PracCodes

Repository for mathematical codes ( 2 variants - optimized, non-optimized )

• Overview (NON OPTIMIZED)
  • Table of Contents (NON OPTIMIZED)
• Optimized Experimental (build)
  • Overview (OPTIMIZED)
  • Table of Contents (OPTIMIZED) still in development
  • API
    • Current Api Support
• Last Update

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Last Update

Update 05.10.2024 INFO:

• optimized.lineq.lineq_sub.
  • add functions for linear equations systems
    • iter_solve_simple(matrix, vector, eps=1e-12, max_iter=1000, eigen_max_iter=1000, eigen_eps=1e-12):

      Simple iteration to solve a system of linear equations.
      Need positive definite and symmetric matrix.
      

$\text{Sylvester's criterion}$

Sylvester's criterion states that a $n \times n$ Hermitian matrix $M$ is positive-definite if and only if all the following matrices have a positive determinant:

• the upper left 1-by-1 corner of $M$,
• the upper left 2-by-2 corner of $M$,
• the upper left 3-by-3 corner of $M$,
• $\quad \vdots$
• $M$ itself.

In other words, all of the leading principal minors must be positive. By using appropriate permutations of rows and columns of $M$, it can also be shown that the positivity of any nested sequence of $n$ principal minors of $M$ is equivalent to $M$ being positive-definite.

Iterative Methods

Important

• Disabled GIL for lowlevel functions.
• Be careful.

• Fixed memory leak in optimized.lineq.lineq_sub.
• Fixed memory leak in optimized.lineq.matrix_methods.
• Fixed random_double function in optimized.lineq.matrix_methods. -> now work correctly.
• Fixed random in optimized.lineq.matrix_methods.Module.module MatrixMethods class -> now work correctly.
• Fixed variables definitions in .pyx files in optimized.lineq.matrix_methods, optimized.lineq.lineq_sub, optimized.lineq.generator, optimized.lineq.checker.

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Update 28.09.2024 INFO:

• optimized.lineq.lineq_sub.
  • development started.
  • add functions for linear equations systems:

    • solve_tridiagonal(matrix, vector):

      Solve a system of linear equations with tridiagonal matrix
      

      Matrix must be tridiagonal:

      $a_{11}$	$b_{12}$	0	...	...	...	0
      $c_{21}$	$a_{22}$	$b_{23}$	...	...	...	0
      0	$c_{32}$	$a_{33}$	$b_{34}$	...	...	0
      ...	0	$c_{43}$	$a_{44}$	$b_{45}$	...	0
      ...	...	...	...	...	...	0
      0	0	...	0	$c_{n-1 \ n-2}$	$a_{n-1 \ n-1}$	$b_{n-1 \ n}$
      0	0	...	0	0	$c_{n \ n-1}$	$a_{nn}$

      Tridiagonal matrix algorithm (Thomas algorithm)

    • solve_gauss(matrix, vector):

      Solve a system of linear equations with gauss method
      

      Gaussian elimination

    • solve_lu(matrix, vector):

      Solve a system of linear equations with LU method
      

$$ \begin{aligned} (1) \ & A\cdot\bar{x} = \bar{b} \\ (2) \ & A = L \cdot U \\ (3) \ & L \cdot U = A \\ (4) \ & U \cdot \bar{x} = \bar{y}\\ (5) \ & L \cdot \bar{y} = \bar{b} \\ (6) \ & L \text{ is a lower triangular matrix, so (5) is easy to solve for } \bar{y} \\ (7) \ & U \text{ is an upper triangular matrix, so (4) is easy to solve for } \bar{x} \\ \end{aligned} $$

$$ \begin{aligned} \text{Algorithm complexity:} \ LU_{\text{complexity}} & => \frac{2 \cdot n^3}{3} + O(n^2) \\ \text{Solving (5) and (4)} & => n^2 + O(n) \end{aligned} $$

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UPDATE 01.09.2024 INFO:

• run_api.py updated.
  • Argparser added.

Tip

usage: optimized_api [-h] [-r]

optimized_api FLASK app

options:

-h, --help show this help message and exit
-r, --rebuild, -re Rebuild optimized_api

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UPDATE #2 23.08.2024 INFO:

• GUI updated.
  • Add dark mode.
  • Add new accordion fields.
  • Add new input fields.
  • Add result copy button.
  • Add global_info and global_info.GlobalRet return fields.
  • Add new styles to statics.
  • Add new .js files to statics.

Note

api_key in config.ini does not work.

• Enjoy 😸

UPDATE 23.08.2024 INFO:

• Started creating GUI for API. Now you can use only lineq.generator GUI.

• GUI LOCAL link -> localhost:8000/main (localhost:8000/ works too (without GUI)) after running run_api.py.

