exiting due to drv_not_detected – Kubernetes error resolution

exiting due to drv_not_detected: no possible driver

😄 minikube v1.17.1 sur Darwin 10.15.7
👎 Unable to pick a default driver. Here is what was considered, in preference order:
▪ parallels : Not installed: exec: “prlctl”: executable file not found in $PATH
▪ podman : Not installed: exec: “podman”: executable file not found in $PATH
▪ virtualbox : Not installed: unable to find VBoxManage in $PATH
▪ vmware : Not installed: exec: “docker-machine-driver-vmware”: executable file not found in $PATH
▪ vmwarefusion : Not installed: the ‘vmwarefusion’ driver is no longer available
▪ docker : Not installed: exec: “docker”: executable file not found in $PATH
▪ hyperkit : Not installed: exec: “hyperkit”: executable file not found in $PATH

❌ Exiting due to DRV_NOT_DETECTED: No possible driver was detected. Try specifying –driver, or see https://minikube.sigs.k8s.io/docs/start/

😄  minikube v1.17.1 sur Darwin 10.15.7
👎  Unable to pick a default driver. Here is what was considered, in preference order:
    ▪ parallels : Not installed: exec: "prlctl": executable file not found in $PATH
    ▪ podman : Not installed: exec: "podman": executable file not found in $PATH
    ▪ virtualbox : Not installed: unable to find VBoxManage in $PATH
    ▪ vmware : Not installed: exec: "docker-machine-driver-vmware": executable file not found in $PATH
    ▪ vmwarefusion : Not installed: the 'vmwarefusion' driver is no longer available
    ▪ docker : Not installed: exec: "docker": executable file not found in $PATH
    ▪ hyperkit : Not installed: exec: "hyperkit": executable file not found in $PATH

❌  Exiting due to DRV_NOT_DETECTED: No possible driver was detected. Try specifying --driver, or see https://minikube.sigs.k8s.io/docs/start/

When you try to launch :

minikube start

You get this error :

😄  minikube v1.17.1 sur Darwin 10.15.7
👎  Unable to pick a default driver. Here is what was considered, in preference order:
    ▪ parallels : Not installed: exec: "prlctl": executable file not found in $PATH
    ▪ podman : Not installed: exec: "podman": executable file not found in $PATH
    ▪ virtualbox : Not installed: unable to find VBoxManage in $PATH
    ▪ vmware : Not installed: exec: "docker-machine-driver-vmware": executable file not found in $PATH
    ▪ vmwarefusion : Not installed: the 'vmwarefusion' driver is no longer available
    ▪ docker : Not installed: exec: "docker": executable file not found in $PATH
    ▪ hyperkit : Not installed: exec: "hyperkit": executable file not found in $PATH

❌  Exiting due to DRV_NOT_DETECTED: No possible driver was detected. Try specifying --driver, or see https://minikube.sigs.k8s.io/docs/start/

Solution setup Docker with homebrew- Unable to pick a default driver :

You can setup Docker with Homebrew Cask : Homebrew Cask is a Homebrew extension for installing GUI software on Mac os like docker.

brew cask install docker

if you get :

Error: Calling `brew cask install` is disabled! Use brew install [--cask] instead.

Then use instead this command and it will works :

brew install docker --cask

Check docker version :

docker --version

If the command doesn’t works :

docker --version
zsh: command not found: docker

So you can run docker app in finder or in command line it will start docker desktop :

open /Applications/Docker.app

Then you can try again minikube :

minikube start

External links – exiting due to drv_not_detected: no possible driver:

https://www.cprime.com/resources/blog/docker-on-mac-with-homebrew-a-step-by-step-tutorial/

https://github.com/Homebrew/homebrew-cask

https://kubernetes.io/fr/docs/setup/learning-environment/minikube/

Internal links :

http://128mots.com/index.php/2021/01/31/installer-kubernetes-mac/

runtimeerror: attempting to deserialize object on a cuda device

runtimeerror: attempting to deserialize object on a cuda device but torch.cuda.is_available() is false. if you are running on a cpu-only machine, please use torch.load with map_location=torch.device(‘cpu’) to map your storages to the cpu, How to solve the error presented here with Pytorch in python in the context of deeplearning?

runtimeerror: attempting to deserialize object on a cuda device but torch.cuda.is_available() is false. if you are running on a cpu-only machine, please use torch.load with map_location=torch.device('cpu') to map your storages to the cpu, How to solve the error presented here with Pytorch in python in the context of deeplearning?

Introduction

First of all, usually this error is encountered when trying to run your model code on the machine’s CPU instead of the GPU.

lib/python3.6/site-packages/torch/serialization.py", ... in validate_cuda_device
    raise RuntimeError('Attempting to deserialize object on a CUDA '
RuntimeError: Attempting to deserialize object on a CUDA device but 
  torch.cuda.is_available() is False. If you are running on a CPU-only machine, 
  please use torch.load with map_location='cpu' to map your storages to the CPU.

In this case you encounter an error which is a raised RuntimeError exception.

This means that you are looking to deserialize an object using code that runs with the GPU while the GPU is disabled.

Explanation – runtimeerror: attempting to deserialize object on a cuda device

Then, The error then occurs when you try to load the pytorch model using the torch.load instruction (see https://pytorch.org/docs/stable/generated/torch.load.html)

Example :

torch.load('mymodel.pt')

So when the reloading is done with the wrong configuration you get the error:

lib/python3.6/site-packages/torch/serialization.py", ... in validate_cuda_device
    raise RuntimeError('Attempting to deserialize object on a CUDA '
RuntimeError: Attempting to deserialize object on a CUDA device but 
  torch.cuda.is_available() is False. If you are running on a CPU-only machine, 
  please use torch.load with map_location='cpu' to map your storages to the CPU.

Solution

Also, As you can see in the Pytorch documentation (see https://pytorch.org/docs/stable/generated/torch.load.html) there is a map_location parameter – (a function, torch.device, string or a dict specifying how to remap storage locations).

This is where we must force the parameter to specify the location to use.

Note that if your model is registered and saved as using the GPU you will have to specify GPU otherwise you will have to put CPU. The objective here is to put a consistent parameter between what has been saved and what is reloaded.

And If you want to force CPU usage :

torch.load('mymodel.pt',map_location='cpu')

For CPU usage you can also use :

torch.load('mymodel.pt', map_location=torch.device('cpu'))
# Load on first GPU
torch.load('mymodel.pt', map_location=lambda storage, loc: storage.cuda(1))
# Lord on GPU 0 and 1
torch.load('mymodel.pt', map_location={'cuda:1':'cuda:0'})

External links :

https://pytorch.org/tutorials/beginner/saving_loading_models.html

https://pytorch.org/tutorials/recipes/recipes/save_load_across_devices.html

https://discuss.pytorch.org/t/saving-and-loading-a-model-in-pytorch/2610

Internal links – runtimeerror: attempting to deserialize object on a cuda device but torch.cuda.is_available() is false :

http://128mots.com/index.php/en/2020/11/20/deep-learning-pytorch-from-0-to-1-2/

http://128mots.com/index.php/en/category/non-classe-en/

importerror: iprogress not found. please update jupyter and ipywidgets

importerror: iprogress not found. And this is the solution if you get this error .

When trying to install Jupyter Widgets : Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html

importerror: iprogress not found. please update jupyter and ipywidgets

Error

You can check on the https://ipywidgets.readthedocs.io/en/stable/user_install.html to get the complete user install guide for Jupyter Widgets.

ImportError: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html

To solve this problem you need to setup Iprogress on jupyter lab :

pip install ipywidgets
jupyter nbextension enable --py widgetsnbextension

importerror: iprogress not found – Internal Links :

http://128mots.com/index.php/category/python/

http://128mots.com/index.php/category/les-reseaux-sociaux/

http://128mots.com/index.php/en/2021/01/21/greedy-algorithm-python/

Note for old version of jupyter

Installing ipywidgets automatically configures Jupyter Notebook to use widgets.

This package does this by depending on the widgetsnbextension package. This package configures Jupyter Notebook to display and use widgets.

If you have an old version of Jupyter Notebook installed, you may need to manually enable the ipywidgets notebook extension with.

jupyter nbextension enable --py widgetsnbextension

Note for separate environnements between JupyterLab and IPython

If JupyterLab and the IPython kernel are installed in different environments.

You need to do it in 2 steps :

  1. Install jupyterlab_widgets
conda install -n base -c conda-forge jupyterlab_widgets
  1. Install ipywidgets on each kernels
conda install -n py36 -c conda-forge ipywidgets

importerror: iprogress not found – External Links :

https://ipywidgets.readthedocs.io/en/stable/user_install.html

https://ipywidgets.readthedocs.io/en/stable/examples/Using%20Interact.html

Example using Python Jupyter Lab :

Now, to give change to an x ​​value of using these coins and banknotes, then we will check the first element in the array. And if it’s greater than x, we move on to the next element. Otherwise let’s keep it. Now, after taking a valuable coin or bill from the array of coinAndBill [i], the total value x we ​​need to do will become x – coinAndBill [i].

Here is the associated greedy python algorithm:

  pieceEtBillets = [500,200,100,50,20,10,5,2,1]
  i = 0
  while(x>0):
    if(pieceEtBillets[i] > x):
      i = i+1
    else:
      print(str(pieceEtBillets[i]))
      x -= pieceEtBillets[i];
renduMonnaieGlouton(33)#Exemple sur 33 euros

Greedy algorithm python – Coin change problem

A greedy python algorithm (greedy algorithm python) greedily selects the best choice at every step. He hopes that these choices lead to the optimal overall solution to the problem. So, a greedy algorithm does not always give the best solution. However in many problems this is the case.

A greedy python algorithm (greedy algorithm python) greedily selects the best choice at every step. He hopes that these choices lead to the optimal overall solution to the problem. So, a greedy algorithm does not always give the best solution. However in many problems this is the case.

Greedy Algorithm: Introduction

The problem of giving change is formulated as follows. How to return a given sum with a minimum of coins and banknotes?

Here is an example in python of the resolution of the problem:

If we consider the Euro monetary system without the cents we have the whole

EURO = (1, 2, 5, 10, 20, 50, 100, 200, 500)

Greedy algorithm python : Coin change problem

Now, to give change to an x ​​value of using these coins and banknotes, then we will check the first element in the array. And if it’s greater than x, we move on to the next element. Otherwise let’s keep it. Now, after taking a valuable coin or bill from the array of coinAndBill [i], the total value x we ​​need to do will become x – coinAndBill [i].

