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;
; NAME:
; cgHistogram
;
; PURPOSE:
; This program is used as a wrapper to the Histogram command in IDL. It removes the
; very real possibility that the Histogram command will return incorrect values silently.
;
;******************************************************************************************;
; ;
; Copyright (c) 2013, by Fanning Software Consulting, Inc. All rights reserved. ;
; ;
; Redistribution and use in source and binary forms, with or without ;
; modification, are permitted provided that the following conditions are met: ;
; ;
; * Redistributions of source code must retain the above copyright ;
; notice, this list of conditions and the following disclaimer. ;
; * Redistributions in binary form must reproduce the above copyright ;
; notice, this list of conditions and the following disclaimer in the ;
; documentation and/or other materials provided with the distribution. ;
; * Neither the name of Fanning Software Consulting, Inc. nor the names of its ;
; contributors may be used to endorse or promote products derived from this ;
; software without specific prior written permission. ;
; ;
; THIS SOFTWARE IS PROVIDED BY FANNING SOFTWARE CONSULTING, INC. ''AS IS'' AND ANY ;
; EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES ;
; OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT ;
; SHALL FANNING SOFTWARE CONSULTING, INC. BE LIABLE FOR ANY DIRECT, INDIRECT, ;
; INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED ;
; TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; ;
; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ;
; ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT ;
; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ;
; SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ;
;******************************************************************************************;
;
;+
; This program is used as a wrapper to the Histogram command in IDL. It works around a bug
; in the Histogram command when byte data is binned in versions prior to IDL 8.2, and it takes
; care to match the data type of the `BinSize` keyword to the data type of the data being binned.
; If this matching is not done, Histogram silently returns incorrect results. I have added the ability to
; smooth the data (with the `Smooth` keyword) and to return the relative frequency of the histogram,
; rather than the histogram counts (with the `Frequency` keyword). The relative frequency is a
; number between 0 and 1. I have also added the ability to specify "missing" data that should not be
; binned.
;
; :Categories:
; General
;
; :Params:
; data: in, required,
; The data from which the histogram is created.
;
; :Keywords:
; binsize: in, optional
; The binsize of the histogram. By default, Scott's Choice of bin size for histograms is used::
;
; binsize = (3.5 * StdDev(data)) / N_Elements(data)^(0.3333)
;
; If BINSIZE in not defined, and NBINS is defined, the BINSIZE is calcuated as::
;
; binsize = (Max(dataToHistogram) - Min(dataToHistogram)) / (NBINS -1)
;
; While it is pointed out in the HISTOGRAM documentation, it is extremely
; important that the BINSIZE be of the same data type as the data you are going to
; calculate the histogram of. If it is not, VERY strange things can happen, but the
; worst is that HISTOGRAM silently returns incorrect results. I try hard to avoid this
; result in this program.
; frequency: in, optional, type=boolean, default=0
; If this keyword is set, the relative frequency is returned, rather than the
; histogram counts. Relative frequency is a number between 0 and 1. The total of
; all the relative frequencies should equal 1.0.
; input: in, optional
; Set this keyword to a named variable that contains an array to be added to the
; output of cgHistogram. The density function of `data` is added to the existing
; contents of `Input` and returned as the result. The array is converted to
; longword type if necessary and must have at least as many elements as are
; required to form the histogram. Multiple histograms can be efficiently
; accumulated by specifying partial sums via this keyword.
; l64: in, optional, type=boolean, default=0
; If set, the return value of HISTOGRAM are 64-bit integers, rather than
; the default 32-bit integers. Set by default if 64-bit integers are passed in.
; locations: out, optional
; Starting locations of each bin. `Locations` has the same number of elements as the result,
; and has the same data type as the input data array.
; max: in, optional
; The maximum value to use in calculating input histogram.
; min: in, optional
; The minimum value to use in calculating input histogram.
; missing: in, optional
; The value that should be represented as "missing" and not used in the histogram.
; Be aware that if the input data is not of type "float" or "double" that the input
; data will be converted to floating point prior to calculating the histogram.
; nan: in, optional, type=boolean, default=0
; If set, ignore NAN values in calculating and plotting histogram. Set by default if the
; `Missing` keyword is used.
