Single/Multi Dimensional matrix operations using multi threading in Python.

Adding or subtracting or multiplication or Division of matrices takes O(n²) time without threads, but using threads does not reduce the time complexity of the program. For achieving we split the task into cores as if there were 4 cores, split matrix part and split matrix computation into 4 parts, each core taking over one of the operations, and finally each task completed Then all 4 threads join the main program and display the final output.This method only works when we have more then one CPU core if we have only one core the Don’t create the thread because we divide the task and perform on only one CPU so it is waste of time to dividing a task and then compute.

Same process is being followed for all the operations as depicted in the above picture.

For using multithreading concept we import the ‘Process’ library from ‘multiprocessing’ class. In ‘multithreading’ , processes are spawned by creating a “Process” object and then calling its ‘start()’ method. Process follows the API of “threading.Thread”.

Multiprocessing is a package that supports spawning processes using an API similar to the threading module. The multiprocessing package provides both local and remote parallelism, effectively bypassing the global interpreter lock using subprocesses instead of threads. Thus, multiprocessing modules allow programmers to take full advantage of multiple processors on a particular machine. Works on both Unix and Windows.

Some of the following keywords are used while demonstrating the multithreading in python:

1-start():

Start the thread activity. Must be called at most once per thread object. Ensures that the object’s ‘run()’ method is invoked in a separate thread of control.

2-run():

A method representing thread activity. You can override this method in a subclass. The standard run() method invokes the callable object passed to the object’s constructor as the target argument, if any, with positional and keyword arguments taken from the args and kwargs arguments.

3-join(timeout=None)

Wait until the thread ends. This blocks the calling thread until the thread whose join() method is called terminates — either normally or via an unhandled exception — or until an optional timeout occurs. If the timeout argument is present and not None, it should be a floating-point number specifying the timeout for the operation in seconds (or fractions thereof). Since join() always returns None , you must call is_alive() after join() to decide if a timeout occurred — if the thread is still alive, the join() call has timed out.

4-native_id

Thread ID (TID) of this thread assigned by the OS (kernel). This is a non-negative integer or none if the thread has not been started. See the ‘get_native_id()’ function. This value can be used to uniquely identify that particular thread system-wide (until the thread terminates, after which the value can be recycled by the OS).One Dimensional Array Operations:

Basic Methods

The fundamental operations enabled by an array are listed below.

• Traverse prints each array element one at a time.
• Insert a new element at the specified index.
• Delete the element at the specified index.
• Searches for an element based on the specified index or value.
• Update the element at the specified index.

Operation Traverse

Each array element is accessed exactly once for processing during an array traversal operation.

This is also known as a field visit.

Insert Operation:

An insert operation inserts one or more data elements into an array. New elements can be added to the array at the beginning, end, or specified index as needed.
Adding elements to the end of an array is not always necessary.
First-come, first-served field
Insert into an array at a specific index.
Insert into field by index.
Inserts data into the field before the specified index.

Insertion at the Start of a Sequence

When data is inserted at the start, it causes all existing data items to move one step lower. We create and test an algorithm for inserting an element at the start of an array.

Algorithm

Assume that A is an N-element array. MAX specifies the maximum number of items it can hold. First, we find out if there is free space in the field to store an element, and then we start the insertion procedure.

Insertion before an Array’s Given Index

In this case, we are given the position (index) of the field into which we need to insert the new data element (value). The remaining activities are the same as in the previous example, but we search up to index-1, which is one place before the specified index.

Algorithm:

Assume that A is an N-element array. MAX specifies the maximum number of items it can hold.

begin
IF N = MAX, return
ELSE
   N = N + 1
   SEEK Location index
   For All Elements from A[index - 1] to A[N]
      Move to next adjacent location
   A[index - 1] = New_Element   
end

Operation Deletion

Deletion is the process of removing an existing element from an array and reorganizing all its elements.

Algorithm:

Consider the case where LA is a linear array with N entries and K is a positive integer position with value where K<=N. The algorithm for removing an element accessible at the Kth position of LA is as follows.

Start
Set J = K
Repeat steps 4 and 5 while J < N
Set LA[J] = LA[J + 1]
Set J = J+1
Set N = N-1
Stop

Operation of Search

A search for an array element can be done using its value or index.

Algorithm

Consider the case where LA is a linear array with N entries and K is a positive integer position with value where K<=N. The algorithm for finding an element with the value ITEM using a sequential search is as follows.

Start
Set J = 0
Repeat steps 4 and 5 while J < N
IF LA[J] is equal ITEM THEN GOTO STEP 6
Set J = J +1
PRINT J, ITEM
Stop

Operation Update

The update action updates an existing element in the array at a specified index.

Algorithm

Consider the case when LA is a linear array with N items and K is a positive integer’s position with the value where K<=N. The algorithm to update an element accessible at the Kth location of LA is as follows.

Start
Set LA[K-1] = ITEM
Stop

Operation Update

The update action updates an existing element in the array at a specified index.

Algorithm

Consider the case when LA is a linear array with N items and K is a positive integer’s position with the value where K<=N. The algorithm to update an element accessible at the Kth location of LA is as follows.

Start
Set LA[K-1] = ITEM
Stop

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a = [[2, 5], [1, 7]]

b = [[3, 7], [2, 9]]

c = [[0, 0], [0, 0]]

for i in range(0, 2):

for j in range(0, 2):

c[i][j] = 0

for k in range(0, 2):

c[i][j] = c[i][j]+(a[i][k]*b[k][j])

for i in range(0, 2):

for j in range(0, 2):

print(c[i][j])

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