Repatch (from linux) of OSX IRAF

11 files changed, 625 insertions, 0 deletions

diff --git a/math/nlfit/doc/nlerrors.hlp b/math/nlfit/doc/nlerrors.hlp
new file mode 100644
index 00000000..3b463c14
--- /dev/null
+++ b/math/nlfit/doc/nlerrors.hlp
@@ -0,0 +1,67 @@
+.help nlerrors Feb91 "Nlfit Package"
+.ih
+NAME
+nlerrors -- compute the fit statistics and errors in the parameters
+.ih
+SYNOPSIS
+nlerrors[rd] (nl, z, zfit, w, npts, variance, chisqr, errors)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	z[npts]		# array of input function values
+real/double	zfit[npts]	# array of fitted function values
+real/double	w[npts]		# array of weights
+int		npts		# number of data points
+real/double	variance	# the computed variance of the fit
+real/double	chisqr		# the computed reduced chi-square of the fit
+real/double	errors[*]	# errors in the fitted parameters
+.fi
+.ih
+ARGUMENTS
+.ls nl     
+Pointer to the curve descriptor structure.
+.le
+.ls z   
+Array of function values.
+.le
+.ls zfit  
+Array of fitted function values.
+.le
+.ls w
+Array of weights.
+.le
+.ls npts
+The number of data points.
+.le
+.ls variance
+The computed variance of the fit.
+.le
+.ls chisqr
+The computed reduced chi-squared of the fit.
+.le
+.ls errors
+Array of errors in the computed parameters.
+.le
+.ih
+DESCRIPTION
+Compute the variance and reduced chi-squared of the fit and the
+errors in the fitted parameters.
+.ih
+NOTES
+The reduced chi-squared of the fit is the square root of the sum of the
+weighted squares of the residuals divided by the number of degrees of freedom.
+The variance of the fit is the square root of the sum of the
+squares of the residuals divided by the number of degrees of freedom.
+If the weighting is uniform, then the reduced chi-squared is equal to the
+variance of the fit.
+The error of the j-th parameter is the square root of the j-th diagonal
+element of the inverse of the data matrix. If the weighting is uniform,
+then the errors are scaled by the square root of the variance of the data.
+
+The zfit array can be computed by a call to the nlvector[rd] routine.
+The size of the array required to hold the output error array can be
+determined by a call to nlstati.
+.ih
+SEE ALSO
+nlvector,nlstat
+.endhelp
diff --git a/math/nlfit/doc/nleval.hlp b/math/nlfit/doc/nleval.hlp
new file mode 100644
index 00000000..f0bbb400
--- /dev/null
+++ b/math/nlfit/doc/nleval.hlp
@@ -0,0 +1,35 @@
+.help nleval Feb91 "Nlfit Package"
+.ih
+NAME
+nleval -- evaluate the fitted function at a single point
+.ih
+SYNOPSIS
+z = nleval[rd] (nl, x, nvars)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	x[nvars]	# array of variables
+int		nvars		# the number of variables
+.fi
+.ih
+ARGUMENTS
+.ls nl    
+Pointer to the curve descriptor structure.
+.le
+.ls x   
+Array of variable values at which the curve is to be evaluated.
+.le
+.ls nvars
+The number of variables.
+.le
+.ih
+DESCRIPTION
+Evaluate the curve at the specified point. NLEVAL is a real or double
+function which returns the fitted z value.
+.ih
+NOTES
+NLEVAL uses the parameter array stored in the curve descriptor structure.
+.ih
+SEE ALSO
+nlvector
+.endhelp
diff --git a/math/nlfit/doc/nlfit.hd b/math/nlfit/doc/nlfit.hd
new file mode 100644
index 00000000..13bb3065
--- /dev/null
+++ b/math/nlfit/doc/nlfit.hd
@@ -0,0 +1,12 @@
+# Help directory for the NLFIT (non-linear least-squares fitting) package.
