update ast 8.6.2

1 files changed, 0 insertions, 2011 deletions

diff --git a/ast/ratemap.c b/ast/ratemap.c
deleted file mode 100644
index 1e343a6..0000000
--- a/ast/ratemap.c
+++ /dev/null
@@ -1,2011 +0,0 @@
-/*
-*class++
-*  Name:
-*     RateMap
-
-*  Purpose:
-*     Mapping which represents differentiation.
-
-*  Constructor Function:
-c     astRateMap
-f     AST_RATEMAP
-
-*  Description:
-*     A RateMap is a Mapping which represents a single element of the
-*     Jacobian matrix of another Mapping. The Mapping for which the
-*     Jacobian is required is specified when the new RateMap is created,
-*     and is referred to as the "encapsulated Mapping" below.
-*
-*     The number of inputs to a RateMap is the same as the number of inputs
-*     to its encapsulated Mapping. The number of outputs from a RateMap
-*     is always one. This one output equals the rate of change of a
-*     specified output of the encapsulated Mapping with respect to a
-*     specified input of the encapsulated Mapping (the input and output
-*     to use are specified when the RateMap is created).
-*
-*     A RateMap which has not been inverted does not define an inverse
-*     transformation. If a RateMap has been inverted then it will define
-*     an inverse transformation but not a forward transformation.
-
-*  Inheritance:
-*     The RateMap class inherits from the Mapping class.
-
-*  Attributes:
-*     The RateMap class does not define any new attributes beyond those
-*     which are applicable to all Mappings.
-
-*  Functions:
-c     The RateMap class does not define any new functions beyond those
-f     The RateMap 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
-
-*  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:
-*     DSB: David S. Berry (Starlink)
-
-*  History:
-*     10-FEB-2004 (DSB):
-*        Original version.
-*     14-FEB-2006 (DSB):
-*        Override astGetObjSize.
-*     10-MAY-2006 (DSB):
-*        Override astEqual.
-*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 RateMap
-
-/* Include files. */
-/* ============== */
-/* Interface definitions. */
-/* ---------------------- */
-
-#include "globals.h"             /* Thread-safe global data access */
-#include "error.h"               /* Error reporting facilities */
-#include "memory.h"              /* Memory allocation facilities */
-#include "object.h"              /* Base Object class */
-#include "pointset.h"            /* Sets of points/coordinates */
-#include "mapping.h"             /* Coordinate Mappings (parent class) */
-#include "channel.h"             /* I/O channels */
-#include "ratemap.h"             /* Interface definition for this class */
-#include "unitmap.h"             /* Unit Mappings */
-#include "frame.h"               /* Frames */
-
-/* Error code definitions. */
-/* ----------------------- */
-#include "ast_err.h"             /* AST error codes */
-
-/* C header files. */
-/* --------------- */
-#include <stdarg.h>
-#include <stddef.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 int (* parent_getobjsize)( AstObject *, int * );
-static AstPointSet *(* parent_transform)( AstMapping *, AstPointSet *, int, AstPointSet *, int * );
-static int *(* parent_mapsplit)( AstMapping *, int, const int *, AstMapping **, int * );
-
-#if defined(THREAD_SAFE)
-static int (* parent_managelock)( AstObject *, int, int, AstObject **, int * );
-#endif
-
-
-#ifdef THREAD_SAFE
-/* Define how to initialise thread-specific globals. */
-#define GLOBAL_inits \
-   globals->Class_Init = 0;
-
-/* Create the function that initialises global data for this module. */
-astMAKE_INITGLOBALS(RateMap)
-
-/* Define macros for accessing each item of thread specific global data. */
-#define class_init astGLOBAL(RateMap,Class_Init)
-#define class_vtab astGLOBAL(RateMap,Class_Vtab)
-
-
-#include <pthread.h>
-
-
-#else
-
-
-/* Define the class virtual function table and its initialisation flag
-   as static variables. */
-static AstRateMapVtab 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. */
-AstRateMap *astRateMapId_( void *, int, int, const char *, ... );
-
-/* Prototypes for Private Member Functions. */
-/* ======================================== */
-static AstMapping *RemoveRegions( AstMapping *, int * );
-static AstPointSet *Transform( AstMapping *, AstPointSet *, int, AstPointSet *, 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 *MapSplit( AstMapping *, int, const int *, AstMapping **, int * );
-static int Equal( AstObject *, AstObject *, int * );
-static int GetObjSize( AstObject *, int * );
-
-#if defined(THREAD_SAFE)
-static int ManageLock( AstObject *, int, int, AstObject **, int * );
-#endif
-
-/* Member functions. */
-/* ================= */
-static int Equal( AstObject *this_object, AstObject *that_object, int *status ) {
-/*
-*  Name:
-*     Equal
-
-*  Purpose:
-*     Test if two RateMaps are equivalent.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     int Equal( AstObject *this, AstObject *that, int *status )
-
-*  Class Membership:
-*     RateMap 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 RateMaps are equivalent.
-
-*  Parameters:
-*     this
-*        Pointer to the first Object (a RateMap).
-*     that
-*        Pointer to the second Object.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     One if the RateMaps 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: */
-   AstRateMap *that;
-   AstRateMap *this;
-   int nin;
-   int nout;
-   int result;
-   int that_inv;
-   int this_inv;
-
-/* Initialise. */
-   result = 0;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Obtain pointers to the two RateMap structures. */
-   this = (AstRateMap *) this_object;
-   that = (AstRateMap *) that_object;
-
-/* Check the second object is a RateMap. We know the first is a
-   RateMap since we have arrived at this implementation of the virtual
-   function. */
-   if( astIsARateMap( 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 RateMaps differ, it may still be possible
-   for them to be equivalent. First compare the RateMaps if their Invert
-   flags are the same. In this case all the attributes of the two RateMaps
-   must be identical. */
-         if( astGetInvert( this ) == astGetInvert( that ) ) {
-
-/* Temporarily re-instate the original Invert flag values. */
-            this_inv = astGetInvert( this->map );
-            that_inv = astGetInvert( that->map );
-            astSetInvert( this->map, this->invert );
-            astSetInvert( that->map, that->invert );
-
-            if( astEqual( this->map, that->map ) &&
-                this->iin == that->iin &&
-                this->iout == that->iout ){
-               result = 1;
-            }
-
-/* Restore the original Invert flag values. */
-            astSetInvert( this->map, this_inv );
-            astSetInvert( that->map, that_inv );
-
-/* If the Invert flags for the two RateMaps differ, the attributes of the two
-   RateMaps must be inversely related to each other. */
-         } else {
-
-/* In the specific case of a RateMap, 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 int GetObjSize( AstObject *this_object, int *status ) {
-/*
-*  Name:
-*     GetObjSize
-
-*  Purpose:
-*     Return the in-memory size of an Object.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     int GetObjSize( AstObject *this, int *status )
-
-*  Class Membership:
-*     RateMap member function (over-rides the astGetObjSize protected
-*     method inherited from the parent class).
