update ast 8.6.2

1 files changed, 2011 insertions, 0 deletions

diff --git a/ast/ratemap.c b/ast/ratemap.c
new file mode 100644
index 0000000..1e343a6
--- /dev/null
+++ b/ast/ratemap.c
@@ -0,0 +1,2011 @@
+/*
+*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. */
+
+
+
+