+
+$nlfit	= "math$nlfit/"
+
+nlerrors	hlp = nlerrors.hlp,	src = nlfit$nlerrorsr.x
+nleval		hlp = nleval.hlp,	src = nlfit$nlevalr.x
+nlinit		hlp = nlinit.hlp,	src = nlfit$nlinitr.x
+nlfit		hlp = nlfit.hlp,	src = nlfit$nlfitr.x
+nlfree		hlp = nlfree.hlp,	src = nlfit$nlfreer.x
+nlpget		hlp = nlpget.hlp,	src = nlfit$nlpgetr.x
+nlstat		hlp = nlstat.hlp,	src = nlfit$nlstatr.x
+nlvector	hlp = nlvector.hlp,	src = nlfit$nlvectorr.x
diff --git a/math/nlfit/doc/nlfit.hlp b/math/nlfit/doc/nlfit.hlp
new file mode 100644
index 00000000..8ed82512
--- /dev/null
+++ b/math/nlfit/doc/nlfit.hlp
@@ -0,0 +1,81 @@
+.help nlfit Feb91 "Nlfit Package"
+.ih
+NAME
+nlfit -- fit a curve to a set of data values
+.ih
+SYNOPSIS
+nlfit (nl, x, z, w, npts, nvars, wtflag, ier)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	x[npts*nvars]	# variable values (stored as x[nvars,npts])
+real/double	z[npts]		# array of z values
+real/double	w[npts]		# array of weights
+int		npts		# number of data points
+int		wtflag		# type of weighting
+int		ier		# error code
+.fi
+.ih
+ARGUMENTS
+.ls nl    
+Pointer to the curve descriptor structure.
+.le
+.ls x    
+Array of x values.
+.le
+.ls z
+Array of function values.
+.le
+.ls w
+Array of weights.
+.le
+.ls npts
+The number of data points.
+.le
+.ls wtflag
+Type of weighting. The options are WTS_USER, WTS_UNIFORM, WTS_CHISQ and
+WTS_SCATTER. If wtflag = WTS_USER individual weights for each data point
+are supplied by the calling program and points with zero-valued weights are
+not included in the fit. If wtflag = WTS_UNIFORM, all weights are assigned
+values of 1. If wtflag = WTS_CHISQ the weights are set equal to the
+reciprocal of the function value. If wtflag = WTS_SCATTER the fitting
+routine adds a scatter term to the weights if the reduced chi-squared of
+the fit is significantly greater than 1.
+.le
+.ls ier
+Error code for the fit. The options are DONE, SINGULAR,
+NO_DEG_FREEDOM and NOT_DONE. If ier = SINGULAR, the numerical routines
+will compute a
+solution but one or more of the coefficients will be
+zero. If ier = NO_DEG_FREEDOM, there were too few data points to solve the
+matrix equations and the routine returns without fitting the data.
+If ier = NOT_DONE, the fit could not achieve the desired tolerance with
+the given input data in the specified maximum number of iterations.
+.le
+.ih
+DESCRIPTION
+NLFIT accumulate the data into the appropriate internal matrices and vectors
+and does the fit.
+.ih
+NOTES
+The permitted values of the input wtflag argument to nlfit[rd] are the
+following.
+
+.nf
+define	WTS_USER			# User enters weights
+define	WTS_UNIFORM			# Equal weights
+define	WTS_CHISQ 			# Chi-squared weights
+define	WTS_SCATTER			# Weights include scatter term
+.fi
+
+The permitted error values returned from nlfit[rd] are the following.
