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$$$$ IPOL     NOTICE  GOUNAND   12/09/10    21:15:07     7495           
                                             DATE     12/09/10

  Operateur IPOL                           Voir aussi :
    --------------   
    1)   OBJET2 = 'IPOL'  OBJET1 | LREEL1 LREEL2 |
                                 | EVOL1         |

                          ('SPLI' ('DGAU' FLOT1) ('DDRO' FLOT2)) ;


    2)   OBJET2 = 'IPOL'  TABLE T  ;
            TABLE : TABLE de soustype 'RESULTAT'
            T     : FLOTTANT

    3)   OBJET2 = 'IPOL'  NUA1 OBJET1 | ('GAUSS') | ;
                                      |  'RATIO'  |


    Description :
    ____________

    The IPOL operator enables the user to create OBJET2 :

    1)  obtained by interpolating a function in OBJET1. The type and
        characteristics of OBJET2 are the same as those of OBJET1.
        Linear interpolation is used by default. If the keyword 'SPLI'
        is given, cubic spline interpolation is used instead.
        
    2)  calculated by interpolating a CHPOINT or a MCHAML depending on
        the content type of TABLE) from a table which subtype is
        'RESULTAT' at a real value T. 

    3)  obtained as an interpolation of n scalar variables function
        of p scalar values. The value of function at some points is
        stored in a NUAGE type object under (x,f(x)) where x has n
        components and f(x) has p components. OBJET1 is either a field
        by points (CHPOINT) or a field by elements (MCHAML) with n
        components. The name of those components are also in the NUAGE
        type object. OBJET2 has the same type as OBJET1.
         ex: NUA1 of components            'X' 'Y' 'Z'
             OBJET1  of components         'X' 'Y'
             OBJET2  of components         'Z'
        The key-word 'GAUSS' and 'RATIO' let the user select either
        a gaussian function or a rational function (x-> 1/(1+x) ) as
        the weighting function. (GAUSS is the default)

    Contents :
    __________

    1) The possible types for OBJET1 are  : - FLOTTANT
                                            - LISTREEL
                                            - CHPOINT
                                            - MCHAML

     The function is defined by :
       LREEL1  : list of abscissae listed in increasing or decreasing
                 order (LISTREEL type)
       LREEL2  : list of the corresponding ordinates
                 (LISTREEL type)

     or by
       EVOL1   : elementary scalar evolution containing two LISTREELs

    2) When OBJET1 is a CHPOINT type object, the result OBJET2 has the
       nature as OBJET1.

    3) In the case of syntax 1, when cubic spline interpolation is
       chosen, one can prescribe the spline's first derivative on the
       left (resp. right) boundary with the 'DGAU' (resp. 'DDRO')
       keyword. If the first derivative is not given, the natural
       boundary condition (zero second derivative) applies.
       Remark: cubic spline interpolation has a non-local character, it
       depends on all the values of the given function.

    4) In the case of syntax 3, the interpolation method is derived from
       the diffuse element method with first order polynoms.


    Exemple :
    _________

    syntax 2 :
*   The table which sous-type is RESULTAT is initialized by :
    matab = 'TABLE' RESULTAT ;
 
*   then one must have a monotonous sequence of indices (type FLOTTANT)
*   an a corresponding sequences or values of the same given type
*   (CHPOINT ou MCHAML). For example :
    matab. 1.5 = chpo1 ;
    matab. 3.  = chpo2 ;
 
*   and then, one can interpolate
    chpo3  = 'IPOL' matab 2. ;
 
*   which results is the same as the one obtained by the operation :
    chpo3  = ( CHPO1 * (2./3.) ) + (CHPO2 * (1./3.))