/usr/share/gnudatalanguage/mpfit/mpchitest.pro is in gdl-mpfit 1.85+2017.01.03-1.
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; NAME:
; MPCHITEST
;
; AUTHOR:
; Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
; craigm@lheamail.gsfc.nasa.gov
; UPDATED VERSIONs can be found on my WEB PAGE:
; http://cow.physics.wisc.edu/~craigm/idl/idl.html
;
; PURPOSE:
; Compute the probability of a given chi-squared value
;
; MAJOR TOPICS:
; Curve and Surface Fitting, Statistics
;
; CALLING SEQUENCE:
; PROB = MPCHITEST(CHI, DOF, [/SIGMA, /CLEVEL, /SLEVEL ])
;
; DESCRIPTION:
;
; The function MPCHITEST() computes the probability for a value drawn
; from the chi-square distribution to equal or exceed the given value
; CHI. This can be used for confidence testing of a measured value
; obeying the chi-squared distribution.
;
; P_CHI(X > CHI; DOF) = PROB
;
; In specifying the returned probability level the user has three
; choices:
;
; * return the confidence level when the /CLEVEL keyword is passed;
; OR
;
; * return the significance level (i.e., 1 - confidence level) when
; the /SLEVEL keyword is passed (default); OR
;
; * return the "sigma" of the probability (i.e., compute the
; probability based on the normal distribution) when the /SIGMA
; keyword is passed.
;
; Note that /SLEVEL, /CLEVEL and /SIGMA are mutually exclusive.
;
; INPUTS:
;
; CHI - chi-squared value to be tested.
;
; DOF - scalar or vector number, giving the number of degrees of
; freedom in the chi-square distribution.
;
; RETURNS:
;
; Returns a scalar or vector of probabilities, as described above,
; and according to the /SLEVEL, /CLEVEL and /SIGMA keywords.
;
; KEYWORD PARAMETERS:
;
; SLEVEL - if set, then PROB describes the significance level
; (default).
;
; CLEVEL - if set, then PROB describes the confidence level.
;
; SIGMA - if set, then PROB is the number of "sigma" away from the
; mean in the normal distribution.
;
; EXAMPLES:
;
; print, mpchitest(1300d,1252d)
;
; Print the probability for a chi-squared value with 1252 degrees of
; freedom to exceed a value of 1300, as a confidence level.
;
; REFERENCES:
;
; Algorithms taken from CEPHES special function library, by Stephen
; Moshier. (http://www.netlib.org/cephes/)
;
; MODIFICATION HISTORY:
; Completed, 1999, CM
; Documented, 16 Nov 2001, CM
; Reduced obtrusiveness of common block and math error handling, 18
; Nov 2001, CM
; Convert to IDL 5 array syntax (!), 16 Jul 2006, CM
; Move STRICTARR compile option inside each function/procedure, 9 Oct 2006
; Add usage message, 24 Nov 2006, CM
; Really add usage message, with /CONTINUE, 23 Sep 2009, CM
;
; $Id: mpchitest.pro,v 1.10 2009/10/05 16:22:44 craigm Exp $
;-
; Copyright (C) 1997-2001, 2006, 2009, Craig Markwardt
; This software is provided as is without any warranty whatsoever.
; Permission to use, copy, modify, and distribute modified or
; unmodified copies is granted, provided this copyright and disclaimer
; are included unchanged.
;-
forward_function cephes_igamc, cephes_igam
;; Set machine constants, once for this session. Double precision
;; only.
pro cephes_setmachar
COMPILE_OPT strictarr
common cephes_machar, cephes_machar_vals
if n_elements(cephes_machar_vals) GT 0 then return
if (!version.release) LT 5 then dummy = check_math(1, 1)
mch = machar(/double)
machep = mch.eps
maxnum = mch.xmax
minnum = mch.xmin
maxlog = alog(mch.xmax)
minlog = alog(mch.xmin)
maxgam = 171.624376956302725D
cephes_machar_vals = {machep: machep, maxnum: maxnum, minnum: minnum, $
maxlog: maxlog, minlog: minlog, maxgam: maxgam}
if (!version.release) LT 5 then dummy = check_math(0, 0)
return
end
function cephes_igam, a, x
;
; Incomplete gamma integral
;
;
;
; SYNOPSIS:
;
; double a, x, y, igam();
;
; y = igam( a, x );
;
; DESCRIPTION:
;
; The function is defined by
;
; x
; -
; 1 | | -t a-1
; igam(a,x) = ----- | e t dt.