-
-*  Description:
-*     This function returns the in-memory size of the supplied RateMap,
-*     in bytes.
-
-*  Parameters:
-*     this
-*        Pointer to the RateMap.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     The Object size, in bytes.
-
-*  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: */
-   AstRateMap *this;         /* Pointer to RateMap structure */
-   int result;                /* Result value to return */
-
-/* Initialise. */
-   result = 0;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Obtain a pointers to the RateMap structure. */
-   this = (AstRateMap *) this_object;
-
-/* Invoke the GetObjSize method inherited from the parent class, and then
-   add on any components of the class structure defined by thsi class
-   which are stored in dynamically allocated memory. */
-   result = (*parent_getobjsize)( this_object, status );
-   result += astGetObjSize( this->map );
-
-/* If an error occurred, clear the result value. */
-   if ( !astOK ) result = 0;
-
-/* Return the result, */
-   return result;
-}
-
-void astInitRateMapVtab_(  AstRateMapVtab *vtab, const char *name, int *status ) {
-/*
-*+
-*  Name:
-*     astInitRateMapVtab
-
-*  Purpose:
-*     Initialise a virtual function table for a RateMap.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     void astInitRateMapVtab( AstRateMapVtab *vtab, const char *name )
-
-*  Class Membership:
-*     RateMap vtab initialiser.
-
-*  Description:
-*     This function initialises the component of a virtual function
-*     table which is used by the RateMap 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 astIsARateMap) 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. */
-
-/* None. */
-
-/* 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_getobjsize = object->GetObjSize;
-   object->GetObjSize = GetObjSize;
-
-   mapping->RemoveRegions = RemoveRegions;
-
-#if defined(THREAD_SAFE)
-   parent_managelock = object->ManageLock;
-   object->ManageLock = ManageLock;
-#endif
-
-   parent_transform = mapping->Transform;
-   mapping->Transform = Transform;
-
-   parent_mapsplit = mapping->MapSplit;
-   mapping->MapSplit = MapSplit;
-
-/* Store replacement pointers for methods which will be over-ridden by
-   new member functions implemented here. */
-   object->Equal = Equal;
-   mapping->MapMerge = MapMerge;
-
-/* Declare the copy constructor, destructor and class dump function. */
-   astSetCopy( vtab, Copy );
-   astSetDelete( vtab, Delete );
-   astSetDump( vtab, Dump, "RateMap", "Differential Mapping" );
-
-/* 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) );
-   }
-}
-
-#if defined(THREAD_SAFE)
-static int ManageLock( AstObject *this_object, int mode, int extra,
-                       AstObject **fail, int *status ) {
-/*
-*  Name:
-*     ManageLock
-
-*  Purpose:
-*     Manage the thread lock on an Object.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "object.h"
-*     AstObject *ManageLock( AstObject *this, int mode, int extra,
-*                            AstObject **fail, int *status )
-
-*  Class Membership:
-*     RateMap member function (over-rides the astManageLock protected
-*     method inherited from the parent class).
-
-*  Description:
-*     This function manages the thread lock on the supplied Object. The
-*     lock can be locked, unlocked or checked by this function as
-*     deteremined by parameter "mode". See astLock for details of the way
-*     these locks are used.
-
-*  Parameters:
-*     this
-*        Pointer to the Object.
-*     mode
-*        An integer flag indicating what the function should do:
-*
-*        AST__LOCK: Lock the Object for exclusive use by the calling
-*        thread. The "extra" value indicates what should be done if the
-*        Object is already locked (wait or report an error - see astLock).
-*
-*        AST__UNLOCK: Unlock the Object for use by other threads.
-*
-*        AST__CHECKLOCK: Check that the object is locked for use by the
-*        calling thread (report an error if not).
-*     extra
-*        Extra mode-specific information.
-*     fail
-*        If a non-zero function value is returned, a pointer to the
-*        Object that caused the failure is returned at "*fail". This may
-*        be "this" or it may be an Object contained within "this". Note,
-*        the Object's reference count is not incremented, and so the
-*        returned pointer should not be annulled. A NULL pointer is
-*        returned if this function returns a value of zero.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*    A local status value:
-*        0 - Success
-*        1 - Could not lock or unlock the object because it was already
-*            locked by another thread.
-*        2 - Failed to lock a POSIX mutex
-*        3 - Failed to unlock a POSIX mutex
-*        4 - Bad "mode" value supplied.
-
-*  Notes:
-*     - This function attempts to execute even if an error has already
-*     occurred.
-*/
-
-/* Local Variables: */
-   AstRateMap *this;       /* Pointer to RateMap structure */
-   int result;             /* Returned status value */
-
-/* Initialise */
-   result = 0;
-
-/* Check the supplied pointer is not NULL. */
-   if( !this_object ) return result;
-
-/* Obtain a pointers to the RateMap structure. */
-   this = (AstRateMap *) this_object;
-
-/* Invoke the ManageLock method inherited from the parent class. */
-   if( !result ) result = (*parent_managelock)( this_object, mode, extra,
-                                                fail, status );
-
-/* Invoke the astManageLock method on any Objects contained within
-   the supplied Object. */
-   if( !result ) result = astManageLock( this->map, mode, extra, fail );
-
-   return result;
-
-}
-#endif
-
-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 RateMap.
-
-*  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:
-*     RateMap 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 RateMap 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 RateMap 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 RateMap which is to be merged with
-*        its neighbours. This should be a cloned copy of the RateMap
-*        pointer contained in the array element "(*map_list)[where]"
-*        (see below). This pointer will not be annulled, and the
-*        RateMap it identifies will not be modified by this function.
