upgrade ast 8.7.1

1 files changed, 2629 insertions, 0 deletions

diff --git a/ast/lutmap.c b/ast/lutmap.c
new file mode 100644
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+++ b/ast/lutmap.c
@@ -0,0 +1,2629 @@
+/*
+*class++
+*  Name:
+*     LutMap
+
+*  Purpose:
+*     Transform 1-dimensional coordinates using a lookup table.
+
+*  Constructor Function:
+c     astLutMap
+f     AST_LUTMAP
+
+*  Description:
+*     A LutMap is a specialised form of Mapping which transforms
+*     1-dimensional coordinates by using linear interpolation in a
+*     lookup table.
+*
+*     Each input coordinate value is first scaled to give the index of
+*     an entry in the table by subtracting a starting value (the input
+*     coordinate corresponding to the first table entry) and dividing
+*     by an increment (the difference in input coordinate value
+*     between adjacent table entries).
+*
+*     The resulting index will usually contain a fractional part, so
+*     the output coordinate value is then generated by interpolating
+*     linearly between the appropriate entries in the table. If the
+*     index lies outside the range of the table, linear extrapolation
+*     is used based on the two nearest entries (i.e. the two entries
+*     at the start or end of the table, as appropriate). If either of the
+*     entries used for the interplation has a value of AST__BAD, then the
+*     interpolated value is returned as AST__BAD.
+*
+*     If the lookup table entries increase or decrease monotonically
+*     (ignoring any flat sections), then the inverse transformation may
+*     also be performed.
+
+*  Inheritance:
+*     The LutMap class inherits from the Mapping class.
+
+*  Attributes:
+*     In addition to those attributes common to all Mappings, every
+*     LutMap also has the following attributes:
+*
+*     - LutEpsilon: The relative error of the values in the table.
+*     - LutInterp: The interpolation method to use between table entries.
+
+*  Functions:
+c     The LutMap class does not define any new functions beyond those
+f     The LutMap class does not define any new routines beyond those
+*     which are applicable to all Mappings.
+
+*  Copyright:
+*     Copyright (C) 1997-2006 Council for the Central Laboratory of the
+*     Research Councils
+*     Copyright (C) 2007-2011 Science & Technology Facilities Council.
+*     All Rights Reserved.
+
+*  Licence:
+*     This program is free software: you can redistribute it and/or
+*     modify it under the terms of the GNU Lesser General Public
+*     License as published by the Free Software Foundation, either
+*     version 3 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 Lesser General Public License for more details.
+*
+*     You should have received a copy of the GNU Lesser General
+*     License along with this program.  If not, see
+*     <http://www.gnu.org/licenses/>.
+
+*  Authors:
+*     RFWS: R.F. Warren-Smith (Starlink)
+*     DSB: David S. Berry (JAC, UCLan)
+
+*  History:
+*     8-JUL-1997 (RFWS):
+*        Original version.
+*     10-JUL-1997 (RFWS):
+*        Added the MapMerge function.
+*     8-JAN-2003 (DSB):
+*        Changed private InitVtab method to protected astInitLutMapVtab
+*        method.
+*     12-JAN-2004 (DSB):
+*        Check for AST__BAD values in the supplied lut array.
+*     17-MAR-2006 (DSB):
+*        - MapMerge changed so that a LutMap will cancel with its own
+*        inverse.
+*        - Added attribute LutInterp
+*     10-MAY-2006 (DSB):
+*        Override astEqual.
+*     4-OCT-2006 (DSB):
+*        - Correct "mintick" to "lutinterp" in SetAttrib.
+*        - Do not include bad values in the dumped LUT array.
+*     8-NOV-2007 (DSB):
+*        - Take account of the requested invert flag when comparing two
+*        neighbouring LutMaps for equality in MapMerge.
+*     19-NOV-2010 (DSB):
+*        Added (protected) astGetLutMapInfo function.
+*     24-JAN-2011 (DSB):
+*        Implement an inverse transformation even if the coordinate
+*        array contains sections of equal or bad values. The inverse
+*        transformation will generate bad values if used within such
+*        regions of the coordinate array.
+*     6-JUL-2011 (DSB):
+*        Avoid indexing the lut array beyond the end when doing an
+*        inverse transform.
+*     2-OCT-2012 (DSB):
+*        Check for Infs as well as NaNs.
+*     21-MAY-2015 (DSB):
+*        Aded LutEpsilon
+*     23-SEP-2015 (DSB):
+*        The GetMonotonic function had a bug that caused all LutMaps
+*        to be considered monotonic, and thus have an inverse
+*        transformation.
+*class--
+*/
+
+/* Module Macros. */
+/* ============== */
+/* Set the name of the class we are implementing. This indicates to
+   the header files that define class interfaces that they should make
+   "protected" symbols available. */
+#define astCLASS LutMap
+
+#define LINEAR 0
+#define NEAR 1
+
+/* Include files. */
+/* ============== */
+/* Interface definitions. */
+/* ---------------------- */
+
+#include "globals.h"             /* Thread-safe global data access */
+#include "error.h"               /* Error reporting facilities */
+#include "memory.h"              /* Memory management facilities */
+#include "object.h"              /* Base Object class */
+#include "pointset.h"            /* Sets of points/coordinates */
+#include "mapping.h"             /* Coordinate mappings (parent class) */
+#include "winmap.h"              /* Linear mappings between windows */
+#include "channel.h"             /* I/O channels */
+#include "unitmap.h"             /* Unit mappings */
+#include "lutmap.h"              /* Interface definition for this class */
+#include "globals.h"             /* Thread-safe global data access */
+
+/* Error code definitions. */
+/* ----------------------- */
+#include "ast_err.h"             /* AST error codes */
+
+/* C header files. */
+/* --------------- */
+#include <float.h>
+#include <math.h>
+#include <limits.h>
+#include <stdarg.h>
+#include <stddef.h>
+#include <stdio.h>
+#include <string.h>
+
+/* Module Variables. */
+/* ================= */
+
+/* Address of this static variable is used as a unique identifier for
+   member of this class. */
+static int class_check;
+
+/* Pointers to parent class methods which are extended by this class. */
+static AstPointSet *(* parent_transform)( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static const char *(* parent_getattrib)( AstObject *, const char *, int * );
+static int (* parent_testattrib)( AstObject *, const char *, int * );
+static void (* parent_clearattrib)( AstObject *, const char *, int * );
+static void (* parent_setattrib)( AstObject *, const char *, int * );
+
+/* Define macros for accessing each item of thread specific global data. */
+#ifdef THREAD_SAFE
+
+/* Define how to initialise thread-specific globals. */
+#define GLOBAL_inits \
+   globals->Class_Init = 0; \
+   globals->GetAttrib_Buff[ 0 ] = 0;
+
+/* Create the function that initialises global data for this module. */
+astMAKE_INITGLOBALS(LutMap)
+
+/* Define macros for accessing each item of thread specific global data. */
+#define class_init astGLOBAL(LutMap,Class_Init)
+#define class_vtab astGLOBAL(LutMap,Class_Vtab)
+#define getattrib_buff astGLOBAL(LutMap,GetAttrib_Buff)
+
+
+
+/* If thread safety is not needed, declare and initialise globals at static
+   variables. */
+#else
+
+static char getattrib_buff[ 101 ];
+
+
+/* Define the class virtual function table and its initialisation flag
+   as static variables. */
+static AstLutMapVtab class_vtab;   /* Virtual function table */
+static int class_init = 0;       /* Virtual function table initialised? */
+
+#endif
+
+/* External Interface Function Prototypes. */
+/* ======================================= */
+/* The following functions have public prototypes only (i.e. no
+   protected prototypes), so we must provide local prototypes for use
+   within this module. */
+AstLutMap *astLutMapId_( int, const double [], double, double, const char *, ... );
+
+/* Prototypes for Private Member Functions. */
+/* ======================================== */
+static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
+static int GetLinear( AstMapping *, int * );
+static int GetMonotonic( int, const double *, int *, double **, int **, int **, int * );
+static int MapMerge( AstMapping *, int, int, int *, AstMapping ***, int **, int * );
+static void Copy( const AstObject *, AstObject *, int * );
+static void Delete( AstObject *, int * );
+static void Dump( AstObject *, AstChannel *, int * );
+static int Equal( AstObject *, AstObject *, int * );
+static double *GetLutMapInfo( AstLutMap *, double *, double *, int *, int * );
+
+static const char *GetAttrib( AstObject *, const char *, int * );
+static int TestAttrib( AstObject *, const char *, int * );
+static void ClearAttrib( AstObject *, const char *, int * );
+static void SetAttrib( AstObject *, const char *, int * );
+
+static int GetLutInterp( AstLutMap *, int * );
+static int TestLutInterp( AstLutMap *, int * );
+static void ClearLutInterp( AstLutMap *, int * );
+static void SetLutInterp( AstLutMap *, int, int * );
+
+static double GetLutEpsilon( AstLutMap *, int * );
+static int TestLutEpsilon( AstLutMap *, int * );
+static void ClearLutEpsilon( AstLutMap *, int * );
+static void SetLutEpsilon( AstLutMap *, double, int * );
+
+/* Member functions. */
+/* ================= */
+static void ClearAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     ClearAttrib
+
+*  Purpose:
+*     Clear an attribute value for a LutMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     void ClearAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     LutMap member function (over-rides the astClearAttrib protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function clears the value of a specified attribute for a
+*     LutMap, so that the default value will subsequently be used.
+
+*  Parameters:
+*     this
+*        Pointer to the LutMap.
+*     attrib
+*        Pointer to a null-terminated string specifying the attribute
+*        name.  This should be in lower case with no surrounding white
+*        space.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   AstLutMap *this;             /* Pointer to the LutMap structure */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the LutMap structure. */
+   this = (AstLutMap *) this_object;
+
+/* Check the attribute name and clear the appropriate attribute. */
+
+/* LutInterp. */
+/* ---------- */
+   if ( !strcmp( attrib, "lutinterp" ) ) {
+      astClearLutInterp( this );
+
+/* LutEpsilon. */
+/* ------------- */
+   } else if ( !strcmp( attrib, "lutepsilon" ) ) {
+      astClearLutEpsilon( this );
+
+/* If the attribute is still not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      (*parent_clearattrib)( this_object, attrib, status );
+   }
+}
+
+static int Equal( AstObject *this_object, AstObject *that_object, int *status ) {
+/*
+*  Name:
+*     Equal
+
+*  Purpose:
+*     Test if two LutMaps are equivalent.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     int Equal( AstObject *this, AstObject *that, int *status )
+
+*  Class Membership:
+*     LutMap member function (over-rides the astEqual protected
+*     method inherited from the astMapping class).
