Changeset 3757 for trunk/doc/pslib/psLibSDRS.tex

Timestamp:

Apr 21, 2005, 3:32:15 PM (21 years ago)

Author:

Paul Price

Message:

Changes after conversation with George

File:

• trunk/doc/pslib/psLibSDRS.tex (modified) (7 diffs)

trunk/doc/pslib/psLibSDRS.tex

@@ -1 @@
-%%% $Id: psLibSDRS.tex,v 1.204 2005-04-21 23:48:57 price Exp $
+%%% $Id: psLibSDRS.tex,v 1.205 2005-04-22 01:32:15 price Exp $
 \documentclass[panstarrs,spec]{panstarrs}
 
@@ -2224 +2224 @@
 use Chebyshev polynomials ($\sum_{i=0}^n a_i T_i(x)$), which have
 properties which are useful in the modeling of data over a defined
-domain.
+domain.  Note that Chebyshev polynomials should only have inputs in
+the range $-1 \le x \le +1$ (because they are bounded over this
+range), but we will not enforce this.
 
 This leads us to define the following polynomial types:
@@ -2339 +2341 @@
 implementation).  The \code{knots} member specifies the boundaries
 between each spline piece (including the two ends).  The \code{knots}
-vector may be of type U32, F32 or F64.
+vector may be of type U32 or F32.
 
 Of course, we require the appropriate constructors and destructor:
@@ -2368 +2370 @@
 
 \begin{verbatim}
-psF64 psSpline1DEval(const psSpline1D *spline, float x);
+float psSpline1DEval(const psSpline1D *spline, float x);
 psVector *psSpline1DEvalVector(const psSpline1D *spline, const psVector *x);
 \end{verbatim}
@@ -2487 +2489 @@
 for types \code{psF32}, \code{psF64}.
 
-\subsubsubsection{Pre-defined Functions for LM}
-
-We define some commonly used functions for use with the LM
-minimization, used for the purpose of performing $\chi^2$ fitting:
-
-\begin{verbatim}
-psMinimizeLMChi2Func psMinimizeLMChi2Gauss1D;
-psMinimizeLMChi2Func psMinimizeLMChi2Gauss2D;
-\end{verbatim}
-
-\code{psMinimizeChi2LMGauss1D} shall take as \code{params}, the
-normalization, center, and standard deviation of a Gaussian to be fit,
-and as \code{x}, a vector containing a single value.  It shall return
-the value of the Gaussian at the value, and the derivatives
-(\code{deriv}) with respect to each of the parameters.
-
-\code{psMinimizeChi2LMGauss2D} shall take, as \code{params}, the
-normalization, center (two values), standard deviation (two values)
-and position angle of a 2-dimensional Gaussian, and as \code{x}, a
-vector containing a position, $(x,y)$.  It shall return the value of
-the 2-dimensional Gaussian at the specified point, along with the
-derivatives with respect to each of the parameters.
+%% \subsubsubsection{Pre-defined Functions for LM}
+
+%% We define some commonly used functions for use with the LM
+%% minimization, used for the purpose of performing $\chi^2$ fitting:
+
+%% \begin{verbatim}
+%% psMinimizeLMChi2Func psMinimizeLMChi2Gauss1D;
+%% psMinimizeLMChi2Func psMinimizeLMChi2Gauss2D;
+%% \end{verbatim}
+
+%% \code{psMinimizeChi2LMGauss1D} shall take as \code{params}, the
+%% normalization, center, and standard deviation of a Gaussian to be fit,
+%% and as \code{x}, a vector containing a single value.  It shall return
+%% the value of the Gaussian at the value, and the derivatives
+%% (\code{deriv}) with respect to each of the parameters.
+
+%% \code{psMinimizeChi2LMGauss2D} shall take, as \code{params}, the
+%% normalization, center (two values), standard deviation (two values)
+%% and position angle of a 2-dimensional Gaussian, and as \code{x}, a
+%% vector containing a position, $(x,y)$.  It shall return the value of
+%% the 2-dimensional Gaussian at the specified point, along with the
+%% derivatives with respect to each of the parameters.
 
 \subsubsection{Powell}
@@ -2587 +2589 @@
 
 \begin{verbatim}
-psSpline1D *psVectorFitSpline1D(psSpline1D *mySpline,
-                                const psVector *x,
-                                const psVector *y);
+psSpline1D *psVectorFitSpline1D(const psVector *x,
+                                const psVector *y
+                                int nKnots);
 \end{verbatim}
 \code{psVectorFitSpline1D} shall return the spline that best fits the
 given combination of ordinates (\code{x}) and coordinates (\code{y}).
-The function shall construct a new \code{psSpline1D} based on knots
-determined from \code{x}: the domain boundaries are the data values in
-\code{x}.  As is the case for \code{psVectorFitPolynomial1D}, if
-\code{x} is \code{NULL}, then the index of \code{y} shall be used as
-the ordinate.  This function must be valid only for types
-\code{psF32}, \code{psF64}.
+The function shall construct a new \code{psSpline1D} using
+\code{nKnots} knots uniformly distributed over \code{x}.  As is the
+case for \code{psVectorFitPolynomial1D}, if \code{x} is \code{NULL},
+then the index of \code{y} shall be used as the ordinate.  This
+function must be valid only for types \code{psF32}, \code{psF64}.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -3226 +3227 @@
 \end{itemize}
 The corresponding APIs follow.
+
+In the event of an error, the matrix functions shall return \code{NULL}.
 
 \begin{verbatim}