Pattern Ahead

Stephen Hards
Mathematical Software Team

A powerful extension to Mathcad 11 enables engineering data patterns and relationships to be analysed. And as part of Mathcad, it means the results are instantly part of an engineering worksheet and a publication-quality document.

Designed with industrial applications in mind, the new Data Analysis Extension Pack for Mathcad 11 should appeal to a broad base of professionals from engineers to statisticians. Mathcad is of course already ideal for exploratory data analysis and ‘what-if’ scenarios; the new Extension Pack is aimed at offering the very latest technology in fitting algorithms for quicker, more robust and more accurate solutions.

Users instantly get added functionality in their copy of Mathcad 11, enabling the import of multiple and large-scale files in multiple file formats, including an interactive data preview to help import complicated file formats correctly.

No two technical professionals gather data in the same formats from the same types of system, so a lot of work has gone into ensuring that data can be used in many formats, including multiple, large datasets with inconsistent column formatting and labelling/headers. A Data Import wizard component allows you to read files in ASCII, fixed-width, binary, Excel, and other formats, to preview contents, visually select rows and columns for import, choose fillers for missing values, and specify delimiters.

The software is also adept at handling data on a very small or very large scale, which makes it difficult to fit, as well as data with hundreds of measurements that must be reduced to a more compact representation. Considerable effort has gone into the ability to evaluate data visually and qualitatively to determine the best course of analysis. Matrix utility functions are available for flexible table lookup, data ranking, and empirical maxima and minima searches.

There’s much more besides. The Data Analysis Extension Pack offers functions that help you manipulate raw data matrices, functions that calculate statistical quantities for vectors and matrices of data, and functions that detect, mark, and eliminate outliers from data for subsequent processing. There are functions that perform parametric fits to data or return information on the quality of fit, functions that interpolate between data points, and statistical functions for EDA, outlier detection, and missing value NaN (not a number) support. Flexible non-parametric fitting algorithms are available using statistical methods to create optimal solutions, and returning more information about the fit, as well as robust, generalised parametric nonlinear fitting functions, which support weighting and constraints.

Documentation includes examples of commonly used analysis scenarios with real data, written in Mathcad for reuse. There’s also detailed documentation of existing Mathcad functions for data analysis, which in conjunction with Mathcad programs and scriptable components, shows you new ways to use the already powerful toolset in Mathcad.

Service Release for Mathcad 11 crams in the features
Service Release 2 for Mathcad 11 has just been launched, and contains several new features, outlined below. It’s available free to registered Mathcad 11 users with current maintenance from the Adept Scientific website.

A new right-click menu for pdesolve lists four options for a differencing method: Polynomial, CentralDiff, Diff5Point and Diff5PointRecursive. Switching between methods when solving a partial differential equation may yield more stable or accurate results, depending on the problem you are solving.

Strings now support a “newline” character to wrap text used as an error message. Typing “\n” in a string will cause text to wrap at that point when the string is displayed using the error function.

The medsmooth function will now filter all the data, instead of leaving points less than half the window width away from the ends untouched. All smoothing functions will now accept united vectors as inputs, and output smoothed vectors with the same units. The linfit function no longer requires sorted vectors, and will handle repeated values. The histogram and hist functions now create appropriate end bins for small-valued data.

To accommodate proper operation over a wider range of data values, the regress, slope, and intercept functions have been updated to pre-scale data before calculating coefficients. After calculating the regression coefficients, they rescale them to the original data range. This should result in closer fits with smaller errors for a wider range of data input values over a larger number of polynomial orders. And lookup functions can now handle input matrices with different types (e.g., strings and numbers).

If you’re running Mathcad 11 with current maintenance, you can download this latest service release from http://www.adeptscience.co.uk/go?pg=AA502.