I need to explain 3-way tensors by using these diagram and also I want to know that how to draw them and in which software?
If you want to draw these diagrams or diagrams like these you can use any vector drawing tool. For example, there is an open source and free tool called Inkscape (https://inkscape.org/en/download/) which can be used for this purpose.
I do not know of any tool that can "generate" this kind of diagram in line art (grid & face projection) from perspective like shown on those four diagrams. I believe that a tool like Inkscape (or any other vector drawing tool) is the best option.
Bare in mind that this means that you will have to draw it manually. Also, for precision, you will have to enable the grid and grid snapping to make sure that all is nice and parallel in each axis of the projection.
On the other hand, you can also use any CAD tool, like AutoCad (commercial) or CoffeeSCad (http://coffeescad.net/) if you want to make more elaborate representations. This is probably too much, so Inkscape will mostly do.
Hi Kirandeep, I am not certain I fully understand your question:
Do you ask what software you can use to just draw schematic diagrams? Or do you ask for software to calculate Tensor Decompositions?
If the first, I'd say any (vector-) drawing program will do - Inkscape comes to mind as a decent free software, but for simple tasks like this, there are even nice free online drawing tools and e.g. addons you can install into the Google Chrome browser for free that can do this. If you have access to the "big players", any of CorelDraw, Illustrator, AutoCAD,... will do as well, of course.
If you are asking about the actual calculations, in the PDF you linked from page 489 onwards, there is a section about software - MATLAB, Maple and Mathematica are mentioned, and most programming languages will also allow you to do these calculations (C++ is mentioned in the document, but many others will have libraries/packages to do this).
I am not certain if there are any tools to automatically generate nice, simple schematic diagrams as on p. 458ff from a specific, numerical problem/calculation.
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