numerical differentiation function

[etienne grossmann]

  Hello,

  this is just to say that I added a numerical differentiation
function to the archive of 'Miscellaneous' functions, at

   http://anonimo.isr.ist.utl.pt:8080/~etienne/octave/ 

  Cheers,

  Etienne


The help text goes like this : (comments, suggestions etc are welcome)

======================================================================

       df = ndiff( func [, options], argument(s) )

 Numerical differentiation of 'func'.

 By default, differentiation is with respect to the first argument
 found after the eventual options.

 If this variable (call it 'x') is of size RxC, and the output 'y' of
 'func' is SxD, then 'df' will be (S*D)x(R*C).

                  df(i,j) = dy(i)/dx(j)

 OPTIONS :
 ---------
 "dx"    , small_value     : value of the small perturbation in 'x'.
                                                      Default = 1e-6 

 "varnum", integer         : Number, in argument list, of the
                             differentiation variable.   Default = 1

 "rstack"  : allow stacking of arguments in rows. This means that

             [ func(x1) ; func(x2) ] == func( [ x1 ; x2 ] )

             (for differentiation of a one-arg function). When this
             option is passed, a 'func' is called once only.

 "cstack"  : allow stacking of arguments in columns. This means that

             [ func(x1) , func(x2) ] == func( [ x1 , x2 ] )

             (for differentiation of a one-arg function). When this
             option is passed, a 'func' is called once only.

 "assym:   : Perform calculation using an assymetric finite difference
             scheme rather than the symmetric scheme. With this
             option, 'func' is evaluated at R*C+1 points rather than
             the 2*R*C that are necessary for the symmetric scheme.
             Beware that error is then linear in the value of 'dx'
             rather than quadratic.

 EXAMPLES :
 ----------
 function y = foo(x,y,z) ... end

 df = ndiff("foo","varnum",2,x0,y0,z0)
 ## Returns an approximation of the differential of 'foo' wrt. 'y', at
 ## (x0,y0,z0). 

 df = ndiff("foo",x0,y0,z0)
 ## Returns an approximation of the differential of 'foo' wrt. 'x', at
 ## (x0,y0,z0). 



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