+
+.nf
+define	DONE			0	# Solution converged
+define	SINGULAR		1	# Singular matrix
+define	NO_DEG_FREEDOM		2	# Too few points
+define	NOT_DONE		3	# Solution did not converge
+.fi
+.ih
+SEE ALSO
+.endhelp
diff --git a/math/nlfit/doc/nlfit.men b/math/nlfit/doc/nlfit.men
new file mode 100644
index 00000000..5fb68623
--- /dev/null
+++ b/math/nlfit/doc/nlfit.men
@@ -0,0 +1,8 @@
+      nlerrors - Compute the fits statistics and errors in the parameters
+	 nlfit - Fit the function
+	nlfree - Free memory allocated by nlinit
+	nlinit - Initialize the fitting routines
+	nlpget - Get the values of the fitted parameters
+        nlstat - Get the value of an NLFIT parameter
+	nleval - Evaluate the curve at a given point
+      nlvector - Evaluate the curve at an array of points 
diff --git a/math/nlfit/doc/nlfree.hlp b/math/nlfit/doc/nlfree.hlp
new file mode 100644
index 00000000..9688d5e7
--- /dev/null
+++ b/math/nlfit/doc/nlfree.hlp
@@ -0,0 +1,26 @@
+.help nlfree Feb91 "Nlfit Package"
+.ih
+NAME
+nlfree -- free the curve descriptor structure
+.ih
+SYNOPSIS
+nlfree[rd] (nl)
+
+.nf
+pointer	nl	# curve descriptor
+.fi
+.ih
+ARGUMENTS
+.ls nl     
+Pointer to the curve descriptor structure.
+.le
+.ih
+DESCRIPTION
+Frees the curve descriptor structure.
+.ih
+NOTES
+NLFREE should be called after each curve fit.
+.ih
+SEE ALSO
+nlinit
+.endhelp
diff --git a/math/nlfit/doc/nlinit.hlp b/math/nlfit/doc/nlinit.hlp
new file mode 100644
index 00000000..94e5e5a9
--- /dev/null
+++ b/math/nlfit/doc/nlinit.hlp
@@ -0,0 +1,86 @@
+.help nlinit Feb91 "Nlfit Package"
+.ih
+NAME
+nlinit -- initialise curve descriptor
+.ih
+SYNOPSIS
+include <math/nlfit.h>
+
+nlinit[rd] (nl, fnc, dfnc, params, dparams, nparams, plist, nfparams,
+                tol, itmax)
+
+.nf
+pointer		nl		# curve descriptor
+int		fnc		# address of first user-supplied function
+int		dfnc		# address of second user-supplied function
+real/double	params[nparams]	# list of initial parameter values
+real/double	dparams[nparams]# list of parameter increments
+int		nparams		# number of parameters
+int		plist[nparams]	# list of parameters to be fit
+int		nfparams	# number of parameters to be fit
+real/double	tol		# fitting tolerance
+int		itmax		# maximum number of iterations
+.fi
+.ih
+ARGUMENTS
+.ls nl             
+Pointer to the curve descriptor structure.
+.le
+.ls fnc       
+The address of the user-supplied subroutine fncname for evaluating the function
+to be fit. The calling sequence of fncname is the following.
+
+.nf
+fncname (x, nvars, params, nparams, zfit)
+.fi
+.le
+.ls dfnc       
+The address of the user-supplied subroutine dfncname for evaluating the
+function to be fit and its derivatives with respect to the parameters.
+The calling sequence of dfncname is the following.
+
+.nf
+dfncname (x, nvars, params, dparams, nparams, zfit, derivs)
+.fi
+.le
+.ls params
+An array containing initial values of all the parameters, including both
+those to be fit and those that are to be held constant.
+.le
+.ls dparams
+An array parameter increment values over which the derivatives are to be
+computed empirically. If equations are supplied for the derivatives
+inside dfnc, the dparams array is not used.
+.le
+.ls nparams
+The total number of parameters in the user-supplied function.
+.le
+.ls plist
+The list of parameters to be fit. Plist is an integer array containing
+the indices of those parameters in params to be fit.
+.le
+.ls nfparams
+The total number of parameters to be fit.
+.le
+.ls tol   
+The fitting tolerance. If the difference in the chi-squared
+from one iteration to the next is less than the fitting tolerance
+times the current chi-squared, the fit has converged.
+.le
+.ls itmax
+The maximum number of fitting iterations. Itmax must be greater than
+or equal to 3.
