====== Functions y=f(t) ======

Functions are quite useful to describe how some parameters evolve, over time for example. They can be used to [[doc:user:conditions:displacements|prescribe displacements]] or to define [[doc:user:elements:volumes:start|hardening laws]].

===== PieceWiseLinearFunction =====

A piecewise linear function is defined one point at a time:


    fct = PieceWiseLinearFunction()
    fct.setData(abs1, ord1)
    fct.setData(abs2, ord2)
    ...

where

| ''abs1'', ''abs2'', ... | list of abscissae |
| ''ord1'', ''ord2'', ... | list of ordinates |

{{ doc:user:piecewise.gif |Piecewise linear function}}

__Remark:__ As can be seen above, the first and last segments are extrapolated if a value of the function is required outside its domain.

===== CyclicPieceWiseLinearFunction =====
The ''CyclicPieceWiseLinearFunction'' allows to duplicate infinitely  a ''PieceWiseLinearFunction''.

{{ :doc:user:cyclicpiecewiselinearfunction.png?600 |}}

2 constrains are applied on Data : 
  - the first abcisse must be equal to 0.0 (abs1 = 0.0)
  - the cycle must be closed (ord1 = ordLast)

===== PythonOneParameterFunction =====

If a function is mathematically too complex to be defined with a ''PieceWiseLinearFunction'', it can be defined analytically, with a ''PythonOneParameterFunction'' object.

  def f(x):
      [function calculating y=f(x)]
      return y
  fct1 = PythonOneParameterFunction(f)

For example, this is used to:
    * Set the node density for a 1D mesher ([[doc:user:geometry:mesh:1d]]).
    * define elaborated prescribed displacements ([[doc:user:conditions:displacements]]).
    * Define a hardening function with Python ([[doc:user:elements:volumes:start]]).

===== Examples =====

The ramp function:

    fct1 = PieceWiseLinearFunction()
    fct1.setData(0,0)
    fct1.setData(1,1)

can be also defined with a classical python function:

    def f(x):
        return x
    fct1 = PythonOneParameterFunction(f)

or, using python ''lambda'' function:

    f = lambda x: x
    fct1 = PythonOneParameterFunction(f)

===== Advanced use =====
{{:doc:user:ico-advanced.png?40 |Advanced}}
The value can also be displayed for each estimation, and a more complex function can also be defined using all Python tools. For example, a load function can be first defined with a parabola, then with a straight line, the change between these two being controlled by an conditional structure.

    def f(a):
        val=0
        if(a‹0.5):
             val=a*a
        else:
             x=0.5*0.5;
             val=x+(a-0.5)/(1-0.5)*(1-x)
        print 'value=', val
        return val	
    fct1 = PythonOneParameterFunction(f)