Here is the associated greedy python algorithm:

def renduMonnaieGlouton(x):
  pieceEtBillets = [500,200,100,50,20,10,5,2,1]
  i = 0

  while(x>0):
    if(pieceEtBillets[i] > x):
      i = i+1
    else:
      print(str(pieceEtBillets[i]))
      x -= pieceEtBillets[i];

renduMonnaieGlouton(33)#Exemple sur 33 euros

The output for 33 euro is then:

20
10
2
1

Another example with 55 euro of greedy python algorithm:

def renduMonnaieGlouton(x):
  pieceEtBillets = [500,200,100,50,20,10,5,2,1]
  i = 0

  while(x>0):
    if(pieceEtBillets[i] > x):
      i = i+1
    else:
      print(str(pieceEtBillets[i]))
      x -= pieceEtBillets[i];

renduMonnaieGlouton(55)#Exemple sur 55 euros

Output :

50
5

Conclusion

The problem of giving change is NP-difficult relative to the number of coins and notes of the monetary system considered (euro in this example). To go further, we can demonstrate that for certain so-called canonical money systems, the use of a greedy algorithm is optimal. A monetary system is said to be canonical if for any sum s the greedy algorithm leads to a minimal decomposition.

NP difficulty is the defining property of a class of problems informally “at least as difficult as the most difficult NP problems”.

A simple example of an NP-hard problem is the sum of subset problem. If P is different from NP then it is unlikely to find a polynomial time algorithm that exactly solves this problem.

External links :

http://math.univ-lyon1.fr/irem/IMG/pdf/monnaie.pdf

http://www.dil.univ-mrs.fr/~gcolas/algo-licence/slides/gloutons.pdf

Internal links python greedy algorithm :

http://128mots.com/index.php/category/python/

http://128mots.com/index.php/category/non-classe/

Levenshtein Python Algo implementation Wagner & Fischer

Here is the levenshtein python implementation of the Wagner & Fischer algorithm (Wagner-Fischer). It allows to calculate the distance of Levenshtein (distance between two strings of characters).

Here is the python implementation of the Wagner & Fischer algorithm (Wagner-Fischer). It allows to calculate the distance of Levenshtein (distance between two strings of characters).

First, the goal of the algorithm is to find the minimum cost. Minimal cost to transform one channel into another. Then a recursive function allows to return the minimum number of transformation. And to transform a substring of A with n characters into a substring of B with the same number of characters. The solution is given. We must calculate the distance between the 2 letters at the same position in the chain A and B. Then Either the letters and the previous letter are identical. Either there is a difference and in this case we calculate 3 costs. So the first is to delete a letter from the chain A. And insert a letter in the chain A to substitute a letter from the chain A. Then we can then find the minimum cost.

Example of levenshtein python implementation :

import numpy as np

def levenshtein(chaine1, chaine2):
    taille_chaine1 = len(chaine1) + 1
    taille_chaine2 = len(chaine2) + 1
    levenshtein_matrix = np.zeros ((taille_chaine1, taille_chaine2))
    for x in range(taille_chaine1):
        levenshtein_matrix [x, 0] = x
    for y in range(taille_chaine2):
        levenshtein_matrix [0, y] = y

    for x in range(1, taille_chaine1):
        for y in range(1, taille_chaine2):
            if chaine1[x-1] == chaine2[y-1]:
                levenshtein_matrix [x,y] = min(
                    levenshtein_matrix[x-1, y] + 1,
                    levenshtein_matrix[x-1, y-1],
                    levenshtein_matrix[x, y-1] + 1
                )
            else:
                levenshtein_matrix [x,y] = min(
                    levenshtein_matrix[x-1,y] + 1,
                    levenshtein_matrix[x-1,y-1] + 1,
                    levenshtein_matrix[x,y-1] + 1
                )
    return (levenshtein_matrix[taille_chaine1 - 1, taille_chaine2 - 1])

print("distance de levenshtein = " + str(levenshtein("Lorem ipsum dolor sit amet", "Laram zpsam dilir siy amot")))

To calculate the Levenshtein distance with a non-recursive algorithm. We use a matrix which contains the Levenshtein distances. Then These are the distances between all the prefixes of the first string and all the prefixes of the second string.

Also we can dynamically calculate the values ​​in this matrix. The last calculated value will be the Levenshtein distance between the two whole chains.

Finally there are many use cases of the Levenshtein distance. Levenshtein distance is used in domains. Computational linguistics, molecular biology. And again bioinformatics, machine learning. Also deep learning, DNA analysis. In addition, a program that does spell checking uses, for example, the Levenshtein distance.

Links on the Wagner & Fischer algorithm (Wagner-Fischer) and the Levenshtein python distance or other language:

https://graal.hypotheses.org/tag/algorithme-de-wagner-fischer

https://fr.wikipedia.org/wiki/Algorithme_de_Wagner-Fischer

https://fr.wikipedia.org/wiki/Distance_de_Levenshtein

https://medium.com/@sddkal/wagner-fischer-algorithm-be0d96893f6d

https://www.python-course.eu/levenshtein_distance.php

Internal links on algorithms

http://128mots.com/index.php/category/python/

http://128mots.com/index.php/category/graphes/

Quantum sort : sorting algorithm IBM Qiskit tutorial python

In this article, I propose a quantum sort algorithm with Qiskit tutorial in python that allows you to sort a list of integers coded on two qubits. I have found that there is little literature on the subject. This algorithm can be used and can be used as a basis for solving sorting problems on an unsorted list of integers.

Introduction

We consider the following problem: Given a list of four integers between 0 and 3 that are strictly different sort the given list. The solution proposed is a quantum sort algorithm.

Quantum sort : sorting algorithm IBM Qiskit python IBM Qiskit tutorial
Figure 1 : Problem to solve with Quantum sorting algorithm

A classic sorting algorithm such as merge sorting solves the problem, see in more detail my article on the subject:

Merge sorting follows the divide and conquer paradigm of dividing the initial task into two similar smaller tasks.

Some concepts of quantum algorithm and IBM Qiskit tutorial

I recall here some concept that we are going to use in our quantum sorting algorithm, so I advise you to consult the IBM Qiskit site to learn more https://qiskit.org/textbook/what-is-quantum.html and also to read the very good book “Programming Quantum Computers: Essential Algorithms and Code Samples” by Eric R. Johnston, Nic Harrigan, Mercedes Gimeno-Segovia:

Circuits

The principle in quantum algorithm is to manipulate qubits for inputs which we have in outputs which we need, the process can be represented in the form of circuit (inputs on the left, output on the right). We can perform different operations by means of quantum gate (which act on the qubits in a way similar in classical algorithm to logic gates like AND, OR, Exclusive OR…).

In this article I will rely on Qiskit which is the IBM framework for quantum computing.

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from numpy import pi

qreg_qubit = QuantumRegister(2, 'qubit')
creg_classic = ClassicalRegister(2, 'classic')
circuit = QuantumCircuit(qreg_qubit, creg_classic)

circuit.reset(qreg_qubit[0])
circuit.reset(qreg_qubit[1])
circuit.x(qreg_qubit[0])
circuit.measure(qreg_qubit[0], creg_classic[0])
circuit.measure(qreg_qubit[1], creg_classic[1])

In this first algorithm, a quantum register is initialized to the state | 01> measures in a classical register the quantum state of a register of 2 qubits. The circuit can be drawn using the circuit.draw () instruction or via Circuit Composer from IBM Quantum Experience: https://quantum-computing.ibm.com/

Quantum sort : sorting algorithm IBM Qiskit python IBM Qiskit tutorial
Quantum state of a single qubit:

The state of a qubit can be expressed as a state vector:

    \[|q\rangle = \cos{(\tfrac{\theta}{2})}|0\rangle + e^{i\phi}\sin{\tfrac{\theta}{2}}|1\rangle\]

With alpha and beta which are complex numbers (ie a real and imaginary part) in this case there is the relation (mathematical reminder on complex numbers: https://www.mathsisfun.com/numbers/complex-numbers.html):

    \[|\psi\rangle = \alpha|0\rangle + \beta|1\rangle\]

If we go into trigonometric and exponential form we have with θ and ϕ which are real numbers.

    \[\sqrt{|\alpha|^2 + |\beta|^2} = 1\]

So if we measure a qubit q we have:

    \[|q\rangle = \alpha|0\rangle + \beta|1\rangle\]

That is, there is a probability of measuring the qubit in state | 0> and a probability of measuring the qubit in state | 1>. The measurement of a qubit reveals whether it is in state 1 or in state 0, in general the measurement is placed at the end of the circuit because it affects the state of the qubit accordingly.

Quantum gates

Here are some quantum gates to know that we will use in our quantum sorting algorithm:

Gate X (Pauli-X) :

Gate X is used to return the state of the qubit without modifying the phase:

    \[X = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} = |0\rangle\langle1| + |1\rangle\langle0|\]

<

See the example above with the use of qiskit.

Gate Y (Pauli-Y) :

The pauli Y gate allows you to return the phase and the qubit at the same time:

Example if we consider here the initialized state | 0> of the qubit and its phase of 0, there is then a 100% chance of measuring the state | 0>.

Quantum sort : sorting algorithm IBM Qiskit python IBM Qiskit tutorial

Applying the quantum gate Y has the following effect on the state and phase of the qubit:

Quantum sort : sorting algorithm IBM Qiskit python IBM Qiskit tutorial

There is then a 100% chance of measuring state 1 and the phase is reversed (see the bloch sphere above)

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from numpy import pi

qreg_qubit = QuantumRegister(1, 'qubit')
creg_classic = ClassicalRegister(1, 'classic')
circuit = QuantumCircuit(qreg_qubit, creg_classic)

circuit.reset(qreg_qubit[0])
circuit.y(qreg_qubit[0])
circuit.measure(qreg_qubit[0], creg_classic[0])

Gate Z (Pauli-Z) :

The Z gate is used to return only the phase and not the state of the qubit.

Note that the Y and Z gates can be represented by the following matrices:

    \[Y = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} \quad\quad\quad\quad Z = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}\]

    \[Y = -i|0\rangle\langle1| + i|1\rangle\langle0| \quad\quad Z = |0\rangle\langle0| - |1\rangle\langle1|\]

Voir : https://qiskit.org/textbook/ch-states/single-qubit-gates.html

Hadamard Gate

The Hadamard gate (H gate) is an important quantum gate which allows to create a superposition of | 0⟩ and | 1⟩.

The matrix of this gate is:

    \[H = \tfrac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}\]

SWAP Gate

A SWAP gate allows the state of two qubits to be exchanged:

SWAP state example | 1⟩ from qubit 0 to qbit 2

IBM Qiskit tutorial

And state SWAP | 0⟩ from qubit 1 to qbit 2

Quantum sort : sorting algorithm IBM Qiskit python IBM Qiskit tutorial

In Python with the Qiskit framework we have:

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from numpy import pi

qreg_qubit = QuantumRegister(3, 'qubit')
creg_classic = ClassicalRegister(1, 'classic')
circuit = QuantumCircuit(qreg_qubit, creg_classic)

circuit.reset(qreg_qubit[0])
circuit.reset(qreg_qubit[1])
circuit.reset(qreg_qubit[2])
circuit.x(qreg_qubit[0])
circuit.swap(qreg_qubit[1], qreg_qubit[2])
circuit.measure(qreg_qubit[2], creg_classic[0])

Toffoli Gate

The Toffoli quantum gate is three qubits (two commands and one target).
It performs a phase reversal (quantum gate X on the target) only if both controls are in state | 1⟩.
A Toffoli is equivalent to an UNControlled gate (it is also called the CCX gate).