+.le
+.ih
+DESCRIPTION
+Allocate space for the curve descriptor structure and the arrays and
+vectors used by the numerical routines. Initialize all arrays and vectors
+to zero. Return the curve descriptor to the calling routine.
+.ih
+NOTES
+NLINIT must be the first NLFIT routine called. NLINIT returns a NULL pointer
+if it encounters an illegal parameter list.
+.ih
+SEE ALSO
+nlfree
+.endhelp
diff --git a/math/nlfit/doc/nllmfit.hlp b/math/nlfit/doc/nllmfit.hlp
new file mode 100644
index 00000000..59309133
--- /dev/null
+++ b/math/nlfit/doc/nllmfit.hlp
@@ -0,0 +1,172 @@
+.help nlfit Feb91 "Math Package"
+.ih
+NAME
+nlfit -- Levenberg-Marquardt non-linear least-squares fitting package
+.ih
+SYNOPSIS
+The principal entry points into the NLFIT package are listed below.
+
+.nf
+	nlinit - Initialize the fitting routines
+        nlstat - Get the value of an NLFIT parameter
+	nlpget - Get the values of the fitted parameters
+	nlfree - Free memory allocated by nlinit
+	 nlfit - Fit the function
+	nleval - Evaluate the curve at a given point
+      nlvector - Evaluate the curve at an array of points 
+      nlerrors - Compute the fits statistics and errors in the parameters
+.fi
+
+The calling sequences for the above routines are listed below. The [ird]
+stand for integer, real and double precision versions of each routine
+respectively.
+
+.nf
+            nlinit[rd] (nl, address(fnc), address(dfnc), params, dparams,
+	        nparams, plist, nfparams, tol, itmax)
+        ival = nlstati (nl, param)
+  [rd]val = nlstat[rd] (nl, param)
+            nlpget[rd] (nl, params, nparams)
+            nlfree[rd] (nl)
+             nlfit[rd] (nl, x, z, w, npts, nvars, wtflag, ier)
+  [rd]val = nleval[rd] (nl, x, nvars)
+          nlvector[rd] (nl, x, zfit, npts, nvars)
+          nlerrors[rd] (nl, z, zfit, wts, npts, variance, chisqr, errors)
+.fi
+
+The user supplied functions fnc and dfnc must have the following form.
+	
+.nf
+	       fnc (x, nvars, params, nparams, zfit)
+	      dfnc (x, nvars, params, dparams, nparams, zfit, derivs)
+.fi
+
+The addresses of these functions can be obtained by a call to lcopr as
+follows.
+
+.nf
+		address = locpr (fnc)
+.fi
+
+.ih
+DESCRIPTION
+The NLFIT package provides a set of routines for fitting data to non-linear
+functions of several variables using least squares techniques.
+NLFIT uses the Levenberg-Marquardt
+method to solve for the parameters of a user specified non-linear equation.
+The user must supply two subroutines. The first subroutine evaluates the
+function in terms of its parameters. The second subroutine evaluates the
+function and its derivatives in terms of its parameters.  The user must
+also supply initial
+guesses for the parameters and parameter increments, the list of
+parameters to be varied during the fitting process, a fitting
+tolerance and the maximum number of iterations. 
+.ih
+NOTES
+The poackage definitions for NLFIT can be found in the file 
+lib$math/nlfit.h. In order to make these definitions available
+to the calling program, the user must insert the statement
+"include <math/nlfit.h>" inside the calling program.
+
+The permitted values for the param argument in nlstat[ird] are the following.
+
+.nf
+define	NLNPARAMS	integer		# Number of parameters
+define	NLNFPARAMS	integer         # Number of fitted parameters
+define	NLITMAX		integer		# Maximum number of iterations
+define	NLITER		integer		# Current number of iterations
+define	NLNPTS		integer         # Number of points
+define	NLSUMSQ		real/double	# Current reduced chi-squared
+define	NLOLDSQ		real/double     # Previous reduced chi-squared
+define	NLLAMBDA	real/double     # Value of lambda factor
+define	NLTOL		real/double	# Fitting tolerance in %chi-squared
+define	NLSCATTER	real/double     # Mean scatter in the fit
+.fi
+
+The permitted values of the wtflag argument in nlfit[rd] are the following.
