Matrix Operations

This program provides a way to represent square matrices and perform basic matrix operations. The primary operations supported are addition, subtraction, multiplication, and submatrix extraction.

Code Structure

1. Header File (matrix.h):

   • Defines the Matrix class that holds the details and operations of the square matrices.
   • Member functions include:
     • Basic constructors and destructors.
     • Overloaded operators for input/output.
     • Arithmetic operations such as addition, subtraction, and multiplication.
     • Submatrix extraction.
   • Note: Matrix dimensions are assumed to be powers of 2 for simplicity.

2. Implementation File 1 (matrix.cpp):

   • Implements all the member functions and constructors defined in the Matrix class.
   • This file also provides utility functions, for example, ceilLogAndCompute, to ensure matrix sizes are powers of 2.

3. Implementation File 2 (main.cpp):

   • Contains a simple matrix multiplication benchmark (matmultNaive) which multiplies two square matrices using a direct O(n^3) method.
   • Also uses an IPM_timer to measure the performance of this naive matrix multiplication.
   • Main function (main) reads the size of the matrix from command line arguments and then multiplies two matrices of the given size.

How to Run

1. Compilation: Ensure you have all required dependencies, especially the ipm-2.0a/IPM_timer.h header. Once done, you can compile the project with:

   g++ matrix.cpp main.cpp -o matrix_operations
   

   This will create an executable named matrix_operations.

2. Usage: Run the executable with the size of the matrix (a power of 2) as an argument. For example:

   ./matrix_operations 4
   

   This command will multiply two 4x4 matrices and display the results along with the time taken.

Notes

• All matrices are assumed to be square.
• The size of the matrix is expected to be a power of 2 due to certain optimization techniques applied in the Matrix class.
• Matrix multiplication uses the conventional O(n^3) approach.
• Ensure proper error handling when reading input from files or the command line.

Example

Running:

./matrix_operations 2

Will yield something like:

*************
* Matrix 1  *
*************
1.0 1.99
1.0 1.99

*************
* Matrix 2  *
*************
1.0 1.99
1.0 1.99

************
* Product: *
************
2.99 5.9601
2.99 5.9601

Elapsed time to compute: [Some value]u
MFlops: [Some value]

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This README provides a comprehensive understanding of the code and its execution. Make sure to adjust paths and filenames accordingly if any changes are made to the codebase.