Example below with 2 command qubits in state | 1⟩ there is then a 100% chance of measuring the state | 1⟩ on the target qubit of the tofoli gate which was initially initialized to state | 0⟩ (or a reversal of the state).

Quantum sort : sorting algorithm IBM Qiskit python

Example below in the opposite case (there is then 0% chance of measuring state | 1⟩ or 100% chance of measuring state | 0⟩):

Quantum sort : sorting algorithm IBM Qiskit python
Classical gate AND gate, OR gate equivalence in quantum gate – IBM Qiskit tutorial

We see here how to combine doors to create a behavior equivalent to what we are used to using in classical circuits.

Gate AND :

From Qbit a and b and a qubit with a forced initialization to state | 0⟩ we can obtain the operation a AND b using a Toffoli quantum gate and a SWAP mate.

Quantum sort : sorting algorithm IBM Qiskit python
Le circuit suivant effectue un classique ET sur un algorithme quantique

It should be noted that at the end of this circuit we find the state A AND B on qubit B the state of qubit B is ultimately on qubit C.

The equivalent python code is as follows:

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from numpy import pi

qreg_a = QuantumRegister(1, 'a')
qreg_b = QuantumRegister(1, 'b')
qreg_c = QuantumRegister(1, 'c')
creg_aANDb = ClassicalRegister(1, 'aANDb')
creg_aState = ClassicalRegister(1, 'aState')
creg_bState = ClassicalRegister(1, 'bState')
circuit = QuantumCircuit(qreg_a, qreg_b, qreg_c, creg_aANDb, creg_aState, creg_bState)

circuit.reset(qreg_c[0])
circuit.ccx(qreg_a[0], qreg_b[0], qreg_c[0])
circuit.swap(qreg_b[0], qreg_c[0])
circuit.measure(qreg_b[0], creg_aANDb[0])
circuit.measure(qreg_a[0], creg_aState[0])
circuit.measure(qreg_c[0], creg_bState[0])

The equivalent of this code in OpenQASM assembler is:

OPENQASM 2.0;
include "qelib1.inc";

qreg a[1];
qreg b[1];
qreg c[1];
creg aANDb[1];
creg aState[1];
creg bState[1];

reset c[0];
ccx a[0],b[0],c[0];
swap b[0],c[0];
measure b[0] -> aANDb[0];
measure a[0] -> aState[0];
measure c[0] -> bState[0];

We will use this gate (in Quantum sort algorithm for example) to perform our quantum list sorting, here are some tests:

For | 0⟩ AND | 0⟩ you have | 0⟩ on qubit B:

IBM Qiskit tutorial

For | 0⟩ AND | 1⟩ you have | 0⟩ on qubit B:

IBM Qiskit tutorial

For | 1⟩ AND | 0⟩ you have | 0⟩ on qubit B:

Finally for | 1⟩ AND | 1⟩ you have good | 1⟩ on qubit B with a probability of 100%:

IBM Qiskit tutorial

Gate OR :

We will use it in Quantum sort algorithm.

To realize an OR gate we combine 4 X quantum gates, a Toffoli gate and a SWAP quantum gate, also the state of C must be initialized to the state | 1>:

IBM Qiskit tutorial

The code for this door in Qiskit:

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from numpy import pi

qreg_a = QuantumRegister(1, 'a')
qreg_b = QuantumRegister(1, 'b')
qreg_c = QuantumRegister(1, 'c')
creg_aORb = ClassicalRegister(1, 'aORb')
creg_aState = ClassicalRegister(1, 'aState')
creg_bState = ClassicalRegister(1, 'bState')
circuit = QuantumCircuit(qreg_a, qreg_b, qreg_c, creg_aORb, creg_aState, creg_bState)

circuit.reset(qreg_a[0])
circuit.reset(qreg_b[0])
circuit.x(qreg_b[0])
circuit.x(qreg_c[0])
circuit.x(qreg_a[0])
circuit.ccx(qreg_a[0], qreg_b[0], qreg_c[0])
circuit.x(qreg_a[0])
circuit.x(qreg_b[0])
circuit.swap(qreg_b[0], qreg_c[0])
circuit.measure(qreg_b[0], creg_aORb[0])
circuit.measure(qreg_a[0], creg_aState[0])
circuit.measure(qreg_c[0], creg_bState[0])

in OpenQASM :

OPENQASM 2.0;
include "qelib1.inc";

qreg a[1];
qreg b[1];
qreg c[1];
creg aORb[1];
creg aState[1];
creg bState[1];

reset a[0];
reset b[0];
x b[0];
x c[0];
x a[0];
ccx a[0],b[0],c[0];
x a[0];
x b[0];
swap b[0],c[0];
measure b[0] -> aORb[0];
measure a[0] -> aState[0];
measure c[0] -> bState[0];

If we test we get a OR gate :

Here for | 0⟩ OR | 0⟩ you have good | 0⟩ on qubit B with a probability of 100%:

Here for | 0⟩ OR | 1⟩ you have good | 1⟩ on qubit B with a probability of 100%:

For | 1⟩ OR | 0⟩ you have good | 1⟩ on qubit B with a probability of 100%:

Quantum sort algorithm.

Finally for | 1⟩ OR | 1⟩ you have good | 1⟩ on qubit B with a probability of 100%:

Quantum sort algorithm.

Quantum sort : Quantum sorting algorithm

Quantum sort algorithm

To solve this problem we will first create a quantum circuit (used in Quantum sort algorithm) that allows you to measure if a figure is lower than another for this the intuition is to be based on a circuit similar to a classic circuit of comparison of magnitude at 2 qubit .

Quantum magnitude comparator for Quantum sort algorithm:

We consider a digit A stored in a 2 qubit register (A0, A1) and a digit B stored in another register (B0, B1):

Link here: https://www.electronics-tutorials.ws/combination/comb_8.html

To know if A> B with 2 registers of 2 Qubits, the equation must be applied:

(A_{1}\overline{B_{1}})+((A_{1}A_{0}+A_{0}\overline{B_{1}})\overline{B_{0}})

The equivalent circuit to create this is:

Here in the example the 2 bits compared by this circuit are in register a and register B

Quantum qubit magnitude comparator

The equivalent code for this comparator in OpenQASM is:

I have created a GATE comparator4 which has the following OPENQASM equivalent code:

gate comparator4 a, b, c, d, f, g, i, j, k, l {
  x d;
  x j;
  x l;
  andG1 b, d, f;
  andG2 a, b, g;
  andG3 a, f, i;
  orG1 b, f, j;
  x c;
  andG4 c, f, k;
  x c;
  orG2 d, f, l;
  swap d, i;
  x d;
  swap b, g;
}

So we see that this custom quantum gate is made up of a quantum AND gate and a custom quantum OR gate that I created in the following way. If we unfold the doors andG1, andG2, andG3, orG1, orG2 we have:

The OpenQASM equivalent code to write the different gate andG1, andG2, andG3, orG1, orG2 to create comparator 4 is:

gate andG1 a, b, c {
  ccx a, b, c;
  swap b, c;
}

gate andG2 a, b, c {
  ccx a, b, c;
  swap b, c;
}

gate andG3 a, b, c {
  ccx a, b, c;
  swap b, c;
}

gate orG1 a, b, c {
  x a;
  x b;
  ccx a, b, c;
  x a;
  x b;
  swap b, c;
}

gate andG4 a, b, c {
  ccx a, b, c;
  swap b, c;
}

gate orG2 a, b, c {
  x a;
  x b;
  ccx a, b, c;
  x a;
  x b;
  swap b, c;
}
Circuit for checking a sorted list

If we consider here a list of 4 digits stored in the 4 registers of 2 qubits: a, b, m, n. The circuit above is used to test whether the input list is sorted or not. For this I cascaded 3 quantum magnitude comparators (seen in detail in the previous paragraph). Thus the circuit obtained will test if a> b and put the result on the qbit c then check if b> m and store the result on the qbit o and finally it tests if m> n and store the result on the qubit q.

The last quantum gate andOnCompare makes it possible to apply a mutliple AND part: if c AND o AND q are in the quantum state | 1> then the qubit q is set in the quantum state | 1> otherwise it is in the quantum | 0>:

Below is the code of the door andOnCompare in openQASM:

gate andOnCompare a, b, c, d, f {
  ccx a, b, d;
  swap b, d;
  ccx b, c, f;
  swap c, f;
}

We have thus created a verification circuit that a list of 4 digits stored in registers a, b, m, n is sorted in a decreasing way or not. The result is stored in the qubit q which has a 100% chance of being measured at state | 1> if the list is sorted otherwise 100% to be at | 0> if the list a, b, m, n is not in decreasing order.

In the general diagram above we notice that in the example:

a=0,b=2,m=3,n=1

in this case this circuit will return the quantum state | 0> on the qubit q

Creation of a circuit of permutations

The idea of ​​our algorithm is to permute these 4 digits using control qubits which will be in superimposed state.

The permutation circuit is as follows:

A register of 6 Qubit “control” allows to control the permutation of the list knowing that there are for 4 elements: 4 * 3 * 2 * 1 possible permutations that is to say 24 possibilities the 6 qubits allow to generate these different states.

4 Hadamard quantum gates are used to implement these permutations and take advantage of the superposition of the Qubit ‘control’ register

In other words in the circuit above we see that we start the circuit by initializing the registers a, b, m, n with its list of unsorted numbers, here (a = 0, b = 2, m = 3, n = 1).

The permutation circuit which is controlled by a superimposed qubit register allows the list to be permuted in quantum superposition.

Thus we obtain on the qubit q0 the quantum state | 1> if the permuted list is sorted in a decreasing way otherwise the quantum state | 0>.

The OpenQASM code of the quantum algorithm for performing permutations is as follows:

gate permuter a, b, c, d, f, g, i, j, k, l, m, n, o, p {
  cswap k, a, c;
  cswap l, a, f;
  cswap m, a, i;
  cswap k, b, d;
  cswap l, b, g;
  cswap m, b, j;
  cswap n, c, f;
  cswap o, c, i;
  cswap n, d, g;
  cswap o, d, j;
  cswap p, f, i;
  cswap p, g, j;
}
Amplification of the result

I’m going to call this part of my algorithm amplification: the idea is to put the qubit a, b, m, n at | 00>, | 00>, | 00>, | 00> if the list is unsorted. If the list is sorted then the quantum state of a, b, m, n should not be changed.

So we should measure the following result: | 00>, | 00>, | 00>, | 00> when the list is unsorted and a, b, m, n with the input digits in sorted order (in the case in our example this means that there is a probability of measuring the state | 11>, | 10>, | 01>, | 00> either 3,2,1,0 or the sorted list).

The circuit of the quantum amplifier is as follows:

The circuit is based on a series of quantum gate AND applied to the output state q0 AND the number of the list. When the qubit q0 indicates that the list is sorted it is at | 1> and leaves the state of the qubits a, b, m, n at their input state (or permuted by superposition). When the qubit q0 indicates that the list is unsorted it is in the state | 0> the application of the AND gate will thus set the qubits a, b, m, n to | 0>.