• Examples -> images.api_gui

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Update 22.08.2024 INFO:

• optimized.lineq.matrix_methods.python_interface-API is ready for 100% use.
• optimized.lineq.generator.python_interface-API is ready for 100% use.
• optimized.lineq.checker.python_interface-API is ready for 100% use.
  • all API functions you can see in Current Api Support

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Update 19.08.2024 INFO:

• Continued working on API after a break. API for generator, checker will be finished soon. Then I will continue optimizing the rest of the modules, namely lineq.lineq, ( lineq.Utils.Prettier, lineq.Utils.S_R may not be changed, but will be moved to a new module without optimization, or will be completely removed ). lineq.Utils.timer will be definitely removed.

• optimized.lineq.matrix_methods.python_interface API is ready for 100% use.

  • all API functions you can see in Current Api Support

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Update 10.08.2024 INFO:

• Fixed a bug in the rand function of the optimized/lineq/matrix_methods/lowlevel/mm.c file (file). The function was returning extremely large numbers instead of a random number within the specified range.

• Updated the docstrings in the optimized.lineq.generator.python_interface module. optimized.lineq.generator.python_interface

• Added new information to the API data.json file. API-DATA.

• Added new API functions. Check the Current Api Support for all functions.

• New API return system -> Added in each return global_info -> request.headers, host, url, etc...

  • some screenshots

  

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Update #2 04.08.2024 INFO:

Add new API functions Current Api Support Check usage instructions in API-DATA or just run run_api.py and check home page. All info in:

• API
  • Current Api Support

Update 04.08.2024 INFO:

Started developing the API for the optimized codes. Already ready for use determinant function API. Info in data. To run the API, run run_api. Local API is available at http://127.0.0.1:8000/.

• Use examples:

  • browser list mode (img1): http://127.0.0.1:5000/det/?type=list&matrix=[[1,2,3],[4,5,6],[7,1.2,7]]

  • browser str mode (img2): http://127.0.0.1:5000/det/?matrix=1%202%203\n4%205%206\n7%208%209

  • curl list mode (img3):

  curl `http://127.0.0.1:5000/det/?type=list&matrix=%5B%5B1%2C2%2C3%5D%2C%5B4%2C5%2C6%5D%2C%5B7%2C1.2%2C7%5D%5D`

  

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Update 02.08.2024 INFO:

Rewritted build.py script.

New Build System

• Build Management: Manages cleaning up previous builds, compiling modules, and organizing build artifacts.
• Dependency Check: Automatically checks for and installs necessary dependencies such as Cython.
• Configuration Loading: Loads build settings and module configurations from the file cfg. If the file does not exist, a default configuration is created.
• Build Result Visualization: Displays a tree structure with icons indicating the success or failure of each module.
• Automated Testing: Runs tests on successfully built libraries to ensure their correctness.

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Update 29.07.2024 INFO:

I have rewritten the Checker module and updated matrix filling in matrix_methods module.

• Introduced the Checker class for matrix validation

  • Methods included:
    • diagonal_domination(matrix) -> bool: Checks matrix diagonal domination
    • symmetric_check(matrix) -> bool: Checks matrix symmetry
    • sylvesters_criterion(matrix) -> bool: Checks matrix against Sylvester's criterion

• I also updated the matrix filling in both the matrix_methods and Checker modules. I replaced the cycle with a for loop and used memset(*, 0, sizeof(*)) to set the matrix elements to zero.

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Update 26.07.2024 INFO:

The updated Python interface for optimized.lineq.matrix_methods is now ready for use. It is optimized for 100% efficiency.

The new code is significantly faster, with an average improvement of more than 50 times.

The Generator has also been rewritten.

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Update 26.07.2024 INFO:

In the lineq/LinEq/Utils/Matrix_methods.py file, the determinant function has been fixed.

I have started rewriting the code. In the Optimized-Experimental directory, you will find experimental versions of the codes with optimizations. These versions are about 50 times faster. However, you need the Cython library for this!

I have rewritten the lineq.matrix_methods module in the optimized/lineq/matrix_methods/ directory.

Here are the links to the source code:

• The C code can be found in the code file.
• The Python code is available in the code file. This file is ready for 50% use. All functions work if imported from the build.matrix_methods file. However, in the Python file, only 50% of the code is implemented.

The source codes are located in the optimized/{module_name}/{util_name}/lowlevel directory, where {module_name} represents the module name and {util_name} represents the utility name.

To build the optimized version, run the build.bat [DELETED, use python script]UPD 02.08.2024 build.py file from the optimized directory. Please note that this feature does not work with older versions of the project. Wait for a new version to be ready with all optimizations implemented.