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covar2ellipse.pro
NAME: MPCHILIM
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 confidence limits for chi-square statistic
MAJOR TOPICS: Curve and Surface Fitting, Statistics
CALLING SEQUENCE: DELCHI = MPCHILIM(PROB, DOF, [/SIGMA, /CLEVEL, /SLEVEL ])
DESCRIPTION:
The function MPCHILIM() computes confidence limits of the chi-square statistic for a desired probability level. The returned values, DELCHI, are the limiting chi-squared values: a chi-squared value of greater than DELCHI will occur by chance with probability PROB:
P_CHI(CHI > DELCHI; DOF) = PROB
In specifying the probability level the user has three choices:
* give the confidence level (default);
* give the significance level (i.e., 1 - confidence level) and pass the /SLEVEL keyword; OR
* give the "sigma" of the probability (i.e., compute the probability based on the normal distribution) and pass the /SIGMA keyword.
Note that /SLEVEL, /CLEVEL and /SIGMA are mutually exclusive.
INPUTS:
PROB - scalar or vector number, giving the desired probability level as described above.
DOF - scalar or vector number, giving the number of degrees of freedom in the chi-square distribution.
RETURNS:
Returns a scalar or vector of chi-square confidence limits.
KEYWORD PARAMETERS:
SLEVEL - if set, then PROB describes the significance level.
CLEVEL - if set, then PROB describes the confidence level (default).
SIGMA - if set, then PROB is the number of "sigma" away from the mean in the normal distribution.
EXAMPLES:
print, mpchilim(0.99d, 2d, /clevel)
Print the 99% confidence limit for a chi-squared of 2 degrees of freedom.
print, mpchilim(5d, 2d, /sigma)
Print the "5 sigma" confidence limit for a chi-squared of 2 degrees of freedom. Here "5 sigma" indicates the gaussian probability of a 5 sigma event or greater. P_GAUSS(5D) = 1D - 5.7330314e-07
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 Usage message with /CONTINUE, 23 Sep 2009, CM
$Id: mpchilim.pro,v 1.8 2009/09/23 20:12:46 craigm Exp $
Routines
result = covar2ellipse(covar, nsigma=nsigma)NAME: COVAR2ELLIPSE()
cephes_setmacharresult = cephes_polevl(x, coef)function
result = cephes_ndtri(y0)result = cephes_igam(a, x)Incomplete gamma integral
result = cephes_igamc(a, x)Complemented incomplete gamma integral
result = cephes_igami(a, y0)Inverse of complemented imcomplete gamma integral
result = mpchilim(p, dof, sigma=sigma, clevel=clevel, slevel=slevel)GLS routines to calculate linear fit
Routine details
top source covar2ellipse
result = covar2ellipse(covar, nsigma=nsigma)
NAME: COVAR2ELLIPSE()
PURPOSE: Given a 2D covariance matrix, compute the parameters of the confidence ellipse.
INPUTS: covar - 2D covariance matrix
OPTIONAL INPUTS: nsigma - desired confidence interval; default is 1-sigma
KEYWORD PARAMETERS:
OUTPUTS: ellipse - data structure containing the parameters of the ellipse
OPTIONAL OUTPUTS:
COMMENTS: Based entirely on D. Coe's beautiful Fisher-matrix write-up, astro-ph/0906.3123.
EXAMPLES:
MODIFICATION HISTORY: J. Moustakas, 2010 Jul 09, UCSD
Copyright (C) 2010, John Moustakas
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
Parameters
- covar
Keywords
- nsigma
Statistics
| Lines: | 25 lines |
| McCabe complexity: | 1 |
top source cephes_polevl
result = cephes_polevl(x, coef)
function
Parameters
- x
- coef
Statistics
| Lines: | 7 lines |
| McCabe complexity: | 1 |
top source cephes_ndtri
result = cephes_ndtri(y0)
Parameters
- y0
Statistics
| Lines: | 118 lines |
| McCabe complexity: | 6 |
top source cephes_igam
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
Parameters
- a
- x
Statistics
| Lines: | 63 lines |
| McCabe complexity: | 1 |
top source cephes_igamc
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
Parameters
- a
- x
Statistics
| Lines: | 96 lines |
| McCabe complexity: | 3 |
top source cephes_igami
Inverse of complemented imcomplete gamma integral
SYNOPSIS:
double a, x, p, igami();
x = igami( a, p );
DESCRIPTION:
Given p, the function finds x such that
igamc( a, x ) = p.
Starting with the approximate value
3 x = a t
where
t = 1 - d - ndtri(p) sqrt(d)
and
d = 1/9a,
the routine performs up to 10 Newton iterations to find the root of igamc(a,x) - p = 0.
ACCURACY:
Tested at random a, p in the intervals indicated.
a p Relative error: arithmetic domain domain # trials peak rms IEEE 0.5,100 0,0.5 100000 1.0e-14 1.7e-15 IEEE 0.01,0.5 0,0.5 100000 9.0e-14 3.4e-15 IEEE 0.5,10000 0,0.5 20000 2.3e-13 3.8e-14
Parameters
- a
- y0
Statistics
| Lines: | 145 lines |
| McCabe complexity: | 21 |
File attributes
| Modification date: | Mon Apr 29 10:31:39 2013 |
| Lines: | 677 |