+
+.nf
+define	WTS_USER			# User enters weights
+define	WTS_UNIFORM			# Equal weights
+define	WTS_CHISQ 			# Chi-squared weights
+define	WTS_SCATTER			# Weights include scatter term
+.fi
+
+The permitted error values returned from nlfit[rd] are the following.
+
+.nf
+define	DONE			0	# Solution converged
+define	SINGULAR		1	# Singular matrix
+define	NO_DEG_FREEDOM		2	# Too few points
+define	NOT_DONE		3	# Solution did not converge
+.fi
+.ih
+REFERENCES
+1. Bevington,P.R., 1969, Data Reduction and Error Analysis for the Physical
+Sciences, Chapter 11, page 235.
+
+2. Press, W.H. et al., 1986, Numerical Recipes: The Art of Scientific
+Computing, Chapter 14, page 523
+.ih
+EXAMPLES
+.nf
+Example 1: Fit a curve to the data using uniform weighting. Fit all the
+parameters.
+
+    # Include nlfit definitions
+    include <math/nlfit.h>
+
+    # Declare the variables
+    int	nparams, nfparams, itmax, npts, nvars, ier
+    int	plist[nparams]
+    real tol, variance, chisqr
+    real params[nparams], dparams[nparams], vars[nvars,npts], z[npts]
+    real w[npts], zfit[npts], errors[nparams]
+
+    # Declare the functions
+    extern fncname(), dfncname()
+    int	locpr()
+
+    begin
+            ... get data, set initial values of all parameters, parameter
+	    ... increments, tol and itmax
+
+            # Define list of variables to be fitted
+            nfparams = nparams
+            do i = 1, nparams
+	        plist[i] = i
+
+	    # Fit only parameters 1,3 and 5
+	    #nfparams = 3
+	    #plist[1] = 1
+	    #plist[2] = 3
+	    #plist[3] = 5
+
+            # Initialize the fitting routines
+            call nlinitr (nl, locpr (fncname), locpr (dfncname),
+	        params, dparams, nparams, plist, nfparams, tol, itmax)
+
+            # Fit the data
+            call nlfitr (nl, x, z, w, npts, nvars, WTS_UNIFORM, ier)
+            if (ier != DONE)
+	        ... take error action
+
+            # Compute the statistics of the fit
+            call nlvectorr (nl, x, zfit, npts, nvars)
+            call nlerrorsr (nl, z, zfit, wts, npts, variance, chisqr,
+	        errors)
+
+            # Get the values of the fitted parameters
+            call nlpgetr (nl, params, nparams)
+            call nlfreer (nl)
+
+            # Print the parameters and their errors.
+            do i = 1, nparams {
+	        call printf ("%d  %g  %g\n")
+	        call pargi (i)
+	        call pargr (params[i])
+	        call pargr (errors[i])
+	    }
+    end
+.fi
+.endhelp
diff --git a/math/nlfit/doc/nlpget.hlp b/math/nlfit/doc/nlpget.hlp
new file mode 100644
index 00000000..07f2ef5e
--- /dev/null
+++ b/math/nlfit/doc/nlpget.hlp
@@ -0,0 +1,38 @@
+.help nlpget Feb91 "Nlfit Package"
+
+.ih
+NAME
+nlpget -- get the number and values of the fitted parameters
+.ih
+SYNOPSIS
+nlpget[rd] (nl, params, nparams)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	params[nparams]	# the parameters array
+int		nparams		# the number of parameters
+.fi
+.ih
+ARGUMENTS
+.ls nl
+Pointer to the curve descriptor.
+.le
+.ls params
+Array of fitted parameters.
+.le
+.ls nparameters
+The total number of parameters.
