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;
; NAME:
; cgRandomWald
;
; PURPOSE:
;
; This function creates a vector of N random numbers using an Inverse Gaussian Distribution,
; which is also known as the Wald Distribution. The reference for the code can be found at
; http://en.wikipedia.org/wiki/Inverse_Gaussian_distribution.
;******************************************************************************************;
; ;
; Copyright (c) 2012, 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 function creates a vector of N random numbers using an Inverse Gaussian Distribution,
; which is also known as the Wald Distribution. The reference for the code can be found at
; http://en.wikipedia.org/wiki/Inverse_Gaussian_distribution.
;
; :Categories:
; Utility
;
; :Params:
; seed: in, optional
; The seed for the random number generator. If undefined, on output will
; have the seed used by the IDL RandomU function. See the documentation
; for RandomU for additional information.
; dims: in, optional, type=integer
; A scalar or integer array defining the dimensions of the result. If no dimensions
; are specified, a single random number is returned. If `Dims` is a scalar, a 1D vector
; of that number of values will be returned.
;
; :Keywords:
; mu: in, optional, type=double, default=1.0
; The mean of the distribution.
; lambda: in, optional, type=double, default=1.0
; The shape parameter of the distribution. As lambda tends to infinity, the inverse
; distribution becomes more like a normal distribution.
;
; :Examples:
; For example, to create 100 random numbers, using the Wald distribution::
; wald = cgRandomWald(seed, 100)
; To create a 20-column by 10-row array of random numbers::
; wald = cgRandoWald(seed, [20,10])
;
; :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:
; Written, 25 Oct 2012, by David W. Fanning.
;
; :Copyright:
; Copyright (c) 2012, Fanning Software Consulting, Inc.
;-
FUNCTION cgRandomWald, seed, dims, MU=mu, LAMBDA=lambda
Compile_Opt idl2
; Return to the caller on an error.
On_Error, 2
; Handle the number of input parameters appropriately.
CASE N_Params() OF
0: dims = 1
1: dims = 1
2:
ENDCASE
; Check for keywords.
IF N_Elements(mu) EQ 0 THEN mu = 1D ELSE mu = Double(mu)
IF N_Elements(lambda) EQ 0 THEN lambda = 1D ELSE lambda = Double(lambda)
; Define parameters for the inverse Gaussian distribution.
nu = RandomN(seed, dims)
z = RandomU(seed, dims)
randomNumbers = DblArr(dims)
; Implement the algorithm given in the Wikipedia reference above.
y = nu^2
x = mu + mu^2.0*y/(2.0*lambda) - mu/2.0/lambda*SQRT(4.0*mu*lambda*y + mu^2*y^2)
indices = Where(z LE mu/(mu+x), Complement=cindices, indicesCnt, NComplement=cindicesCnt)
IF indicesCnt GT 0 THEN randomNumbers[indices] = x[indices]
IF cindicesCnt GT 0 THEN randomNumbers[cindices] = (mu^2/x)[cindices]
RETURN, randomNumbers
END
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