The amplifier code is as follows according to a quantum algorithm encoded in OpenQASM:

gate amplifier2 a, b, c, d, f, g, i, j, k, l, m, n, o, p, q, r, v {
  ccx a, k, l;
  swap a, l;
  ccx b, k, m;
  swap b, m;
  ccx c, k, n;
  swap c, n;
  ccx d, k, o;
  swap d, o;
  ccx f, k, p;
  swap f, p;
  ccx g, k, q;
  swap g, q;
  ccx i, k, r;
  swap i, r;
  ccx j, k, v;
  swap j, v;
}
Complete quantum algorithm for descending sorting of a list of four digits:

Here is the circuit used to sort the following list: a = 0, b = 2, m = 3, n = 1.

It is easily possible to initialize the circuit with another list by modifying the initialization of registers a, b, m, n. Also the current algorithm allows to sort numbers coded on 2 qubits it remains possible to modify the algorithm according to the same principle to sort numbers stored on 3 qubits and consider a list of more than 4 elements (it is then necessary to multiply the number of qubit registers to store the entry list).

The complete code is as follows in openQASM:

OPENQASM 2.0;
include "qelib1.inc";
gate andG1 a, b, c {
  ccx a, b, c;
  swap b, c;
}

gate andG2 a, b, c {
  ccx a, b, c;
  swap b, c;
}

gate andG3 a, b, c {
  ccx a, b, c;
  swap b, c;
}

gate orG1 a, b, c {
  x a;
  x b;
  ccx a, b, c;
  x a;
  x b;
  swap b, c;
}

gate andG4 a, b, c {
  ccx a, b, c;
  swap b, c;
}

gate orG2 a, b, c {
  x a;
  x b;
  ccx a, b, c;
  x a;
  x b;
  swap b, c;
}

gate comparator a, b, c, d, f, g, i, j, k, l {
  x d;
  x j;
  x l;
  andG1 b, d, f;
  andG2 a, b, g;
  andG3 a, f, i;
  orG1 b, f, j;
  x c;
  andG4 c, f, k;
  orG2 d, f, l;
}

gate comparator2 a, b, c, d, f, g, i, j, k, l {
  x d;
  x j;
  x l;
  andG1 b, d, f;
  andG2 a, b, g;
  andG3 a, f, i;
  orG1 b, f, j;
  x c;
  andG4 c, f, k;
  orG2 d, f, l;
  x d;
  swap b, g;
}

gate comparator3 a, b, c, d, f, g, i, j, k, l {
  x d;
  x j;
  x l;
  andG1 b, d, f;
  andG2 a, b, g;
  andG3 a, f, i;
  orG1 b, f, j;
  x c;
  andG4 c, f, k;
  orG2 d, f, l;
  swap d, i;
  x d;
  swap b, g;
}

gate comparator4 a, b, c, d, f, g, i, j, k, l {
  x d;
  x j;
  x l;
  andG1 b, d, f;
  andG2 a, b, g;
  andG3 a, f, i;
  orG1 b, f, j;
  x c;
  andG4 c, f, k;
  x c;
  orG2 d, f, l;
  swap d, i;
  x d;
  swap b, g;
}

gate permutation a, b, c, d, f, g, i, j, k, l, m, n, o, p {
  ccx a, c, k;
  ccx a, f, l;
  ccx a, i, m;
  ccx b, d, k;
  ccx b, g, l;
  ccx b, j, m;
  ccx c, f, n;
  ccx c, i, o;
  ccx d, g, n;
  ccx d, j, o;
  ccx f, i, p;
  ccx g, j, p;
}

gate andOnCompare a, b, c, d, f {
  ccx a, b, d;
  swap b, d;
  ccx b, c, f;
  swap c, f;
}

gate permuter a, b, c, d, f, g, i, j, k, l, m, n, o, p {
  cswap k, a, c;
  cswap l, a, f;
  cswap m, a, i;
  cswap k, b, d;
  cswap l, b, g;
  cswap m, b, j;
  cswap n, c, f;
  cswap o, c, i;
  cswap n, d, g;
  cswap o, d, j;
  cswap p, f, i;
  cswap p, g, j;
}

gate amplifier a, b, c, d, f, g, i, j, k, l, m, n, o, p, q, r, v {
  ccx l, a, m;
  swap a, m;
  ccx l, b, n;
  swap b, n;
  ccx l, c, o;
  swap c, o;
  ccx l, d, p;
  swap d, p;
  ccx l, f, q;
  swap f, q;
  ccx l, f, q;
  swap f, q;
  ccx l, g, r;
  swap g, r;
  ccx l, i, v;
  swap i, v;
  ccx l, j, k;
  swap j, k;
}

gate amplifier1 a, b, c, d, f, g, i, j, k, l, m, n, o, p, q, r, v {
  ccx a, l, m;
  swap a, m;
  ccx b, l, n;
  swap b, n;
  ccx c, l, o;
  swap c, o;
  ccx d, l, p;
  swap d, p;
  ccx f, l, q;
  swap f, q;
  ccx f, l, q;
  swap f, q;
  ccx g, l, r;
  swap g, r;
  ccx i, l, v;
  swap i, v;
  ccx j, k, l;
  swap j, k;
}

gate amplifier2 a, b, c, d, f, g, i, j, k, l, m, n, o, p, q, r, v {
  ccx a, k, l;
  swap a, l;
  ccx b, k, m;
  swap b, m;
  ccx c, k, n;
  swap c, n;
  ccx d, k, o;
  swap d, o;
  ccx f, k, p;
  swap f, p;
  ccx g, k, q;
  swap g, q;
  ccx i, k, r;
  swap i, r;
  ccx j, k, v;
  swap j, v;
}

qreg a[2];
qreg b[2];
qreg m[2];
qreg n[2];
qreg c[1];
qreg o[1];
qreg q[1];
qreg d[1];
qreg g[1];
qreg j[1];
qreg k[1];
qreg l[1];
qreg r[1];
qreg uu[1];
qreg zz[1];
qreg control[6];
creg sorted[8];

reset a[0];
reset a[1];
reset b[0];
reset b[1];
reset m[0];
reset m[1];
reset n[0];
reset n[1];
reset c[0];
reset o[0];
reset q[0];
reset d[0];
reset g[0];
reset j[0];
reset k[0];
reset l[0];
reset r[0];
reset uu[0];
h control[0];
h control[1];
h control[2];
h control[3];
h control[4];
h control[5];
reset a[0];
reset a[1];
reset b[0];
x b[1];
x m[0];
x m[1];
reset n[1];
reset c[0];
reset d[0];
reset g[0];
reset j[0];
reset k[0];
reset l[0];
x n[0];
permuter a[0],a[1],b[0],b[1],m[0],m[1],n[0],n[1],control[0],control[1],control[2],control[3],control[4],control[5];
comparator4 a[0],a[1],b[0],b[1],c[0],d[0],g[0],j[0],k[0],l[0];
reset zz[0];
reset d[0];
reset g[0];
reset j[0];
reset k[0];
reset l[0];
comparator4 b[0],b[1],m[0],m[1],o[0],d[0],g[0],j[0],k[0],l[0];
reset d[0];
reset g[0];
reset j[0];
reset k[0];
reset l[0];
comparator4 m[0],m[1],n[0],n[1],q[0],d[0],g[0],j[0],k[0],l[0];
andOnCompare c[0],o[0],q[0],r[0],uu[0];
reset d[0];
reset g[0];
reset j[0];
reset k[0];
reset l[0];
reset r[0];
reset uu[0];
amplifier2 a[0],a[1],b[0],b[1],m[0],m[1],n[0],n[1],q[0],d[0],g[0],j[0],k[0],l[0],r[0],uu[0],zz[0];
measure a[0] -> sorted[0];
measure a[1] -> sorted[1];
measure b[0] -> sorted[2];
measure b[1] -> sorted[3];
measure m[0] -> sorted[4];
measure m[1] -> sorted[5];
measure n[0] -> sorted[6];
measure n[1] -> sorted[7];

Here is the Python Qiskit code for my quantum sorting algorithm:

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from numpy import pi

qreg_a = QuantumRegister(2, 'a')
qreg_b = QuantumRegister(2, 'b')
qreg_m = QuantumRegister(2, 'm')
qreg_n = QuantumRegister(2, 'n')
qreg_c = QuantumRegister(1, 'c')
qreg_o = QuantumRegister(1, 'o')
qreg_q = QuantumRegister(1, 'q')
qreg_d = QuantumRegister(1, 'd')
qreg_g = QuantumRegister(1, 'g')
qreg_j = QuantumRegister(1, 'j')
qreg_k = QuantumRegister(1, 'k')
qreg_l = QuantumRegister(1, 'l')
qreg_r = QuantumRegister(1, 'r')
qreg_uu = QuantumRegister(1, 'uu')
qreg_zz = QuantumRegister(1, 'zz')
qreg_control = QuantumRegister(6, 'control')
creg_sorted = ClassicalRegister(8, 'sorted')
circuit = QuantumCircuit(qreg_a, qreg_b, qreg_m, qreg_n, qreg_c, qreg_o, qreg_q, qreg_d, qreg_g, qreg_j, qreg_k, qreg_l, qreg_r, qreg_uu, qreg_zz, qreg_control, creg_sorted)

