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Last modified: Wed May 20 22:19:22 1998.
NAME:
CURVEFIT
PURPOSE:
Non-linear least squares fit to a function of an arbitrary
number of parameters. The function may be any non-linear
function. If available, partial derivatives can be calculated by
the user function, else this routine will estimate partial derivatives
with a forward difference approximation.
CATEGORY:
E2 - Curve and Surface Fitting.
CALLING SEQUENCE:
Result = CURVEFIT(X, Y, W, A, SIGMAA, FUNCTION_NAME = name, $
ITMAX=ITMAX, ITER=ITER, TOL=TOL, /NODERIVATIVE)
INPUTS:
X: A row vector of independent variables. This routine does
not manipulate or use values in X, it simply passes X
to the user-written function.
Y: A row vector containing the dependent variable.
W: A row vector of weights, the same length as Y.
For no weighting,
w(i) = 1.0.
For instrumental weighting,
w(i) = 1.0/y(i), etc.
A: A vector, with as many elements as the number of terms, that
contains the initial estimate for each parameter. If A is double-
precision, calculations are performed in double precision,
otherwise they are performed in single precision.
KEYWORDS:
FUNCTION_NAME: The name of the function (actually, a procedure) to
fit. If omitted, "FUNCT" is used. The procedure must be written as
described under RESTRICTIONS, below.
ITMAX: Maximum number of iterations. Default = 20.
ITER: The actual number of iterations which were performed
TOL: The convergence tolerance. The routine returns when the
relative decrease in chi-squared is less than TOL in an
interation. Default = 1.e-3.
CHI2: The value of chi-squared on exit
NODERIVATIVE: If this keyword is set then the user procedure will not
be requested to provide partial derivatives. The partial
derivatives will be estimated in CURVEFIT using forward
differences. If analytical derivatives are available they
should always be used.
OUTPUTS:
Returns a vector of calculated values.
A: A vector of parameters containing fit.
OPTIONAL OUTPUT PARAMETERS:
Sigmaa: A vector of standard deviations for the parameters in A.
COMMON BLOCKS:
NONE.
SIDE EFFECTS:
None.
RESTRICTIONS:
The function to be fit must be defined and called FUNCT,
unless the FUNCTION_NAME keyword is supplied. This function,
(actually written as a procedure) must accept values of
X (the independent variable), and A (the fitted function's
parameter values), and return F (the function's value at
X), and PDER (a 2D array of partial derivatives).
For an example, see FUNCT in the IDL User's Libaray.
A call to FUNCT is entered as:
FUNCT, X, A, F, PDER
where:
X = Variable passed into CURVEFIT. It is the job of the user-written
function to interpret this variable.
A = Vector of NTERMS function parameters, input.
F = Vector of NPOINT values of function, y(i) = funct(x), output.
PDER = Array, (NPOINT, NTERMS), of partial derivatives of funct.
PDER(I,J) = DErivative of function at ith point with
respect to jth parameter. Optional output parameter.
PDER should not be calculated if the parameter is not
supplied in call. If the /NODERIVATIVE keyword is set in the
call to CURVEFIT then the user routine will never need to
calculate PDER.
PROCEDURE:
Copied from "CURFIT", least squares fit to a non-linear
function, pages 237-239, Bevington, Data Reduction and Error
Analysis for the Physical Sciences.
"This method is the Gradient-expansion algorithm which
combines the best features of the gradient search with
the method of linearizing the fitting function."
Iterations are performed until the chi square changes by
only TOL or until ITMAX iterations have been performed.
The initial guess of the parameter values should be
as close to the actual values as possible or the solution
may not converge.
EXAMPLE: Fit a function of the form f(x) = a * exp(b*x) + c to
sample pairs contained in x and y.
In this example, a=a(0), b=a(1) and c=a(2).