-*     where
-*        Index in the "*map_list" array (below) at which the pointer
-*        to the nominated RateMap 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: */
-   AstMapping *emap1;
-   AstMapping *emap2;
-   AstMapping *emap;
-   AstMapping *smap;
-   AstRateMap *map;
-   AstRateMap *rmap1;
-   AstRateMap *rmap2;
-   int cancel;
-   int map_inv;
-   int nax;
-   int old_inv2;
-   int old_inv;
-   int old_winv;
-   int result;
-
-/* Initialise. */
-   result = -1;
-
-/* Check the inherited status. */
-   if ( !astOK ) return result;
-
-/* Initialisation to avoid compiler warnings. */
-   nax = 0;
-
-/* Get a pointer to this RateMap. */
-   map = (AstRateMap *) this;
-
-/* Temporarily set its Invert flag to the requested value. */
-   map_inv = astGetInvert( map );
-   astSetInvert( map, ( *invert_list )[ where ] );
-
-/* Get the encapsulated Mapping, and temporarily set its Invert attribute
-   back to the value it had when the RateMap was created, saving the current
-   Invert value so that it can be re-instated later. */
-   emap = map->map;
-   old_inv = astGetInvert( emap );
-   astSetInvert( emap, map->invert );
-
-/* First try to simplify the RateMap by simplifying its encapsulated
-   Mapping. */
-   smap = astSimplify( emap );
-
-/* If any simplification took place, create a new RateMap with the
-   simplified mapping. */
-   if( smap != emap ) {
-      (void) astAnnul( ( *map_list )[ where ] );
-      ( *map_list )[ where ] = (AstMapping *) astRateMap( smap, map->iout, map->iin, "", status );
-      result = where;
-
-/* The only other simplication which can be performed is to cancel a RateMap
-   with its own inverse in series. */
-   } else if( series ) {
-
-/* Indicate we have nothing to cancel with as yet. */
-      cancel = -1;
-
-/* First consider the lower neighbour. */
-      if( where > 0 && astIsARateMap( ( *map_list )[ where - 1 ] ) ) {
-
-/* Check the Invert flags are opposite */
-         if( ( *invert_list )[ where ] != ( *invert_list )[ where - 1 ] ) {
-            rmap1 = map;
-            rmap2 = (AstRateMap *) ( *map_list )[ where - 1 ];
-
-/* Check the input and output indices are equal. */
-            if( rmap1->iin == rmap2->iin &&
-                rmap1->iout == rmap2->iout ) {
-
-/* Check the encapsulated Mappings are equal. */
-               emap1 = emap;
-               emap2 = rmap2->map;
-               old_winv = astGetInvert( rmap2 );
-               astSetInvert( rmap2, ( *invert_list )[ where - 1 ] );
-               old_inv2 = astGetInvert( emap2 );
-               astSetInvert( emap2,  rmap2->invert );
-
-               if( astEqual( emap1, emap2 ) ) cancel = where - 1;
-
-               astSetInvert( emap2,  old_inv2 );
-               astSetInvert( rmap2, old_winv );
-
-               nax = astGetNout( rmap1 );
-            }
-         }
-      }
-
-/* Likewise consider the upper neighbour. */
-      if( cancel == -1 && where + 1 < *nmap &&
-          astIsARateMap( ( *map_list )[ where + 1 ] ) ) {
-
-         if( ( *invert_list )[ where ] != ( *invert_list )[ where + 1 ] ) {
-            rmap1 = map;
-            rmap2 = (AstRateMap *) ( *map_list )[ where + 1 ];
-            if( rmap1->iin == rmap2->iin &&
-                rmap1->iout == rmap2->iout ) {
-               emap1 = emap;
-               emap2 = rmap2->map;
-               old_winv = astGetInvert( rmap2 );
-               astSetInvert( rmap2, ( *invert_list )[ where + 1 ] );
-               old_inv2 = astGetInvert( emap2 );
-               astSetInvert( emap2,  rmap2->invert );
-
-               if( astEqual( emap1, emap2 ) ) cancel = where + 1;
-
-               astSetInvert( emap2,  old_inv2 );
-               astSetInvert( rmap2, old_winv );
-
-               nax = astGetNin( rmap1 );
-            }
-         }
-      }
-
-/* If we can cancel with a neightbour, do so. */
-      if( cancel != -1 ) {
-         (void) astAnnul( ( *map_list )[ where ] );
-         (void) astAnnul( ( *map_list )[ cancel ] );
-         ( *map_list )[ where ] = (AstMapping *) astUnitMap( nax, "", status );
-         ( *invert_list )[ where ] = 0;
-         ( *map_list )[ cancel ] = (AstMapping *) astUnitMap( nax, "", status );
-         ( *invert_list )[ cancel ] = 0;
-          result = ( cancel < where ) ? cancel : where;
-      }
-   }
-
-/* Free resources. */
-   smap = astAnnul( smap );
-
-/* Reset the original Invert attribute for the encapsulated Mapping. */
-   astSetInvert( emap, old_inv );
-
-/* Reset the original Invert attribute for the specified RateMap */
-   astSetInvert( map, map_inv );
-
-/* If an error occurred, clear the result value. */
-   if ( !astOK ) result = -1;
-
-/* Return the result. */
-   return result;
-}
-
-static int *MapSplit( AstMapping *this_map, int nin, const int *in, AstMapping **map, int *status ){
-/*
-*  Name:
-*     MapSplit
-
-*  Purpose:
-*     Create a Mapping representing a subset of the inputs of an existing
-*     RateMap.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     int *MapSplit( AstMapping *this, int nin, const int *in, AstMapping **map, int *status )
-
-*  Class Membership:
-*     RateMap method (over-rides the protected astMapSplit method
-*     inherited from the Mapping class).
-
-*  Description:
-*     This function creates a new Mapping by picking specified inputs from
-*     an existing RateMap. This is only possible if the specified inputs
-*     correspond to some subset of the RateMap outputs. That is, there
-*     must exist a subset of the RateMap outputs for which each output
-*     depends only on the selected RateMap inputs, and not on any of the
-*     inputs which have not been selected. If this condition is not met
-*     by the supplied RateMap, then a NULL Mapping is returned.