+
+*  Description:
+*     This function returns a boolean result (0 or 1) to indicate whether
+*     two LutMaps are equivalent.
+
+*  Parameters:
+*     this
+*        Pointer to the first Object (a LutMap).
+*     that
+*        Pointer to the second Object.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     One if the LutMaps are equivalent, zero otherwise.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global status set, or if it should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstLutMap *that;
+   AstLutMap *this;
+   int i;
+   int nin;
+   int nout;
+   int result;
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain pointers to the two LutMap structures. */
+   this = (AstLutMap *) this_object;
+   that = (AstLutMap *) that_object;
+
+/* Check the second object is a LutMap. We know the first is a
+   LutMap since we have arrived at this implementation of the virtual
+   function. */
+   if( astIsALutMap( that ) ) {
+
+/* Get the number of inputs and outputs and check they are the same for both. */
+      nin = astGetNin( this );
+      nout = astGetNout( this );
+      if( astGetNin( that ) == nin && astGetNout( that ) == nout ) {
+
+/* If the Invert flags for the two LutMaps differ, it may still be possible
+   for them to be equivalent. First compare the LutMaps if their Invert
+   flags are the same. In this case all the attributes of the two LutMaps
+   must be identical. */
+         if( astGetInvert( this ) == astGetInvert( that ) ) {
+
+            if( astEQUAL( this->start, that->start ) &&
+                astEQUAL( this->inc, that->inc ) &&
+                this->nlut == that->nlut &&
+                this->lutinterp == that->lutinterp ){
+
+               result = 1;
+               for( i = 0; i < this->nlut; i++ ) {
+                  if( !astEQUAL( (this->lut)[ i ], (that->lut)[ i ] ) ) {
+                     result = 0;
+                     break;
+                  }
+               }
+            }
+
+/* If the Invert flags for the two LutMaps differ, the attributes of the two
+   LutMaps must be inversely related to each other. */
+         } else {
+
+/* In the specific case of a LutMap, Invert flags must be equal. */
+            result = 0;
+         }
+      }
+   }
+
+/* If an error occurred, clear the result value. */
+   if ( !astOK ) result = 0;
+
+/* Return the result, */
+   return result;
+}
+
+static const char *GetAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     GetAttrib
+
+*  Purpose:
+*     Get the value of a specified attribute for a LutMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     const char *GetAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     LutMap member function (over-rides the protected astGetAttrib
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function returns a pointer to the value of a specified
+*     attribute for a LutMap, formatted as a character string.
+
+*  Parameters:
+*     this
+*        Pointer to the LutMap.
+*     attrib
+*        Pointer to a null-terminated string containing the name of
+*        the attribute whose value is required. This name should be in
+*        lower case, with all white space removed.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     - Pointer to a null-terminated string containing the attribute
+*     value.
+
+*  Notes:
+*     - The returned string pointer may point at memory allocated
+*     within the LutMap, or at static memory. The contents of the
+*     string may be over-written or the pointer may become invalid
+*     following a further invocation of the same function or any
+*     modification of the LutMap. A copy of the string should
+*     therefore be made if necessary.
+*     - A NULL pointer will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*/
+
+/* Local Variables: */
+   AstLutMap *this;             /* Pointer to the LutMap structure */
+   astDECLARE_GLOBALS           /* Pointer to thread-specific global data */
+   const char *result;          /* Pointer value to return */
+   double luteps;               /* LutEpsilon attribute value */
+   int lutinterp;               /* LutInterp attribute value */
+
+/* Initialise. */
+   result = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(this_object);
+
+/* Obtain a pointer to the LutMap structure. */
+   this = (AstLutMap *) this_object;
+
+/* Compare "attrib" with each recognised attribute name in turn,
+   obtaining the value of the required attribute. If necessary, write
+   the value into "getattrib_buff" as a null-terminated string in an appropriate
+   format.  Set "result" to point at the result string. */
+
+/* LutInterp. */
+/* ---------- */
+   if ( !strcmp( attrib, "lutinterp" ) ) {
+      lutinterp = astGetLutInterp( this );
+      if ( astOK ) {
+         (void) sprintf( getattrib_buff, "%d", lutinterp );
+         result = getattrib_buff;
+      }
+
+/* LutEpsilon. */
+/* ------------- */
+   } else if ( !strcmp( attrib, "lutepsilon" ) ) {
+      luteps = astGetLutEpsilon( this );
+      if ( astOK ) {
+         (void) sprintf( getattrib_buff, "%.*g", AST__DBL_DIG, luteps );
+         result = getattrib_buff;
+      }
+
+/* If the attribute name was not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      result = (*parent_getattrib)( this_object, attrib, status );
+   }
+
+/* Return the result. */
+   return result;
+
+}
+
+static int GetLinear( AstMapping *this_mapping, int *status ) {
+/*
+*  Name:
+*     GetLinear
+
+*  Purpose:
+*     Determine if a LutMap implements a linear coordinate transformation.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     int GetLinear( AstMapping *this, int *status )
+
+*  Class Membership:
+*     LutMap member function.
+
+*  Description:
+*     This function returns a boolean value to indicate if the LutMap
+*     supplied is equivalent to a linear coordinate
+*     transformation. This will be the case if the lookup table
+*     elements increase or decrease linearly.
+
+*  Parameters:
+*     this
+*        Pointer to the LutMap.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*    - A value of zero will be returned if this function is invoked
+*    with the global error status set, or if it should fail for any
+*    reason.
+*/
+
+/* Local Variables: */
+   AstLutMap *this;              /* Pointer to the LutMap structure */
+   double *lut;                  /* Pointer to the lookup table */
+   double eps;                   /* Relative error on the table values */
+   double fract;                 /* Fractional position within table */
+   double hi;                    /* Largest value */
+   double interp;                /* Interpolated value */
+   double lo;                    /* Smallest value */
+   double tol1;                  /* First tolerance estimate */
+   double tol2;                  /* Second tolerance estimate */
+   double tol;                   /* Tolerance value used */
+   int ilut;                     /* Loop counter for table elements */
+   int linear;                   /* Result to be returned */
+   int nlut;                     /* Number of lookup table elements */
+
+/* Initialise. */
+   linear = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return linear;
+
+/* Obtain a pointer to the LutMap structure. */
+   this = (AstLutMap *) this_mapping;
+
+/* Nearest neighbour LutMaps are not considered to be linear because of
+   the discontinuities at the start and end of the table. */
+   if( astGetLutInterp( this ) != NEAR ) {
+
+/* Obtain the lookup table details. */
+      lut = this->lut;
+      nlut = this->nlut;
+
+/* Loop to identify the largest and smallest values in the lookup
+      table. */
+      lo = DBL_MAX;
+      hi = -DBL_MAX;
+      for ( ilut = 0; ilut < nlut; ilut++ ) {
+         if ( lut[ ilut ] > hi ) hi = lut[ ilut ];
+         if ( lut[ ilut ] < lo ) lo = lut[ ilut ];
+      }
+
+/* Check if the values are all the same (this makes the LutMap
+      linear, although it will have no inverse). */
+      linear = ( hi == lo );
+      if ( !linear ) {
+
+/* Get the relative error associated with the table values. */
+         eps = astGetLutEpsilon( this );
+
+/* Form a tolerance estimate based on the overall range of values in
+   the lookup table. */
+         tol1 = fabs( hi - lo ) * eps;
+
+/* Now loop to inspect all the lookup table elements except the first
+      and last. */
+         linear = 1;
+         for ( ilut = 1; ilut < ( nlut - 1 ); ilut++ ) {
+
+/* Calculate the fractional position of the current element within the
+      table. */
+            fract = ( (double) ilut ) / ( (double) ( nlut - 1 ) );
+
+/* Calculate the value it should have if the table is linear by
+      interpolating between the first and last values. */
+            interp = lut[ 0 ] * ( 1.0 - fract ) + lut[ nlut - 1 ] * fract;
+
+/* Form a second tolerance estimate from this interpolated
+   value. Select whichever tolerance estimate is larger (this avoids
+   problems when values are near zero). */
+            tol2 = fabs( interp ) * eps;
+            tol = ( tol1 > tol2 ) ? tol1 : tol2;
+
+/* Test for linearity within a small multiple of the tolerance. */
+            linear = ( fabs( lut[ ilut ] - interp ) <= ( 2.0 * tol ) );
+            if ( !linear ) break;
+         }
+      }
+   }
+
+/* Return the result. */
+   return linear;
+}
+
+static double *GetLutMapInfo( AstLutMap *this, double *start, double *inc,
+                              int *nlut, int *status ){
+/*
+*  Name:
+*     GetLutMapInfo
+
+*  Purpose:
+*     Return information about a LutMap.
+
+*  Type:
+*     Protected virtual function.
+
+*  Synopsis:
+*     #include "permmap.h"
+*     double *astGetLutMapInfo( AstLutMap *this, double *start, double *inc,
+*                               int *nlut, int *status )
+
+*  Class Membership:
+*     LutMap method
+
+*  Description:
+*     This function returns information about the supplied LutMap.
+
+*  Parameters:
+*     this
+*        Pointer to the LutMap.
+*     start
+*        Pointer to a double in which to return the "start" value
+*        supplied when the LutMap was created.
+*     inc
+*        Pointer to a double in which to return the "inc" value
+*        supplied when the LutMap was created.
+*     nlut
+*        Pointer to a double in which to return the number of values in
+*        the LUT.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     A pointer to a dynamically allocated array holding a copy of the
+*     look-up table. This is an array of "nlut" elements, giving the
+*     output values for input values "start", "start+inc", "start+2*inc",
+*     etc. The pointer should be freed using astFree when no longer
+*     needed.
+
+*  Notes:
+*     - A value of NULL will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*/
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Store the scalar values. */
+   *start = this->start;
+   *inc = this->inc;
+   *nlut = this->nlut;
+
+/* Return a copy of the look up table. */
+   return astStore( NULL, this->lut, sizeof( double )*this->nlut );
+}
+
+static int GetMonotonic( int nlut, const double *lut, int *nluti, double **luti,
+                         int **flagsi, int **indexi, int *status ) {
+/*
+*  Name:
+*     GetMonotonic
+
+*  Purpose:
+*     Determine if a array is monotonic increasing or decreasing.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     int GetMonotonic( int nlut, const double *lut, int *nluti, double **luti,
+*                       int **flagsi, int **indexi, int *status )
+
+*  Class Membership:
+*     LutMap member function.
+
+*  Description:
+*     This function returns a flag indiciating the supplied array is
+*     monotonic increasing, monotonic decreasing, or non-monotonic.
+*     Sections of equal or bad values do not invalidate an otherwise
+*     monotonic array.
+*
+*     It also returns information needed to implement the inverse
+*     transformation of a LutMap.