The partials are easily computed symbolicaly:
df/da = exp(b*x), df/db = a * x * exp(b*x), and df/dc = 1.0
Here is the user-written procedure to return F(x) and
the partials, given x:
pro gfunct, x, a, f, pder ; Function + partials
bx = exp(a(1) * x)
f= a(0) * bx + a(2) ;Evaluate the function
if N_PARAMS() ge 4 then $ ;Return partials?
pder= [[bx], [a(0) * x * bx], [replicate(1.0, N_ELEMENTS(y))]]
end
x=findgen(10) ;Define indep & dep variables.
y=[12.0, 11.0,10.2,9.4,8.7,8.1,7.5,6.9,6.5,6.1]
w=1.0/y ;Weights
a=[10.0,-0.1,2.0] ;Initial guess
yfit=curvefit(x,y,w,a,sigmaa,function_name='gfunct')
print, 'Function parameters: ', a
print, yfit
end
MODIFICATION HISTORY:
Written, DMS, RSI, September, 1982.
Does not iterate if the first guess is good. DMS, Oct, 1990.
Added CALL_PROCEDURE to make the function's name a parameter.
(Nov 1990)
12/14/92 - modified to reflect the changes in the 1991
edition of Bevington (eq. II-27) (jiy-suggested by CreaSo)
Mark Rivers, U of Chicago, Feb. 12, 1995
- Added following keywords: ITMAX, ITER, TOL, CHI2, NODERIVATIVE
These make the routine much more generally useful.
- Removed Oct. 1990 modification so the routine does one iteration
even if first guess is good. Required to get meaningful output
for errors.
- Added forward difference derivative calculations required for
NODERIVATIVE keyword.
- Fixed a bug: PDER was passed to user's procedure on first call,
but was not defined. Thus, user's procedure might not calculate
it, but the result was then used.
(See /deep0/marc/idlshare/Nbody/profiles/my_curvefit.pro)
NAME:
FIT_GEN
PURPOSE:
Fit an NFW profile to the density profile of a dark matter
halo.
CATEGORY:
Nbody/profile
CALLING SEQUENCE:
fitted = fit_gen( r, den, fit_param, fit_errors, weight )
INPUTS:
r -- Radii at which the density is tabulated.
den -- Tabulated density to which the NFW profile should be
fit.
fit_param -- On input, a guess as to the scale radius and
characteristic density of the profile. ALSO USED
FOR OUTPUT.
weight -- Vector of weights to be used in fitting. Default is
same weight (1.0) for each point.
KEYWORD PARAMETERS:
/FIXED_MASS -- Set this keyword to require that the total mass
of the halo be the number of particles. This
reduces the number of parameters being fit to
one, the scale radius.
OUTPUTS:
fitted -- The best fit density profile, evaluated at the
points r.
fit_param -- On output, the parameters of the fit. ALSO USED
FOR INPUT.
fit_errors -- The standard deviations in the fits parameters,
as determined by the CURVEFIT procedure.
COMMON BLOCKS:
COMMON nfw_fit_params, UseFixedParmsCmn, BetaFixed, AlphaFixed
UseFixedParms -- Set to one if this routine is to use the
fixed values of alpha and beta specified in
the common block.
BetaFixed -- Value of Beta to use if Beta is to be held
fixed.
AlphaFixed -- Value of Beta to use if Beta is to be held
fixed.
SIDE EFFECTS:
NOTES:
The density profiles fit here are the following:
\rho = \rho_a/r^\beta/(r+a)^\alpha
We actually fit to the log of this,
log(\rho) = \log(\rho_a) - \beta \log(r)
- \alpha \log(r+a).
The input parmaters are used as follows:
Params(0) = \rho_a
Params(1) = a
Params(2) = \alpha
Params(3) = \beta.
HOWEVER, if Params(3) is not passed, we set \beta=1, and if
Params(2) is not passed, we set \alpha=2.
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
log_nfw_fit
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/fit_gen.pro)
NAME:
FIT_HERN
PURPOSE:
Fit a Hernquist profile to the density profile of a dark matter
halo.
