Many problems, especially in scientific computing, end up being formulated as matrix operations. This can be anything from PDE-solvers (PDE - Partial Differential Equation) up to image-processing or ML-algorithms. The list is endless. Usually one has written on paper some final equations which describe your model or whatever it is, and it involves some matrix algebra like this: A = B + C Okay, looks quite easy on paper. Now, when it comes to implementation of this in JavaScript, whatever technique you are going to use (for-loops, iterators, ...), your code won't resemble above easy to read line. There is a huge amount of good matrix-libraries available, and usually they let you write something like this: A = B.add(C) This still looks not quite different from our paper version, but imagine our paper version would be this: A = (B * (C + D)) * (E + F) To put this into one line by using the '.add' notation might hurt a little and one would tend to split the code into multiple lines. Though, due to all these parenthesis, readability would be destroyed: H1 = E.add(F); H2 = C.add(D); H3 = B.multiply(H2); A = H3.multiply(H1); const const const const If we were in context of a language like C++, we can give sense to expressions involving mathematical operators between any custom types - a concept called Operator Overloading. At the time of writing, JavaScript is lacking this nice feature though. We can find some resort if we take a look at 'Tagged Templates' (see https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Template_literals). In essence they give us a way to interpret a given string together with value filled placeholders: A: Matrix = ...; B: Matrix = ...; C: Matrix = calc ; const const const ` + ` ${A} ${B} Here 'Matrix' shall be some type representing a matrix. The 'calc' is a tagged template function, written by us, and it will be called with all string parts and values for given placeholders. In other words we somewhere define a function like this: { } ( ) function calc stringParts: TemplateStringsArray, ...values: any[] '1.) parse the expression 2.) calculate it by using given placeholder-values 3.) return the result' Our main task remains to implement the 'calc' function such that it can cope with any kind of expression from matrix-algebra. You can do it on your own, it is quite a learning-full experience, or you can use my package provided here: https://www.npmjs.com/package/@applied.math.coding/lina With this at hand you can write expressions like these: calc ; A = calc ; calc ; ` = 3 * - ` ${A} ${B} ${C} `3 * - ` ${B} ${C} `pow( , 5)` ${A} The library also supports some form of slicing which becomes very handy in some occasions: calc ; ` )` ${A.slice( , , , ) = cos(${B.slice( , , , )} 1 1 5 5 1 1 5 5 It also has some support of creating a matrix-type from given array: A = mat([[ , ], [ , ]]); const 1 2 3 4 Or just create a new instance of some dimensions and with all values set to 0: A = zeros( , ); const 10 10 calc ; ` =sqrt(abs( )) + 7` ${A} ${A} Note: when you add or multiply a number with a matrix-type, as in above example, the parser is handling this by element-wise applying the operation to the matrix. And finally our initial example would look like this: calc ; ` = ( * ( + )) * ( + )` ${A} ${B} ${C} ${D} ${E} ${F} For more you can look into its docs or tests. Please keep the following in mind: The library is not intended for use in computation intensive environments. It rather should be used for educational purposes or for presentation of some computations on a web-page. I used it successfully in some small project which intended to explain the solution procedure of a PDE. I hope this helps or contributes to getting new ideas!
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