+
+*  Parameters:
+*     nlut
+*        The length of the array.
+*     lut
+*        The array to check.
+*     nluti
+*        Address of an int in which to store the length of the returned
+*        "luti" and "flags" arrays.
+*     luti
+*        Address at which to return a pointer to a newly allocated array
+*        containing "*nluti" elements. This is a copy of the supplied
+*        "lut" array but with any bad or NaN values omitted. Subsequent
+*        elements are shuffled down to fill the holes left by removing
+*        these bad values. A NULL pointer is returned if there are no bad
+*        values in "lut".
+*     flagsi
+*        Address at which to return a pointer to a newly allocated array
+*        containing "*nluti" elements. Each element is non-zero if the
+*        corresponding value stored in "luti" was adjacent to a bad value
+*        in the supplied "lut" array. A NULL pointer is returned if there
+*        are no bad values in "lut".
+*     indexi
+*        Address at which to return a pointer to a newly allocated array
+*        containing "*nluti" elements. Each element is the index within
+*        "lut" of the corresponding value stored in "luti". A NULL pointer
+*        is returned if there are no bad values in "lut".
+*     status
+*        Pointer to the inherited status variable.
+
+*  Notes:
+*    - A value of zero will be returned if this function is invoked
+*    with the global error status set, or if it should fail for any
+*    reason.
+*/
+
+/* Local Variables: */
+   const double *p3;
+   double *p1;
+   double lval;
+   int *p2;
+   int *p4;
+   int ilut;
+   int nbad;
+   int result;
+
+/* Initialise. */
+   result = 0;
+   *nluti = 0;
+   *luti = NULL;
+   *flagsi = NULL;
+   *indexi = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* As yet we have not found a good value. */
+   lval = AST__BAD;
+
+/* As yet we have not found a bad value. */
+   nbad = 0;
+
+/* Loop  round the supplied array, ignoring bad (AST__BAD or NaN) values. */
+   for ( ilut = 0; ilut < nlut; ilut++ ) {
+      if( !astISBAD( lut[ ilut ] ) ) {
+
+/* If this is the first good value, record it. */
+         if( lval == AST__BAD ) {
+            lval = lut[ ilut ];
+
+/* If this is not the first good value, ignore it if it is equal to the
+   previous god value. */
+         } else if( lut[ ilut ] != lval ) {
+
+/* Set the returned flag on the basis of the first pair of good values. */
+            if( result == 0 ) {
+               result = ( lut[ ilut ] > lval ) ? 1 : -1;
+
+/* For subsequent pairs of good values, check the pair increases or
+   decreases in the same way as the first pair. Reset the returned value
+   to zero and break if not. */
+            } else if( result == 1 && lut[ ilut ] < lval ) {
+               result = 0;
+               break;
+
+            } else if( result == -1 && lut[ ilut ] >lval ) {
+               result = 0;
+               break;
+            }
+
+/* Record the current good value. */
+            lval = lut[ ilut ];
+         }
+      } else {
+         nbad++;
+      }
+   }
+
+/* If any bad values were found, we now allocate the required returned
+   arrays. */
+   if( nbad ) {
+      *nluti = nlut - nbad;
+      *luti = astMalloc( sizeof( double )*( *nluti ) );
+      *flagsi = astMalloc( sizeof( double )*( *nluti ) );
+      *indexi = astMalloc( sizeof( double )*( *nluti ) );
+
+      if( astOK ) {
+
+/* Into "luti" copy all good values from "lut", shuffling down values to
+   fill holes left by bad values. Into "flagsi", store a flag indicating
+   if the corresponding "luti" value was adjacent to a bad value in the
+   full "lut" array. */
+         p1 = *luti;
+         p2 = *flagsi;
+         p3 = lut;
+         p4 = *indexi;
+
+/* Do the first input point (it has no lower neighbour). */
+         if( !astISBAD( *p3 ) ) {
+            *(p1++) = *p3;
+            *(p2++) = astISBAD( p3[ +1 ] );
+            *(p4++) = 0;
+         }
+
+/* Do all remaining input points except for the last one. */
+         for ( ilut = 1,p3++; ilut < nlut-1; ilut++,p3++ ) {
+            if( !astISBAD( *p3 ) ) {
+               *(p1++) = *p3;
+               *(p2++) = astISBAD( p3[ -1 ] ) || astISBAD( p3[ +1 ] );
+               *(p4++) = ilut;
+            }
+         }
+
+/* Do the last input point (it has no upper neighbour). */
+         if( !astISBAD( *p3 ) ) {
+            *p1 = *p3;
+            *p2 = astISBAD( p3[ -1 ] );
+            *p4 = ilut;
+         }
+      }
+   }
+
+
+/* Return the result. */
+   return result;
+}
+
+void astInitLutMapVtab_(  AstLutMapVtab *vtab, const char *name, int *status ) {
+/*
+*+
+*  Name:
+*     astInitLutMapVtab
+
+*  Purpose:
+*     Initialise a virtual function table for a LutMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     void astInitLutMapVtab( AstLutMapVtab *vtab, const char *name )
+
+*  Class Membership:
+*     LutMap vtab initialiser.
+
+*  Description:
+*     This function initialises the component of a virtual function
+*     table which is used by the LutMap class.
+
+*  Parameters:
+*     vtab
+*        Pointer to the virtual function table. The components used by
+*        all ancestral classes will be initialised if they have not already
+*        been initialised.
+*     name
+*        Pointer to a constant null-terminated character string which contains
+*        the name of the class to which the virtual function table belongs (it
+*        is this pointer value that will subsequently be returned by the Object
+*        astClass function).
+*-
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstObjectVtab *object;        /* Pointer to Object component of Vtab */
+   AstMappingVtab *mapping;      /* Pointer to Mapping component of Vtab */
+
+/* Check the local error status. */
+   if ( !astOK ) return;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Initialize the component of the virtual function table used by the
+   parent class. */
+   astInitMappingVtab( (AstMappingVtab *) vtab, name );
+
+/* Store a unique "magic" value in the virtual function table. This
+   will be used (by astIsALutMap) to determine if an object belongs
+   to this class.  We can conveniently use the address of the (static)
+   class_check variable to generate this unique value. */
+   vtab->id.check = &class_check;
+   vtab->id.parent = &(((AstMappingVtab *) vtab)->id);
+
+/* Initialise member function pointers. */
+/* ------------------------------------ */
+/* Store pointers to the member functions (implemented here) that
+   provide virtual methods for this class. */
+   vtab->ClearLutInterp = ClearLutInterp;
+   vtab->GetLutInterp = GetLutInterp;
+   vtab->SetLutInterp = SetLutInterp;
+   vtab->TestLutInterp = TestLutInterp;
+   vtab->ClearLutEpsilon = ClearLutEpsilon;
+   vtab->GetLutEpsilon = GetLutEpsilon;
+   vtab->SetLutEpsilon = SetLutEpsilon;
+   vtab->TestLutEpsilon = TestLutEpsilon;
+   vtab->GetLutMapInfo = GetLutMapInfo;
+
+/* Save the inherited pointers to methods that will be extended, and
+   replace them with pointers to the new member functions. */
+   object = (AstObjectVtab *) vtab;
+   mapping = (AstMappingVtab *) vtab;
+
+   parent_clearattrib = object->ClearAttrib;
+   object->ClearAttrib = ClearAttrib;
+   parent_getattrib = object->GetAttrib;
+   object->GetAttrib = GetAttrib;
+   parent_setattrib = object->SetAttrib;
+   object->SetAttrib = SetAttrib;
+   parent_testattrib = object->TestAttrib;
+   object->TestAttrib = TestAttrib;
+
+   parent_transform = mapping->Transform;
+   mapping->Transform = Transform;
+
+/* Store replacement pointers for methods which will be over-ridden by
+   new member functions implemented here. */
+   object->Equal = Equal;
+   mapping->MapMerge = MapMerge;
+
+/* Declare the class dump, copy and delete functions.*/
+   astSetDump( vtab, Dump, "LutMap",
+               "Map 1-d coordinates using a lookup table" );
+   astSetCopy( (AstObjectVtab *) vtab, Copy );
+   astSetDelete( (AstObjectVtab *) vtab, Delete );
+
+/* If we have just initialised the vtab for the current class, indicate
+   that the vtab is now initialised, and store a pointer to the class
+   identifier in the base "object" level of the vtab. */
+   if( vtab == &class_vtab ) {
+      class_init = 1;
+      astSetVtabClassIdentifier( vtab, &(vtab->id) );
+   }
+}
+
+static int MapMerge( AstMapping *this, int where, int series, int *nmap,
+                     AstMapping ***map_list, int **invert_list, int *status ) {
+/*
+*  Name:
+*     MapMerge
+
+*  Purpose:
+*     Simplify a sequence of Mappings containing a LutMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "mapping.h"
+*     int MapMerge( AstMapping *this, int where, int series, int *nmap,
+*                   AstMapping ***map_list, int **invert_list, int *status )
+
+*  Class Membership:
+*     LutMap method (over-rides the protected astMapMerge method
+*     inherited from the Mapping class).
+
+*  Description:
+*     This function attempts to simplify a sequence of Mappings by
+*     merging a nominated LutMap in the sequence with its neighbours,
+*     so as to shorten the sequence if possible.
+*
+*     In many cases, simplification will not be possible and the
+*     function will return -1 to indicate this, without further
+*     action.
+*
+*     In most cases of interest, however, this function will either
+*     attempt to replace the nominated LutMap with one which it
+*     considers simpler, or to merge it with the Mappings which
+*     immediately precede it or follow it in the sequence (both will
+*     normally be considered). This is sufficient to ensure the
+*     eventual simplification of most Mapping sequences by repeated
+*     application of this function.
+*
+*     In some cases, the function may attempt more elaborate
+*     simplification, involving any number of other Mappings in the
+*     sequence. It is not restricted in the type or scope of
+*     simplification it may perform, but will normally only attempt
+*     elaborate simplification in cases where a more straightforward
+*     approach is not adequate.
+
+*  Parameters:
+*     this
+*        Pointer to the nominated LutMap which is to be merged with
+*        its neighbours. This should be a cloned copy of the LutMap
+*        pointer contained in the array element "(*map_list)[where]"
+*        (see below). This pointer will not be annulled, and the
+*        LutMap it identifies will not be modified by this function.
+*     where
+*        Index in the "*map_list" array (below) at which the pointer
+*        to the nominated LutMap resides.
+*     series
+*        A non-zero value indicates that the sequence of Mappings to
+*        be simplified will be applied in series (i.e. one after the
+*        other), whereas a zero value indicates that they will be
+*        applied in parallel (i.e. on successive sub-sets of the
+*        input/output coordinates).
