This project provides a suite of functions for performing advanced matrix operations with a focus on parallel computation. The implementation leverages superpose and collapse to parallelize tasks where possible.

The project is organized into three main functional areas:

1. Matrix Row Normalization (L2 Norm)
2. Upper and Lower Triangular Matrix Extraction
3. Parallel Trace of Matrix Powers

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📜 File Structure

The library is composed of the following files:

• triangular_matrix.metta: Contains logic for extracting upper and lower triangular matrices .
• trace_matrix.metta: Implements functions for matrix transposition, multiplication, exponentiation, and trace calculation .
• row_normalization.metta: Provides tools for normalizing matrix rows using the L2 norm .

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✨ Core Functionalities

1. Matrix Row Normalization (L2 Norm)

This feature normalizes each row of a given matrix, ensuring that each row vector has an L2 norm (length) of 1.

Key Functions

• calc_l2_norm $row: Computes the L2 norm for a single row vector. It squares all elements in parallel using superpose, sums the results, and then takes the square root .
• normalize_row $row: Normalizes a single row by dividing each of its elements by the row's L2 norm .
• normalize $matrix: Applies the normalize_row function to every row in the input matrix to produce the final normalized matrix .

Example

Normalizing a 2x2 matrix:

!(normalize
   (
      (3 4)
      (1 2)
   )
)

; Expected output: (
                     (0.6      0.8) 
                     (0.447..  0.894...)
                  )

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2. Upper and Lower Triangular Matrix Extraction

These functions create a new matrix containing only the upper or lower triangular part of a given square matrix, setting all other elements to zero .

Key Functions

• to_upr_matrix $matrix: (Generates Upper Triangular) This function processes a matrix and replaces elements below the main diagonal with zeros, effectively creating an upper triangular matrix .
• to_lwr_matrix $matrix: (Generates Lower Triangular) This function processes a matrix and replaces elements above the main diagonal with zeros, creating a lower triangular matrix .

Examples

• Generating an Upper Triangular Matrix (using to_upr_matrix):

  !(to_upr_matrix (
     (1 2 3 4)
     (4 5 6 7)
     (7 8 9 2)
     (4 8 2 9)
  ))
  
  ; Output: (
       (1 2 3 4)
       (0 5 6 7)
       (0 0 9 2)
       (0 0 0 9)
    )
  

• Generating a Lower Triangular Matrix (using to_lwr_matrix):

  !(to_lwr_matrix (
     (1 2 3 4)
     (4 5 6 7)
     (7 8 9 2)
     (4 8 2 9)
  ))
  
  ; Output: (
       (1 0 0 0) 
       (4 5 0 0) 
       (7 8 9 0) 
       (4 8 2 9)
    )
  

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3. Parallel Trace of Matrix Powers

This functionality computes the trace (the sum of the diagonal elements) of a matrix raised to the k-th power, i.e., $Trace(A^k)$.

Key Functions

• matrix_mul $m1 $m2: Multiplies two matrices. Parallelization is achieved by transposing the second matrix and using superpose to calculate the products of all corresponding row-column pairs simultaneously .
• matrix_power $m $k: Raises a matrix $m to the power of $k by recursively applying the parallel matrix_mul function .
• calc_trace $matrix $power: The main function that orchestrates the operation. It first computes the matrix power using matrix_power and then sums the diagonal elements of the resulting matrix to find the trace .

Example

Calculate the trace of a matrix raised to the power of 2:

!(calc_trace ((1 2) (3 4)) 22)

; This first computes A^2 =  ((7 10) (15 22))
; Then, it computes the trace = 7 + 22 = 29

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© Aug 2025 - Built by Haileiyesus Mesafint as part of iCog-Labs AGI Internship.