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$$$$ GANE     NOTICE  CHAT      11/09/12    21:16:22     7124           
                                             DATE     11/09/12

    Operator GA(us-)NE(wton)                See also : MOCA, LEVM
    -------------------------                          AJUSTE, EXCE

    TAB2=GANE TAB1 ('AMOR' FLOT1);
    
    CHPO1 RIGI1=GANE TAB1 'MATR' ('AMOR' FLOT1);

     
    Description:
    ____________
    
    The GANE operator constructs the matrix and the second member of
    the Gauss-Newton or the Levenberg-Marquardt methods. 
    
    - Giving the key word 'MATR', these objects are given back in CHPO1
      (object of type 'CHPOINT') and RIGI1 (object of type
      'RIGIDITE'). 
      
    - Without this keyword, the system is solved. The result (descent
      direction) is stored in TAB2 (object of type 'TABLE').
      
    - The key-word 'AMOR' allows to introduce the viscosity parameter
      nu=FLOT1 (object of type 'FLOTTANT') of the L-M method. When
      'AMOR' is not given, nu=0 (G-N method).
    
    The function to minimize is 2F(X)={f(X)}.{f(X)}, and [J(X)]=df/dX
    
    The descent direction is H solution of:
      [[transpose([J])[J]]+[nu*I]]{H}  = -{transpose([J]){f}}

    For an application, see the test case gane.dgibi.
    
    Contents:
    _________
    
    TAB1   :  Table of type 'VECTEUR' containing
              TAB1 . 0 = f(X)
              TAB1 . 1 = df/dX1
                   .
              TAB1 . n = df/dXn
              
    FLOT1  :  Flottant=nu
              
    CHPO1  :  -{transpose([J]){f}}
    RIGI1  :  [transpose([J])[J]]
    
    TAB2   :  TABLE of type 'VECTEUR' containing
              TAB2 . 1 = H1
                   .           
              TAB2 . n = Hn