Algebra Matrix

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• Algebra Matrix
  • User Documentation
    • Overview
    • How to Use the Program
      • Example Usage:
        • Input:
        • Output:
      • Notes:
  • Program Documentation
    • Program Title: Merging Two Arrays
      • Problem:
      • Programming Language:
      • Author:
      • Version:
      • Program Flowchart
      • Program Structure:
        • 2. User Input for Arrays A and B:
        • 3. Processing Elements of C to matrix_algebra:
        • 4. Displaying the Arrays:
      • Example Run:
        • Input:
        • Output:
      • Enhancements and Notes:

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User Documentation

Overview

This program allows the user to input three integers on one dimensional array, nine integers on multidimensional array with three rows and columns. Third array will add the product on two array.

How to Use the Program

1. Run the Program: Execute the compiled program named matrix_algebra.

2. Input Values:

   1. One Dimensional Array
   • The program will prompt you to enter three integers for Array A.
   2. Multidimensional Array
   • Next Array will prompt you to enter nine integers for Array B which consists of 3 rows and 3 columns.

3. Processing:

   • The program will create additional Array which is the product of two other matrices with the following formula:

           C[0] = {(A[0] * B[0][0]) + (A[1] * B[0][1]) + (A[2] * B[0][2])}
           C[1] = {(A[0] * B[1][0]) + (A[1] * B[1][1]) + (A[2] * B[1][2])}
           C[2] = {(A[0] * B[2][0]) + (A[1] * B[2][1]) + (A[2] * B[1][2])}

4. Output Display:

   • Array N and Array B will be displayed.

   • The matrix algebra (matrix_algebra) will also be displayed.

Example Usage:

Input:

ARRAY A:
Enter element for A[0]: 1
Enter element for A[1]: 2
Enter element for A[2]: 3

ARRAY B:
Enter element for B[0][0]: 1
Enter element for B[0][1]: 2
Enter element for B[0][2]: 3
Enter element for B[1][0]: 4
Enter element for B[1][1]: 5
Enter element for B[1][2]: 6
Enter element for B[2][0]: 7
Enter element for B[2][1]: 8
Enter element for B[2][2]: 9

Output:

ARRAY A:
A[0] = 1    A[1] = 2    A[2] = 3

ARRAY B:
B[0][0] = 1    B[0][1] = 2    B[0][2] = 3
B[1][0] = 4    B[1][1] = 5    B[1][2] = 6
B[2][0] = 7    B[2][1] = 8    B[2][2] = 9

ARRAY C:
C[0] = 14    C[1] = 32    C[2] = 50

Notes:

1. Only integer values should be entered.

2. No sorting is applied to the final merged array.

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Program Documentation

Program Title: Merging Two Arrays

Problem:

Write a program that will input 3 integers in an array A(one dimensional - 3 digits) and another 9 integers in an array B(multidimensional - 3 rows and 3 columns). After which process two arrays in one array called matrix_algebra such that on each elements of Array C are the products of two matrices:

    Formula for Array C: 
      C[0] = {(A[0] * B[0][0]) + (A[1] * B[0][1]) + (A[2] * B[0][2])}
      C[1] = {(A[0] * B[1][0]) + (A[1] * B[1][1]) + (A[2] * B[1][2])}
      C[2] = {(A[0] * B[2][0]) + (A[1] * B[2][1]) + (A[2] * B[1][2])}

Programming Language:

C++ Programming

Author:

Ariel Rivera

Version:

================================================================
Author             Date            Description          Version
----------------------------------------------------------------
Ariel Rivera       2025-03-23      Initial Build        1.0.0
================================================================

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Program Flowchart

Working...

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Program Structure:

1. Declaration: Constant Declaration:

   • _size = 3: Defines the maximum array size to ensure sufficient storage space for merging.

   Variable Declaration:

   • A[_size]: Stores the one dimensional array.
   • B[_size][_size]: Stores the multidimensional array.
   • C[_size]: Stores the processed array.

2. User Input:

   • The user is prompted to enter three integers for array A.
   • The user is then prompted to enter nine integers for array B.
   • No Error Validation added. User must refrain from entering out-of-bound data from the array. Can be enhancement feature

3. Process:

   • Each element of C is the product of elements of A[index] and B[rows][columns].