+*     nmap
+*        Address of an int which counts the number of Mappings in the
+*        sequence. On entry this should be set to the initial number
+*        of Mappings. On exit it will be updated to record the number
+*        of Mappings remaining after simplification.
+*     map_list
+*        Address of a pointer to a dynamically allocated array of
+*        Mapping pointers (produced, for example, by the astMapList
+*        method) which identifies the sequence of Mappings. On entry,
+*        the initial sequence of Mappings to be simplified should be
+*        supplied.
+*
+*        On exit, the contents of this array will be modified to
+*        reflect any simplification carried out. Any form of
+*        simplification may be performed. This may involve any of: (a)
+*        removing Mappings by annulling any of the pointers supplied,
+*        (b) replacing them with pointers to new Mappings, (c)
+*        inserting additional Mappings and (d) changing their order.
+*
+*        The intention is to reduce the number of Mappings in the
+*        sequence, if possible, and any reduction will be reflected in
+*        the value of "*nmap" returned. However, simplifications which
+*        do not reduce the length of the sequence (but improve its
+*        execution time, for example) may also be performed, and the
+*        sequence might conceivably increase in length (but normally
+*        only in order to split up a Mapping into pieces that can be
+*        more easily merged with their neighbours on subsequent
+*        invocations of this function).
+*
+*        If Mappings are removed from the sequence, any gaps that
+*        remain will be closed up, by moving subsequent Mapping
+*        pointers along in the array, so that vacated elements occur
+*        at the end. If the sequence increases in length, the array
+*        will be extended (and its pointer updated) if necessary to
+*        accommodate any new elements.
+*
+*        Note that any (or all) of the Mapping pointers supplied in
+*        this array may be annulled by this function, but the Mappings
+*        to which they refer are not modified in any way (although
+*        they may, of course, be deleted if the annulled pointer is
+*        the final one).
+*     invert_list
+*        Address of a pointer to a dynamically allocated array which,
+*        on entry, should contain values to be assigned to the Invert
+*        attributes of the Mappings identified in the "*map_list"
+*        array before they are applied (this array might have been
+*        produced, for example, by the astMapList method). These
+*        values will be used by this function instead of the actual
+*        Invert attributes of the Mappings supplied, which are
+*        ignored.
+*
+*        On exit, the contents of this array will be updated to
+*        correspond with the possibly modified contents of the
+*        "*map_list" array.  If the Mapping sequence increases in
+*        length, the "*invert_list" array will be extended (and its
+*        pointer updated) if necessary to accommodate any new
+*        elements.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     If simplification was possible, the function returns the index
+*     in the "map_list" array of the first element which was
+*     modified. Otherwise, it returns -1 (and makes no changes to the
+*     arrays supplied).
+
+*  Notes:
+*     - A value of -1 will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*/
+
+/* Local Variables: */
+   AstLutMap *map;               /* Pointer to LutMap */
+   AstLutMap *neb;               /* Pointer to neighbouring LutMap */
+   AstMapping *new;              /* Pointer to replacement Mapping */
+   double a1;                    /* First input coordinate value */
+   double a2;                    /* Second input coordinate value */
+   double b1;                    /* First output coordinate value */
+   double b2;                    /* Second output coordinate value */
+   int equal;                    /* Are LutMaps equal? */
+   int i;                        /* Mapping index */
+   int ilo;                      /* Index of lower LutMap */
+   int invneb;                   /* Should the neigbour be used inverted? */
+   int old_inv;                  /* Original Invert value for neigbour */
+   int result;                   /* Result value to return */
+   int simpler;                  /* Mapping simplified? */
+
+/* Initialise the returned result. */
+   result = -1;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointer to the nominated LutMap. */
+   map = (AstLutMap *) ( *map_list )[ where ];
+
+/* See if the LutMap is linear. If so, it can probably be
+   simplified. */
+   simpler = GetLinear( (AstMapping *) map, status );
+   if ( simpler ) {
+
+/* Obtain the range of input values corresponding to the first and
+   last lookup table elements. */
+      a1 = map->start;
+      a2 = map->start + map->inc * ( map->nlut - 1 );
+
+/* Obtain the corresponding range of output values and check these
+   values are not the same. */
+      b1 = map->lut[ 0 ];
+      b2 = map->lut[ map->nlut - 1 ];
+      if ( b1 != b2 ) {
+
+/* Create a new WinMap that implements an equivalent linear Mapping,
+   allowing for the invert flag associated with the LutMap. */
+         if ( !( *invert_list )[ where ] ) {
+            new = (AstMapping *) astWinMap( 1, &a1, &a2, &b1, &b2, "", status );
+         } else {
+            new = (AstMapping *) astWinMap( 1, &b1, &b2, &a1, &a2, "", status );
+         }
+
+/* If OK, annul the original LutMap pointer and substitute the new
+   one. Also clear the associated invert flag. */
+         if ( astOK ) {
+            (void) astAnnul( ( *map_list )[ where ] );
+            ( *map_list )[ where ] = new;
+            ( *invert_list )[ where ] = 0;
+
+/* Assign the result value. */
+            result = where;
+         }
+      }
+
+/* Otherwise, see if the LutMap is in series with its own inverse. If so
+   the pair of LutMaps can be replaced by a UnitMap. */
+   } else if( series ) {
+
+/* Is the higher neighbour a LutMap? If so get a pointer to it, and
+   note the index of the lower of the two adjacent LutMaps. */
+      if( where < ( *nmap - 1 ) &&
+          astIsALutMap( ( *map_list )[ where + 1 ] ) ){
+         neb = (AstLutMap *) ( *map_list )[ where + 1 ];
+         invneb = ( *invert_list )[ where + 1 ];
+         ilo = where;
+
+/* If not, is the lower neighbour a LutMap? If so get a pointer to it,
+   and note the index of the lower of the two adjacent LutMaps. */
+      } else if( where > 0 &&
+                 astIsALutMap( ( *map_list )[ where - 1 ] ) ){
+         neb = (AstLutMap *) ( *map_list )[ where - 1 ];
+         invneb = ( *invert_list )[ where - 1 ];
+         ilo =  where - 1;
+
+      } else {
+         neb = NULL;
+      }
+
+/* If a neighbouring LutMap was found, we can replace the pair by a
+   UnitMap if the two LutMaps are equal but have opposite values for
+   their Invert flags. Temporarily invert the neighbour, then compare
+   the two LutMaps for equality, then re-invert the neighbour. */
+      if( neb ) {
+         old_inv = astGetInvert( neb );
+         astSetInvert( neb, invneb );
+         astInvert( neb );
+         equal = astEqual( map, neb );
+         astSetInvert( neb, old_inv );
+
+/* If the two LutMaps are equal but opposite, annul the first of the two
+   Mappings, and replace it with a UnitMap. Also set the invert flag. */
+         if( equal ) {
+            new = (AstMapping *) astUnitMap( 1, "", status );
+            (void) astAnnul( ( *map_list )[ ilo ] );
+            ( *map_list )[ ilo ] = new;
+            ( *invert_list )[ ilo ] = 0;
+
+/* Annul the second of the two Mappings, and shuffle down the rest of the
+   list to fill the gap. */
+            (void) astAnnul( ( *map_list )[ ilo + 1 ] );
+            for ( i = ilo + 2; i < *nmap; i++ ) {
+               ( *map_list )[ i - 1 ] = ( *map_list )[ i ];
+               ( *invert_list )[ i - 1 ] = ( *invert_list )[ i ];
+            }
+
+/* Clear the vacated element at the end. */
+            ( *map_list )[ *nmap - 1 ] = NULL;
+            ( *invert_list )[ *nmap - 1 ] = 0;
+
+/* Decrement the Mapping count and return the index of the first
+   modified element. */
+            ( *nmap )--;
+            result = where;
+         }
+      }
+   }
+
+/* If an error occurred, clear the returned result. */
+   if ( !astOK ) result = -1;
+
+/* Return the result. */
+   return result;
+}
+
+static void SetAttrib( AstObject *this_object, const char *setting, int *status ) {
+/*
+*  Name:
+*     SetAttrib
+
+*  Purpose:
+*     Set an attribute value for a LutMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     void SetAttrib( AstObject *this, const char *setting )
+
+*  Class Membership:
+*     LutMap member function (over-rides the astSetAttrib protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function assigns an attribute value for a LutMap, the
+*     attribute and its value being specified by means of a string of
+*     the form:
+*
+*        "attribute= value "
+*
+*     Here, "attribute" specifies the attribute name and should be in
+*     lower case with no white space present. The value to the right
+*     of the "=" should be a suitable textual representation of the
+*     value to be assigned and this will be interpreted according to
+*     the attribute's data type.  White space surrounding the value is
+*     only significant for string attributes.
+
+*  Parameters:
+*     this
+*        Pointer to the LutMap.
+*     setting
+*        Pointer to a null-terminated string specifying the new attribute
+*        value.
+*/
+
+/* Local Variables: */
+   AstLutMap *this;              /* Pointer to the LutMap structure */
+   double luteps;                /* LutEpsilon attribute value */
+   int lutinterp;                /* LutInterp attribute value */
+   int len;                      /* Length of setting string */
+   int nc;                       /* Number of characters read by astSscanf */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the LutMap structure. */
+   this = (AstLutMap *) this_object;
+
+/* Obtain the length of the setting string. */
+   len = (int) strlen( setting );
+
+/* Test for each recognised attribute in turn, using "astSscanf" to parse
+   the setting string and extract the attribute value (or an offset to
+   it in the case of string values). In each case, use the value set
+   in "nc" to check that the entire string was matched. Once a value
+   has been obtained, use the appropriate method to set it. */
+
+/* LutInterp. */
+/* ---------- */
+   if ( nc = 0,
+        ( 1 == astSscanf( setting, "lutinterp= %d %n", &lutinterp, &nc ) )
+        && ( nc >= len ) ) {
+      astSetLutInterp( this, lutinterp );
+
+/* LutEpsilon. */
+/* ------------- */
+   } else if ( nc = 0,
+        ( 1 == astSscanf( setting, "lutepsilon= %lf %n", &luteps, &nc ) )
+        && ( nc >= len ) ) {
+      astSetLutEpsilon( this, luteps );
+
+/* If the attribute is still not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      (*parent_setattrib)( this_object, setting, status );
+   }
+}
+
+static int TestAttrib( AstObject *this_object, const char *attrib, int *status ) {
+/*
+*  Name:
+*     TestAttrib
+
+*  Purpose:
+*     Test if a specified attribute value is set for a LutMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     int TestAttrib( AstObject *this, const char *attrib, int *status )
+
+*  Class Membership:
+*     LutMap member function (over-rides the astTestAttrib protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function returns a boolean result (0 or 1) to indicate whether
+*     a value has been set for one of a LutMap's attributes.
