$$\renewcommand\AA{\unicode{x212B}}$$

# UserFunction1D v1¶

## Summary¶

Fits a histogram from a workspace to a user defined function.

Fit

## Properties¶

Name

Direction

Type

Default

Description

InputWorkspace

Input

MatrixWorkspace

Mandatory

Name of the input Workspace

WorkspaceIndex

Input

number

0

The Workspace to fit, uses the workspace numbering of the spectra (default 0)

StartX

Input

number

Optional

A value of x in, or on the low x boundary of, the first bin to include in the fit (default lowest value of x)

EndX

Input

number

Optional

A value in, or on the high x boundary of, the last bin the fitting range (default the highest value of x)

Fix

Input

string

A list of comma separated parameter names which should be fixed in the fit

MaxIterations

Input

number

500

Stop after this number of iterations if a good fit is not found

OutputStatus

Output

string

OutputChi2overDoF

Output

number

Function

Input

string

Mandatory

The fit function

InitialParameters

Input

string

The comma separated list of initial values of the fit parameters in the form varName=value

Output

Input

string

If not empty OutputParameters TableWorksace and OutputWorkspace will be created.

## 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 TableWorkspace set in OutputParameters property. Also for displaying purposes OutputWorkspace is returned. It contains the initial spectrum, the fitted spectrum and their difference.

## Example¶

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

Categories: AlgorithmIndex | Optimization\FitAlgorithms