; docformat = 'rst' ; ; NAME: ; cgPercentiles ; ; PURPOSE: ; This program calculates user-specified percentiles of a data set. ; ;******************************************************************************************; ; ; ; 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 calculates user-specified percentiles of a data set. ; A percentile is the value of a variable below which a certain percent ; of observations fall. In other words, 75% of the values in a data set ; fall below the 75th percentile of the data. Computing percentiles is ; really nothing more than counting in a sorted input array. A box-and-whisker ; plot usually will display the 25th, 50th, and 75th percentiles. ; ; A `commercial version ` ; of this program, containing a DIMENSION keyword, can be purchased from the Coyote Store. The ; DIMENSION keyword allows the user to calculate the percentiles over a particular dimension ; of a multi-dimensional data set. ; ; :Categories: ; Math ; ; :Returns: ; The return value is either a scalar or vector of data values corresponding to ; the number of percentiles asked for with the `Percentiles` keyword, or a -1 if ; there is an error in the program. ; ; :Params: ; data: in, required ; The data from which percentiles are desired. A vector or an array. ; ; :Keywords: ; percentiles: in, optional, type=float ; Set this keyword to a scalar or vector of values between 0.0 and 1.0 ; to indicate the percentile desired. A value of 0.5 indicates the 50th ; percentile. Default value is [0.25, 0.50, 0.75]. ; ; :Examples: ; To return percentile values for 0.25, 0.50, and 0.75 of a data set:: ; IDL> data = Randomu(3L, 100) * 100 ; IDL> Print, cgPercentiles(data, Percentiles=[0.25, 0.5, 0.75]) ; 27.4920 45.3172 69.3138 ; ; :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, 3 June 2013 by David W. Fanning. ; ; :Copyright: ; Copyright (c) 2013, Fanning Software Consulting, Inc. ;- FUNCTION cgPercentiles, data, Percentiles=percentiles Compile_Opt idl2 ; Error handling. Catch, theError IF theError NE 0 THEN BEGIN Catch, /Cancel void = cgErrorMsg() RETURN, -1 ENDIF ; Assume the worst. result = -1 ; Input data is required. IF N_Elements(data) EQ 0 THEN Message, 'Input data is required.' ; Need default values for percentiles? IF N_Elements(percentiles) EQ 0 THEN percentiles = [0.25, 0.50, 0.75] ; Percentile values must be GE 0 and LE 1.0. index = Where((percentiles LT 0.0) OR (percentiles GT 1.0), count) IF count GT 0 THEN Message, 'Percentiles must be numbers between 0.0 and 1.0.' ; Count the data elements. num = N_Elements(data) ; Sort the data and find percentiles. sortIndex = Sort(data) sortIndices = cgScaleVector(Findgen(num+1), 0.0, 1.0) dataIndices = Value_Locate(sortIndices, percentiles) result = data[sortIndex[dataIndices]] RETURN, result END