+
+*  Parameters:
+*     this
+*        Pointer to the LutMap.
+*     attrib
+*        Pointer to a null-terminated string specifying the attribute
+*        name.  This should be in lower case with no surrounding white
+*        space.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     One if a value has been set, otherwise zero.
+
+*  Notes:
+*     - A value of zero will be returned if this function is invoked
+*     with the global status set, or if it should fail for any reason.
+*/
+
+/* Local Variables: */
+   AstLutMap *this;             /* Pointer to the LutMap structure */
+   int result;                   /* Result value to return */
+
+/* Initialise. */
+   result = 0;
+
+/* Check the global error status. */
+   if ( !astOK ) return result;
+
+/* Obtain a pointer to the LutMap structure. */
+   this = (AstLutMap *) this_object;
+
+/* Check the attribute name and test the appropriate attribute. */
+
+/* LutInterp. */
+/* ---------- */
+   if ( !strcmp( attrib, "lutinterp" ) ) {
+      result = astTestLutInterp( this );
+
+/* LutEpsilon. */
+/* ------------- */
+   } else if ( !strcmp( attrib, "lutepsilon" ) ) {
+      result = astTestLutEpsilon( this );
+
+/* If the attribute is still not recognised, pass it on to the parent
+   method for further interpretation. */
+   } else {
+      result = (*parent_testattrib)( this_object, attrib, status );
+   }
+
+/* Return the result, */
+   return result;
+}
+
+static AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+                               int forward, AstPointSet *out, int *status ) {
+/*
+*  Name:
+*     Transform
+
+*  Purpose:
+*     Apply a LutMap to transform a set of points.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
+*                             int forward, AstPointSet *out, int *status )
+
+*  Class Membership:
+*     LutMap member function (over-rides the astTransform protected
+*     method inherited from the Mapping class).
+
+*  Description:
+*     This function takes a LutMap and a set of points encapsulated
+*     in a PointSet and transforms the points so as to apply the
+*     lookup table transformation.
+
+*  Parameters:
+*     this
+*        Pointer to the LutMap.
+*     in
+*        Pointer to the PointSet holding the input coordinate data.
+*     forward
+*        A non-zero value indicates that the forward coordinate
+*        transformation should be applied, while a zero value requests
+*        the inverse transformation.
+*     out
+*        Pointer to a PointSet which will hold the transformed
+*        (output) coordinate values. A NULL value may also be given,
+*        in which case a new PointSet will be created by this
+*        function.
+*     status
+*        Pointer to the inherited status variable.
+
+*  Returned Value:
+*     Pointer to the output (possibly new) PointSet.
+
+*  Notes:
+*     - A null pointer will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*     - The number of coordinate values per point in the input
+*     PointSet must equal 1.
+*     - If an output PointSet is supplied, it must have space for
+*     sufficient number of points (with 1 coordinate value per point)
+*     to accommodate the result. Any excess space will be ignored.
+*/
+
+/* Local Variables: */
+   AstLutMap *map;               /* Pointer to LutMap to be applied */
+   AstPointSet *result;          /* Pointer to output PointSet */
+   double **ptr_in;              /* Pointer to input coordinate data */
+   double **ptr_out;             /* Pointer to output coordinate data */
+   double *lut;                  /* Pointer to LUT */
+   double d1;                    /* Offset to I1 value */
+   double d2;                    /* Offset to I2 value */
+   double fract;                 /* Fractional interpolation distance */
+   double scale;                 /* Normalising scale factor */
+   double value_in;              /* Input coordinate value */
+   double value_out;             /* Output coordinate value */
+   double x;                     /* Value normalised to LUT increment */
+   double xi;                    /* Integer value of "x" */
+   int *flags;                   /* Flags indicating an adjacent bad value */
+   int *index;                   /* Translates reduced to original indices */
+   int i1;                       /* Lower adjacent LUT index */
+   int i2;                       /* Upper adjacent LUT index */
+   int i;                        /* New LUT index */
+   int istart;                   /* Original LUT index at start of interval */
+   int ix;                       /* "x" converted to an int */
+   int near;                     /* Perform nearest neighbour interpolation? */
+   int nlut;                     /* Number of LUT entries */
+   int nlutm1;                   /* Number of LUT entries minus one */
+   int npoint;                   /* Number of points */
+   int ok;                       /* Lookup table is not flat */
+   int point;                    /* Loop counter for points */
+   int up;                       /* LUT values are increasing? */
+
+/* Check the global error status. */
+   if ( !astOK ) return NULL;
+
+/* Obtain a pointer to the LutMap. */
+   map = (AstLutMap *) this;
+
+/* Apply the parent mapping using the stored pointer to the Transform
+   member function inherited from the parent Mapping class. This
+   function validates all arguments and generates an output PointSet
+   if necessary, but does not actually transform any coordinate
+   values. */
+   result = (*parent_transform)( this, in, forward, out, status );
+
+/* We will now extend the parent astTransform method by performing the
+   calculations needed to generate the output coordinate values. */
+
+/* Determine the numbers of points from the input PointSet and obtain
+   pointers for accessing the input and output coordinate values. */
+   npoint = astGetNpoint( in );
+   ptr_in = astGetPoints( in );
+   ptr_out = astGetPoints( result );
+
+/* Determine whether to apply the forward or inverse mapping,
+   according to the direction specified and whether the mapping has
+   been inverted. */
+   if ( astGetInvert( map ) ) forward = !forward;
+
+/* Forward transformation. */
+/* ----------------------- */
+   if( astOK ){
+      if ( forward ) {
+
+/* Obtain lookup table details. */
+         lut = map->lut;
+         nlut = map->nlut;
+         near = ( astGetLutInterp( map ) == NEAR );
+         nlutm1 = nlut - 1;
+
+/* Calculate the scale factor required. */
+         scale = 1.0 / map->inc;
+
+/* Loop to transform each input point. */
+         for ( point = 0; point < npoint; point++ ) {
+
+/* Extract the input coordinate value. */
+            value_in = ptr_in[ 0 ][ point ];
+
+/* First check if this is the same value as we transformed last. If
+   so, re-use the last result. */
+            if ( value_in == map->last_fwd_in ) {
+               value_out = map->last_fwd_out;
+
+/* Check for bad input coordinates and generate a bad result if
+   necessary. */
+            } else if ( value_in == AST__BAD ) {
+               value_out = AST__BAD;
+
+/* For nearest-neighbour interpolation, return the value of the lookup table
+   entry corresponding to the input coordinate. */
+            } else if( near ){
+               x = ( value_in - map->start ) * scale;
+               xi = floor( x + 0.5 );
+               ix = (int) xi;
+               if ( ix < 0 || ix >= nlut ) {
+                  value_out = AST__BAD;
+               } else {
+                  value_out = lut[ ix ];
+               }
+
+/* Otherwise, (for linear interpolation) identify the lookup table entry
+   corresponding to the input coordinate. */
+            } else {
+               x = ( value_in - map->start ) * scale;
+               xi = floor( x );
+               ix = (int) xi;
+
+/* If the input value lies below the first lookup table entry,
+   extrapolate using the first two table values. */
+               if ( ix < 0 ) {
+                  if( lut[ 0 ] != AST__BAD && lut[ 1 ] != AST__BAD ) {
+                     value_out = lut[ 0 ] + x * ( lut[ 1 ] - lut[ 0 ] );
+                  } else {
+                     value_out = AST__BAD;
+                  }
+
+/* If the input value lies above the last lookup table entry (or equals
+   it), extrapolate using the last two table values. */
+               } else if ( ix >= nlutm1 ) {
+                  if( lut[ nlutm1 ] != AST__BAD &&
+                      lut[ nlut - 2 ] != AST__BAD ) {
+                     value_out = lut[ nlutm1 ] +
+                                 ( x - (double) ( nlutm1 ) ) *
+                                 ( lut[ nlutm1 ] - lut[ nlut - 2 ] );
+                  } else {
+                     value_out = AST__BAD;
+                  }
+
+/* Otherwise, interpolate between the adjacent entries. */
+               } else {
+                  if( lut[ ix ] != AST__BAD &&
+                      lut[ ix + 1 ] != AST__BAD ) {
+                     fract = x - xi;
+                     value_out = lut[ ix ] * ( 1.0 - fract ) +
+                                 lut[ ix + 1 ] * fract;
+                  } else {
+                     value_out = AST__BAD;
+                  }
+               }
+            }
+
+/* Assign the output coordinate value. */
+            ptr_out[ 0 ][ point ] = value_out;
+
+/* Retain the input and output coordinate values for possible re-use
+   in future. */
+            map->last_fwd_in = value_in;
+            map->last_fwd_out = value_out;
+         }
+
+/* Inverse transformation. */
+/* ----------------------- */
+      } else {
+
+/* Obtain details of the lookup table to be used by the inverse
+   transformation. This is the same as the forward transformation lookup
+   table, except that any bad values are omitted. Also, get a pointer to a
+   array of flags that indicate if the corresponding lookup table entries
+   were adjacent to a bad value or not in the full lookup table. */
+         if( map->luti ) {
+            lut = map->luti;
+            flags = map->flagsi;
+            nlut = map->nluti;
+            index = map->indexi;
+         } else {
+            lut = map->lut;
+            flags = NULL;
+            nlut = map->nlut;
+            index = NULL;
+         }
+         near = ( astGetLutInterp( map ) == NEAR );
+         nlutm1 = nlut - 1;
+
+/* Loop to transform each input point. */
+         for ( point = 0; point < npoint; point++ ) {
+
+/* Extract the input coordinate value. */
+            value_in = ptr_in[ 0 ][ point ];
+
+/* First check if this is the same value as we transformed last. If
+   so, re-use the last result. */
+            if ( value_in == map->last_inv_in ) {
+               value_out = map->last_inv_out;
+