circuit.x(qreg_b[1])
circuit.x(qreg_m[0])
circuit.x(qreg_m[1])
circuit.x(qreg_n[0])
circuit.x(qreg_j[0])
circuit.x(qreg_l[0])
circuit.h(qreg_control[0])
circuit.cswap(qreg_control[0], qreg_a[0], qreg_b[0])
circuit.cswap(qreg_control[0], qreg_a[1], qreg_b[1])
circuit.h(qreg_control[1])
circuit.cswap(qreg_control[1], qreg_a[0], qreg_m[0])
circuit.cswap(qreg_control[1], qreg_a[1], qreg_m[1])
circuit.h(qreg_control[2])
circuit.cswap(qreg_control[2], qreg_a[0], qreg_n[0])
circuit.cswap(qreg_control[2], qreg_a[1], qreg_n[1])
circuit.h(qreg_control[3])
circuit.cswap(qreg_control[3], qreg_b[0], qreg_m[0])
circuit.cswap(qreg_control[3], qreg_b[1], qreg_m[1])
circuit.h(qreg_control[4])
circuit.cswap(qreg_control[4], qreg_b[0], qreg_n[0])
circuit.x(qreg_b[0])
circuit.cswap(qreg_control[4], qreg_b[1], qreg_n[1])
circuit.x(qreg_b[1])
circuit.ccx(qreg_a[1], qreg_b[1], qreg_c[0])
circuit.ccx(qreg_a[0], qreg_a[1], qreg_d[0])
circuit.swap(qreg_a[1], qreg_d[0])
circuit.x(qreg_a[1])
circuit.swap(qreg_b[1], qreg_c[0])
circuit.ccx(qreg_a[0], qreg_c[0], qreg_g[0])
circuit.swap(qreg_c[0], qreg_g[0])
circuit.x(qreg_c[0])
circuit.ccx(qreg_a[1], qreg_c[0], qreg_j[0])
circuit.x(qreg_c[0])
circuit.swap(qreg_c[0], qreg_j[0])
circuit.reset(qreg_j[0])
circuit.x(qreg_j[0])
circuit.x(qreg_a[1])
circuit.swap(qreg_a[1], qreg_d[0])
circuit.reset(qreg_d[0])
circuit.ccx(qreg_b[0], qreg_c[0], qreg_k[0])
circuit.swap(qreg_c[0], qreg_k[0])
circuit.x(qreg_c[0])
circuit.reset(qreg_k[0])
circuit.x(qreg_b[0])
circuit.x(qreg_b[1])
circuit.ccx(qreg_b[1], qreg_c[0], qreg_l[0])
circuit.x(qreg_c[0])
circuit.swap(qreg_c[0], qreg_l[0])
circuit.reset(qreg_l[0])
circuit.x(qreg_l[0])
circuit.x(qreg_b[1])
circuit.swap(qreg_b[1], qreg_g[0])
circuit.reset(qreg_g[0])
circuit.x(qreg_b[1])
circuit.h(qreg_control[5])
circuit.cswap(qreg_control[5], qreg_m[0], qreg_n[0])
circuit.x(qreg_m[0])
circuit.x(qreg_n[0])
circuit.cswap(qreg_control[5], qreg_m[1], qreg_n[1])
circuit.x(qreg_m[1])
circuit.ccx(qreg_b[1], qreg_m[1], qreg_o[0])
circuit.ccx(qreg_b[0], qreg_b[1], qreg_d[0])
circuit.swap(qreg_b[1], qreg_d[0])
circuit.x(qreg_b[1])
circuit.swap(qreg_m[1], qreg_o[0])
circuit.ccx(qreg_b[0], qreg_o[0], qreg_g[0])
circuit.swap(qreg_o[0], qreg_g[0])
circuit.x(qreg_o[0])
circuit.ccx(qreg_b[1], qreg_o[0], qreg_j[0])
circuit.x(qreg_o[0])
circuit.swap(qreg_o[0], qreg_j[0])
circuit.reset(qreg_j[0])
circuit.x(qreg_j[0])
circuit.x(qreg_b[1])
circuit.swap(qreg_b[1], qreg_d[0])
circuit.reset(qreg_d[0])
circuit.ccx(qreg_m[0], qreg_o[0], qreg_k[0])
circuit.swap(qreg_o[0], qreg_k[0])
circuit.reset(qreg_k[0])
circuit.x(qreg_o[0])
circuit.x(qreg_m[0])
circuit.x(qreg_m[1])
circuit.ccx(qreg_m[1], qreg_o[0], qreg_l[0])
circuit.x(qreg_o[0])
circuit.swap(qreg_o[0], qreg_l[0])
circuit.ccx(qreg_c[0], qreg_o[0], qreg_r[0])
circuit.reset(qreg_l[0])
circuit.x(qreg_l[0])
circuit.swap(qreg_o[0], qreg_r[0])
circuit.reset(qreg_r[0])
circuit.x(qreg_m[1])
circuit.swap(qreg_m[1], qreg_g[0])
circuit.reset(qreg_g[0])
circuit.x(qreg_m[1])
circuit.x(qreg_n[1])
circuit.ccx(qreg_m[1], qreg_n[1], qreg_q[0])
circuit.ccx(qreg_m[0], qreg_m[1], qreg_d[0])
circuit.swap(qreg_m[1], qreg_d[0])
circuit.x(qreg_m[1])
circuit.swap(qreg_n[1], qreg_q[0])
circuit.ccx(qreg_m[0], qreg_q[0], qreg_g[0])
circuit.swap(qreg_q[0], qreg_g[0])
circuit.x(qreg_q[0])
circuit.ccx(qreg_m[1], qreg_q[0], qreg_j[0])
circuit.x(qreg_q[0])
circuit.swap(qreg_q[0], qreg_j[0])
circuit.reset(qreg_j[0])
circuit.x(qreg_m[1])
circuit.swap(qreg_m[1], qreg_d[0])
circuit.reset(qreg_d[0])
circuit.ccx(qreg_n[0], qreg_q[0], qreg_k[0])
circuit.swap(qreg_q[0], qreg_k[0])
circuit.reset(qreg_k[0])
circuit.x(qreg_q[0])
circuit.x(qreg_n[0])
circuit.x(qreg_n[1])
circuit.ccx(qreg_n[1], qreg_q[0], qreg_l[0])
circuit.x(qreg_q[0])
circuit.swap(qreg_q[0], qreg_l[0])
circuit.reset(qreg_l[0])
circuit.ccx(qreg_o[0], qreg_q[0], qreg_uu[0])
circuit.swap(qreg_q[0], qreg_uu[0])
circuit.reset(qreg_uu[0])
circuit.ccx(qreg_a[0], qreg_q[0], qreg_d[0])
circuit.swap(qreg_a[0], qreg_d[0])
circuit.x(qreg_n[1])
circuit.swap(qreg_n[1], qreg_g[0])
circuit.reset(qreg_g[0])
circuit.ccx(qreg_a[1], qreg_q[0], qreg_g[0])
circuit.swap(qreg_a[1], qreg_g[0])
circuit.ccx(qreg_b[0], qreg_q[0], qreg_j[0])
circuit.swap(qreg_b[0], qreg_j[0])
circuit.ccx(qreg_b[1], qreg_q[0], qreg_k[0])
circuit.swap(qreg_b[1], qreg_k[0])
circuit.ccx(qreg_m[0], qreg_q[0], qreg_l[0])
circuit.swap(qreg_m[0], qreg_l[0])
circuit.ccx(qreg_m[1], qreg_q[0], qreg_r[0])
circuit.swap(qreg_m[1], qreg_r[0])
circuit.ccx(qreg_n[0], qreg_q[0], qreg_uu[0])
circuit.swap(qreg_n[0], qreg_uu[0])
circuit.x(qreg_n[1])
circuit.ccx(qreg_n[1], qreg_q[0], qreg_zz[0])
circuit.swap(qreg_n[1], qreg_zz[0])
circuit.measure(qreg_a[0], creg_sorted[0])
circuit.measure(qreg_a[1], creg_sorted[1])
circuit.measure(qreg_b[0], creg_sorted[2])
circuit.measure(qreg_b[1], creg_sorted[3])
circuit.measure(qreg_m[0], creg_sorted[4])
circuit.measure(qreg_m[1], creg_sorted[5])
circuit.measure(qreg_n[0], creg_sorted[6])
circuit.measure(qreg_n[1], creg_sorted[7])

Quantum sorting algorithm circuit test with IBM qiskit (python)

The tests are carried out by starting the algorithm on the quantum simulator:

To start the quantum algorithm, you must first initialize:

%matplotlib inline
# Importing standard Qiskit libraries
from qiskit import QuantumCircuit, execute, Aer, IBMQ
from qiskit.compiler import transpile, assemble
from qiskit.tools.jupyter import *
from qiskit.visualization import *
from iqx import *

# Loading your IBM Q account(s)
provider = IBMQ.load_account()

And to perform the test for example by executing the quantum circuit 100 times and displaying the probability of measurement in the form of a histogram:

backend = Aer.get_backend('qasm_simulator')
results = execute(circuit, backend=backend, shots=100).result()
answer = results.get_counts()
plot_histogram(answer)

We obtain the result which confirms that with Quantum sort algorithm we have more change in measuring the quantum state of the sorted list than the other combinations (in my test 5%):

After 200 shots i get :

Quantum Sort & Internal links :

http://128mots.com/index.php/en/category/non-classe-en/

Pytorch tutorial Deep Learning with Python

Introduction

When I wrote this blog post (this Pytorch tutorial), I remembered the challenge I set for myself at the beginning of the year to learn deep learning, I did not even know Python at the time. What makes things difficult is not necessarily the complexity of the concepts, but it starts with questions like: What framework to use for deep learning? Which activation function should I choose? Which cost function is best suited for my problem?

My personal experience has been to study the PyTorch framework and especially for the theory the online course made available for free by Yan LeCun whom I thank (link here https://atcold.github.io/pytorch-Deep-Learning/) . I still have to learn and work in the field but through this blog post, I would like to share and give you an overview of what I have learned about deep learning this year.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial

Deep Learning: Which activation and cost function to choose?

The objective of this article is to sweep through this central topic in DeepLearning of choosing the activation and cost (loss) function according to the problem you are looking to solve by means of a DeepLearning algorithm.

We are talking about the activation function of the last layer of your model, that is to say the one that gives you the result.

This result is used in the algorithm which checks for each learning the difference between the result predicted by the neural network and the real result (gradient descent algorithm), for this we apply to the result a cost function (loss function) which represents this difference and which you seek to minimize as you practice in order to reduce the error. (See this article here to learn more : https://machinelearnia.com/descente-de-gradient/)

Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Source https://upload.wikimedia.org/wikipedia/commons/6/68/Gradient_descent.jpg :
L’algorithe de descente de Gradient permet de trouver le minimum de n’importe quelle fonction convexe pas à pas. – Pytorch tutorial

As a reminder, the machine learns by minimizing the cost function, iteratively by successive training steps, the result of the cost function and taken into account for the adjustment of the parameters of the neurons (weight and bias for example for linear layers) .

This choice of activation function on the last layer and the cost function to be minimized (loss function) is therefore crucial since these two elements combined will determine how you are going to solve a problem using your neural network.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial
https://upload.wikimedia.org/wikipedia/commons/6/60/ArtificialNeuronModel_english.png – Pytorch tutorial

This article also presents simple examples that use the Pytorch framework in my opinion a very good tool for machine learning.

The question here to ask is the following:

  • Am I looking to create a model that performs binary classification? (In this case you are trying to predict a probability that the result of an entry will be 0 or 1)
    Am I looking to calculate / predict a numeric value with my neural network? (In this case you are trying to predict a decimal value for example at the output that corresponds to your input)
  • Am I looking to create a model that performs single or multiple label classification for a set of classes? (In this case, you are trying to predict for each output class the probability that an input matches this class)
  • Am I looking to create a model that searches for multiple classes within a set of possible classes? (In this case, you are trying to predict for each class at the exit its attendance rate at the entrance).

Binary classification problem:

You are trying to predict by means of your DeepLearning algorithm whether a result is true or false, and more precisely it is a probability that a result of 1 or that of a result of 0 that you will get.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial

The output size of your neural network is 1 (final layer) and you seek to obtain a result between 0 and 1 which will be assimilated to the probability that the result is 1 (example at the output of the network if you obtain 0.65 this will correspond to 65% chance that the result is true).
Application example: Predicting the probability that the home team in a football match will win. The closer the value is to 1 the more the home team has a chance of winning, and conversely the closer the score is to 0 the more chance the home team has of losing.
It is possible to qualify this result using a threshold, for example by admitting that if the output is> 0.5 then the result is true if not false.