-
-*  Parameters:
-*     this
-*        Pointer to the RateMap to be split (the RateMap is not actually
-*        modified by this function).
-*     nin
-*        The number of inputs to pick from "this".
-*     in
-*        Pointer to an array of indices (zero based) for the inputs which
-*        are to be picked. This array should have "nin" elements. If "Nin"
-*        is the number of inputs of the supplied RateMap, then each element
-*        should have a value in the range zero to Nin-1.
-*     map
-*        Address of a location at which to return a pointer to the new
-*        Mapping. This Mapping will have "nin" inputs (the number of
-*        outputs may be different to "nin"). A NULL pointer will be
-*        returned if the supplied RateMap has no subset of outputs which
-*        depend only on the selected inputs.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     A pointer to a dynamically allocated array of ints. The number of
-*     elements in this array will equal the number of outputs for the
-*     returned Mapping. Each element will hold the index of the
-*     corresponding output in the supplied RateMap. The array should be
-*     freed using astFree when no longer needed. A NULL pointer will
-*     be returned if no output Mapping can be created.
-
-*  Notes:
-*     - If this function is invoked with the global error status set,
-*     or if it should fail for any reason, then NULL values will be
-*     returned as the function value and for the "map" pointer.
-*/
-
-/* Local Variables: */
-   AstMapping *emap;          /* Pointer to Mapping encapsulated by RateMap */
-   AstMapping *remap;         /* Split Mapping encapsulated by RateMap */
-   AstRateMap *this;          /* Pointer to RateMap structure */
-   int *eres;                 /* Outputs used by split Mapping */
-   int *result;               /* Array holding returned output inedx */
-   int ax1;                   /* New index of output being differentiated */
-   int ax2;                   /* New index of output being varied */
-   int i;                     /* Loop count */
-   int nout;                  /* No. of outputs in the split Mapping */
-   int old_inv;               /* Original Invert flag for emap */
-
-/* Initialise */
-   result = NULL;
-   *map = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Invoke the parent astMapSplit method to see if it can do the job. */
-   result = (*parent_mapsplit)( this_map, nin, in, map, status );
-
-/* If not, we provide a special implementation here. Note we cannot
-   produce the Mapping if the RaterMap has been inverted. */
-   if( !result && !astGetInvert( this_map ) ) {
-
-/* Get a pointer to the RateMap structure. */
-      this = (AstRateMap *) this_map;
-
-/* Temporarily reset the Invert attribute of the encapsulated Mapping
-   back to the value it had when the RateMap was created. */
-      emap = this->map;
-      old_inv = astGetInvert( emap );
-      astSetInvert( emap, this->invert );
-
-/* Attempt to split the encapsulated Mapping */
-      eres = astMapSplit( emap, nin, in, &remap );
-
-/* We can only continue if this was succesful. */
-      if( eres ) {
-
-/* Check that the input which the RateMap varies is one of the selected
-   inputs. */
-         ax2 = -1;
-         for( i = 0; i < nin; i++ ) {
-            if( in[ i ] == this->iin ) {
-               ax2 = i;
-               break;
-            }
-         }
-
-/* Check that the output which the RateMap differentiates is one of the
-   outputs of the "remap" Mapping. */
-         ax1 = -1;
-         nout = astGetNout( remap );
-         for( i = 0; i < nout; i++ ) {
-            if( eres[ i ] == this->iout ) {
-               ax1 = i;
-               break;
-            }
-         }
-
-/* If possible create the required Mapping and returned array. */
-         if( ax1 != -1 && ax2 != -1 ) {
-            *map = (AstMapping *) astRateMap( remap, ax1, ax2, "", status );
-            result = astMalloc( sizeof( int ) );
-            if( astOK ) *result= 0;
-         }
-
-/* Free resources */
-         eres = astFree( eres );
-         remap = astAnnul( remap );
-      }
-
-/* Re-instate the original Invert flag in the Mapping encapsulated by the
-   supplied RateMap. */
-      astSetInvert( emap, old_inv );
-   }
-
-/* Free returned resources if an error has occurred. */
-   if( !astOK ) {
-      result = astFree( result );
-      *map = astAnnul( *map );
-   }
-
-/* Return the list of output indices. */
-   return result;
-}
-
-static AstMapping *RemoveRegions( AstMapping *this_mapping, int *status ) {
-/*
-*  Name:
-*     RemoveRegions
-
-*  Purpose:
-*     Remove any Regions from a Mapping.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     AstMapping *RemoveRegions( AstMapping *this, int *status )
-
-*  Class Membership:
-*     RateMap method (over-rides the astRemoveRegions method inherited
-*     from the Mapping class).
-
-*  Description:
-*     This function searches the supplied Mapping (which may be a
-*     compound Mapping such as a CmpMap) for any component Mappings
-*     that are instances of the AST Region class. It then creates a new
-*     Mapping from which all Regions have been removed. If a Region
-*     cannot simply be removed (for instance, if it is a component of a
-*     parallel CmpMap), then it is replaced with an equivalent UnitMap
-*     in the returned Mapping.
-*
-*     The implementation provided by the RateMap class invokes the
-*     astRemoveRegions method on the encapsulated Mapping, and returns a
-*     new RateMap containing the resulting Mapping.
-
-*  Parameters:
-*     this
-*        Pointer to the original Region.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     A pointer to the modified mapping.
-
-*  Notes:
-*     - A NULL pointer value will be returned if this function is
-*     invoked with the AST error status set, or if it should fail for
-*     any reason.