CATEGORY:
Nbody/profile
CALLING SEQUENCE:
fitted = fit_hern( r, den, fit_param, fit_errors, weight )
INPUTS:
r -- Radii at which the density is tabulated.
den -- Tabulated density to which the Hernquist profile should be
fit.
fit_param -- On input, a guess as to the scale radius and
characteristic density of the profile. ALSO USED
FOR OUTPUT.
weight -- Vector of weights to be used in fitting. Default is
same weight (1.0) for each point.
KEYWORD PARAMETERS:
/FIXED_MASS -- Set this keyword to require that the total mass
of the halo be the number of particles. This
reduces the number of parameters being fit to
one, the scale radius.
OUTPUTS:
fitted -- The best fit density profile, evaluated at the
points r.
fit_param -- On output, the parameters of the fit. ALSO USED
FOR INPUT.
fit_errors -- The standard deviations in the fits parameters,
as determined by the CURVEFIT procedure.
COMMON BLOCKS:
COMMON nfw_fit_params, UseFixedParmsCmn, BetaFixed, AlphaFixed
UseFixedParms -- Set to one if this routine is to use the
fixed values of alpha and beta specified in
the common block.
BetaFixed -- Value of Beta to use if Beta is to be held
fixed.
AlphaFixed -- Value of Beta to use if Beta is to be held
fixed.
SIDE EFFECTS:
NOTES:
The density profiles fit here are the following:
\rho = \rho_a/r/(r+a)^3
We actually fit to the log of this,
log(\rho) = \log(\rho_a) - \log(r)
- \log(r+a).
The input parmaters are used as follows:
Params(0) = \rho_a
Params(1) = a
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
log_nfw_fit
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/fit_hern.pro)
NAME:
FIT_NFW
PURPOSE:
Fit an NFW profile to the density profile of a dark matter
halo.
CATEGORY:
Nbody/profile
CALLING SEQUENCE:
fitted = fit_nfw( r, den, fit_param, fit_errors, weight )
INPUTS:
r -- Radii at which the density is tabulated.
den -- Tabulated density to which the NFW profile should be
fit.
fit_param -- On input, a guess as to the scale radius and
characteristic density of the profile. ALSO USED
FOR OUTPUT.
weight -- Vector of weights to be used in fitting. Default is
same weight (1.0) for each point.
KEYWORD PARAMETERS:
/FIXED_MASS -- Set this keyword to require that the total mass
of the halo be the number of particles. This
reduces the number of parameters being fit to
one, the scale radius.
OUTPUTS:
fitted -- The best fit density profile, evaluated at the
points r.
fit_param -- On output, the parameters of the fit. ALSO USED
FOR INPUT.
fit_errors -- The standard deviations in the fits parameters,
as determined by the CURVEFIT procedure.
COMMON BLOCKS:
COMMON nfw_fit_params, UseFixedParmsCmn, BetaFixed, AlphaFixed
UseFixedParms -- Set to one if this routine is to use the
fixed values of alpha and beta specified in
the common block.
BetaFixed -- Value of Beta to use if Beta is to be held
fixed.
AlphaFixed -- Value of Beta to use if Beta is to be held
fixed.
SIDE EFFECTS:
NOTES:
The density profiles fit here are the following:
\rho = \rho_a/r^\beta/(r+a)^\alpha
We actually fit to the log of this,
log(\rho) = \log(\rho_a) - \beta \log(r)
- \alpha \log(r+a).
The input parmaters are used as follows:
Params(0) = \rho_a
Params(1) = a
Params(2) = \alpha
Params(3) = \beta.
HOWEVER, if Params(3) is not passed, we set \beta=1, and if
Params(2) is not passed, we set \alpha=2.
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
log_nfw_fit
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/fit_nfw.pro)
NAME:
FIT_NFW
PURPOSE:
Fit an NFW profile to the density profile of a dark matter
halo.
