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 |                         ABBREVIATED FUNCTION                    |
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 MEANING: User-supplied function that may be used in abbreviated code.
 CONTEXT: Fortran coded function

 USAGE:
 SUBROUTINE FUNCA(X,X1,X2)
 DOUBLE PRECISION X,X1,X2,FUNCA
 DIMENSION X(9),X1(9),X2(9,9)

 The constant "9" must be used exactly as shown.

 DISCUSSION:
 The FORTRAN function FUNCA may be used  in  abbreviated  code.   Simi-
 larly,  the functions FUNCB and FUNCC may be used; their constructions
 would be similar to that of FUNCA.  In abbreviated code, the  function
 is  referenced with a single argument, either a (scalar) expression or
 a vector (See abbreviated code).  In the code defining  the  function,
 the function has three arguments.

 Input Argument:

  X   The value of the argument (which may be a vector).

 Output Argument:

  FUNCA
      The value of the function is to be stored in FUNCA.

 There are two other outputs.

  X1  X1(n) is  the  first-partial  derivative  of  the  function  with
      respect to the nth element of the argument.
      If the value of X(n) will not be a value of  a  random  variable,
      X1(n) need not be set.
      If the argument X is a (scalar) expression, only X1(1) is needed.

  X2  X2(n,m) is the second-partial derivative  of  the  function  with
      respect to the nth and mth elements of the argument.
      If the value of either X(n) or X(m) will not be a value of a ran-
      dom  variable,  X2(n,m) need not be set. Nor need any value of X2
      be set if a test of MSEC=1 is false (See ROCM12).
      If the argument is a (scalar) expression,  only  X2(1,1)  may  be
      needed.   If the argument is a vector and if the value of X2(n,m)
      is needed, then the value of X2(m,n)  is  needed  as  well,  even
      though these two values will be identical.

 (See Abbreviated function example).

 REFERENCES: none                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      


  
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