 1D
; cross-spectrum S21 (real_part)]
;
; KEYWORDS: image2 = optional second image (2D flarr) same size than 'image'.
; If called, 'wt' and 'S1a' will return repestively the cross-wavelet
; coefficients and the cross-wavelet power spectrum of both images
; apodize = R will weight the map with a cosine tapper
; equal to 1 for radii < R ( 0 < R < 1 required) Ex.:0.98
; header = header of the image updated with the padding
;
; PROCEDURE CALLS: APODIZE, XYMAP,ralonge,ralonge_hdless
;
;
; HISTORY: 2013 V1.0 Jean-Francois ROBITAILLE
;
;-
;------------------------------------------------------------------------------
if N_params() LT 6 then begin
print,'Syntax: FAN_TRANSFORM, image, arrdim, reso, wt, tab_k, S1a , image2=image2, S11=S11, S22=S22, S12=S12, S21=S21, apodize=radius, header=header'
return
endif
ko= 5.336
delta= ( 2*sqrt(-2*alog(0.75)) )/ko
N=size(image)
na=N[1]
nb=N[2]
na2=arrdim[0]
nb2=arrdim[1]
;Apodisation
;----------------------------------------
tapper = APODIZE(na, nb, radius)
moyenne=mean(image)
image = image-moyenne
image = image * tapper
if not keyword_set(header) then begin
ralonge_hdless,image,imager,na2,nb2
endif else begin
ralonge,image,imager,na2,nb2,header
endelse
if keyword_set(image2) then begin
moyenne2 = mean(image2)
image2 = image2-moyenne2
image2 = image * tapper
if not keyword_set(header) then begin
ralonge_hdless,image2,image2r,na2,nb2
endif else begin
ralonge,image2,image2r,na2,nb2,header
endelse
endif
tapper = 0 ; release the memory for tapper
na=na2
nb=nb2
;Spectral Logarithm sample
;-------------------------------------
M=fix(alog(na2)/delta)
a2=fltarr(M)
a2[0]=na2
a2=alog(a2)
for i=0, M-2 do begin
a2[i+1]=a2[i]-0.284306
endfor
a2=exp(a2)
tab_k = 1. /(a2*reso)
;Creation of the UV-plane
;-------------------------------------
xymap, na, nb, x, y
if (na mod 2) eq 0 then begin
x = ( 1.*x - na/2. ) / na
shiftx = na/2
ishiftx = na/2
endif else begin
x = ( 1.*x - (na - 1)/2. ) / na
shiftx = (na-1.)/2.+1
ishiftx = (na-1.)/2.
endelse
if (nb mod 2) eq 0 then begin
y = ( 1.*y - nb/2.) / nb
shifty = nb/2
ishifty = nb/2
endif else begin
y = ( 1.*y - (nb - 1)/2.) / nb
shifty = (nb-1.)/2.+1
ishifty = (nb-1.)/2.
endelse
;-------------------------------------
wt=complexarr(na2,nb2,M)*0.
S1a=fltarr(M)
S11=dblarr(na,nb,M)*0.
if keyword_set(image2) then begin
S22=dblarr(na,nb,M)*0.
S21=complexarr(na,nb,M)*0.
S12=complexarr(na,nb,M)*0.
endif
;if keyword_set(S12) then begin
; S12=dblarr(na,nb,M)*0.
;endif
;Parameters and loops
;-------------------------------------
a = ko * a2 ;according to Kirby 2005
N=fix(!pi/delta)
imFT=FFT(imager,-1)
imFT=shift(imFT,shiftx,shifty)
if keyword_set(image2) then begin
im2FT=FFT(image2r,-1)
im2FT=shift(im2FT,shiftx,shifty)
endif
FOR j=0, M-1 DO BEGIN
FOR i=0, N-1 DO BEGIN
uvplan=0.
t=delta*i
;"Daughter Wavelet" parameters
;--------------------------------------------
uvplan= exp( -0.5*( (a[j]*x - ko*cos(t))^2. + (a[j]*y - ko*sin(t))^2. ) )
;Energy normalisation
;--------------------------------------------
uvplan= uvplan * a[j]
;Wavelet Transform
;--------------------------------------------
W1FT=imFT*uvplan
W1FT2=shift(W1FT,ishiftx,ishifty)
W1=FFT(W1FT2,1)
wt[*,*,j] = wt[*,*,j] + W1
S11[*,*,j] = S11[*,*,j] + abs(W1)^2
if keyword_set(image2) then begin
W2FT=im2FT*uvplan
W2FT2=shift(W2FT,ishiftx,ishifty)
W2=FFT(W2FT2,1)
S22[*,*,j] = S22[*,*,j] + abs(W2)^2
S21[*,*,j] = S21[*,*,j] + conj(W2)*W1
S12[*,*,j] = S12[*,*,j] + conj(W1)*W2
endif
;if keyword_set(S12) then begin
; S12[*,*,j] = S12[*,*,j] + conj(W1)*W2
;endif
ENDFOR
if not keyword_set(image2) then begin
S1a[j]=total(S11[*,*,j]) * delta / (float(N)*float(na2)*float(nb2))
endif else begin
S1a[j]=total(real_part(S21[*,*,j])) * delta / (float(N)*float(na2)*float(nb2))
endelse
ENDFOR
RETURN
END