Developing a matrix arithmetic parser using JavaScript

Question

Developing a matrix arithmetic parser using JavaScript

Currently, I am in the process of developing a program that can solve matrix equations. My main focus right now is on making sure the parser functions correctly. However, I am feeling lost and unsure of where to begin.

In my program, I utilize an array of strings to keep track of both matrices and operators. For instance, if we take the equation

[[0, 0],[4, 5]] + [[4, 8], [12, 6]]

it would be organized as:

variables = ["$", "+", "$"]
matrices = [[[0, 0],[4, 5]], [[4, 8], [12, 6]]

Here, each "$" symbol represents a distinct matrix stored in a separate array. Additionally, I aim to encapsulate matrices within different expressions like so:

det([[0, 0],[4, 5]]) + inv([[0, 0],[4, 5]] + [[4, 8], [12, 6]])

where "det" and "inv" signify determinant and inverse operations respectively.

If represented in code, the above expression would look like this:

variables = ["d", "e", "t", "(", "$", ")", "+", "i", "n", "v", "(", "$", "+", "$", ")"]
matrices = [ [[0, 0],[4, 5]], [[0, 0],[4, 5]],  [[4, 8], [12, 6]] ]

My initial thought is to utilize context-free grammars for constructing a parse tree, as regular expressions may not be suitable due to the presence of parentheses... (?). Another idea I have is to convert the expressions into postfix notation and test its feasibility.

javascript parsing

Answer 1

Answer №1

Constructing a parse tree with the help of a context-free grammar seems like the most effective method in my opinion. (If you're not familiar with context-free grammars and don't have access to a suitable textbook, consider checking out the Wikipedia article on the topic.)

If you search around, you'll discover numerous instances of how to formulate a context-free grammar for arithmetic expressions. (The provided Wikipedia link showcases an example arithmetic grammar.) It's true that most of these examples are geared towards basic calculators rather than matrix arithmetic. However, this distinction doesn't significantly impact the approach.

The key understanding for developing parsers is that syntax remains consistent regardless of the nature of the calculated primitive elements – be it integers, floating-point numbers, complex numbers, or arrays. The variance primarily lies in the syntax for representing a literal object. Furthermore, the format of operators doesn't affect the underlying grammar structure, allowing for a uniform style even when evaluating boolean expressions using operators such as and, or, and not.

In scenarios involving a standard numeric calculator, literal objects (numbers) typically emerge from the lexer effortlessly due to their lack of internal complexity. Conversely, matrices possess internal structuring, making regex-based lexers less efficient for parsing structured data. A more effective strategy involves treating a matrix literal as a sequence of tokens comprising numbers alongside symbols like [, ], and ,, and integrating corresponding productions into your context-free grammar for matrix parsing.

In essence, a matrix can be viewed as a collection of vectors separated by commas, with each vector containing a comma-separated list of numbers. This structure is syntactically analogous to any other comma-separated or delimited list variant, irrespective of the specific delimiter used. Similar production requirements also apply when parsing argument lists within function call expressions.

A fundamental form of a context-free grammar for a delimited list typically follows this schema, replacing X with the actual element type:

/* Parses lists containing one or more elements */
list_of_X: X
         | list_of_X ',' X

In cases where empty lists are permissible (less common with matrices but prevalent in function calls), you can combine the above pattern with another concept:

optional_list_of_X: %empty
                  | list_of_X

Your grammar would then involve rules like:

expression: matrix
          | /* ... all other expression forms */

matrix: '[' list_of_vector ']'
vector: '[' list_of_number ']'

For illustration purposes, I've utilized Bison syntax since it's commonly employed for writing context-free grammars. Keep in mind that every parser generator comes with its unique conventions and quirks.

Answer 2

Constructing a parse tree with the help of a context-free grammar seems like the most effective method in my opinion. (If you're not familiar with context-free grammars and don't have access to a suitable textbook, consider checking out the Wikipedia article on the topic.)

If you search around, you'll discover numerous instances of how to formulate a context-free grammar for arithmetic expressions. (The provided Wikipedia link showcases an example arithmetic grammar.) It's true that most of these examples are geared towards basic calculators rather than matrix arithmetic. However, this distinction doesn't significantly impact the approach.

The key understanding for developing parsers is that syntax remains consistent regardless of the nature of the calculated primitive elements – be it integers, floating-point numbers, complex numbers, or arrays. The variance primarily lies in the syntax for representing a literal object. Furthermore, the format of operators doesn't affect the underlying grammar structure, allowing for a uniform style even when evaluating boolean expressions using operators such as and, or, and not.

In scenarios involving a standard numeric calculator, literal objects (numbers) typically emerge from the lexer effortlessly due to their lack of internal complexity. Conversely, matrices possess internal structuring, making regex-based lexers less efficient for parsing structured data. A more effective strategy involves treating a matrix literal as a sequence of tokens comprising numbers alongside symbols like [, ], and ,, and integrating corresponding productions into your context-free grammar for matrix parsing.

In essence, a matrix can be viewed as a collection of vectors separated by commas, with each vector containing a comma-separated list of numbers. This structure is syntactically analogous to any other comma-separated or delimited list variant, irrespective of the specific delimiter used. Similar production requirements also apply when parsing argument lists within function call expressions.

A fundamental form of a context-free grammar for a delimited list typically follows this schema, replacing X with the actual element type:

/* Parses lists containing one or more elements */
list_of_X: X
         | list_of_X ',' X

In cases where empty lists are permissible (less common with matrices but prevalent in function calls), you can combine the above pattern with another concept:

optional_list_of_X: %empty
                  | list_of_X

Your grammar would then involve rules like:

expression: matrix
          | /* ... all other expression forms */

matrix: '[' list_of_vector ']'
vector: '[' list_of_number ']'

For illustration purposes, I've utilized Bison syntax since it's commonly employed for writing context-free grammars. Keep in mind that every parser generator comes with its unique conventions and quirks.

Developing a matrix arithmetic parser using JavaScript

Answer №1

Similar questions

Unable to interact with the page while executing printing functionality in

In Typescript, we can streamline this code by assigning a default value of `true` to `this.active` if `data.active

Rearranging table rows with jQuery based on numerical values within child elements

Link a function to a button in a 3rd party library

What is the best method for retrieving a child control from a TR element?

I possess an array of objects that includes both images and documents. My goal is to examine the mime_type of each object and select the first element in React to be displayed within an <img> tag

Using Rails to Pass Front-End JavaScript Data from an External API to the Controller

Retrieving status code without reliance on a back-end language (maybe through JavaScript?)

Utilizing Sequelize validation through condition objects

AgGrid supports multi-line content within its cells

Modify the background color of React-select when it is in a disabled state

Utilize JavaScript declarations on dynamically added strings during Ajax loading

issue with integrating promise in angular 4

Ways to deactivate the submit button using Cookies, sessions, or local storage

IntelliJ does not support the use of newlines within Vue.js component templates

How to create a manual mock for @material-ui withStyles in React using Jest

Guide to switching classes with jquery

Adjusting the CSS class name based on the screen size and applying styles to that class only during the "onload" event

Prop type failure: The `actions` prop is specified as mandatory in the `Testing` component, however, its value is currently undefined

Encountering a WriteableDraft error in Redux when using Type Definitions in TypeScript