-*/
-
-/* Local Variables: */
-   AstMapping *newmap;           /* New component Mapping */
-   AstMapping *result;           /* Result pointer to return */
-   AstRateMap *new;              /* Pointer to new RateMap */
-   AstRateMap *this;             /* Pointer to RateMap structure */
-
-/* Initialise. */
-   result = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return result;
-
-/* Get a pointer to the RateMap. */
-   this = (AstRateMap *) this_mapping;
-
-/* Invoke the astRemoveRegions method on the component Mapping. */
-   newmap = astRemoveRegions( this->map );
-
-/* If the Mapping was not modified, just return a clone of the supplied
-   pointer. */
-   if( this->map == newmap ) {
-      result = astClone( this );
-
-/* Otherwise, we need to create a new RateMap to return. */
-   } else {
-
-/* If the new Mapping is a Frame (as will be the case if the original
-   Mapping was a Region), use a UnitMap instead. */
-      if( astIsAFrame( newmap ) ) {
-         (void) astAnnul( newmap );
-         newmap = (AstMapping *) astUnitMap( astGetNin( this ), " ", status );
-      }
-
-/* Take a deep copy of the supplied RateMap and then modify the Mapping
-   so that we retain any extra information in the supplied RateMap. */
-      new = astCopy( this );
-      (void) astAnnul( new->map );
-      new->map = astClone( newmap );
-      result = (AstMapping *) new;
-   }
-
-/* Free resources. */
-   newmap = astAnnul( newmap );
-
-/* Annul the returned Mapping if an error has occurred. */
-   if( !astOK ) result = astAnnul( result );
-
-/* Return the result. */
-   return result;
-}
-
-static AstPointSet *Transform( AstMapping *this, AstPointSet *in,
-                               int forward, AstPointSet *out, int *status ) {
-/*
-*  Name:
-*     Transform
-
-*  Purpose:
-*     Apply a RateMap to transform a set of points.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     AstPointSet *Transform( AstMapping *this, AstPointSet *in,
-*                             int forward, AstPointSet *out, int *status )
-
-*  Class Membership:
-*     RateMap member function (over-rides the astTransform method inherited
-*     from the Mapping class).
-
-*  Description:
-*     This function takes a RateMap and a set of points encapsulated in a
-*     PointSet and transforms the points so as to apply the required Mapping.
-*     This implies applying each of the RateMap's component Mappings in turn,
-*     either in series or in parallel.
-
-*  Parameters:
-*     this
-*        Pointer to the RateMap.
-*     in
-*        Pointer to the PointSet associated with the input coordinate values.
-*     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
-*     match the number of coordinates for the RateMap being applied.
-*     -  If an output PointSet is supplied, it must have space for sufficient
-*     number of points and coordinate values per point to accommodate the
-*     result. Any excess space will be ignored.
-*/
-
-/* Local Variables: */
-   AstMapping *emap;
-   AstPointSet *result;
-   AstRateMap *map;
-   double **ptr2;
-   double **ptr;
-   double *pout;
-   double *work;
-   int ic;
-   int iin;
-   int iout;
-   int ipoint;
-   int ncoord;
-   int npoint;
-   int old_inv;
-
-/* Check the global error status. */
-   if ( !astOK ) return NULL;
-
-/* Obtain a pointer to the RateMap. */
-   map = (AstRateMap *) 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 now extend the parent astTransform method by applying the component
-   Mappings of the RateMap to generate the output coordinate values. */
-
-/* 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;
-
-/* The RateMap class does not have an inverse transformation. */
-   if( !forward ) {
-      astError( AST__INTER, "astTransform(%s): The %s class does not have "
-                "an inverse transformation (AST internal programming error).", status,
-                astGetClass( this ), astGetClass( this ) );
-
-/* Otherwise use the astRate method on the encapsulated Maping to
-   determine the required rate of change at each supplied input point. */
-   } else {
-
-/* Temporarily reset the Invert attribute of the encapsulated Mapping
-   back to the value it had when the RateMap was created. */
-      emap = map->map;
-      old_inv = astGetInvert( emap );
-      astSetInvert( emap, map->invert );
-
-/* Note the indices of the input and output to use. */
-      iin = map->iin;
-      iout = map->iout;
-
-/* Get pointers to the axis values in the supplied PointSet. */
-      ptr = astGetPoints( in );
-      ncoord = astGetNcoord( in );
-      npoint = astGetNpoint( in );
-
-/* Work space to hold an input position. */
-      work = astMalloc( sizeof( double )*(size_t) ncoord );
-
-/* Get a pointer to the axis values in the results PointSet. */
-      ptr2 = astGetPoints( result );
-      pout = ptr2[ 0 ];
-      if( astOK ) {
-
-/* Loop round each point in the supplied PointSet. */
-         for( ipoint = 0; ipoint < npoint; ipoint++ ) {
-
-/* Copy this point into the work array. */
-            for( ic = 0; ic < ncoord; ic++ ) work[ ic ] = ptr[ ic ][ ipoint ];
-
-/* Find the rate of change of the specified output of the encapsulated
-   Mapping with respect to the specified input. */
-            *(pout++) = astRate( emap, work, iout, iin );
-         }
-      }
-
-/* Re-instate the original Invert flag. */
-      astSetInvert( emap, old_inv );
-
-/* Free resources */
-      work = astFree( work );
-
-   }
-
-/* If an error occurred, clean up by deleting the output PointSet (if
-   allocated by this function) and setting a NULL result pointer. */
-   if ( !astOK ) {
-      if ( !out ) result = astDelete( result );
-      result = NULL;
-   }
-
-/* Return a pointer to the output PointSet. */
-   return result;
-}
-
-/* Copy constructor. */
-/* ----------------- */
-static void Copy( const AstObject *objin, AstObject *objout, int *status ) {
-/*
-*  Name:
-*     Copy
-
-*  Purpose:
-*     Copy constructor for RateMap objects.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     void Copy( const AstObject *objin, AstObject *objout, int *status )
-
-*  Description:
-*     This function implements the copy constructor for RateMap objects.
-
-*  Parameters:
-*     objin
-*        Pointer to the object to be copied.
-*     objout
-*        Pointer to the object being constructed.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     void
-
-*  Notes:
-*     -  This constructor makes a deep copy, including a copy of the component
-*     Mappings within the RateMap.
-*/
-
-/* Local Variables: */
-   AstRateMap *in;                /* Pointer to input RateMap */
-   AstRateMap *out;               /* Pointer to output RateMap */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain pointers to the input and output RateMaps. */
-   in = (AstRateMap *) objin;
-   out = (AstRateMap *) objout;
-
-/* For safety, start by clearing any references to the input component
-   Mappings from the output RateMap. */
-   out->map = NULL;
-
-/* Make copies of these Mappings and store pointers to them in the output
-   RateMap structure. */
-   out->map = astCopy( in->map );
-}
-
-/* Destructor. */
-/* ----------- */
-static void Delete( AstObject *obj, int *status ) {
-/*
-*  Name:
-*     Delete
-
-*  Purpose:
-*     Destructor for RateMap objects.