Final activation function (case of binary classification):

The final activation function should return a result between 0 and 1, the correct choice in this case may be the sigmoid function. The sigmoid function will easily translate a result between 0 and 1 and therefore is ideal for translating the probability that we are trying to predict.

If you want to plot the sigmoid function in Python here is some code that should help you (see alsohttps://squall0032.tumblr.com/post/77300791096/plotting-a-sigmoid-function-using-python-matplotlib) :

import math
import numpy as np
import matplotlib.pyplot as plt
def sigmoid(x):
    a = []
    for item in x:
        a.append(1/(1+math.exp(-item)))
    return a
x = np.arange(-10., 10., 0.2)
sig = sigmoid(x)
plt.plot(x,sig)
plt.show()
Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Tracé de la fonction sigmoid, fonction utilisée comme fonction d’activation finale dans le cas d’un algorithme de Deep Learning – Pytorch tutorial
The cost function – Loss function (case of binary classification):

You have to determine during training the difference between the probability that the model predicts (translated via the final sigmoid function) and the true and known response (0 or 1). The function to use is Binary Cross Entrropy because this function allows to calculate the difference between 2 probability.
The optimizer will then use this result to adjust the weights and biases in your model (or other parameters depending on the architecture of your model).

Example :

In this example I will create a neural network with 1 linear layer and a final sigmoid activation function.

First, I perform all the imports that we will use in this post:

import numpy as np
import pandas as pd 
import matplotlib.pyplot as plt
from collections import OrderedDict
import math
from random import randrange
import torch 
from torch.autograd import Variable
import torch.nn as nn 
from torch.autograd import Function 
from torch.nn.parameter import Parameter 
from torch import optim 
import torch.nn.functional as F 
from torchvision import datasets, transforms
from echoAI.Activation.Torch.bent_id import BentID
from sklearn.model_selection import train_test_split
import sklearn.datasets
from sklearn.metrics import accuracy_score
import hiddenlayer as hl
import warnings
warnings.filterwarnings("ignore")
from torchviz import make_dot, make_dot_from_trace

The following lines allow you not to display the warnings in python:

import warnings
warnings.filterwarnings("ignore")

I will generate 1000 samples generated by the sklearn library allowing me to have a set of tests for a binary classification problem. The test set covers 2 decimal inputs and a binary output (0 or 1). I also display the result as a point cloud:

inputData,outputData = sklearn.datasets.make_moons(1000,noise=0.3) 
plt.scatter(inputData[:,0],inputData[:,1],s=40,c=outputData,cmap = plt.cm.get_cmap("Spectral"))
Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Creation of 1000 samples with a result of 0 or 1 via sklearn

The test set generated here corresponds to a data set with 2 classes (class 0 and 1).

The goal of my neural network is therefore a binary classification of the input.

I will take 20% of this test set as test data and the remaining 80% as training data. I split the test set again to create a validation set on the training dataset.

X_train, X_test, y_train, y_test = train_test_split(inputData, outputData, test_size=0.20, random_state=42)
Input Data
Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Output data

In my example I’m going to create a network with any architecture what interests us is to show how the last layer works:

fc1 = nn.Linear(2, 2)
fc2 = nn.Linear(2, 1)

model = nn.Sequential(OrderedDict([
                      ('lin1', fc1),
                      ('BentID1', BentID()),
                      ('lin2', fc2),
                      ('sigmoid', nn.Sigmoid())
                        ]))
model = model.double()

I added a line to transform the pytorch model to use the double type. This avoids an error of the type:

Expected object of scalar type Double but got scalar type Float for argument

Also it will be necessary to use dtype = torch.double when creating torch.tensor at each training.

As indicated in my documents above the cost function is the Binary Cross Entropy function in this case (BCELoss : https://pytorch.org/docs/stable/generated/torch.nn.BCELoss.html#torch.nn.BCELoss) :

loss = nn.BCELoss()

I am using the Adam optimizer with a learning rate of 0.01:
Deep learning optimizers are algorithms or methods used to modify attributes of your neural network such as weights and bias in such a way that the loss function is minimized.

The learning rate is a hyperparameter that controls how much the model should be changed in response to the estimated error each time the model weights are updated.

Here I am using the Adam optimization algorithm. In Deep Learning Adam is a stochastic gradient descent method that calculates individual adaptive learning rates for different parameters from estimates of the first and second order moments of the gradients.
More information on optimizing Adam: https://machinelearningmastery.com/adam-optimization-algorithm-for-deep-learning/
and in PyToch doc : https://pytorch.org/docs/stable/optim.html?highlight=adam#torch.optim.Adam

optimizer = optim.Adam(model.parameters(), lr=0.01)

I previously split the training data a second time to take 20% of the data as validation data. They allow us at each training to validate that we are not doing over-training (over-adjustment, or over-interpretation, or simply in English overfitting).

X_train, X_valid, y_train, y_valid = train_test_split(X_train, y_train, test_size=0.20, random_state=42)

In this example I have chosen to implement the EarlyStopping algorithm with a patience of 5. This means that if the cost function of the validation data increases during 15 training sessions (ie the distance between the prediction and the true data). After 15 training sessions with an increasing distance, we reload the previous data which represents the configuration of the neural network producing a distance of the minimum cost function (in the case of our example this consists in reloading the weight and the bias for the 2 layers linear). As long as the function decreases, the configuration of the neural network is saved (weight and bias of the linear layers in our example).

Here I have chosen to display the weights and bias of the 2 linear layers every 10 workouts, to give you an idea of how the Adam optimization algorithm works:

I used https://github.com/waleedka/hiddenlayer to display various graphs around training and validation metrics. The graphics are thus refreshed during use.

history1 = hl.History()
canvas1 = hl.Canvas()

Here is the main code of the learning loop:

bestvalidloss = np.inf
saveWeight1 = fc1.weight 
saveWeight2 = fc2.weight 
saveBias1 = fc1.bias
saveBias2 = fc2.bias
wait = 0
for epoch in range(1000):
    model.train()
    optimizer.zero_grad()
    result = model(torch.tensor(X_train,dtype=torch.double))
    lossoutput = loss(result, torch.tensor(y_train,dtype=torch.double))
    lossoutput.backward()
    optimizer.step()
    print("EPOCH " + str(epoch) + "- train loss = " + str(lossoutput.item()))
    if((epoch+1)%10==0):
        #AFFICHE LES PARAMETRES DU RESEAU TOUT LES 10 entrainements
        print("*************** PARAMETERS WEIGHT & BIAS *********************")
        print("weight linear1= " + str(fc1.weight))
        print('Bias linear1=' + str(fc1.bias))
        print("weight linear2= " + str(fc2.weight))
        print('bias linear2=' + str(fc2.bias))
        print("**************************************************************")
    model.eval()
    validpred = model(torch.tensor(X_valid,dtype=torch.double))
    validloss = loss(validpred, torch.tensor(y_valid,dtype=torch.double))
    print("EPOCH " + str(epoch) + "- valid loss = " + str(validloss.item()))
    
    # Store and plot train and valid loss.
    history1.log(epoch, trainloss=lossoutput.item(),validloss=validloss.item())
    canvas1.draw_plot([history1["trainloss"], history1["validloss"]])
    
    if(validloss.item() < bestvalidloss):
        bestvalidloss = validloss.item()
        #
        saveWeight1 = fc1.weight 
        saveWeight2 = fc2.weight 
        saveBias1 = fc1.bias
        saveBias2 = fc2.bias
        wait = 0
    else:
        wait += 1
        if(wait > 15):
            #Restauration des mailleurs parametre et early stopping
            fc1.weight = saveWeight1
            fc2.weight = saveWeight2
            fc1.bias = saveBias1
            fc2.bias = saveBias2
            print("##############################################################")
            print("stop valid because loss is increasing (EARLY STOPPING) afte EPOCH=" + str(epoch))
            print("BEST VALID LOSS = " + str(bestvalidloss))
            print("BEST PARAMETERS WHEIGHT AND BIAS = ")
            print("FIRST LINEAR : WEIGHT=" + str(saveWeight1) + " BIAS = " + str(saveBias1))
            print("SECOND LINEAR : WEIGHT=" + str(saveWeight2) + " BIAS = " + str(saveBias2))
            print("##############################################################")
            break
        else:
            continue

Here is an overview of the result, training stops after about 200 epochs (an “epoch” is a term used in machine learning to refer to a passage of the complete training data set). In my example I didn’t use a batch to load the data so the epoch count is the iteration count.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial

Evolution of the cost function on the training test and the validation test

Here’s a look at the prediction results:

result = model(torch.tensor(X_test,dtype=torch.double))
plt.scatter(X_test[:,0],X_test[:,1],s=40,c=y_test,cmap = plt.cm.get_cmap("Spectral"))
plt.title("True")
plt.colorbar()
plt.show()
plt.scatter(X_test[:,0],X_test[:,1],s=40,c=result.data.numpy(),cmap = plt.cm.get_cmap("Spectral"))
plt.title("predicted")
plt.colorbar()
plt.show()
Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Results: The first graph shows the “true” answer the second shows the predicted answer (the color varies according to the predicted probability) – Pytorch tutorial

To display the architecture of the neural network I used the hidden layer library which requires the installation of graphviz to avoid the following error:

RuntimeError: Make sure the Graphviz executables are on your system's path


To resolve this error see https://graphviz.org/download/

On Mac OS X, for example, I installed via Homebrew:

brew install graphviz

Here is an overview of the hidden layer graph:

# HiddenLayer graph
hl.build_graph(model, torch.zeros(2,dtype=torch.double))
Hidden Layer architecture pour le classifier binaire – Pytorch tutorial

I also used PyTorchViz https://github.com/szagoruyko/pytorchviz/blob/master/examples.ipynb to display a graph of Pytorch operations during the forward of an entry and thus we can clearly see what will happen pass during the backward (ie the application the calculation of the dols / dx differential for all the parameters x of the network which has requires_grad = True).

make_dot(model(torch.ones(2,dtype=torch.double)), params=dict(model.named_parameters()))
Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Architecture diagram of the neural network created with PyTorch – Pytorch tutorial

Regression problem (numeric / decimal value calculation):

In this case, you are trying to predict a continuous numerical quantity using your DeepLearning algorithm.
In this case, the gradient descent algorithm consists in comparing the difference between the numerical value predicted by the network and the true value.
The output size of the network will be 1 since there is only one value to predict.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Final activation function (decimal or numeric value case):

The activation function to use in this case depends on the range in which your data is located.

For a data between -infinite and + infinite then you can use a linear function at the output of your network.

Linear function graph function. https://pytorch.org/docs/stable/generated/torch.nn.Linear.html. The particularity is that this linear function (of the type y = ax + b) contains learnable parameters (weight and bias which are modified by the optimizer over the training sessions, i.e. y = weight * x + bias).

Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Source https://upload.wikimedia.org/wikipedia/commons/9/9c/Linear_function_kx.png: Linear functions.

