Benchmark: Solving System of Linear Equations with Matrix v2

HTML Preparation code:

<!-- JStat -->
<script src="https://cdn.jsdelivr.net/jstat/latest/jstat.min.js"></script>
<!-- NumericJS -->
<script src="https://cdn.rawgit.com/sloisel/numeric/master/src/numeric.js"></script>
<!-- Math.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/3.9.0/math.min.js"></script>

Script Preparation code:

var A = [[11, -1, 0], [-1, 12, -1], [0, -1, 11]],
    B = [[87], [12] , [0]];

var Numeric_LUa = numeric.LU(A),
    math_LUa = math.lup(A);

Tests:

jStat
jStat.gauss_elimination(A, B);
Numeric JS (uses LUsolve under the hood)
numeric.solve(A, B);
Numeric JS (LU Decomposed first)
numeric.LUsolve(Numeric_LUa, B);
math.js
math.lusolve(A, B);
math.js (LU Decomposed first)
math.lusolve(math_LUa, B);

Rendered benchmark preparation results:

Suite status: <idle, ready to run>

Previous results

Test case name	Result
jStat
Numeric JS (uses LUsolve under the hood)
Numeric JS (LU Decomposed first)
math.js
math.js (LU Decomposed first)

Fastest: N/A

Slowest: N/A

Latest run results:

Run details: (Test run date: 3 months ago)

User agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/131.0.0.0 Safari/537.36

Browser/OS: Chrome 131 on Windows

View result in a separate tab

Test name	Executions per second
jStat	2358601.8 Ops/sec
Numeric JS (uses LUsolve under the hood)	930884.4 Ops/sec
Numeric JS (LU Decomposed first)	1385989.8 Ops/sec
math.js	464471.1 Ops/sec
math.js (LU Decomposed first)	839937.2 Ops/sec

Autogenerated LLM Summary (model llama3.2:3b, generated 6 months ago):

LLMs can make mistakes. Check important info.

Let's break down the provided benchmark definition and test cases.

**Benchmark Definition:**

The benchmark is designed to solve a system of linear equations using matrix operations. The script preparation code provides two matrices, A and B, which are used as input for the benchmarks. The Html Preparation Code includes links to external libraries: JStat (a statistical analysis library), NumericJS (a numerical computation library), and Math.js (a mathematical expression library).

**Test Cases:**

The benchmark compares four different approaches:

1. **jStat.gauss_elimination(A, B)**: This test case uses the `gaussElimination` function from the JStat library to solve the system of linear equations.
2. **numeric.solve(A, B)**: This test case uses the `solve` function from the NumericJS library to solve the system of linear equations. Note that this function is actually using an LU decomposition under the hood (more on this later).
3. **numeric.LUsolve(Numeric_LUa, B)**: This test case explicitly performs an LU decomposition using the `LU` function from the NumericJS library and then uses the `LUsolve` function to solve the system of linear equations.
4. **math.lusolve(A, B)**: This test case uses the `lusolve` function from the Math.js library to solve the system of linear equations. Note that this function is also performing an LU decomposition (more on this later).

**Options Compared:**

The benchmark is comparing four different approaches:

* Using a separate `gauss_elimination` function vs. using a built-in `solve` function with LU decomposition.
* Performing explicit LU decomposition using the `LU` function and then solving the system of linear equations vs. using an existing implementation in the library.

**Pros and Cons:**

Here are some pros and cons for each approach:

1. **jStat.gauss_elimination(A, B)**:
	* Pros: Simple to implement, easy to understand.
	* Cons: May not be as efficient or optimized as other approaches.
2. **numeric.solve(A, B) (uses LUsolve under the hood)**:
	* Pros: Built-in implementation in the library, potentially more efficient than explicit LU decomposition.
	* Cons: May require additional setup or initialization compared to other approaches.
3. **numeric.LUsolve(Numeric_LUa, B)**:
	* Pros: Allows for explicit control over the LU decomposition process.
	* Cons: Requires manual implementation of the LU decomposition algorithm.
4. **math.lusolve(A, B) (LU Decomposed first)**:
	* Pros: Similar to NumericJS approach, allows for explicit control over the LU decomposition process.
	* Cons: May require additional setup or initialization compared to other approaches.

**Libraries and Their Purpose:**

1. **JStat**: A statistical analysis library that provides a `gaussElimination` function for solving systems of linear equations.
2. **NumericJS**: A numerical computation library that provides functions for performing LU decomposition (e.g., `LU`, `LUsolve`) and other matrix operations.
3. **Math.js**: A mathematical expression library that provides a `lusolve` function for solving systems of linear equations using LU decomposition.

**Special JS Features or Syntax:**

None mentioned in the provided benchmark definition.

**Alternatives:**

Other alternatives for solving systems of linear equations include:

1. Using a dedicated linear algebra library, such as LinAlg.js.
2. Implementing a custom algorithm for Gaussian elimination or LU decomposition.
3. Using a different numerical computation library, such as TensorFlow.js.

Note that the choice of approach will depend on the specific requirements and constraints of your project.

Related benchmarks:

Solving System of Linear Equations with Matrix v2 (version: 0)

Comparing performance of: jStat vs Numeric JS (uses LUsolve under the hood) vs Numeric JS (LU Decomposed first) vs math.js vs math.js (LU Decomposed first)

Created: 8 years ago by: Registered User

Jump to the latest result

jStat

Numeric JS (uses LUsolve under the hood)

Numeric JS (LU Decomposed first)

math.js

math.js (LU Decomposed first)

Suite status: <idle, ready to run>

Experimental features:

Fastest: N/A

Slowest: N/A

Autogenerated LLM Summary (model llama3.2:3b, generated 6 months ago):