+/* Check for bad input coordinates and generate a bad result if
+   necessary. */
+            } else if ( value_in == AST__BAD ) {
+               value_out = AST__BAD;
+
+/* Otherwise, we can determine an inverse. Note the inverse transformation
+   will not be defined, so will not be attempted, unless all the table
+   entries are monotonically increasing or decreasing, possibly with sections
+   of equal or bad values. */
+            } else {
+               up = ( lut[ nlutm1 ] > lut[ 0 ] );
+
+/* Perform a binary search to identify two adjacent lookup table
+   elements whose values bracket the input coordinate value. */
+               i1 = -1;
+               i2 = nlutm1;
+               while ( i2 > ( i1 + 1 ) ) {
+                  i = ( i1 + i2 ) / 2;
+                  *( ( ( value_in >= lut[ i ] ) == up ) ? &i1 : &i2 ) = i;
+               }
+
+/* If the lower table value is equal to the required value, and either of
+   its neighbours is also equal to the required value, then we have been
+   asked to find the inverse in a flat region of the table, so return
+   a bad value. Likewise, if the upper table value is equal to the required
+   value, and either of its neighbours is also equal to the required value,
+   then we have been asked to find the inverse in a flat region of the table,
+   so return a bad value. */
+               ok = 1;
+               if( lut[ i1 ] == value_in ) {
+                  if( i1 > 0 && lut[ i1 - 1 ] == value_in ) ok = 0;
+                  if( lut[ i2 ] == value_in ) ok = 0;
+               } else if( lut[ i2 ] == value_in ) {
+                  if( i2 < nlutm1 && lut[ i2 + 1 ] == value_in ) ok = 0;
+                  if( lut[ i1 ] == value_in ) ok = 0;
+               }
+
+               if( !ok ) {
+                  value_out = AST__BAD;
+
+/* If both of the two table elements were adjacent to a bad value in the
+   full lookup table, return a bad output value. */
+               } else if( flags && ( flags[ i1 ] && flags[ i2 ] ) ) {
+                  value_out = AST__BAD;
+
+/* Nearest neighbour interpolation: return the closest of i1 or i2. Return
+   AST__BAD if the supplied value is less than either or greater than
+   either.  */
+               } else if( near ) {
+                  d1 = lut[ i1 ] - value_in;
+                  d2 = lut[ i2 ] - value_in;
+                  if( ( d1 > 0.0 && d2 > 0.0 ) ||
+                      ( d1 < 0.0 && d2 < 0.0 ) ) {
+                     value_out = AST__BAD;
+
+                  } else {
+
+                     if( fabs( d1 ) < fabs( d2 ) ){
+                        istart = index ? index[ i1 ] : i1;
+                     } else {
+                        istart = index ? index[ i2 ] : i2;
+                     }
+                     value_out = map->start + map->inc * istart;
+
+                  }
+
+/* Linear interpolation... */
+               } else {
+
+/* We are interested in the lower bracketing table element. If
+   necessary, restrict this element's index to lie within the
+   table. This causes extrapolation to occur (instead of
+   interpolation) if the input value actually lies outside the range
+   of the lookup table. */
+                  if ( i1 < 0 ) i1 = 0;
+                  if ( i1 > ( nlut - 2 ) ) i1 = nlut - 2;
+
+/* Interpolate (or extrapolate) to derive the output coordinate
+   value. */
+                  istart = index ? index[ i1 ] : i1;
+                  value_out = map->start + map->inc * ( (double) istart +
+                                             ( ( value_in - lut[ i1 ] ) /
+                                             ( lut[ i1 + 1 ] - lut[ i1 ] ) ) );
+               }
+            }
+
+/* Assign the output coordinate value. */
+            ptr_out[ 0 ][ point ] = value_out;
+
+/* Retain the input and output coordinate values for possible re-use
+   in future. */
+            map->last_inv_in = value_in;
+            map->last_inv_out = value_out;
+         }
+      }
+   }
+
+/* Return a pointer to the output PointSet. */
+   return result;
+}
+
+/* Functions which access class attributes. */
+/* ---------------------------------------- */
+/* Implement member functions to access the attributes associated with
+   this class using the macros defined for this purpose in the
+   "object.h" file. For a description of each attribute, see the class
+   interface (in the associated .h file). */
+
+/*
+*att++
+*  Name:
+*     LutInterp
+
+*  Purpose:
+*     Look-up table interpolation method.
+
+*  Type:
+*     Public attribute.
+
+*  Synopsis:
+*     Integer.
+
+*  Description:
+*     This attribute indicates the method to be used when finding the
+*     output value of a LutMap for an input value part way between two
+*     table entries. If it is set to 0 (the default) then linear
+*     interpolation is used. Otherwise, nearest neighbour interpolation
+*     is used.
+*
+*     Using nearest neighbour interpolation causes AST__BAD to be returned
+*     for any point which falls outside the bounds of the table. Linear
+*     interpolation results in an extrapolated value being returned based
+*     on the two end entries in the table.
+*
+*     Note, the value of this attribute may changed only if the LutMap
+*     has no more than one reference. That is, an error is reported if the
+*     LutMap has been cloned, either by including it within another object
+*     such as a CmpMap or FrameSet or by calling the
+c     astClone
+f     AST_CLONE
+*     function.
+
+*  Applicability:
+*     LutMap
+*        All LutMaps have this attribute.
+
+*att--
+*/
+astMAKE_CLEAR1(LutMap,LutInterp,lutinterp,-INT_MAX)
+astMAKE_GET(LutMap,LutInterp,int,LINEAR,( ( this->lutinterp == -INT_MAX ) ?
+                                          LINEAR : this->lutinterp ))
+astMAKE_SET1(LutMap,LutInterp,int,lutinterp,(( value == LINEAR ) ? LINEAR : NEAR ))
+astMAKE_TEST(LutMap,LutInterp,( this->lutinterp != -INT_MAX ))
+
+/*
+*att++
+*  Name:
+*     LutEpsilon
+
+*  Purpose:
+*     The relative error of the values held in the took-up table.
+
+*  Type:
+*     Public attribute.
+
+*  Synopsis:
+*     Double precision.
+
+*  Description:
+*     This attribute holds the relative error of the values held in the
+*     took-up table. It is used when simplifying a LutMap, to determine
+*     if the LutMap should be considered linear. Setting a larger value
+*     makes it more likely that a LutMap will be replaced by a WinMap
+*     (i.e. a linear Mapping) when simplified.
+*
+*     The default value is the value of the system constant DBL_EPSILON
+*     (typically around 1e-16 or 2E-16). If the values in the look-up
+*     table were derived from single precision data, it may be appropriate
+*     to set this attribute to a value around 1E-7.
+*
+*     Note, the value of this attribute may changed only if the LutMap
+*     has no more than one reference. That is, an error is reported if the
+*     LutMap has been cloned, either by including it within another object
+*     such as a CmpMap or FrameSet or by calling the
+c     astClone
+f     AST_CLONE
+*     function.
+
+*  Applicability:
+*     LutMap
+*        All LutMaps have this attribute.
+
+*att--
+*/
+astMAKE_CLEAR1(LutMap,LutEpsilon,lutepsilon,AST__BAD)
+astMAKE_GET(LutMap,LutEpsilon,double,DBL_EPSILON,( ( this->lutepsilon == AST__BAD ) ?
+                                          DBL_EPSILON : this->lutepsilon ))
+astMAKE_SET1(LutMap,LutEpsilon,double,lutepsilon,(value))
+astMAKE_TEST(LutMap,LutEpsilon,( this->lutepsilon != AST__BAD ))
+
+/* Copy constructor. */
+/* ----------------- */
+static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
+/*
+*  Name:
+*     Copy
+
+*  Purpose:
+*     Copy constructor for LutMap objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Copy( const AstObject *objin, AstObject *objout, int *status )
+
+*  Description:
+*     This function implements the copy constructor for LutMap objects.
+
+*  Parameters:
+*     objin
+*        Pointer to the LutMap to be copied.
+*     objout
+*        Pointer to the LutMap being constructed.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   AstLutMap *out;               /* Pointer to output LutMap */
+   AstLutMap *in;                /* Pointer to input LutMap */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the input and output LutMaps. */
+   in= (AstLutMap *) objin;
+   out = (AstLutMap *) objout;
+
+/* Nullify all output pointers. */
+   out->lut = NULL;
+   out->luti = NULL;
+   out->flagsi = NULL;
+   out->indexi = NULL;
+
+/* Allocate memory and store a copy of the lookup table data. */
+   out->lut = astStore( NULL, in->lut,
+                        sizeof( double ) * (size_t) in->nlut );
+
+/* Do the arrays used for the inverse transformation, if they exist. */
+   if( in->luti ) out->luti = astStore( NULL, in->luti,
+                                        sizeof( double ) * (size_t) in->nluti );
+   if( in->flagsi ) out->flagsi = astStore( NULL, in->flagsi,
+                                        sizeof( double ) * (size_t) in->nluti );
+   if( in->indexi ) out->indexi = astStore( NULL, in->indexi,
+                                        sizeof( double ) * (size_t) in->nluti );
+}
+
+/* Destructor. */
+/* ----------- */
+static void Delete( AstObject *obj, int *status ) {
+/*
+*  Name:
+*     Delete
+
+*  Purpose:
+*     Destructor for LutMap objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Delete( AstObject *obj, int *status )
+
+*  Description:
+*     This function implements the destructor for LutMap objects.
+
+*  Parameters:
+*     obj
+*        Pointer to the LutMap to be deleted.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Variables: */
+   AstLutMap *this;              /* Pointer to LutMap */
+
+/* Obtain a pointer to the LutMap structure. */
+   this = (AstLutMap *) obj;
+
+/* Free the memory holding the lookup tables, etc. */
+   this->lut = astFree( this->lut );
+   this->luti = astFree( this->luti );
+   this->flagsi = astFree( this->flagsi );
+   this->indexi = astFree( this->indexi );
+}
+
+/* Dump function. */
+/* -------------- */
+static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
+/*
+*  Name:
+*     Dump
+
+*  Purpose:
+*     Dump function for LutMap objects.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     void Dump( AstObject *this, AstChannel *channel, int *status )
+
+*  Description:
+*     This function implements the Dump function which writes out data
+*     for the LutMap class to an output Channel.
+
+*  Parameters:
+*     this
+*        Pointer to the LutMap whose data are being written.
+*     channel
+*        Pointer to the Channel to which the data are being written.
+*     status
+*        Pointer to the inherited status variable.