You can also use the Relu function if your value to predict is strictly positive
the output of ReLu is the maximum value between zero and the input value. An output is zero when the input value is negative and the input value when the input is positive.
Note that unlike the rectified linear activation function Relu does not have an adjustable parameter (learnable).

https://pytorch.org/docs/stable/generated/torch.nn.ReLU.html

Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Fonction d’activation ReLu Source = https://upload.wikimedia.org/wikipedia/commons/f/fe/Activation_rectified_linear.svg

Another possible function is PReLu (parametric linear rectification unit):

Pytorch tutorial deeplearning with python and pytorch mnist tutorial
PReLu activation function
Source https://upload.wikimedia.org/wikipedia/commons/a/ae/Activation_prelu.svg


Also another possible final activation function is Bent identity.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Bent identity activation function Source https://upload.wikimedia.org/wikipedia/commons/c/c3/Activation_bent_identity.svg


Finally I recommend the possible use of Parametric Soft Exponential, I use the echoAi implementation because it is not natively in PyTorch
https://echo-ai.readthedocs.io/en/latest/#torch-soft-exponential

Soft Exponential
Source https://upload.wikimedia.org/wikipedia/commons/b/b5/Activation_soft_exponential.svg
The cost function (regression case, calculation of numerical value):

The cost function which makes it possible to determine the distance between the predicted value and the real value is the average of the squared distance between the 2 predictions. The function to use is mean squared error (MSE): https://pytorch.org/docs/stable/generated/torch.nn.MSELoss.html

Here is a simple example that illustrates the use of each of the final functions:

I started off with the example of house prices which I then adapted to test with each of the functions.

Example: Loading test data

First, I import the necessary libraries:

import numpy as np
import pandas as pd 
import matplotlib.pyplot as plt
from collections import OrderedDict
import math
from random import randrange
import torch 
from torch.autograd import Variable
import torch.nn as nn 
from torch.autograd import Function 
from torch.nn.parameter import Parameter 
from torch import optim 
import torch.nn.functional as F 
from torchvision import datasets, transforms
from echoAI.Activation.Torch.bent_id import BentID
from echoAI.Activation.Torch.soft_exponential import SoftExponential
from sklearn.model_selection import train_test_split
import sklearn.datasets
from sklearn.metrics import accuracy_score
import hiddenlayer as hl
import warnings
warnings.filterwarnings("ignore")
from torchviz import make_dot, make_dot_from_trace
from sklearn.datasets import make_regression
from torch.autograd import Variable

I create the dataset which is quite simple and display it:

house_prices_array = [30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140]
house_price_np = np.array(house_prices_array, dtype=np.float32)
house_price_np = house_price_np.reshape(-1,1)
house_price_tensor = Variable(torch.from_numpy(house_price_np))
house_size = [ 7.5, 7, 6.5, 6.0, 5.5, 5.0, 4.5,3.5,3.2,2.8,3.0,2.5]
house_size_np = np.array(house_size, dtype=np.float32)
house_size_np = house_size_np.reshape(-1, 1)
house_size_tensor = Variable(torch.from_numpy(house_size_np))
import matplotlib.pyplot as plt
plt.scatter(house_prices_array, house_size_np)
plt.xlabel("House Price $")
plt.ylabel("House Sizes")
plt.title("House Price $ VS House Size")
plt.show()

In the example, we see that the function to find is close to
f (x) = – 0.05 * x + 9
Example: – 0.05 * 40 + 9 = 7 and -0.05 * 30 + 9 = 7.5

I set the bias and the weight to -0.01 and 8 to limit the training time.

Linear activation function (Solving regression problem):
fc1 = nn.Linear(1, 1)

model = nn.Sequential(OrderedDict([
                       ('lin', fc1)
                        ]))

model = model.float()
fc1.weight.data.fill_(-0.01)
fc1.bias.data.fill_(8)

I declare MSELoss and an Adam optimizer tuned with a learning rate 0.01

loss = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.01)

Here is the training loop:

history1 = hl.History()
canvas1 = hl.Canvas()
for epoch in range(100):
    model.train()
    optimizer.zero_grad()
    result = model(house_price_tensor)
    lossoutput = loss(result, house_size_tensor)
    lossoutput.backward()
    optimizer.step()
    print("EPOCH " + str(epoch) + "- train loss = " + str(lossoutput.item()))
    history1.log(epoch, trainloss=lossoutput.item())
    canvas1.draw_plot([history1["trainloss"]])

After a hundred training sessions we obtain an MSELoss = 0.13

Pytorch tutorial deeplearning with python and pytorch mnist tutorial

If I display the weights and biases found by the model I get in my example:

print("weight" + str(fc1.weight))
print("bias" + str(fc1.bias))

The network therefore executes here the function f (x) = -0.0408 * x + 8.1321

I then display the predicted result to compare it with the actual result:

result = model(house_price_tensor)
plt.scatter(house_prices_array, house_size_np)
plt.title("True")
plt.show()
plt.scatter(house_prices_array,result.detach().numpy())
plt.title("predicted")
plt.show()
Pytorch tutorial deeplearning with python and pytorch mnist tutorial

Here is a preview of the architecture diagram for a simple Pytorch neuron network with Linear function, we see the multiplication operator and the addition operator to execute y = ax + b.

hl.build_graph(model, torch.ones(1,dtype=torch.float))
Diagramme of the neural network pytorch – Pytorch tutorial
Pytorch tutorial deeplearning with python and pytorch mnist tutorial

ReLu activation function (Regression problem solving):

ReLu is not an activation function with “learnable” parameters (modified by the optimizer) so I add a linear layer upstream for the test:

The result is identical, which is logical since in my case reLu only passes the result which is strictly positive

In the previous example, a ReLu layer must be added at the output after the linear layer:

fc1 = nn.Linear(1, 1)

model = nn.Sequential(OrderedDict([
                       ('lin', fc1),
                       ('relu',nn.ReLU())
                        ]))

model = model.float()
fc1.weight.data.fill_(-0.01)
fc1.bias.data.fill_(8)
Model architecture with linear layer + ReLu layer

The same for PrRelu in my case:
These two functions simply make a flat pass between the linear function and the output. ReLu remains interesting if you want to set to 0 all the outputs concerning a negative input.

Bent Identity Function (Regression Problem Solving):

Bent identity there is no learning parameter but the function does not just forward the input it applies the curved identity function to it which slightly modifies the result:

fc1 = nn.Linear(1, 1)

model = nn.Sequential(OrderedDict([
                       ('lin', fc1),
                       ('BentID',BentID())
                        ]))

model = model.float()
fc1.weight.data.fill_(-0.01)
fc1.bias.data.fill_(8)

In our case after 100 training sessions the network found the following weights for the linear function upstream of bent identity the final loss is 0.78 so less good than with the linear function (the network converges less quickly):

In our case, the function applied by the network will therefore be:

-0.0481 ((math.sqt(x**2 + 1) -1)/2 + x) + 7.7386

Result obtained with Bent Identity:

hl.build_graph(model, torch.ones(1,dtype=torch.float))

I display the architecture of the Pytorch network which is now linear layer + bent identity layer :

Also :

make_dot(model(torch.ones(1,dtype=torch.float)), params=dict(model.named_parameters()))
Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Soft Exponential – (Regression problem solving)


Soft Exponential has a trainable alpha parameter.We are going to place a linear function upstream and softExponential in output and check the approximation performed in this case:

fc1 = nn.Linear(1, 1)
fse = SoftExponential(1,torch.tensor([-0.9],dtype=torch.float))
model = nn.Sequential(OrderedDict([
                       ('lin', fc1),
                       ('SoftExponential',fse)
                        ]))

model = model.float()
fc1.weight.data.fill_(-0.01)
fc1.bias.data.fill_(8)

After 100 training sessions the results on the linear layer parameters and the soft exponential layer parameters are as follows:

print("weight" + str(fc1.weight))
print("bias" + str(fc1.bias))
print("fse alpha" + str(fse.alpha))

The result is not really good since the approximation is not done in the right direction,

We therefore notice that we could invert the function in our case to define a Soft Exponential customize activation function with a bias criterion and that is what we will do here.

Custom function – (Regression problem solving)

We declare a custom activation function to PyTorch compared to the original soft exponential I added the beta bias criterion as well as the torch.div inversion (1, …)

class SoftExponential2(nn.Module):
    def __init__(self, in_features, alpha=None,beta=None):
        super(SoftExponential2, self).__init__()
        self.in_features = in_features
        # initialize alpha
        if alpha is None:
            self.alpha = Parameter(torch.tensor(0.0))  # create a tensor out of alpha
        else:
            self.alpha = Parameter(torch.tensor(alpha))  # create a tensor out of alpha
        if beta is None:
            self.beta = Parameter(torch.tensor(0.0))  # create a tensor out of alpha
        else:
            self.beta = Parameter(torch.tensor(beta))  # create a tensor out of alpha

        self.alpha.requiresGrad = True  # set requiresGrad to true!
        self.beta.requiresGrad = True  # set requiresGrad to true!

    def forward(self, x):
        if self.alpha == 0.0:
            return x

        if self.alpha < 0.0:
            return torch.add(torch.div(1,(-torch.log(1 - self.alpha * (x + self.alpha)) / self.alpha)),self.beta)

        if self.alpha > 0.0:
            return torch.add(torch.div(1,((torch.exp(self.alpha * x) - 1) / self.alpha + self.alpha)),self.beta)

We now have 2 parameters that can be trained in this custom function in Pytorch.

By also lowering the learning rate to 0.01 after 100 training sessions and initializing alpha = 0 .1 and beta = 0.7 I arrive at a loss <5

fse = SoftExponential2(1,torch.tensor([0.1],dtype=torch.float),torch.tensor([7.0],dtype=torch.float))

model = nn.Sequential(OrderedDict([
                       ('SoftExponential',fse)
                        ]))

model = model.float()
fc1.weight.data.fill_(-0.01)
fc1.bias.data.fill_(8)
print("fse alpha" + str(fse.alpha))
print("fse beta" + str(fse.beta))

Network architecture applied for my custom soft exponentialt inversion function with addition of a bias criterion.

Categorization problem (predict a class among several classes possible) – single-label classifier with pytorch

You are looking to predict the probability that your entry will match a single class and exit betting multiple possible classes.
For example you want to predict the type of vehicle on an image allowed the classes: car, truck, train

The dimensioning of your output network corresponds to n neurons for n classes. And for each output neurons corresponding to a possible class to be predicted, we will obtain a probability between 0 and 1 which will represent the probability that the input corresponds to this class at the output. So for each class this comes down to solving a binary classification problem in part 1 but in addition to which it must be considered that an input can only correspond to a single output class.

Activation function Categorization problem (predict a class among several possible classes):

The activation function to be used on the final layer is a Softfmax function with n dimensions corresponding to the number of classes to be predicted.
Softmax is a mathematical function that converts a vector of numbers (tensor) into a vector of probabilities, where the probabilities of each value are proportional to the relative scale of each value in the vector.


