PRO HISTOGAUSS,SAMPLE,A,XX,YY,GX,GY,NOPLOT=noplot,NOFIT=SIMPL, \$ CHARSIZE=CSIZE, FONT=font, _EXTRA = _extra,Window=window ; ;+ ;NAME: ; HISTOGAUSS ; ; PURPOSE: ; Histograms data and overlays it with a Gaussian. Draws the mean, sigma, ; and number of points on the plot. ; ; CALLING SEQUENCE: ; HISTOGAUSS, Sample, A, [XX, YY, GX, GY, /NOPLOT, /NOFIT, FONT=, ; CHARSIZE = ] ; ; INPUT: ; SAMPLE = Vector to be histogrammed ; ; OUTPUT ARGUMENTS: ; A = coefficients of the Gaussian fit: Height, mean, sigma ; A[0]= the height of the Gaussian ; A[1]= the mean ; A[2]= the standard deviation ; A[3]= the half-width of the 95% conf. interval of the standard ; mean ; A[4]= 1/(N-1)*total( (y-mean)/sigma)^2 ) = a measure of ; normality ; ; Below: superceded. The formula is not entirely reliable. ; A[4]= measure of the normality of the distribution. =1.0, perfectly ; normal. If no more than a few hundred points are input, there are ; formulae for the 90 and 95% confidence intervals of this quantity: ; M=ALOG10(N-1) ; N = number of points ; T90=ABS(.6376-1.1535*M+.1266*M^2) ; = 90% confidence interval ; IF N LT 50 THEN T95=ABS(-1.9065-2.5465*M+.5652*M^2) \$ ; ELSE T95=ABS( 0.7824-1.1021*M+.1021*M^2) ;95% conf. ; (From Martinez, J. and Iglewicz, I., 1981, Biometrika, 68, 331-333.) ; ; XX = the X coordinates of the histogram bins (CENTER) ; YY = the Y coordinates of the histogram bins ; GX = the X coordinates of the Gaussian fit ; GY = the Y coordinates of the Gaussian fit ; ; OPTIONAL INPUT KEYWORDS: ; /NOPLOT - If set, nothing is drawn ; /FITIT If set, a Gaussian is actually fitted to the distribution. ; By default, a Gaussian with the same mean and sigma is drawn; ; the height is the only free parameter. ; CHARSIZE Size of the characters in the annotation. Default = 0.82. ; FONT - scalar font graphics keyword (-1,0 or 1) for text ; /WINDOW - set to plot to a resizeable graphics window ; _EXTRA - Any value keywords to the cgPLOT command (e.g. XTITLE) may also ; be passed to HISTOGAUSS ; SUBROUTINE CALLS: ; BIWEIGHT_MEAN, which determines the mean and std. dev. ; AUTOHIST, which draws the histogram ; GAUSSFIT() (IDL Library) which does just that ; ; REVISION HISTORY: ; Written, H. Freudenreich, STX, 12/89 ; More quantities returned in A, 2/94, HF ; Added NOPLOT keyword and print if Gaussian, 3/94 ; Stopped printing confidence limits on normality 3/31/94 HF ; Added CHARSIZE keyword, changed annotation format, 8/94 HF ; Simplified calculation of Gaussian height, 5/95 HF ; Convert to V5.0, use T_CVF instead of STUDENT_T, GAUSSFIT instead of ; FITAGAUSS W. Landsman April 2002 ; Correct call to T_CVF for calculation of A[3], 95% confidence interval ; P. Broos/W. Landsman July 2003 ; Allow FONT keyword to be passed. T. Robishaw Apr. 2006 ; Use Coyote Graphics for plotting W.L. Mar 2011 ; Better formatting of text output W.L. May 2012 ;- On_error,2 compile_opt idl2 if N_params() LT 2 