+.le
+.ih
+DESCRIPTION
+NLPGET fetches the parameters array and the number of parameters from the
+curve descriptor structure. All the parameters, both those that were
+fit and those that were held constant are output.
+.ih
+NOTES
+The array size required to hold the output parameters can be determined
+by a call to nlstati.
+.ih
+SEE ALSO
+nlstat
+.endhelp
diff --git a/math/nlfit/doc/nlstat.hlp b/math/nlfit/doc/nlstat.hlp
new file mode 100644
index 00000000..a745a663
--- /dev/null
+++ b/math/nlfit/doc/nlstat.hlp
@@ -0,0 +1,57 @@
+.help nlstat Feb91 "Nlfit Package"
+.ih
+NAME
+nlstat[ird] -- get an NLFIT parameter
+.ih
+SYNOPSIS
+include <math/nlfit.h>
+
+[ird]val = nlstat[ird] (nl, parameter)
+
+.nf
+pointer	nl		# curve descriptor
+int	parameter	# parameter to be returned
+.fi
+.ih
+ARGUMENTS
+.ls nl     
+The pointer to the curve descriptor structure.
+.le
+.ls parameter
+Parameter to be return.  Definitions in nlfit.h are:
+
+.nf
+NLNPARAMS	integer		# Number of parameters
+NLNFPARAMS	integer         # Number of fitted parameters
+NLITMAX		integer		# Maximum number of iterations
+NLITER		integer		# Current number of iterations
+NLNPTS		integer         # Number of points
+NLSUMSQ		real/double	# Current reduced chi-squared
+NLOLDSQ		real/double     # Previous reduced chi-squared
+NLLAMBDA	real/double     # Value of lambda factor
+NLTOL		real/double	# Fitting tolerance in %chi-squared
+NLSCATTER	real/double     # Mean scatter in the fit
+.fi
+.le
+.ih
+DESCRIPTION
+The values of integer, real or double  parameters are returned.
+The parameters include the number of parameters, the number of fitted
+parameters, the maximum number of iterations, the number of iterations,
+the total number of points, the current chi-squared, the previous
+chi-squared, the lambda factor, the fitting tolerance and the fitted
+scatter term.
+.ih
+EXAMPLES
+.nf
+include <math/nlfit.h>
+
+int	nlstati()
+
+call malloc (buf, nlstati (nl, NLNPARAMS), TY_REAL)
+call nlpgetr (nl, Memr[buf], nparams)
+.fi
+.ih
+SEE ALSO
+nlpget
+.endhelp
diff --git a/math/nlfit/doc/nlvector.hlp b/math/nlfit/doc/nlvector.hlp
new file mode 100644
index 00000000..98308cc3
--- /dev/null
+++ b/math/nlfit/doc/nlvector.hlp
@@ -0,0 +1,43 @@
+.help nlvector Feb91 "Nlfit Package"
+.ih
+NAME
+nlvector -- evaluate the fitted curve at a set of points
+.ih
+SYNOPSIS
+nlvector[rd] (nl, x, zfit, npts, nvars)
+
+.nf
+pointer		nl		# curve descriptor
+real/double	x[nvars*npts]	# array of variables stored as x[nvars,npts]
+real/double	zfit[npts]	# array of fitted function values
+int		npts		# number of data points
+int		nvars		# number of variables
+.fi
+.ih
+ARGUMENTS
+.ls nl   
+Pointer to the curve descriptor structure.
+.le
+.ls x     
+Array of variable values for all the data points.
+.le
+.ls zfit   
+Array of fitted function values.
+.le
+.ls npts   
+The number of data points at which the curve is to be evaluated.
+.le
+.ls nvars
+The number of variables in the fitted function.
+.le
+.ih
+DESCRIPTION
+Fit the curve to an array of data points.
+.ih
+NOTES
+NLVECTOR uses the coefficient array stored in the curfit descriptor
+structure.
+.ih
+SEE ALSO
+nleval
+.endhelp