; - | |
; | (a) -
; 0
;
;
; In this implementation both arguments must be positive.
; The integral is evaluated by either a power series or
; continued fraction expansion, depending on the relative
; values of a and x.
;
; ACCURACY:
;
; Relative error:
; arithmetic domain # trials peak rms
; IEEE 0,30 200000 3.6e-14 2.9e-15
; IEEE 0,100 300000 9.9e-14 1.5e-14
COMPILE_OPT strictarr
common cephes_machar, machvals
MAXLOG = machvals.maxlog
MACHEP = machvals.machep
if x LE 0 OR a LE 0 then return, 0.D
if x GT 1. AND x GT a then return, 1.D - cephes_igamc(a, x)
ax = a * alog(x) - x - lngamma(a)
if ax LT -MAXLOG then begin
; message, 'WARNING: underflow', /info
return, 0.D
endif
ax = exp(ax)
r = a
c = 1.D
ans = 1.D
repeat begin
r = r + 1
c = c * x/r
ans = ans + c
endrep until (c/ans LE MACHEP)
return, ans*ax/a
end
function cephes_igamc, a, x
;
; Complemented incomplete gamma integral
;
;
;
; SYNOPSIS:
;
; double a, x, y, igamc();
;
; y = igamc( a, x );
;
; DESCRIPTION:
;
; The function is defined by
;
;
; igamc(a,x) = 1 - igam(a,x)
;
; inf.
; -
; 1 | | -t a-1
; = ----- | e t dt.
; - | |
; | (a) -
; x
;
;
; In this implementation both arguments must be positive.
; The integral is evaluated by either a power series or
; continued fraction expansion, depending on the relative
; values of a and x.
;
; ACCURACY:
;
; Tested at random a, x.
; a x Relative error:
; arithmetic domain domain # trials peak rms
; IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
; IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
COMPILE_OPT strictarr
if n_params() EQ 0 then begin
message, 'USAGE: PROB = MPCHITEST(CHI, DOF, [/SIGMA, /CLEVEL, /SLEVEL ])', /info
return, !values.d_nan
endif
common cephes_machar, machvals
MAXLOG = machvals.maxlog
MACHEP = machvals.machep
big = 4.503599627370496D15
biginv = 2.22044604925031308085D-16
if x LE 0 OR a LE 0 then return, 1.D
if x LT 1. OR x LT a then return, 1.D - cephes_igam(a, x)
ax = a * alog(x) - x - lngamma(a)
if ax LT -MAXLOG then begin
; message, 'ERROR: underflow', /info
return, 0.D
endif
ax = exp(ax)
y = 1.D - a
z = x + y + 1.D
c = 0.D
pkm2 = 1.D
qkm2 = x
pkm1 = x + 1.D
qkm1 = z * x
ans = pkm1 / qkm1
repeat begin
c = c + 1.D
y = y + 1.D
z = z + 2.D
yc = y * c
pk = pkm1 * z - pkm2 * yc
qk = qkm1 * z - qkm2 * yc
if qk NE 0 then begin
r = pk/qk
t = abs( (ans-r)/r )
ans = r
endif else begin
t = 1.D
endelse
pkm2 = pkm1
pkm1 = pk
qkm2 = qkm1
qkm1 = qk
if abs(pk) GT big then begin
pkm2 = pkm2 * biginv
pkm1 = pkm1 * biginv
qkm2 = qkm2 * biginv
qkm1 = qkm1 * biginv
endif
endrep until t LE MACHEP
return, ans * ax
end
; MPCHITEST
; compute the probability for a chi-squared value to exceed x give
; the number of degrees of freedom dof.
function mpchitest, x, dof, slevel=slevel, clevel=clevel, sigma=sigma
COMPILE_OPT strictarr
if n_params() LT 2 then begin
message, 'USAGE: PROB = MPCHITEST(CHI, DOF, [/SIGMA, /CLEVEL, /SLEVEL ])', /cont
return, !values.d_nan
endif
cephes_setmachar ;; Set machine constants
p = double(x) * 0
for i = 0, n_elements(x)-1 do begin
p[i] = cephes_igamc(0.5D * dof, 0.5D * double(x[i]))
endfor
if keyword_set(clevel) then return, 1D - double(p)
if keyword_set(sigma) then return, mpnormlim(p, /slevel)
return, p
end
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