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# ConvertAxisByFormula v1¶

## Summary¶

Converts the X or Y axis of a MatrixWorkspace via a user defined math formula.

ConvertUnits

## Properties¶

Name

Direction

Type

Default

Description

InputWorkspace

Input

MatrixWorkspace

Mandatory

Name of the input workspace

OutputWorkspace

Output

MatrixWorkspace

Mandatory

Name of the output workspace

Axis

Input

string

X

The axis to modify. Allowed values: [‘X’, ‘Y’]

Formula

Input

string

The formula to use to convert the values, x or y may be used to refer to the axis values. l1, l2, twotheta and signedtwothetamay be used to provide values from the instrument geometry.

AxisTitle

Input

string

The label of he new axis. If not set then the title will not change.

AxisUnits

Input

string

The units of the new axis. If not set then the unit will not change

## Description¶

This algorithm allows users to adjust the axes of a workspace by a user defined math formula. It will adjust the data values (other than in one case the X values) of a workspace, although it will reverse the spectra if needed to keep the X values increasing across the workspace. This only works for MatrixWorkspaces, so will not work on Multi Dimensional Workspaces or Table Workspaces. If you specify one of the known Units then that will be the resulting unit, otherwise like the ConvertSpectrumAxis v2 algorithm the result of this algorithm will have custom units defined for the axis you have altered, and as such may not work in all other algorithms.

The algorithm can operate on the X or Y axis, but cannot alter the values of a spectrum axis (the axis used as the Y axis on newly loaded Raw data). If you wish to alter this axis use the ConvertSpectrumAxis v2 algorithm first.

The formula is defined in a simple math syntax. For example:

• Squaring - x^2

• Square root - sqrt(x)

• Cubing - x^3

• Basic addition - y + 3

• Brackets - (y+1)/20

• Natural Log - ln(x)

• Log 10 - log(x)

• Exponent - exp(y)

• Round to nearest integer - rint(y/10)

• Absolute value - abs(y-100)

• Sine function (angle in radians) - sin(x)

x and y can be used interchangeably to refer to the current axis value.

### Using Constants¶

The following constants are predeined for use in your equations:

• pi - The ratio of a circle’s circumference to its diameter

• h - Planck constant in J*s

• h_bar - Planck constant in J*s, divided by 2 PI

• g - Standard acceleration due to gravity. Precise value in ms-2

• mN - Mass of the neutron in kg

• mNAMU - Mass of the neutron in AMU

### Using geometry variables¶

If the axis you are not transforming is a spectrum axis (the axis used as the Y axis on newly loaded Raw data). Then you may also include geometry variables in your formula and they will be correctly interpreted by the algorithm.

The algorithm supports the following geometry variables: * l1 - the distance between the source and sample * l2 - the distance between the sample and detector * signedtwotheta - the exit angle from the sample when it is determined with respect to the extended incoming beam * twotheta - abs(signedtwotheta)

Refer to the muparser page for a full list of the functions available.

## Usage¶

Example - Squaring the X axis:

# Create sample input workspace
dataX = [1,2,3,4,5]
dataY = [1,1,1,1,1]
input = CreateWorkspace(dataX, dataY)

output = ConvertAxisByFormula(InputWorkspace=input,
Axis="X",
Formula="x^2",
AxisTitle="Squared X",
AxisUnits="x^2")

print("New X values: {}".format(output.getAxis(0).extractValues()))
print("New X units: {}".format(output.getAxis(0).getUnit().symbol()))
print("New X title: {}".format(output.getAxis(0).getUnit().caption()))


Output:

New X values: [  1.   4.   9.  16.  25.]
New X units: x^2
New X title: Squared X


Example - Doubling the Y axis:

from mantid.api import NumericAxis

# Create sample input workspace (with 5 spectra)
dataX = [1,2,3,4,5]
dataY = [1,1,1,1,1]
input = CreateWorkspace(dataX, dataY, NSpec=5)

# Create numeric Y axis with values [1..5]
yAxis = NumericAxis.create(5)
for i in range(0,5):
yAxis.setValue(i, i+1)

# Replace Y axis in the input workspace. This is necessary because CreateWorkspace
# uses TextAxis by default, which are not suitable for conversion.
input.replaceAxis(1, yAxis)

output = ConvertAxisByFormula(InputWorkspace=input,
Axis="Y",
Formula="y*2",
AxisTitle="Doubled Y",
AxisUnits="y*2")

print("New Y values: {}".format(output.getAxis(1).extractValues()))
print("New Y units: {}".format(output.getAxis(1).getUnit().symbol()))
print("New Y title: {}".format(output.getAxis(1).getUnit().caption()))


Output:

New Y values: [  2.   4.   6.   8.  10.]
New Y units: y*2
New Y title: Doubled Y


Example - Converting from Wavelength to Momentum Transfer:

wsWavelength = CreateSampleWorkspace(XUnit='Wavelength', XMin=2, XMax=6, BinWidth=0.05)
# Convert to momentum transfer
# directly using a formula
wsMTbyFormula = ConvertAxisByFormula(InputWorkspace=wsWavelength,  Formula='(4*pi*sin(twotheta/2))/x', AxisUnits='MomentumTransfer')
# using convert units (this will convert via time of flight)
wsMTbyConvertUnits = ConvertUnits(InputWorkspace=wsWavelength, Target='MomentumTransfer')

#check they are the same
isMatched, messageTable = CompareWorkspaces(wsMTbyFormula,wsMTbyConvertUnits,0.00001,checkAxes=True, CheckType=True)
if isMatched:
print("Both methods create matching workspaces.")


Output:

Both methods create matching workspaces.


Categories: AlgorithmIndex | Transforms\Axes