-
-*  Type:
-*     Private function.
-
-*  Synopsis:
-*     void Delete( AstObject *obj, int *status )
-
-*  Description:
-*     This function implements the destructor for RateMap objects.
-
-*  Parameters:
-*     obj
-*        Pointer to the object to be deleted.
-*     status
-*        Pointer to the inherited status variable.
-
-*  Returned Value:
-*     void
-
-*  Notes:
-*     This function attempts to execute even if the global error status is
-*     set.
-*/
-
-/* Local Variables: */
-   AstRateMap *this;              /* Pointer to RateMap */
-
-/* Obtain a pointer to the RateMap structure. */
-   this = (AstRateMap *) obj;
-
-/* Annul the pointers to the component Mappings. */
-   this->map = astAnnul( this->map );
-
-/* Clear the remaining RateMap variables. */
-   this->invert = 0;
-   this->iin = 0;
-   this->iout = 0;
-}
-
-/* Dump function. */
-/* -------------- */
-static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
-/*
-*  Name:
-*     Dump
-
-*  Purpose:
-*     Dump function for RateMap 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 RateMap class to an output Channel.
-
-*  Parameters:
-*     this
-*        Pointer to the RateMap 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 Variables: */
-   AstRateMap *this;              /* Pointer to the RateMap structure */
-   int ival;                     /* Integer value */
-   int set;                      /* Attribute value set? */
-
-/* Check the global error status. */
-   if ( !astOK ) return;
-
-/* Obtain a pointer to the RateMap structure. */
-   this = (AstRateMap *) this_object;
-
-/* Write out values representing the instance variables for the RateMap
-   class.  Accompany these with appropriate comment strings, possibly
-   depending on the values being written.*/
-
-/* In the case of attributes, we first use the appropriate (private)
-   Test...  member function to see if they are set. If so, we then use
-   the (private) Get... function to obtain the value to be written
-   out.
-
-   For attributes which are not set, we use the astGet... method to
-   obtain the value instead. This will supply a default value
-   (possibly provided by a derived class which over-rides this method)
-   which is more useful to a human reader as it corresponds to the
-   actual default attribute value.  Since "set" will be zero, these
-   values are for information only and will not be read back. */
-
-/* Input axis. */
-/* ------------ */
-   ival = this->iin;
-   set = ( ival != 0 );
-   astWriteInt( channel, "IIn", set, 0, ival, "Index of Mapping input" );
-
-/* Output axis. */
-/* ------------ */
-   ival = this->iout;
-   set = ( ival != 0 );
-   astWriteInt( channel, "IOut", set, 0, ival, "Index of Mapping output" );
-
-/* Invert flag. */
-/* ------------ */
-   ival = this->invert;
-   set = ( ival != 0 );
-   astWriteInt( channel, "Inv", set, 0, ival,
-                ival ? "Mapping used in inverse direction" :
-                       "Mapping used in forward direction" );
-
-/* Mapping. */
-/* -------- */
-   astWriteObject( channel, "Map", 1, 1, this->map,
-                   "Mapping to be differentiated" );
-
-}
-
-/* Standard class functions. */
-/* ========================= */
-/* Implement the astIsARateMap and astCheckRateMap functions using the
-   macros defined for this purpose in the "object.h" header file. */
-astMAKE_ISA(RateMap,Mapping)
-astMAKE_CHECK(RateMap)
-
-AstRateMap *astRateMap_( void *map_void, int ax1, int ax2, const char *options, int *status, ...) {
-/*
-*+
-*  Name:
-*     astRateMap
-
-*  Purpose:
-*     Create a RateMap.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     AstRateMap *astRateMap( AstMapping *map, int ax1, int ax2, const char *options, int *status, ... )
-
-*  Class Membership:
-*     RateMap constructor.
-
-*  Description:
-*     This function creates a new RateMap and optionally initialises its
-*     attributes.
-
-*  Parameters:
-*     map
-*        Pointer to the Mapping to differentiate.
-*     ax1
-*        zero-based index of the "map" output which is to be differentiated.
-*     ax2
-*        Zero-based index of the "map" input which is to be varied.
-*     options
-*        Pointer to a null terminated string containing an optional
-*        comma-separated list of attribute assignments to be used for
-*        initialising the new RateMap. The syntax used is the same as for the
-*        astSet method and may include "printf" format specifiers identified
-*        by "%" symbols in the normal way.
-*     status
-*        Pointer to the inherited status variable.
-*     ...
-*        If the "options" string contains "%" format specifiers, then an
-*        optional list of arguments may follow it in order to supply values to
-*        be substituted for these specifiers. The rules for supplying these
-*        are identical to those for the astSet method (and for the C "printf"
-*        function).
-
-*  Returned Value:
-*     A pointer to the new RateMap.
-
-*  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.
-*-
-
-*  Implementation Notes:
-*     - This function implements the basic RateMap constructor which is
-*     available via the protected interface to the RateMap class.  A
-*     public interface is provided by the astRateMapId_ function.
-*     - Because this function has a variable argument list, it is
-*     invoked by a macro that evaluates to a function pointer (not a
-*     function invocation) and no checking or casting of arguments is
-*     performed before the function is invoked. Because of this, the
-*     "map" parameter is of type (void *) and is converted and validated
-*     within the function itself.
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstRateMap *new;              /* Pointer to new RateMap */
-   AstMapping *map;              /* Pointer to Mapping structure */
-   va_list args;                 /* Variable argument list */
-
-/* Initialise. */
-   new = NULL;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* Check the global status. */
-   if ( !astOK ) return new;
-
-/* Obtain and validate pointers to the Mapping structures provided. */
-   map = astCheckMapping( map_void );
-   if ( astOK ) {
-
-/* Initialise the RateMap, allocating memory and initialising the
-   virtual function table as well if necessary. */
-      new = astInitRateMap( NULL, sizeof( AstRateMap ), !class_init, &class_vtab,
-                           "RateMap", map, ax1, ax2 );
-
-/* 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 RateMap'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 RateMap. */
-   return new;
-}
-
-AstRateMap *astRateMapId_( void *map_void, int ax1, int ax2,
-                           const char *options, ... ) {
-/*
-*++
-*  Name:
-c     astRateMap
-f     AST_RATEMAP
-
-*  Purpose:
-*     Create a RateMap.
