### Mathematics

Origin provides a collection of tools for performing mathematical operations on 2D and 3D data. All tools support saving dialog settings as a theme for repeat use, and also support recalculation of results when data or analysis settings are changed.

Multiple analysis operations from these tools can be used in sequence and saved as an Analysis Template for repeated use. The analysis template can also be loaded in Batch Processing to apply to multiple imported files in a single configuration which saves a lot of time. The LabTalk scripting and Origin C programming can further extend Origin's analysis capability with the access to NAG library. The Gadgets for different mathematical operations can be used to easily apply analysis to all curves in all layers.

Calculation on Data Column

The most direct yet powerful way to manipulate data in a column is to use Set Column Values where you are allowed to use various types of variables which are hard to be defined using simple mathematical expressions. It is convenient to use Normalization tool to normalize your data to certain base and apply Average Multiple Curves to quickly output averaged curve with standard errors from all input curves as error bars.

• Set Column Values
• Normalization
• Average Multiple Curves
• Simple Math Calculations on Column

Origin supports interpolation/extrapolation with 1D, 2D and even 3D data with formula column using diverse methods, and supports trace interpolation for XY or XYZ dataset other than ordinary interpolation.

• 1D Interpolation/Extrapolation
• Interpolate/Extrapolate Y From X
• 2D Interpolation/Extrapolation
• 3D Interpolation
• Trace Interpolation and XYZ Trace Interpolation
Interpolate Gadget allows you to visually adjust interpolation/extrapolation range and the analysis operation can be applied to all other curves in all layers at one time.

Differentiation allows derivative calculation up to 9th order and smoothing of differentiated curve while integration is capable of performing integral with baseline to calculate either Mathematical or Absolute area. In addition, surface area and enclose Polygon area calculation are supported.

• Area Calculation
• Polygon Area
• Surface Area Calculation
• 2D Volume Integration and 2D Integration Gadget
2D Integration Gadget can perform volume integration over a specified region with baseline in an image plot or a contour plot, meanwhile extracting crucial parameters about the peak region, such as FWHM, Z Max, (x,y) at Z Max, Surface Area.

Matrix-Based Operations

For mathematical operation on matrix object, Set Matrix Values also allows before formula scripting to enrich types of variables can be used in formula. You can quickly calculate the inverse of a matrix through Inverse and filter matrix object through either customized filters or build in filters.

• Set Matrix Values
• Inverse
• Custom Filter
• Median Filter
• Special Filter

Time-Saving Options

In order to avoid time-consumingly repeating similar analysis operations for different dataset, Origin developed Analysis Template that can be used to save multiple analysis operations in a template which can be later loaded in Batch Processing to apply to all imported files. Besided these powerful mathematical tools mentioned above, Origin's Gadgets, LabTalk scripting and Origin C programming can be used to further extend the graphing and analysis capabilities.

• Analysis Template, Batch Processing
• Script and OC Possibility