w04-g04-matrix-matrix-multiplication

Matrix-Matrix multiplication

Objective

You will implement a matrix-matrix multiplication and optimize it using pointer arithmetrics. You will implement three different approaches and compare their speed.

Implementation

0. Use the file named matrix_matrix_multiplication.cpp as a starting point, which is provided in the tehpc/basics/ directory.

1. Follow instructions in the provided file. And implement the different approach to multiply matrices (see notes below)

2. Make sure that your code is well structured and commented.

3. For all three approaches, measure the execution time for various sizes of matrix, and comment your observations (in your MR).

Notes

Some notes regarding the three approaches:

1. First approach: declare and allocate 2D arrays for matrices $A$, $B$, and $C$. Compute C = AxB using the [] operators (as you would expect).
2. Second approach: continue using the same arrays, but now compute the multiplication by dereferencing the pointers. e.g. the C[i][j] can be accessed by *(*(C+i)+j). Explain what this does.
3. Third approach: declare and allocate 1D arrays for matrices $A1$, $B1$, and $C1$, but with size $N\timesM$. Compute matrix multiplication by using pointer arithmetics, i.e. use pointers p_A1 to point to the array and modify them through the for loops. This means that you will need to use operations, such as ++p_A.

Compile and run your code by:

1. going into the tehpc/build/ folder
2. compile with the following command: g++ -Werror -Wpedantic -g -o matrix_matrix_multiplication ../basics/matrix_matrix_multiplication.cpp
3. run code with ./matrix_matrix_multiplication 4 (or any other number)