CATEGORY:
Nbody/profile
CALLING SEQUENCE:
fitted = fit_nfw( r, den, fit_param, fit_errors, weight )
INPUTS:
r -- Radii at which the density is tabulated.
den -- Tabulated density to which the NFW profile should be
fit.
fit_param -- On input, a guess as to the scale radius and
characteristic density of the profile. ALSO USED
FOR OUTPUT.
weight -- Vector of weights to be used in fitting. Default is
same weight (1.0) for each point.
KEYWORD PARAMETERS:
/FIXED_MASS -- Set this keyword to require that the total mass
of the halo be the number of particles. This
reduces the number of parameters being fit to
one, the scale radius.
OUTPUTS:
fitted -- The best fit density profile, evaluated at the
points r.
fit_param -- On output, the parameters of the fit. ALSO USED
FOR INPUT.
fit_errors -- The standard deviations in the fits parameters,
as determined by the CURVEFIT procedure.
COMMON BLOCKS:
COMMON nfw_fit_params, UseFixedParmsCmn, BetaFixed, AlphaFixed
UseFixedParms -- Set to one if this routine is to use the
fixed values of alpha and beta specified in
the common block.
BetaFixed -- Value of Beta to use if Beta is to be held
fixed.
AlphaFixed -- Value of Beta to use if Beta is to be held
fixed.
SIDE EFFECTS:
NOTES:
The density profiles fit here are the following:
\rho = \rho_a/r^\beta/(r+a)^\alpha
We actually fit to the log of this,
log(\rho) = \log(\rho_a) - \beta \log(r)
- \alpha \log(r+a).
The input parmaters are used as follows:
Params(0) = \rho_a
Params(1) = a
Params(2) = \alpha
Params(3) = \beta.
HOWEVER, if Params(3) is not passed, we set \beta=1, and if
Params(2) is not passed, we set \alpha=2.
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
log_nfw_fit
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/my_nfw_fit.pro)
NAME:
FIT_NFW_VCIRC
PURPOSE:
Fit an NFW profile to the rotation curve of a dark matter
halo.
CATEGORY:
Nbody/profile
CALLING SEQUENCE:
fitted = fit_nfw_vcirc( r, vcirc, fit_param, fit_errors, weight )
INPUTS:
r -- Radii at which the density is tabulated.
vcirc -- Tabulated circular velocity to which the NFW profile
should be fit.
fit_param -- On input, a guess as to the scale radius and
characteristic density of the profile. ALSO USED
FOR OUTPUT.
weight -- Vector of weights to be used in fitting. Default is
same weight (1.0) for each point.
KEYWORD PARAMETERS:
OUTPUTS:
fitted -- The best fit velocity profile, evaluated at the
points r.
fit_param -- On output, the parameters of the fit. ALSO USED
FOR INPUT.
fit_errors -- The standard deviations in the fits parameters,
as determined by the CURVEFIT procedure.
COMMON BLOCKS:
COMMON nfw_fit_params, UseFixedParmsCmn, BetaFixed, AlphaFixed
UseFixedParms -- Set to one if this routine is to use the
fixed values of alpha and beta specified in
the common block.
BetaFixed -- Value of Beta to use if Beta is to be held
fixed.
AlphaFixed -- Value of Beta to use if Beta is to be held
fixed.
SIDE EFFECTS:
NOTES:
The circular velocity fit here is:
V_c = B \sqrt{(\ln{1+r/a} - r/(r+a))/r},
which corresponds to the density profile:
\rho = B^2/(4\pi)/r/(r+a)^2.
The input parmaters are used as follows:
Params(0) = \rho_a
Params(1) = a
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
nfw_vcirc_fit
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/fit_nfw_vcirc.pro)
NAME:
LOG_NFW_FIT
PURPOSE:
Fit log density profile to nbody data.
CATEGORY:
NBody/profile
CALLING SEQUENCE:
log_nfw_fit, x, params, logden, logdenderiv
INPUTS:
X -- Positions at which density profile is to be
evaluated.
Params -- Values of fitting parameters for density
profile. See Notes below for details.
KEYWORD PARAMETERS:
OUTPUTS:
LogDen -- Log of the density evaluated at X.
LogDenDeriv -- Derivative of the log of the density evaluated
at X.
