.. algorithm::

.. summary::

.. relatedalgorithms::

.. properties::

Description
-----------

This algorithm fits a spectrum to a user defined function. The function
is supplied to the algorithm as a text string. The function here is a
mathematical expression using numbers, variable names and internal
function names. Symbols '+', '-', '\*', '/', and '^' can be used for
arithmetic operations. Names can contain only letters, digits, and the
underscore symbol '\_'. The internal functions are:

+---------+---------+-------------------------------------+
| Name    | Argc.   | Explanation                         |
+=========+=========+=====================================+
| sin     | 1       | sine function                       |
+---------+---------+-------------------------------------+
| cos     | 1       | cosine function                     |
+---------+---------+-------------------------------------+
| tan     | 1       | tangens function                    |
+---------+---------+-------------------------------------+
| asin    | 1       | arcus sine function                 |
+---------+---------+-------------------------------------+
| acos    | 1       | arcus cosine function               |
+---------+---------+-------------------------------------+
| atan    | 1       | arcus tangens function              |
+---------+---------+-------------------------------------+
| sinh    | 1       | hyperbolic sine function            |
+---------+---------+-------------------------------------+
| cosh    | 1       | hyperbolic cosine                   |
+---------+---------+-------------------------------------+
| tanh    | 1       | hyperbolic tangens function         |
+---------+---------+-------------------------------------+
| asinh   | 1       | hyperbolic arcus sine function      |
+---------+---------+-------------------------------------+
| acosh   | 1       | hyperbolic arcus tangens function   |
+---------+---------+-------------------------------------+
| atanh   | 1       | hyperbolic arcur tangens function   |
+---------+---------+-------------------------------------+
| log2    | 1       | logarithm to the base 2             |
+---------+---------+-------------------------------------+
| log10   | 1       | logarithm to the base 10            |
+---------+---------+-------------------------------------+
| log     | 1       | logarithm to the base 10            |
+---------+---------+-------------------------------------+
| ln      | 1       | logarithm to base e (2.71828...)    |
+---------+---------+-------------------------------------+
| exp     | 1       | e raised to the power of x          |
+---------+---------+-------------------------------------+
| sqrt    | 1       | square root of a value              |
+---------+---------+-------------------------------------+
| sign    | 1       | sign function -1 if x<0; 1 if x>0   |
+---------+---------+-------------------------------------+
| rint    | 1       | round to nearest integer            |
+---------+---------+-------------------------------------+
| abs     | 1       | absolute value                      |
+---------+---------+-------------------------------------+
| if      | 3       | if ... then ... else ...            |
+---------+---------+-------------------------------------+
| min     | var.    | min of all arguments                |
+---------+---------+-------------------------------------+
| max     | var.    | max of all arguments                |
+---------+---------+-------------------------------------+
| sum     | var.    | sum of all arguments                |
+---------+---------+-------------------------------------+
| avg     | var.    | mean value of all arguments         |
+---------+---------+-------------------------------------+

An example of *Function* property is "a + b\*x + c\*x^2". Variable *x*
is used to represent the values of the X-vector of the input spectrum.
All other variable names are treated as fitting parameters. A parameter
can be given an initial value in the *InitialParameters* property. For
example, "b=1, c=0.2". The order in which the variables are listed is
not important. If a variable is not given a value, it is initialized
with 0.0. If some of the parameters should be fixed in the fit list them
in the *Fix* property in any order, e.g. "a,c".

The resulting parameters are returned in a
:ref:`TableWorkspace <Table Workspaces>` set in ``OutputParameters`` property.
Also for displaying purposes *OutputWorkspace* is returned. It contains
the initial spectrum, the fitted spectrum and their difference.

Example
-------

.. figure:: /images/UserFunction1D.gif

In this example the fitting function is a\*exp(-(x-c)^2\*s). The
parameter *s* is fixed.

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