         C[0] = {(A[0] * B[0][0]) + (A[1] * B[0][1]) + (A[2] * B[0][2])}
         C[1] = {(A[0] * B[1][0]) + (A[1] * B[1][1]) + (A[2] * B[1][2])}
         C[2] = {(A[0] * B[2][0]) + (A[1] * B[2][1]) + (A[2] * B[1][2])}

4. Output:

   • The program prints the original A and B arrays.
   • The program then prints the matrix_algebra containing the product of two matrices.

5. Error Handling:

   • User input where separated on each line to prevent the user on entering out of bound data in an array.

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Code Breakdown:

1. Required Headers:

#include <iostream>

using namespace std;

• using iostream library to handle input/output program.
• using namespace std to allow the developer to use standard library features (like cout, cin, and endl) without having to prefix them with std::.

2. User Input for Arrays A and B:

// asking user to input data in one dimensional array
cout << "ARRAY A: " << endl;
for (int i = 0; i < _size; i++)
{
    cout << "Enter elements for A[" << i << "]: ";
    cin >> A[i];
}

// asking user to input data in multidimensional array
cout << endl
     << "ARRAY B: " << endl;
for (int rows = 0; rows < _size; rows++)
{
    for (int cols = 0; cols < _size; cols++)
    {
        cout << "Enter elements for B[" << rows << "][" << cols << "]: ";
        cin >> B[rows][cols];
    }
}

• The program will ask the user to input 3 elements on Array A.
• The program will ask the user to input 9 elements on Array B.

3. Processing Elements of C to matrix_algebra:

for (int rows = 0; rows < _size; rows++)
{
    C[rows] = 0; // initialize current element to 0 to prevent from adding unnecessary value
    for (int cols = 0; cols < _size; cols++)
    {
        C[rows] += (A[cols] * B[rows][cols]); // on each element of C, value of A[cols] * to value of B[rows][cols]
    }
}

• C[rows] = 0 was define to initialize the value of C[rows] to 0, preventing from adding unnecessary value.
• C[rows] += (A[cols] * B[rows][cols]) to get product of two arrays on each repitition.

4. Displaying the Arrays:

// printing the one dimensional array
cout << endl
     << "ARRAY A: " << endl;
for (int i = 0; i < _size; i++)
{
    cout << "A[" << i << "] = " << A[i] << "\t";
}

// printing the multidimensional array
cout << endl
     << endl
     << "ARRAY B: " << endl;
for (int rows = 0; rows < _size; rows++)
{
    for (int cols = 0; cols < _size; cols++)
    {
        cout << "B[" << rows << "][" << cols << "] = " << B[rows][cols] << "\t";
    }

    cout << endl;
}

// printing the matrix algebra
cout << endl
     << "ARRAY C: " << endl;
for (int i = 0; i < _size; i++)
{
    cout << "C[" << i << "] = " << C[i] << "\t";
}

• Array A, Array B, and Array C were display to ensure the program captured the correct data and process.

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Example Run:

Input:

ARRAY A:
Enter element for A[0]: 1
Enter element for A[1]: 2
Enter element for A[2]: 3

ARRAY B:
Enter element for B[0][0]: 1
Enter element for B[0][1]: 2
Enter element for B[0][2]: 3
Enter element for B[1][0]: 4
Enter element for B[1][1]: 5
Enter element for B[1][2]: 6
Enter element for B[2][0]: 7
Enter element for B[2][1]: 8
Enter element for B[2][2]: 9

Output:

ARRAY A:
A[0] = 1    A[1] = 2    A[2] = 3

ARRAY B:
B[0][0] = 1    B[0][1] = 2    B[0][2] = 3
B[1][0] = 4    B[1][1] = 5    B[1][2] = 6
B[2][0] = 7    B[2][1] = 8    B[2][2] = 9

ARRAY C:
C[0] = 14    C[1] = 32    C[2] = 50

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Enhancements and Notes:

• The program ensures that matrix_algebra get the product of two matrices.
• Future enhancements could include sorting the merged array or allowing dynamic input sizes instead of fixed 5-element arrays.
• Future enhancements could include error handling when user input out-of-bound data in an array.