diff
====

Difference and discrete derivative



Calling Sequence
~~~~~~~~~~~~~~~~


::

    y=diff(x)
    y=diff(x [,n [,dim]])




Arguments
~~~~~~~~~

:x vector or matrix (real, complex, sparse or polynomial)
: :n integer the order of differentiation
: :dim integer or character string with values "r","c" and "*"
: :y scalar or vector/matrix
:



Description
~~~~~~~~~~~

`y=diff(x)` compute the difference function `y=x(2:$)-x(1:$-1)`

`diff(x,n,dim)` is the `n`th difference function along dimension
`dim`.

`diff(x,n,"*")` is equivalent to `diff(x(:),n)`.

Default value for `n` is 1. Default value for `dim` is `"*"`.

`dim='r'` is equivalent to `dim=1` and `dim='c'` is equivalent to
`dim=2`.



Examples
~~~~~~~~


::

    v=(1:8)^3;
    diff(v)
    diff(v,3)
    
    A=[(1:8)^2
       (1:8)^3
       (1:8)^4];
    
    diff(A,3,2)
    
    //approximate differentiation
    step=0.001
    t=0:step:10;
    y=`sin`_(t);
    dy=diff(`sin`_(t))/step; //approximate differentiation of sine function
    `norm`_(dy-`cos`_(t(1:$-1)),%inf)