-
-*  Type:
-*     Public function.
-
-*  Synopsis:
-c     #include "ratemap.h"
-c     AstRateMap *astRateMap( AstMapping *map, int ax1, int ax2,
-c                             const char *options, ... )
-f     RESULT = AST_RATEMAP( MAP, AX1, AX2, OPTIONS, STATUS )
-
-*  Class Membership:
-*     RateMap constructor.
-
-*  Description:
-*     This function creates a new RateMap and optionally initialises
-*     its attributes.
-*
-*     A RateMap is a Mapping which represents a single element of the
-*     Jacobian matrix of another Mapping. The Mapping for which the
-*     Jacobian is required is specified when the new RateMap is created,
-*     and is referred to as the "encapsulated Mapping" below.
-*
-*     The number of inputs to a RateMap is the same as the number of inputs
-*     to its encapsulated Mapping. The number of outputs from a RateMap
-*     is always one. This one output equals the rate of change of a
-*     specified output of the encapsulated Mapping with respect to a
-*     specified input of the encapsulated Mapping (the input and output
-*     to use are specified when the RateMap is created).
-*
-*     A RateMap which has not been inverted does not define an inverse
-*     transformation. If a RateMap has been inverted then it will define
-*     an inverse transformation but not a forward transformation.
-
-*  Parameters:
-c     map
-f     MAP = INTEGER (Given)
-*        Pointer to the encapsulated Mapping.
-c     ax1
-f     AX1 = INTEGER (Given)
-*        Index of the output from the encapsulated Mapping for which the
-*        rate of change is required. This corresponds to the delta
-*        quantity forming the numerator of the required element of the
-*        Jacobian matrix. The first axis has index 1.
-c     ax2
-f     AX2 = INTEGER (Given)
-*        Index of the input to the encapsulated Mapping which is to be
-*        varied. This corresponds to the delta quantity forming the
-*        denominator of the required element of the Jacobian matrix.
-*        The first axis has index 1.
-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 RateMap. 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 RateMap. 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     astRateMap()
-f     AST_RATEMAP = INTEGER
-*        A pointer to the new RateMap.
-
-*  Notes:
-*     - The forward transformation of the encapsulated Mapping must be
-*     defined.
-c     - Note that the component Mappings supplied are not copied by
-c     astRateMap (the new RateMap simply retains a reference to
-c     them). They may continue to be used for other purposes, but
-c     should not be deleted. If a RateMap containing a copy of its
-c     component Mappings is required, then a copy of the RateMap should
-c     be made using astCopy.
-f     - Note that the component Mappings supplied are not copied by
-f     AST_RATEMAP (the new RateMap simply retains a reference to
-f     them). They may continue to be used for other purposes, but
-f     should not be deleted. If a RateMap containing a copy of its
-f     component Mappings is required, then a copy of the RateMap should
-f     be made using AST_COPY.
-*     - 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.
-*--
-
-*  Implementation Notes:
-*     - This function implements the external (public) interface to
-*     the astRateMap constructor function. It returns an ID value
-*     (instead of a true C pointer) to external users, and must be
-*     provided because astRateMap_ has a variable argument list which
-*     cannot be encapsulated in a macro (where this conversion would
-*     otherwise occur).
-*     - Because no checking or casting of arguments is performed
-*     before the function is invoked, the "map" parameter is of type
-*     (void *) and is converted from an ID value to a pointer and
-*     validated within the function itself.
-*     - The variable argument list also prevents this function from
-*     invoking astRateMap_ directly, so it must be a re-implementation
-*     of it in all respects, except for the conversions between IDs
-*     and pointers on input/output of Objects.
-*/
-
-/* Local Variables: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstRateMap *new;              /* Pointer to new RateMap */
-   AstMapping *map;              /* Pointer to Mapping structure */
-   va_list args;                 /* Variable argument list */
-
-/* Pointer to inherited status value */
-   int *status;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(NULL);
-
-/* Initialise. */
-   new = NULL;
-
-/* Get a pointer to the inherited status value. */
-   status = astGetStatusPtr;
-
-/* Check the global status. */
-   if ( !astOK ) return new;
-
-/* Obtain the Mapping pointer from the ID supplied and validate the
-   pointer to ensure it identifies a valid Mapping. */
-   map = astVerifyMapping( astMakePointer( map_void ) );
-   if ( astOK ) {
-
-/* Initialise the RateMap, allocating memory and initialising the
-   virtual function table as well if necessary. */
-      new = astInitRateMap( NULL, sizeof( AstRateMap ), !class_init, &class_vtab,
-                           "RateMap", map, ax1 - 1, ax2 - 1 );
-
-/* 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 RateMap'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 RateMap. */
-   return astMakeId( new );
-}
-
-AstRateMap *astInitRateMap_( void *mem, size_t size, int init,
-                           AstRateMapVtab *vtab, const char *name,
-                           AstMapping *map, int ax1, int ax2, int *status ) {
-/*
-*+
-*  Name:
-*     astInitRateMap
-
-*  Purpose:
-*     Initialise a RateMap.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     AstRateMap *astInitRateMap( void *mem, size_t size, int init,
-*                                 AstRateMapVtab *vtab, const char *name,
-*                                 AstMapping *map, int ax1, int ax2 )
-
-*  Class Membership:
-*     RateMap initialiser.
-
-*  Description:
-*     This function is provided for use by class implementations to initialise
-*     a new RateMap object. It allocates memory (if necessary) to
-*     accommodate the RateMap plus any additional data associated with the
-*     derived class. It then initialises a RateMap 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 RateMap at the start of
-*     the memory passed via the "vtab" parameter.
-
-*  Parameters:
-*     mem
-*        A pointer to the memory in which the RateMap is to be initialised.
-*        This must be of sufficient size to accommodate the RateMap data
-*        (sizeof(RateMap)) 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 RateMap (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
-*        RateMap structure, so a valid value must be supplied even if not
-*        required for allocating memory.