+*/
+
+/* Local Constants: */
+#define KEY_LEN 50               /* Maximum length of a keyword */
+
+/* Local Variables: */
+   AstLutMap *this;              /* Pointer to the LutMap structure */
+   char buff[ KEY_LEN + 1 ];     /* Buffer for keyword string */
+   double dval;                  /* Double value */
+   int ilut;                     /* Loop counter for table elements */
+   int ival;                     /* Integer value */
+   int set;                      /* Attribute value set? */
+
+/* Check the global error status. */
+   if ( !astOK ) return;
+
+/* Obtain a pointer to the LutMap structure. */
+   this = (AstLutMap *) this_object;
+
+/* Write out values representing the instance variables for the LutMap
+   class.  Accompany these with appropriate comment strings, possibly
+   depending on the values being written. */
+
+/* Number of lookup table elements. */
+   astWriteInt( channel, "Nlut", 1, 1, this->nlut,
+                "Number of lookup table elements" );
+
+/* Input coordinate at first element centre. */
+   astWriteDouble( channel, "Start", ( this->start != 0.0 ), 1, this->start,
+                   "Input value at first element" );
+
+/* Element spacing. */
+   astWriteDouble( channel, "Incr", ( this->inc != 1.0 ), 1, this->inc,
+                   "Input value increment between elements" );
+
+/* Interpolation method */
+   set = TestLutInterp( this, status );
+   ival = set ? GetLutInterp( this, status ) : astGetLutInterp( this );
+   astWriteInt( channel, "LutInt", set, 1, ival, "Interpolation method" );
+
+/* Precision */
+   if( TestLutEpsilon( this, status ) ) {
+      dval = GetLutEpsilon( this, status );
+      astWriteDouble( channel, "LutEps", 1, 1, dval, "Table relative error" );
+   }
+
+/* Lookup table contents. */
+   for ( ilut = 0; ilut < this->nlut; ilut++ ) {
+      if( this->lut[ ilut ] != AST__BAD ) {
+         (void) sprintf( buff, "L%d", ilut + 1 );
+         astWriteDouble( channel, buff, 1, 1, this->lut[ ilut ],
+                         ilut ? "" : "Lookup table elements..." );
+      }
+   }
+
+/* Undefine macros local to this function. */
+#undef KEY_LEN
+}
+
+/* Standard class functions. */
+/* ========================= */
+/* Implement the astIsALutMap and astCheckLutMap functions using the
+   macros defined for this purpose in the "object.h" header file. */
+astMAKE_ISA(LutMap,Mapping)
+astMAKE_CHECK(LutMap)
+
+AstLutMap *astLutMap_( int nlut, const double lut[],
+                       double start, double inc,
+                       const char *options, int *status, ...) {
+/*
+*++
+*  Name:
+c     astLutMap
+f     AST_LUTMAP
+
+*  Purpose:
+*     Create a LutMap.
+
+*  Type:
+*     Public function.
+
+*  Synopsis:
+c     #include "lutmap.h"
+c     AstLutMap *astLutMap( int nlut, const double lut[],
+c                           double start, double inc,
+c                           const char *options, ... )
+f     RESULT = AST_LUTMAP( NLUT, LUT, START, INC, OPTIONS, STATUS )
+
+*  Class Membership:
+*     LutMap constructor.
+
+*  Description:
+*     This function creates a new LutMap and optionally initialises
+*     its attributes.
+*
+*     A LutMap is a specialised form of Mapping which transforms
+*     1-dimensional coordinates by using linear interpolation in a
+*     lookup table.  Each input coordinate value is first scaled to
+*     give the index of an entry in the table by subtracting a
+*     starting value (the input coordinate corresponding to the first
+*     table entry) and dividing by an increment (the difference in
+*     input coordinate value between adjacent table entries).
+*
+*     The resulting index will usually contain a fractional part, so
+*     the output coordinate value is then generated by interpolating
+*     linearly between the appropriate entries in the table. If the
+*     index lies outside the range of the table, linear extrapolation
+*     is used based on the two nearest entries (i.e. the two entries
+*     at the start or end of the table, as appropriate).
+*
+*     If the lookup table entries increase or decrease monotonically,
+*     then the inverse transformation may also be performed.
+
+*  Parameters:
+c     nlut
+f     NLUT = INTEGER (Given)
+*        The number of entries in the lookup table. This value must be
+*        at least 2.
+c     lut
+f     LUT( NLUT ) = DOUBLE PRECISION (Given)
+c        An array containing the "nlut"
+f        An array containing the
+*        lookup table entries.
+c     start
+f     START = DOUBLE PRECISION (Given)
+*        The input coordinate value which corresponds to the first lookup
+*        table entry.
+c     inc
+f     INC = DOUBLE PRECISION (Given)
+*        The lookup table spacing (the increment in input coordinate
+*        value between successive lookup table entries). This value
+*        may be positive or negative, but must not be zero.
+c     options
+f     OPTIONS = CHARACTER * ( * ) (Given)
+c        Pointer to a null-terminated string containing an optional
+c        comma-separated list of attribute assignments to be used for
+c        initialising the new LutMap. The syntax used is identical to
+c        that for the astSet function and may include "printf" format
+c        specifiers identified by "%" symbols in the normal way.
+f        A character string containing an optional comma-separated
+f        list of attribute assignments to be used for initialising the
+f        new LutMap. The syntax used is identical to that for the
+f        AST_SET routine.
+c     ...
+c        If the "options" string contains "%" format specifiers, then
+c        an optional list of additional arguments may follow it in
+c        order to supply values to be substituted for these
+c        specifiers. The rules for supplying these are identical to
+c        those for the astSet function (and for the C "printf"
+c        function).
+f     STATUS = INTEGER (Given and Returned)
+f        The global status.
+
+*  Returned Value:
+c     astLutMap()
+f     AST_LUTMAP = INTEGER
+*        A pointer to the new LutMap.
+
+*  Notes:
+*     - If the entries in the lookup table either increase or decrease
+*     monotonically, then the new LutMap's TranInverse attribute will
+*     have a value of one, indicating that the inverse transformation
+*     can be performed. Otherwise, it will have a value of zero, so
+*     that any attempt to use the inverse transformation will result
+*     in an error.
+*     - A null Object pointer (AST__NULL) will be returned if this
+c     function is invoked with the AST error status set, or if it
+f     function is invoked with STATUS set to an error value, or if it
+*     should fail for any reason.
+
+*  Status Handling:
+*     The protected interface to this function includes an extra
+*     parameter at the end of the parameter list descirbed above. This
+*     parameter is a pointer to the integer inherited status
+*     variable: "int *status".
+
+*--
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstLutMap *new;               /* Pointer to new LutMap */
+   va_list args;                 /* Variable argument list */
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* Initialise the LutMap, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitLutMap( NULL, sizeof( AstLutMap ), !class_init, &class_vtab,
+                        "LutMap", nlut, lut, start, inc );
+
+/* If successful, note that the virtual function table has been
+   initialised. */
+   if ( astOK ) {
+      class_init = 1;
+
+/* Obtain the variable argument list and pass it along with the
+   options string to the astVSet method to initialise the new
+   LutMap's attributes. */
+      va_start( args, status );
+      astVSet( new, options, NULL, args );
+      va_end( args );
+
+/* If an error occurred, clean up by deleting the new object. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return a pointer to the new LutMap. */
+   return new;
+}
+
+AstLutMap *astLutMapId_( int nlut, const double lut[],
+                         double start, double inc,
+                         const char *options, ... ) {
+/*
+*  Name:
+*     astLutMapId_
+
+*  Purpose:
+*     Create a LutMap.
+
+*  Type:
+*     Private function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     AstLutMap *astLutMapId( int nlut, const double lut[],
+*                             double start, double inc,
+*                             const char *options, ... )
+
+*  Class Membership:
+*     LutMap constructor.
+
+*  Description:
+*     This function implements the external (public) interface to the
+*     astLutMap constructor function. It returns an ID value (instead
+*     of a true C pointer) to external users, and must be provided
+*     because astLutMap_ has a variable argument list which cannot be
+*     encapsulated in a macro (where this conversion would otherwise
+*     occur).
+*
+*     The variable argument list also prevents this function from
+*     invoking astLutMap_ directly, so it must be a re-implementation
+*     of it in all respects, except for the final conversion of the
+*     result to an ID value.
+
+*  Parameters:
+*     As for astLutMap_.
+
+*  Returned Value:
+*     The ID value associated with the new LutMap.
+*/
+
+/* Local Variables: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+   AstLutMap *new;               /* Pointer to new LutMap */
+   va_list args;                 /* Variable argument list */
+
+   int *status;                  /* Pointer to inherited status value */
+
+/* Get a pointer to the inherited status value. */
+   status = astGetStatusPtr;
+
+/* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(NULL);
+
+/* Check the global status. */
+   if ( !astOK ) return NULL;
+
+/* Initialise the LutMap, allocating memory and initialising the
+   virtual function table as well if necessary. */
+   new = astInitLutMap( NULL, sizeof( AstLutMap ), !class_init, &class_vtab,
+                        "LutMap", nlut, lut, start, inc );
+
+/* If successful, note that the virtual function table has been
+   initialised. */
+   if ( astOK ) {
+      class_init = 1;
+
+/* Obtain the variable argument list and pass it along with the
+   options string to the astVSet method to initialise the new LutMap's
+   attributes. */
+      va_start( args, options );
+      astVSet( new, options, NULL, args );
+      va_end( args );
+
+/* If an error occurred, clean up by deleting the new object. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return an ID value for the new LutMap. */
+   return astMakeId( new );
+}
+
+AstLutMap *astInitLutMap_( void *mem, size_t size, int init,
+                           AstLutMapVtab *vtab, const char *name,
+                           int nlut, const double lut[],
+                           double start, double inc, int *status ) {
+/*
+*+
+*  Name:
+*     astInitLutMap
+
+*  Purpose:
+*     Initialise a LutMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     AstLutMap *astInitLutMap( void *mem, size_t size, int init,
+*                               AstLutMapVtab *vtab, const char *name,
+*                               int nlut, const double lut[],
+*                               double start, double inc )
+
+*  Class Membership:
+*     LutMap initialiser.
+
+*  Description:
+*     This function is provided for use by class implementations to
+*     initialise a new LutMap object. It allocates memory (if
+*     necessary) to accommodate the LutMap plus any additional data
+*     associated with the derived class.  It then initialises a LutMap
+*     structure at the start of this memory. If the "init" flag is
+*     set, it also initialises the contents of a virtual function
+*     table for a LutMap at the start of the memory passed via the
+*     "vtab" parameter.
+
+*  Parameters:
+*     mem
+*        A pointer to the memory in which the LutMap is to be
+*        initialised.  This must be of sufficient size to accommodate
+*        the LutMap data (sizeof(LutMap)) plus any data used by the
+*        derived class. If a value of NULL is given, this function
+*        will allocate the memory itself using the "size" parameter to
+*        determine its size.
+*     size
+*        The amount of memory used by the LutMap (plus derived class
+*        data).  This will be used to allocate memory if a value of
+*        NULL is given for the "mem" parameter. This value is also
+*        stored in the LutMap structure, so a valid value must be
+*        supplied even if not required for allocating memory.
+*     init
+*        A logical flag indicating if the LutMap's virtual function
+*        table is to be initialised. If this value is non-zero, the
+*        virtual function table will be initialised by this function.
+*     vtab
+*        Pointer to the start of the virtual function table to be
+*        associated with the new LutMap.
+*     name
+*        Pointer to a constant null-terminated character string which
+*        contains the name of the class to which the new object
+*        belongs (it is this pointer value that will subsequently be
+*        returned by the astGetClass method).
+*     nlut
+*        The number of elements in the lookup table. This value must
+*        be at least 2.
+*     lut
+*        An array containing the "nlut" lookup table elements.