; nbins: in, optional, type=integer
; The number of output bins in the histogram. The meaning is slightly different from
; the meaning in the HISTOGRAM command. Used only to calculate BINSIZE when BINSIZE is
; not specified. In this case, binsize = rangeofData/(nbins-1). When the number of bins
; is low, the results can be non-intuitive. For this reason, I would discourage the use
; of `NBins` in favor of the `BinSize` keyword.
; omax: out, optional
; The maximum output value used to construct the histogram. (See HISTOGRAM documentation.)
; omin: out, optional
; The minimum output value used to construct the histogram. (See HISTOGRAM documentation.)
; reverse_indices: out, optional
; The list of reverse indices returned from the HISTOGRAM command. (See HISTOGRAM documentation.)
; smooth: in, optional, type=integer, default=0
; Set this keyword to an odd positive integer to smooth the histogram output before plotting.
; The integer will set the width of a smoothing box to be applied to the histogram data with
; the Smooth function. This keyword is ignored if the `Frequency` keyword is set.
;
; :Examples:
; Create a normal distribution of random numbers and take the histogram::
;
; numbers = RandomU(-3L, 1000, /Normal)
; histResults = cgHistogram(numbers, Binsize=0.25)
; cgPlot, histResults
;
; Additional examples of histogram plots can be found here::
;
; http://www.idlcoyote.com/gallery/index.html
;
; :Author:
; FANNING SOFTWARE CONSULTING::
; David W. Fanning
; 1645 Sheely Drive
; Fort Collins, CO 80526 USA
; Phone: 970-221-0438
; E-mail: david@idlcoyote.com
; Coyote's Guide to IDL Programming: http://www.idlcoyote.com
;
; :History:
; Change History::
; Written by: David W. Fanning, 7 March 2013.
;
; :Copyright:
; Copyright (c) 2013, Fanning Software Consulting, Inc.
;-
FUNCTION cgHistogram, $ ; The program name.
data, $ ; The data to draw a histogram of.
BINSIZE=binsize, $ ; The histogram bin size.
FREQUENCY=frequency, $ ; Plot relative frequency, rather than density.
INPUT=input, $ ; Add this array to output of cgHistogram.
L64=l64, $ ; Input for HISTOGRAM.
LOCATIONS=locations, $ ; The starting locations of each bin.
MAX=max, $ ; The maximum value to HISTOGRAM.
MIN=min, $ ; The minimum value to HISTOGRAM.
MISSING=missing, $ ; The value that indicates "missing" data to be excluded from the histgram.
NAN=nan, $ ; Check for NAN.
NBINS=nbins, $ ; The number of bins to display.
OMAX=omax, $ ; The maximum value used to construct the histogram.
OMIN=omin, $ ; The minimum value used to construct the histogram.
REVERSE_INDICES=ri, $ ; The vector that identifies indices in each bin.
SMOOTH=smooth ; Run a smoothing filter of this width over the histogram data before returning.
Compile_Opt idl2
; Catch any error in the cgHistogram program.
Catch, theError
IF theError NE 0 THEN BEGIN
Catch, /Cancel
ok = cgErrorMsg()
IF N_Elements(nancount) EQ 0 THEN BEGIN
IF N_Elements(_data) NE 0 THEN data = Temporary(_data)
ENDIF ELSE BEGIN
IF nancount EQ 0 THEN BEGIN
IF N_Elements(_data) NE 0 THEN data = Temporary(_data)
ENDIF
ENDELSE
RETURN, data
ENDIF
; Check for parameters.
IF N_Elements(data) EQ 0 THEN Message, 'Must pass data to cgHistogram.'
frequency = Keyword_Set(frequency)
l64 = Keyword_Set(l64)
IF N_Elements(smooth) NE 0 THEN BEGIN
IF (smooth MOD 2) NE 0 THEN smooth = smooth + 1
ENDIF
; What kind of data are we doing a HISTOGRAM on?
dataType = Size(data, /TYPE)
; If this is 64-bit integers, set the L64 flag.