-*     init
-*        A logical flag indicating if the RateMap'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 RateMap.
-*     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 Object
-*        astClass function).
-*     map
-*        Pointer to the Mapping.
-*     ax1
-*        Zero-based index of output axis.
-*     ax2
-*        Zero-based index of input axis.
-
-*  Returned Value:
-*     A pointer to the new RateMap.
-
-*  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: */
-   AstRateMap *new;              /* Pointer to new RateMap */
-   int nin;                      /* No. input coordinates for RateMap */
-   int nout;                     /* No. output coordinates for RateMap */
-
-/* Check the global status. */
-   if ( !astOK ) return NULL;
-
-/* If necessary, initialise the virtual function table. */
-   if ( init ) astInitRateMapVtab( vtab, name );
-
-/* Initialise. */
-   new = NULL;
-
-/* Report an error if "map" has no forward transformation. */
-   if( !astGetTranForward( map ) && astOK ) {
-      astError( AST__INTRD, "astInitRateMap(%s): The supplied Mapping "
-              "is not able to transform coordinates in the forward direction.", status,
-              name );
-   }
-
-/* Check that the input and output axis indices are valid. */
-   nin = astGetNin( map );
-   nout = astGetNout( map );
-   if( ( ax1 < 0 || ax1 >= nout ) && astOK ) {
-      astError( AST__INNCO, "astInitRateMap(%s): The output axis %d is out "
-                "of range - it should be in the range 1 to %d.", status, name,
-                ax1 + 1, nout );
-   }
-   if( ( ax2 < 0 || ax2 >= nin ) && astOK ) {
-      astError( AST__INNCO, "astInitRateMap(%s): The input axis %d is out "
-                "of range - it should be in the range 1 to %d.", status, name,
-                ax2 + 1, nin );
-   }
-
-/* Initialise a Mapping structure (the parent class) as the first component
-   within the RateMap structure, allocating memory if necessary. Specify
-   the number of input and output coordinates and in which directions the
-   Mapping should be defined. */
-   if ( astOK ) {
-      new = (AstRateMap *) astInitMapping( mem, size, 0,
-                                          (AstMappingVtab *) vtab, name,
-                                          nin, 1, 1, 0 );
-
-      if ( astOK ) {
-
-/* Initialise the RateMap data. */
-/* --------------------------- */
-/* Store a pointer to the encapsulated Mapping. */
-         new->map = astClone( map );
-
-/* Save the initial values of the inversion flag for this Mapping. */
-         new->invert = astGetInvert( map );
-
-/* Save the input and output axis indices. */
-         new->iout = ax1;
-         new->iin = ax2;
-
-/* If an error occurred, clean up by annulling the Mapping pointers and
-   deleting the new object. */
-         if ( !astOK ) {
-            new->map = astAnnul( new->map );
-            new = astDelete( new );
-         }
-      }
-   }
-
-/* Return a pointer to the new object. */
-   return new;
-}
-
-AstRateMap *astLoadRateMap_( void *mem, size_t size,
-                             AstRateMapVtab *vtab, const char *name,
-                             AstChannel *channel, int *status ) {
-/*
-*+
-*  Name:
-*     astLoadRateMap
-
-*  Purpose:
-*     Load a RateMap.
-
-*  Type:
-*     Protected function.
-
-*  Synopsis:
-*     #include "ratemap.h"
-*     AstRateMap *astLoadRateMap( void *mem, size_t size,
-*                                 AstRateMapVtab *vtab, const char *name,
-*                                 AstChannel *channel )
-
-*  Class Membership:
-*     RateMap loader.
-
-*  Description:
-*     This function is provided to load a new RateMap 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
-*     RateMap 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 RateMap at the start of the memory
-*     passed via the "vtab" parameter.
-
-
-*  Parameters:
-*     mem
-*        A pointer to the memory into which the RateMap is to be
-*        loaded.  This must be of sufficient size to accommodate the
-*        RateMap data (sizeof(RateMap)) 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 RateMap (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 RateMap 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(AstRateMap) is used instead.
-*     vtab
-*        Pointer to the start of the virtual function table to be
-*        associated with the new RateMap. If this is NULL, a pointer to
-*        the (static) virtual function table for the RateMap 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 "RateMap" is used instead.
-
-*  Returned Value:
-*     A pointer to the new RateMap.
-
-*  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: */
-   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
-   AstRateMap *new;               /* Pointer to the new RateMap */
-
-/* Initialise. */
-   new = NULL;
-
-/* Check the global error status. */
-   if ( !astOK ) return new;
-
-/* Get a pointer to the thread specific global data structure. */
-   astGET_GLOBALS(channel);
-
-/* If a NULL virtual function table has been supplied, then this is
-   the first loader to be invoked for this RateMap. In this case the
-   RateMap belongs to this class, so supply appropriate values to be
-   passed to the parent class loader (and its parent, etc.). */
-   if ( !vtab ) {
-      size = sizeof( AstRateMap );
-      vtab = &class_vtab;
-      name = "RateMap";
-
-/* If required, initialise the virtual function table for this class. */
-      if ( !class_init ) {
-         astInitRateMapVtab( 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 RateMap. */
-   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, "RateMap" );
-
-/* Now read each individual data item from this list and use it to
-   initialise the appropriate instance variable(s) for this class. */
-
-/* In the case of attributes, we first read the "raw" input value,
-   supplying the "unset" value as the default. If a "set" value is
-   obtained, we then use the appropriate (private) Set... member
-   function to validate and set the value properly. */
-
-/* Invert flag. */
-/* ------------ */
-      new->invert = astReadInt( channel, "inv", 0 );
-      new->invert = ( new->invert != 0 );
-
-/* Input and output axes. */
-/* ---------------------- */
-      new->iin = astReadInt( channel, "iin", 0 );
-      new->iout = astReadInt( channel, "iout", 0 );
-
-/* Mapping. */
-/* -------- */
-      new->map = astReadObject( channel, "map", NULL );
-
-/* If an error occurred, clean up by deleting the new RateMap. */
-      if ( !astOK ) new = astDelete( new );
-   }
-
-/* Return the new RateMap pointer. */
-   return new;
-}
-
-/* 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. */
-
-/* None. */
-
-
-
-