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A Review of the Free Tela Tensor Language

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The Tela Tensor Language

Tela 3D plot

The 3D plot of the classic sinx/x function you see here was created with Tela, one of the fastest scripting math languages available. It is used and made freely available by the Finnish Meteorological Institute, and created by Pekka Janhunen.

Unlike some of the math languages out there, such as Octave, Tela is an N-dimensional matrix language like Yorick and PDL. That means it can handle matrices of more than 2 dimensions -- up to 5 in fact. It follows Fortran-90 style syntax, and so is similar in syntax to MATLAB, Octave, and Euler.

Tela Syntax

Matrix creating, indexing and referencing is similar to MATLAB and Octave, though not exactly the same:

Create a 3 by 4 matrix
x = #(1,2 ,3 ,4 ; 11,12,13,14 ; 21,22,23,24)

Reference sub matrix, rows 1 to 2, columns 3 to 4
y = x[1:2,3:4]

To combine two x matrices by rows
y = #(x,x)

To combine two x matrices by columns
y = #(x',x')'

Matrix multiply x and y
z = x**y

Take each element of matrix to power of 2
y = x^2

As you can see by the examples, the #(...) operator is used to directly create matrices. Inherently, the operator combines matrices by rows. To combine by columns, use the #(...) operator to combine transposes of the matrices (the ' operator), and transpose the result.

Notice that the operator to take a variable to a power is the ^ operator. The ** operator indicates a matrix multiply in Tela.

Tela has a list type of data object that allows one to hold associated objects of potentially different type or size into a list structure. The object is called voids. A voids object is declared as a specific size, in more than one dimension if desired, and each element of the voids object can be equated with a data item.

Declare a voids object to hold 10 lists of 3 matrices each.
v = voids(10,3)
Set the 1st of 10 lists to 3 matrices, possibly of different size
v[1,1] = x;
v[1,2] = y;
v[1,3] = z;

The voids object can be referenced like a matrix, but each element may itself be a matrix.

Functions are declared similar to the way Octave functions are, except that compound statements (functions, loops, if-then-else) are all indicated by the curly brackets.

To define a function
function [x,y,z] = dosomething(a,b,c){
...
}

To receive multiple arguments
[x,y,z] = dosomething(a,b,c)

As you can see, the syntax is similar in concept, but a bit different in operator syntax from other languages you may have used.

Tela File I/O

Tela is a bit limited in file I/O for my tastes in that it gives little in the way of primitive functions. Without primitive functions, one is limited to files created in certain standard formats. Tela can read and write MATLAB 4 files and HDF files, and PNM graphic files. Tela can also read data from plain ASCII files. As long as the products you interface with uses one of these forms, you are in fine shape. But if you're trying to use data from a C or other language program for example, the burden is on the other language to create data forms compatible with Tela.


Tela Graphics

Sample Tela Plots

Tela definitely has graphics. It relies on the plotmtv plotting package for producing a wide range of graphs. Plotmtv, while called from Tela, can also be directly passed plotting instructions by the user.

And, as with Tela in general, the graphics is fast.

Tela is equipped to produce line plots, multi-line plots (with color), 3D filled and wire-model mesh plots, contour lines, and color contours, many of which are illustrated in the composite above.

Tela Plot Controls

As used with Tela, each graph includes a set of controls at the top of the graph. The image above is an example of the controls, which may vary according to the kind of plot being produced. All plots can be zoomed in or out, and all plots can be exported as GIF or postscript files. Line and point plots can interactively switch the x and y axis and functions between linear and logarithmic presentations. 3D plots can interactively be rotated by steps in the horizontal and vertical axis.

Note that while one may interact with a graph to alter the presentation, the interaction is with plotmtv, not with Tela. Because of this, it appears that Tela provides no mechanism to let the user click locations on a graph and have those locations picked up by Tela. Tela formulates the data and passes it off one way to plotmtv.

Each plot command issued to Tela produces another plot window, so multiple graphs can be displayed and examined at one time. It is also possible to pass control options that will cause plotmtv to plot multiple plots, each on its own axes, on a single window. One can also instruct plotmtv to stack multiple plots, and one can step through the plot window to see each of the plots.

These examples were captured from Tela screen images using the imagemagick import function. When plots are exported to postscript, the blue background becomes a white background for better reproduction in documents. Exported postscripts defaults to black and white, but a color option is available.

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Summary

Tela has a full range of math functions, including regression, statistical, interpolation, and Fourier Transform routines. All of these can operate on N-dimensional matrices, though the FFT routines work on only 1 dimension of a multi-dimensional matrix. Given Tela's speed and ample supply of data handling functions, it is well positioned to be both a model building utility and a data processing utility. The only weakness I see is that for data processing, the file I/O options are limited.

I found the greatest features of Tela to be it's relatively simple syntax, albeit a bit different than other languages, it's ability to handle N-dimensional matrices, and it's absolutely blinding speed. Out of a half-dozen other matrix languages I tried, the only one that came close to Tela's speed was Yorick.

As an example, as I struggled to grasp how to accomplish a convolution filter with the Tela FFT routines, I resorted to a simple 2 dimensional conventional convolution method in the time domain. Common wisdom says that this is a much slower technique than if the convolution can instead be a simple multiply in the frequency domain via FFT transforms. While this proved true in all the the other Matrix languages at my disposal, I was surprised to find that the time-domain convolution in Tela could run as fast as the Frequency domain method in other languages. I was impressed.

In getting to know Tela better, I eventually mastered the FFT convolution technique and created a few image handling routines in Tela. Below is an example of my efforts. I converted one of my moon images to a pgm file, loaded it into Tela with the import_PNM routine, then sharpened it with my newly created Tela sharpen routine. See my Astronomyhints web page for astrophotography details.

Stacked Tycho Moon Image
Sharpened Tycho Moon Image
Stacked Tycho Image
Tela Sharpened Image

Here's my subjective pros and cons on the Tela language.

Pros:
  • Freely available for the Linux operating system.

  • What stands out most is that Tela is Fast.

  • Can work with greater than 2 dimensional matrices (up to five by default).

  • Can support a record structure with the use of the Void operator.

  • Has a simple programming language, similar to Octave.

  • Is integrated with the plotmtv package, and can make 2D and 3D color plots. The plots are interactive by default.

  • Has file I/O support for some common standards such as MATLAB, HDF, and the PNM graphics files.

  • Tela not only does matrix operations fast, but is even amazingly tolerant to moderate use of loops.

  • Has sufficient ASCII file support to move files between most external utilities.

  • Cons:
  • Isn't available for many operating systems.

  • Doesn't have an extensive library of specialized functions.

  • Has limited low-level file I/O support, making it difficult to deal with especially binary files generated externally.

  • While the plotmtv graphics are interactive as to display characteristics, mouse clicks can not deliver information back to a Tela script.