IF dataType GE 14 THEN L64 =1
; Check the data for NANs and alert the user if the NAN keyword is not set.
IF dataType EQ 4 OR datatype EQ 5 THEN BEGIN
goodIndices = Where(Finite(data), count, NCOMPLEMENT=nancount, COMPLEMENT=nanIndices)
IF nancount GT 0 THEN BEGIN
IF ~Keyword_Set(nan) THEN BEGIN
Message, 'NANs found in the data. NAN keyword is set to 1.', /INFORMATIONAL
nan = 1
ENDIF
ENDIF
ENDIF
; The only sensible way to proceed is to make a copy of the data. Otherwise, I'll have
; a devil of a time putting it back together again at the end. There is a bug in
; HISTOGRAM when using BYTE data, so convert that here
IF N_Elements(_data) EQ 0 THEN BEGIN
IF Size(data, /TNAME) EQ 'BYTE' THEN BEGIN
_data = Fix(data)
ENDIF ELSE BEGIN
_data = data
ENDELSE
ENDIF
; If you have any "missing" data, then the data needs to be converted to float
; and the missing data set to F_NAN.
IF N_Elements(missing) NE 0 THEN BEGIN
missingIndices = Where(_data EQ missing, missingCount)
IF missingCount GT 0 THEN BEGIN
CASE datatype OF
4: _data[missingIndices] = !Values.F_NAN
5: _data[missingIndices] = !Values.D_NAN
ELSE: BEGIN
_data = Float(_data)
dataType = 4
_data[missingIndices] = !Values.F_NAN
END
ENDCASE
nan = 1
ENDIF ELSE BEGIN
IF missingCount EQ N_Elements(_data) THEN $
Message, 'All values are "missing"!'
ENDELSE
ENDIF
; Define minimum and maximum input values, if not defined otherwise.
IF N_Elements(min) EQ 0 THEN min = Min(_data, NAN=nan)
IF N_Elements(max) EQ 0 THEN max = Max(_data, NAN=nan)
; Check for histogram keywords.
IF N_Elements(binsize) EQ 0 THEN BEGIN
range = Max(_data < max, /NAN) - Min(_data > min, /NAN)
IF N_Elements(nbins) EQ 0 THEN BEGIN ; Scott's Choice
binsize = (3.5D * StdDev(min > _data < max, /NAN))/N_Elements(_data)^(1./3.0D)
IF (dataType LE 3) OR (dataType GE 12) THEN binsize = Round(binsize) > 1
binsize = Convert_To_Type(binsize, dataType)
ENDIF ELSE BEGIN
binsize = range / (nbins -1)
IF dataType LE 3 THEN binsize = Round(binsize) > 1
binsize = Convert_To_Type(binsize, dataType)
ENDELSE
ENDIF ELSE BEGIN
IF Size(binsize, /TYPE) NE dataType THEN BEGIN
IF dataType LE 3 THEN binsize = Round(binsize) > 1
binsize = Convert_To_Type(binsize, dataType)
ENDIF
ENDELSE
; Calculate the histogram. Can't use the INPUT keyword unless you actuall
; have something in it.
IF N_Elements(input) EQ 0 THEN BEGIN
histdata = Histogram(_data, $
BINSIZE=binsize, $
MAX=max, $
MIN=min, $
NAN=nan, $
LOCATIONS=locations, $
OMAX=omax, $
OMIN=omin, $
REVERSE_INDICES=ri)
ENDIF ELSE BEGIN
histdata = Histogram(_data, $
BINSIZE=binsize, $
INPUT=input, $
MAX=max, $
MIN=min, $
NAN=nan, $
LOCATIONS=locations, $
OMAX=omax, $
OMIN=omin, $
REVERSE_INDICES=ri)
ENDELSE
; Are you returning the frequency rather than the count? You can't smooth the frequency data.
IF frequency THEN BEGIN
histdata = Float(histdata)/N_Elements(_data)
ENDIF ELSE BEGIN
; Do you need to smooth the data?
IF N_Elements(smooth) NE 0 THEN histdata = Smooth(histdata, smooth)
ENDELSE
; Return the data.
RETURN, histdata
END
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