COMMON BLOCKS:
COMMON nfw_fit_params, UseFixedParmsCmn, BetaFixed, AlphaFixed
UseFixedParms -- Set to one if this routine is to use the
fixed values of alpha and beta specified in
the common block.
BetaFixed -- Value of Beta to use if Beta is to be held
fixed.
AlphaFixed -- Value of Beta to use if Beta is to be held
fixed.
SIDE EFFECTS:
NOTES:
The density profiles fit here are the following:
\rho = \rho_a/r^\beta/(r+a)^\alpha
We actually fit to the log of this,
log(\rho) = \log(\rho_a) - \beta \log(r)
- \alpha \log(r+a).
The input parmaters are used as follows:
Params(0) = \rho_a
Params(1) = a
Params(2) = \alpha
Params(3) = \beta.
HOWEVER, if Params(3) is not passed, we set \beta=1, and if
Params(2) is not passed, we set \alpha=2.
UNLESS, that is, UseFixedParmsCmn is nonzero, then use the
values of \alpha and \beta in the common block, but do not
allow them to vary.
EXAMPLE:
x=2.*findgen(100)/99.+.01 & Parmas=[10.,.2,2.5,1.1]
log_nfw_fit,x, Params, Den
returns Den evaluated at X with \rho_a=10., a=.2, \alpha=2.5,
\beta=1.1
x=2.*findgen(100)/99.+.01 & Parmas=[10.,.2]
log_nfw_fit,x, Params, Den
returns Den evaluated at X with \rho_a=10., a=.2, \alpha=2.,
\beta=1.
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/log_nfw_fit.pro)
NAME:
NFW_DELTA_C
PURPOSE:
Return the characteristic density for NFW profile, given
concentration, c.
CATEGORY:
nbody/profiles
CALLING SEQUENCE:
delta_c = nfw_delta_c( c )
INPUTS:
c -- Concentration parameter.
KEYWORD PARAMETERS:
OUTPUTS:
delta_c -- Characteristic density for given value of c.
COMMON BLOCKS:
SIDE EFFECTS:
NOTES:
The formula for \delta_c is (NFW, ApJ v.462, p.563):
\delta_c = \frac{200}{3} \frac{c^3}{\ln{1+c} - c/(c+1)}
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/nfw_delta_c.pro)
NAME:
NFW_DENSITY
PURPOSE:
Return density as a function of radius in NFW halo model.
CATEGORY:
profiles
CALLING SEQUENCE:
Density = nfw_density( Radius, ScaleRadius )
INPUTS:
Radius -- Radii at which the density is desired.
ScaleRadius -- Scale radius that enters into model, in same
units as Radius.
KEYWORD PARAMETERS:
OUTPUTS:
Density -- Density evaluated at input radii.
COMMON BLOCKS:
SIDE EFFECTS:
NOTES:
The density is normalized by the mean density within radius
one.
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/nfw_density.pro)
NAME:
NFW_GEN_FROM_FIT
PURPOSE:
Generate the desired profile (mass, rotation, or density) from
a fit to one of them.
CATEGORY:
Nbody/profile
CALLING SEQUENCE:
func = nfw_gen_from_fit( R, Params )
INPUTS:
R -- Radii at which to evaluate the profile.
Params -- Fitting parameters which describe the fit. It is a
two element vector--see Notes for a description of
the elements.
KEYWORD PARAMETERS:
/DENSITY -- Set to return the NFW density profile (DEFAULT).
/MASS -- Set to return the NFW mass profile.
/VCIRC -- Set to return the NFW cirvular velocity profile.
/FROM_DENSITY -- Set if fit params are to NFW density profile
(DEFAULT).
/FROM_MASS -- Set if fit params are to NFW mass profile (DEFAULT).
/FROM_VCIRC -- Set if fit params are to NFW circular
velocity profile.
OUTPUTS:
func -- either the NFW density, mass or circular velocity,
depending on which keyword has been set, evaluted at R.