+*     start
+*        The input coordinate value which corresponds with the first
+*        lookup table element.
+*     inc
+*        The lookup table element spacing (i.e. the increment in input
+*        coordinate value between successive lookup table elements).
+
+*  Returned Value:
+*     A pointer to the new LutMap.
+
+*  Notes:
+*     - A null pointer will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*-
+*/
+
+/* Local Variables: */
+   AstLutMap *new;       /* Pointer to new LutMap */
+   double *luti;         /* Pointer to table for inverse transformation */
+   double *p;            /* Pointer to next lut element */
+   int *flagsi;          /* Pointer to flags for inverse transformation */
+   int *indexi;          /* Pointer to translation from original to reduced */
+   int dirn;             /* +1 => values increasing, -1 => values decreasing */
+   int ilut;             /* Loop counter for LUT elements */
+   int nluti;            /* Length of "luti" array */
+
+/* Initialise. */
+   new = NULL;
+
+/* Check the global status. */
+   if ( !astOK ) return new;
+
+/* If necessary, initialise the virtual function table. */
+   if ( init ) astInitLutMapVtab( vtab, name );
+
+/* Check that the number of lookup table elements is valid. */
+   if ( nlut < 2 ) {
+      astError( AST__LUTIN, "astInitLutMap(%s): Invalid number of lookup "
+                "table elements (%d).", status, name, nlut );
+      astError( AST__LUTIN, "This value should be at least 2." , status);
+
+/* Also check that the input value increment is not zero. */
+   } else if ( inc == 0.0 ) {
+      astError( AST__LUTII, "astInitLutMap(%s): An input value increment of "
+                "zero between lookup table elements is not allowed.", status, name );
+
+/* Determine if the element values increase or decrease monotonically (except
+   that adjacent entries can be equal). We can only implement the inverse
+   transformation if this is so. The inverse transformation will generate
+   AST__BAD output values for sections of the table that contain equal
+   adjacent values, or hold AST__BAD values. */
+   } else {
+      dirn = GetMonotonic( nlut, lut, &nluti, &luti, &flagsi, &indexi,
+                           status );
+
+/* Initialise a Mapping structure (the parent class) as the first
+   component within the LutMap structure, allocating memory if
+   necessary. Specify that the Mapping should be defined in the
+   forward direction, and conditionally in the inverse direction. */
+      new = (AstLutMap *) astInitMapping( mem, size, 0,
+                                         (AstMappingVtab *) vtab, name,
+                                          1, 1, 1, ( dirn != 0 ) );
+
+      if ( astOK ) {
+
+/* Initialise the LutMap data. */
+/* ---------------------------- */
+         new->nlut = nlut;
+         new->start = start;
+         new->inc = inc;
+         new->lutinterp = LINEAR;
+         new->lutepsilon = AST__BAD;
+         new->nluti = nluti;
+         new->luti = luti;
+         new->flagsi = flagsi;
+         new->indexi = indexi;
+
+/* Allocate memory and store the lookup table. */
+         new->lut = astStore( NULL, lut, sizeof( double ) * (size_t) nlut );
+
+/* Replace an NaN values by AST__BAD */
+         p = new->lut;
+         for ( ilut = 0; ilut < nlut; ilut++, p++ ) {
+            if( !astISFINITE(*p) ) *p = AST__BAD;
+         }
+
+/* Initialise the retained input and output coordinate values. */
+         new->last_fwd_in = AST__BAD;
+         new->last_fwd_out = AST__BAD;
+         new->last_inv_in = AST__BAD;
+         new->last_inv_out = AST__BAD;
+      }
+
+/* If an error occurred, clean up by deleting the new LutMap. */
+      if ( !astOK ) new = astDelete( new );
+   }
+
+/* Return a pointer to the new LutMap. */
+   return new;
+}
+
+AstLutMap *astLoadLutMap_( void *mem, size_t size,
+                           AstLutMapVtab *vtab, const char *name,
+                           AstChannel *channel, int *status ) {
+/*
+*+
+*  Name:
+*     astLoadLutMap
+
+*  Purpose:
+*     Load a LutMap.
+
+*  Type:
+*     Protected function.
+
+*  Synopsis:
+*     #include "lutmap.h"
+*     AstLutMap *astLoadLutMap( void *mem, size_t size,
+*                               AstLutMapVtab *vtab, const char *name,
+*                               AstChannel *channel )
+
+*  Class Membership:
+*     LutMap loader.
+
+*  Description:
+*     This function is provided to load a new LutMap using data read
+*     from a Channel. It first loads the data used by the parent class
+*     (which allocates memory if necessary) and then initialises a
+*     LutMap structure in this memory, using data read from the input
+*     Channel.
+*
+*     If the "init" flag is set, it also initialises the contents of a
+*     virtual function table for a LutMap at the start of the memory
+*     passed via the "vtab" parameter.
+
+
+*  Parameters:
+*     mem
+*        A pointer to the memory into which the LutMap is to be
+*        loaded.  This must be of sufficient size to accommodate the
+*        LutMap data (sizeof(LutMap)) plus any data used by derived
+*        classes. If a value of NULL is given, this function will
+*        allocate the memory itself using the "size" parameter to
+*        determine its size.
+*     size
+*        The amount of memory used by the LutMap (plus derived class
+*        data).  This will be used to allocate memory if a value of
+*        NULL is given for the "mem" parameter. This value is also
+*        stored in the LutMap structure, so a valid value must be
+*        supplied even if not required for allocating memory.
+*
+*        If the "vtab" parameter is NULL, the "size" value is ignored
+*        and sizeof(AstLutMap) is used instead.
+*     vtab
+*        Pointer to the start of the virtual function table to be
+*        associated with the new LutMap. If this is NULL, a pointer
+*        to the (static) virtual function table for the LutMap class
+*        is used instead.
+*     name
+*        Pointer to a constant null-terminated character string which
+*        contains the name of the class to which the new object
+*        belongs (it is this pointer value that will subsequently be
+*        returned by the astGetClass method).
+*
+*        If the "vtab" parameter is NULL, the "name" value is ignored
+*        and a pointer to the string "LutMap" is used instead.
+
+*  Returned Value:
+*     A pointer to the new LutMap.
+
+*  Notes:
+*     - A null pointer will be returned if this function is invoked
+*     with the global error status set, or if it should fail for any
+*     reason.
+*-
+*/
+
+/* Local Constants: */
+   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
+#define KEY_LEN 50               /* Maximum length of a keyword */
+
+/* Local Variables: */
+   AstLutMap *new;               /* Pointer to the new LutMap */
+   char buff[ KEY_LEN + 1 ];     /* Buffer for keyword string */
+   int ilut;                     /* Get a pointer to the thread specific global data structure. */
+   astGET_GLOBALS(channel);
+
+/* Loop counter for table elements */
+
+/* Initialise. */
+   new = NULL;
+
+/* Check the global error status. */
+   if ( !astOK ) return new;
+
+/* If a NULL virtual function table has been supplied, then this is
+   the first loader to be invoked for this LutMap. In this case the
+   LutMap belongs to this class, so supply appropriate values to be
+   passed to the parent class loader (and its parent, etc.). */
+   if ( !vtab ) {
+      size = sizeof( AstLutMap );
+      vtab = &class_vtab;
+      name = "LutMap";
+
+/* If required, initialise the virtual function table for this class. */
+      if ( !class_init ) {
+         astInitLutMapVtab( vtab, name );
+         class_init = 1;
+      }
+   }
+
+/* Invoke the parent class loader to load data for all the ancestral
+   classes of the current one, returning a pointer to the resulting
+   partly-built LutMap. */
+   new = astLoadMapping( mem, size, (AstMappingVtab *) vtab, name,
+                         channel );
+
+   if ( astOK ) {
+
+/* Read input data. */
+/* ================ */
+/* Request the input Channel to read all the input data appropriate to
+   this class into the internal "values list". */
+      astReadClassData( channel, "LutMap" );
+
+/* Now read each individual data item from this list and use it to
+   initialise the appropriate instance variable(s) for this class. */
+
+/* Number of lookup table elements. */
+      new->nlut = astReadInt( channel, "nlut", 2 );
+
+/* Starting input coordinate value. */
+      new->start = astReadDouble( channel, "start", 0.0 );
+
+/* Input coordinate value increment. */
+      new->inc = astReadDouble( channel, "incr", 1.0 );
+
+/* Interpolation method */
+      new->lutinterp = astReadInt( channel, "lutint", LINEAR );
+      if ( TestLutInterp( new, status ) ) SetLutInterp( new, new->lutinterp, status );
+
+/* Precision */
+      new->lutepsilon = astReadDouble( channel, "luteps", AST__BAD );
+      if ( TestLutEpsilon( new, status ) ) SetLutEpsilon( new, new->lutepsilon, status );
+
+/* Allocate memory to hold the lookup table elements. */
+      new->lut = astMalloc( sizeof( double ) * (size_t) new->nlut );
+
+/* If OK, loop to read each element. */
+      if ( astOK ) {
+         for ( ilut = 0; ilut < new->nlut; ilut++ ) {
+            (void) sprintf( buff, "l%d", ilut + 1 );
+            new->lut[ ilut ] = astReadDouble( channel, buff, AST__BAD );
+         }
+
+/* Initialise the retained input and output coordinate values. */
+         new->last_fwd_in = AST__BAD;
+         new->last_fwd_out = AST__BAD;
+         new->last_inv_in = AST__BAD;
+         new->last_inv_out = AST__BAD;
+
+/* See if the array is monotonic increasing or decreasing. */
+         (void) GetMonotonic( new->nlut, new->lut, &(new->nluti),
+                              &(new->luti), &(new->flagsi), &(new->indexi),
+                              status );
+      }
+   }
+
+/* If an error occurred, clean up by deleting the new LutMap. */
+   if ( !astOK ) new = astDelete( new );
+
+/* Return the new LutMap pointer. */
+   return new;
+
+/* Undefine macros local to this function. */
+#undef KEY_LEN
+}
+
+/* Virtual function interfaces. */
+/* ============================ */
+/* These provide the external interface to the virtual functions
+   defined by this class. Each simply checks the global error status
+   and then locates and executes the appropriate member function,
+   using the function pointer stored in the object's virtual function
+   table (this pointer is located using the astMEMBER macro defined in
+   "object.h").
+
+   Note that the member function may not be the one defined here, as
+   it may have been over-ridden by a derived class. However, it should
+   still have the same interface. */
+
+double *astGetLutMapInfo_( AstLutMap *this, double *start, double *inc,
+                           int *nlut, int *status ){
+   if( !astOK ) return NULL;
+   return (**astMEMBER(this,LutMap,GetLutMapInfo))( this, start, inc, nlut,
+                                                    status );
+}
+
+
+