then begin print,'Syntax - HISTOGAUSS, Sample, A, [XX, YY, GX, GY, ' print,' /NOPLOT, /NOFIT, CHARSIZE=, Plotting keywords...]' return endif if (N_elements(FONT) eq 0) then font = !p.font DATA = SAMPLE N = N_ELEMENTS(DATA) ; First make sure that not everything is in the same bin. If most ; data = 0, reject zeroes. If they = some other value, complain and ; give up. A = 0. DATA = DATA[SORT(DATA)] N3 = 0.75*N & N1 = 0.25*N IF DATA[N3] EQ DATA[N1] THEN BEGIN IF DATA[N/2] EQ 0. THEN BEGIN Q = WHERE(DATA NE 0.,NON0) IF (N-NON0) GT 15 THEN BEGIN message,/INF,'Suppressing Zeroes!' DATA=DATA[Q] N=NON0 ENDIF ELSE BEGIN message,' Too Few Non-0 Values!',/CON RETURN ENDELSE Q=0 ENDIF ELSE BEGIN message,/CON,' Too Many Identical Values: ' + strtrim(DATA[N/2],2) RETURN ENDELSE ENDIF A = FLTARR(5) ; The "mean": A[1] = BIWEIGHT_MEAN(DATA,S) ; The "standard deviation": A[2] = S ; The 95% confidence interval: M=.7*(N-1) ;appropriate for a biweighted mean CL = 0.95 two_tail_area = 1 - CL A[3]=ABS( T_CVF(1 - (two_tail_area)/2.0,M) )*S/sqrt(n) ; A measure of the Gaussianness: A[4]=TOTAL((DATA-A[1])^2)/((N-1)*A[2]^2) ;Q=WHERE( ABS(DATA-A(1)) LT (5.*S), COUNT ) ; "robust I" unreliable ;ROB_I=TOTAL((DATA(Q)-A(1))^2)/((COUNT-1)*A(2)^2) ;PRINT,A(4),ROB_I ; Set bounds on the data: U1 = A[1] - 5.*A[2] U2 = A[1] + 5.*A[2] Q = WHERE(DATA LT U1, NQ) IF NQ GT 0 THEN DATA[Q] = U1 Q = WHERE(DATA GT U2, NQ) IF NQ GT 0 THEN DATA[Q] = U2 ; Draw the histogram font_in = !P.FONT & !P.FONT=font AUTOHIST,DATA,X,Y,XX,YY,NOPLOT = noplot, _EXTRA = _extra,Window=window !P.FONT=font_in ; Check for error in AUTOHIST: M = N_ELEMENTS(X) MM = N_ELEMENTS(XX) IF M LT 2 THEN BEGIN XX=0. & YY=0. & A=0. RETURN ; (AUTOHIST has already screamed) ENDIF ; Calculate the height of the Gaussian: Z = EXP(-.5*(X-A[1])^2/A[2]^2 ) XQ1 = A[1] - 1.3*A[2] XQ2 = A[1] + 1.3*A[2] QQ = WHERE((X GT XQ1) AND (X LT XQ2),COUNT) IF COUNT GT 0 THEN HYTE = MEDIAN(Y[QQ]/Z[QQ],/EVEN) ELSE BEGIN print,'HISTOGAUSS: Distribution too Weird!' HYTE = MAX(SMOOTH(Y,5)) ENDELSE A[0]=HYTE ; Fit a Gaussian, unless the /NOFIT qualifier is present IF ~KEYWORD_SET(SIMPL) THEN BEGIN PARM=A[0:2] YFIT = GAUSSFIT(XX,YY,PARM,NTERMS=3) A[0:2]=PARM ENDIF ; It the /NOPLOT qualifier is present, we're done. IF KEYWORD_SET(NOPLOT) THEN RETURN ; Overplot the Gaussian, DU = (U2-U1)/199. GX = U1 + FINDGEN(200)*DU Z = (GX-A[1])/A[2] GY = A[0]*EXP(-Z^2/2. ) cgplot,/over,GX,GY,window=window ; Annotate. MEANST = STRING(A[1],'(G12.5)') SIGST = STRING(A[2],'(G12.5)') NUM = N_ELEMENTS(DATA) NUMST =STRING(N,'(I6)') IF KEYWORD_SET(CSIZE) THEN ANNOT=CSIZE ELSE ANNOT=.82 if FONT EQ 0 then LABL = '#, !Mm!X, !Ms!X=' else LABL='#, !7l!6, !7r!3=' LABL = LABL +numst+','+meanst+','+sigst X1 = !x.crange[0] + annot*(!x.crange[1]-!x.crange[0])/20./0.82 y1 = !y.crange[1] - annot*(!y.crange[1]-!y.crange[0])/23./0.82 cgtext, X1, Y1, LABL, CHARSIZE=ANNOT, FONT=font,window=window RETURN END