COMMON BLOCKS:
SIDE EFFECTS:
NOTES:
The input parameters in Params are:
Params(0) - Normaliztaion factor (i.e. characteristic
density or mass or velocity), from a fit to
an NFW profile.
Params(1) - NFW scale radius, in the same units as R.
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/nfw_gen_from_fit.pro)
NAME:
NFW_MASS
PURPOSE:
Return mass as a function of radius in NFW halo model.
CATEGORY:
profiles
CALLING SEQUENCE:
Mass = nfw_mass( Radius, ScaleRadius )
INPUTS:
Radius -- Radii at which the mass is desired.
ScaleRadius -- Scale radius that enters into model, in same
units as Radius.
KEYWORD PARAMETERS:
OUTPUTS:
Mass -- Mass evaluated at input radii.
COMMON BLOCKS:
SIDE EFFECTS:
NOTES:
The mass is normalized so that the mass within radius one is
one.
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/nfw_mass.pro)
NAME:
NFW_VCIRC
PURPOSE:
Return circular velocity as a function of radius in NFW halo
model.
CATEGORY:
profiles
CALLING SEQUENCE:
Vcirc = nfw_vcirc( Radius, ScaleRadius )
INPUTS:
Radius -- Radii at which the vcirc is desired.
ScaleRadius -- Scale radius that enters into model, in same
units as Radius.
KEYWORD PARAMETERS:
OUTPUTS:
Vcirc -- Vcirc evaluated at input radii.
COMMON BLOCKS:
SIDE EFFECTS:
NOTES:
The circular velocity returned is normalized to the circular
velocity at radius one.
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/nfw_vcirc.pro)
NAME:
NFW_VCIRC_FIT
PURPOSE:
Fit NFW circular velocity profile to rotation curve.
CATEGORY:
NBody/profile
CALLING SEQUENCE:
nfw_vcirc_fit, X, Params, Vcirc, VcircDeriv
INPUTS:
X -- Positions at which density profile is to be
evaluated.
Params -- Values of fitting parameters for density
profile. See Notes below for details.
KEYWORD PARAMETERS:
OUTPUTS:
Vcirc -- Circular velocity evaluated at X.
VcircDeriv -- Derivative of the circular velocity with
respect to the fit parameters, evaluated at X.
COMMON BLOCKS:
COMMON nfw_fit_vcirc_params, UseFixedParmsCmn, BetaFixed, AlphaFixed
UseFixedParms -- Set to one if this routine is to use the
fixed values of alpha and beta specified in
the common block.
BetaFixed -- Value of Beta to use if Beta is to be held
fixed.
AlphaFixed -- Value of Beta to use if Beta is to be held
fixed.
SIDE EFFECTS:
NOTES:
The circular velocity fit here is:
V_c = B \sqrt{(\ln{1+r/a} - r/(r+a))/r},
which corresponds to the density profile:
\rho = B^2/(4\pi)/r/(r+a)^2.
The input parmaters are used as follows:
Params(0) = \rho_a
Params(1) = a
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/nfw_vcirc_fit.pro)
NAME:
PURPOSE:
CATEGORY:
CALLING SEQUENCE:
INPUTS:
KEYWORD PARAMETERS:
OUTPUTS:
COMMON BLOCKS:
SIDE EFFECTS:
NOTES:
We are fitting:
\rho = \rho_f/(a+x)^\alpha
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/log_andi_bad.pro)
NAME:
PURPOSE:
CATEGORY:
CALLING SEQUENCE:
INPUTS:
KEYWORD PARAMETERS:
OUTPUTS:
COMMON BLOCKS:
SIDE EFFECTS:
NOTES:
We are fitting:
\rho = \rho_f/(a+x)/(x^2+a^2)
for \rho_f and a.
EXAMPLE:
LIBRARY FUNCTIONS CALLED:
MODIFICATION HISTORY:
$Id$
$Log$
RELEASE:
$Name$
(See /deep0/marc/idlshare/Nbody/profiles/log_andi_fit.pro)