Copyright Andrei-Marian Rusanescu 311CAb 2023-2024

The objective of the programme is to simulate Octave, open source
Matlab simulator. It has a number of interesting features of matrix
operations, such as multiplication, finding the the transpose, resizing
a matrix using its prior rows and columns, logarithmic complexity
exponentiation of square matrices and Strassen's algorithm for matrix
multiplication implemented in a simpler way.

The key feature of the programme is that everything is done using
dynamic memory allocation, therefore using just enough memory.
Every operation has a specifc command attached to it.

1. The first one should be 'L', which loads up the matrices one by one
in an array of matrices (3D array).
The size of the array is doubled when it gets fully occupied.

2. Next command is 'D' - used for printing the sizes of a specific matrix
in the 3D resizable array.

3. 'P' command prints a specific matrix from the array.

4. The 'C' command concatenates a matrix using its original values.
Basically, the user has to specify how many rows and columns the
resized matrix has and which rows and columns he wants. Very useful
for permutations inside the matrix.

5. For matrix multiplication, the programme has command 'M', which firstly
checks if the matrices are compatible for multiplication, then does the
desired operation and loads the resulted matrix at the end of the array.

6. Command 'O' sorts the array of the matrices using bubble sort.
The matrices are sorted in an ascending order regarding the sum of the
matrix' elements. To avoid overflow, every mathematical operation is
performed % 10007. The programme swaps matrices just like decimal numbers
in a regular array benefiting from the advantages of pointers.

7. 'T' transforms a specific matrix in its' transpose.
The initial matrix is substituted by its' transpose in place.

8. Next feature is command 'R' which multiplies a given matrix by
a number of times using logarithmic complexity exponentiation of
matrices. The power the user wants its' matrix to be raised at is
positive. Also, if the user introduces the power 0, the programme
prints the identity matrix. Old matrix is substituted by the new one.

9. 'F' command frees a specific matrix from the array. If too many
matrices are freed, then the array is resized to half of its size.
All remaining matrices are shifted one by one after freeing a matrix,
using pointers.

10. 'Q' command frees all of the allocated memory, finishing the programme.

11. Last command, 'S', has its purpose in matrix multiplication of very
large matrices. It features Strassen's algorithm for matrix multiplication.
It is implemented in a recursive manner, dividing the matrix by portions
of half of the original dimension until it gets to a 1x1 matrix. Basically
it divides the original matrix in 4 smaller matrices which are also divided
in 4 other small matrices and so on until all matrices are 1x1 and from this
point forward, multiplication is behaving like decimal numbers, a * b.
It does what the command 'M' does but in a more efficient way for larger
matrices.