(Cf https://machinelearningmastery.com/softmax-activation-function-with-python/)

In other words, for an output tensor it will return a probability for each class by scaling each of them so that their sum is equal to one.

https://pytorch.org/docs/stable/generated/torch.nn.Softmax.html

Cost function – Categorization problem (predict a class among several possible classes):

The cost function to be used is close to that used in the case of binary classification but with this notion of probability vector.
Cross Entropy will evaluate the difference between 2 probability distributions. We will therefore use it to compare the predicted value and the true value.

See https://en.wikipedia.org/wiki/Cross_entropy

Based on the tutorial and the data set on this page we have:https://pytorch.org/tutorials/beginner/blitz/cifar10_tutorial.html

For info if you get the following error:

ImportError: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html

You need to setup Iprogress on jupyter lab

pip install ipywidgets
jupyter nbextension enable --py widgetsnbextension

In our example we will first retrieve the input dataset
The dataset used is CIFAR-10, more information here:

https://www.cs.toronto.edu/~kriz/cifar.html

This is already integrated with Pytorch to allow us to perform certain tests.

Exemple (problème de catégorisation) :

Preparation of the dataset:

import torch
import torchvision
import torchvision.transforms as transforms

transform = transforms.Compose(
    [transforms.ToTensor(),
     transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5))])

trainset = torchvision.datasets.CIFAR10(root='./data', train=True,
                                        download=True, transform=transform)
trainloader = torch.utils.data.DataLoader(trainset, batch_size=4,
                                          shuffle=True, num_workers=2)

testset = torchvision.datasets.CIFAR10(root='./data', train=False,
                                       download=True, transform=transform)
testloader = torch.utils.data.DataLoader(testset, batch_size=4,
                                         shuffle=False, num_workers=2)

classes = ('plane', 'car', 'bird', 'cat',
           'deer', 'dog', 'frog', 'horse', 'ship', 'truck')

We then define a function which allows to visualize the imshow image and we display for each image the unique label associated with it:

import matplotlib.pyplot as plt
import numpy as np

# functions to show an image


def imshow(img):
    img = img / 2 + 0.5     # unnormalize
    npimg = img.numpy()
    plt.imshow(np.transpose(npimg, (1, 2, 0)))
    plt.show()


# get some random training images
dataiter = iter(trainloader)
images, labels = dataiter.next()

# show images
imshow(torchvision.utils.make_grid(images))
# print labels
print(' '.join('%5s' % classes[labels[j]] for j in range(4)))

Create a convolutional neural network (more information here: https://towardsdatascience.com/a-comprehensive-guide-to-convolutional-neural-networks-the-eli5-way-3bd2b1164a53)

A convolutional neural network (ConvNet or CNN) is a DeepLearning algorithm that can take an image as input, it sets a score (weight and bias which are learnable parameters) to various aspects / objects of the image and be able to differentiate one from the other.

Source https://upload.wikimedia.org/wikipedia/commons/6/63/Typical_cnn.png

The architecture of a convolutional neuron network is close to that of the model of neuron connectivity in the human brain and was inspired by the organization of the visual cortex.

Individual neurons respond to stimuli only in a restricted region of the visual field known as the receptive field. A collection of these fields overlap to cover the entire visual area.

In our case we are going to use with Pytorch a Conv2d layer and a pooling layer.

https://pytorch.org/docs/stable/generated/torch.nn.Conv2d.html : The Conv2d layer is the 2D convolution layer.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial
Source : https://cdn-media-1.freecodecamp.org/images/gb08-2i83P5wPzs3SL-vosNb6Iur5kb5ZH43

https://www.freecodecamp.org/news/an-intuitive-guide-to-convolutional-neural-networks-260c2de0a050/

A filter in a conv2D layer has a height and a width. They are often smaller than the input image. This filter therefore moves over the entire image during training (this area is called the receptive field).

The Max Pooling layer is a sampling process. The objective is to sub-sample an input representation (image for example), by reducing its size and by making assumptions on the characteristics contained in the grouped sub-regions.

In my example with PyTorch the declaration is made :

import torch.nn as nn
import torch.nn.functional as F


class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(3, 6, 5)
        self.pool = nn.MaxPool2d(2, 2)
        self.conv2 = nn.Conv2d(6, 16, 5)
        self.fc1 = nn.Linear(16 * 5 * 5, 120)
        self.fc2 = nn.Linear(120, 84)
        self.fc3 = nn.Linear(84, 10)

    def forward(self, x):
        x = self.pool(F.relu(self.conv1(x)))
        x = self.pool(F.relu(self.conv2(x)))
        x = x.view(-1, 16 * 5 * 5)
        x = F.relu(self.fc1(x))
        x = F.relu(self.fc2(x))
        x = self.fc3(x)
        return x


net = Net()

Define the criterion of the cost function with CrossEntropyLoss, here we use the SGD opimizer rather than adam (more info here on the comparison between optimizer https://ruder.io/optimizing-gradient-descent/)

import torch.optim as optim

criterion = nn.CrossEntropyLoss()
optimizer = optim.SGD(net.parameters(), lr=0.001, momentum=0.9)

The training loop:

for epoch in range(2):  # loop over the dataset multiple times

    running_loss = 0.0
    for i, data in enumerate(trainloader, 0):
        # get the inputs; data is a list of [inputs, labels]
        inputs, labels = data

        # zero the parameter gradients
        optimizer.zero_grad()

        # forward + backward + optimize
        outputs = net(inputs)
        loss = criterion(outputs, labels)
        loss.backward()
        optimizer.step()

        # print statistics
        running_loss += loss.item()
        if i % 2000 == 1999:    # print every 2000 mini-batches
            print('[%d, %5d] loss: %.3f' %
                  (epoch + 1, i + 1, running_loss / 2000))
            running_loss = 0.0

print('Finished Training')

The Pytorch neuron network is saved

PATH = './cifar_net.pth'
torch.save(net.state_dict(), PATH)

We load a test and use the network to predict the outcome.

dataiter = iter(testloader)
images, labels = dataiter.next()

# print images
imshow(torchvision.utils.make_grid(images))
print('GroundTruth: ', ' '.join('%5s' % classes[labels[j]] for j in range(4)))
Pytorch tutorial deeplearning with python and pytorch mnist tutorial

In this example the “true” labels are “Cat, ship, ship, plane”, we then launch the network to make a prediction:

net = Net()
net.load_state_dict(torch.load(PATH))
outputs = net(images)
_, predicted = torch.max(outputs, 1)
print('Predicted: ', ' '.join('%5s' % classes[predicted[j]]
                              for j in range(4)))

Here is an overview of the architecture of this convolution network.

import hiddenlayer as hl
from torchviz import make_dot, make_dot_from_trace
make_dot(net(images), params=dict(net.named_parameters()))
Pytorch tutorial deeplearning with python and pytorch mnist tutorial

Categorization problem (predict several class among several classes possible) – multiple-label classifier with pytorch – Pytorch tutorial

Overall, it is about predicting several probabilities for each of the classes to indicate their probabilities of presence in the entry. One possible use is to indicate the presence of an object in an image.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial

The problem then comes back to a problem of binary classification for n classes.

The final activation function is sigmoid and the loss function is Binary cross entropy

This internet example perfectly illustrates the use of BCELoss in the case of the prediction of several classes among several possible classes.
https://medium.com/@thevatsalsaglani/training-and-deploying-a-multi-label-image-classifier-using-pytorch-flask-reactjs-and-firebase-c39c96f9c427

In this example: The image dataset used is the CelebFaces Large Scale Attribute Dataset (CelebA).
http://mmlab.ie.cuhk.edu.hk/projects/CelebA.html

In this data dataset there are 200K images with 40 different class labels and each image has a different background footprint and there are a lot of different variations making it difficult for a model to classify each label effectively class.

I suggest you follow the tutorial from the articlehttps://medium.com/@thevatsalsaglani/training-and-deploying-a-multi-label-image-classifier-using-pytorch-flask-reactjs-and-firebase-c39c96f9c427:

  • Step1: Download the file img_align_celeba.zip hard site http://mmlab.ie.cuhk.edu.hk/projects/CelebA.html (it is in a google drive)
  • Step2: Download the list_attr_celeba.txt file which contains the annotations for each image on the same site http://mmlab.ie.cuhk.edu.hk/projects/CelebA.html
  • Step3: Opening the file annotations you can see the 40 labels: 5_o_Clock_Shadow Arched_Eyebrows Attractive Bags_Under_Eyes Bald Bangs Big_Lips Big_Nose Black_Hair Blond_Hair Blurry Brown_Hair Bushy_Eyebrows Chubby Double_Chin Eyeglasses Goatee Gray_Hair Heavy_Makeup High_Cheekbones Male Mouth_Slightly_Open Mustache Narrow_Eyes No_Beard Oval_Face Pale_Skin Pointy_Nose Receding_Hairline Rosy_Cheeks Sideburns Smiling Straight_Hair Wavy_Hair Wearing_Earrings Wearing_Hat Wearing_Lipstick Wearing_Necklace Wearing_Necktie Young
    For each of the images present in the test set there is a value of 1 or -1 specifying for image whether the class is present in the image.
    The objective here will be to predict for each of the classes the probability of its presence in the image.
  • Step4: you can load the notebook which is present on https://github.com/vatsalsaglani/MultiLabelClassifier/blob/master/prediction_celebA.ipynb

Here is the results:

Load of the dataset :


Use of the imshow function (see previous example for single label prediction)

Pytorch tutorial deeplearning with python and pytorch mnist tutorial

Architecture of the convolutional neuron network:

import torch.nn.functional as F
class MultiClassifier(nn.Module):
    def __init__(self):
        super(MultiClassifier, self).__init__()
        self.ConvLayer1 = nn.Sequential(
            nn.Conv2d(3, 64, 3), # 3, 256, 256
            nn.MaxPool2d(2), # op: 16, 127, 127
            nn.ReLU(), # op: 64, 127, 127
        )
        self.ConvLayer2 = nn.Sequential(
            nn.Conv2d(64, 128, 3), # 64, 127, 127   
            nn.MaxPool2d(2), #op: 128, 63, 63
            nn.ReLU() # op: 128, 63, 63
        )
        self.ConvLayer3 = nn.Sequential(
            nn.Conv2d(128, 256, 3), # 128, 63, 63
            nn.MaxPool2d(2), #op: 256, 30, 30
            nn.ReLU() #op: 256, 30, 30
        )
        self.ConvLayer4 = nn.Sequential(
            nn.Conv2d(256, 512, 3), # 256, 30, 30
            nn.MaxPool2d(2), #op: 512, 14, 14
            nn.ReLU(), #op: 512, 14, 14
            nn.Dropout(0.2)
        )
        self.Linear1 = nn.Linear(512 * 14 * 14, 1024)
        self.Linear2 = nn.Linear(1024, 256)
        self.Linear3 = nn.Linear(256, 40)
        
        
    def forward(self, x):
        x = self.ConvLayer1(x)
        x = self.ConvLayer2(x)
        x = self.ConvLayer3(x)
        x = self.ConvLayer4(x)
        x = x.view(x.size(0), -1)
        x = self.Linear1(x)
        x = self.Linear2(x)
        x = self.Linear3(x)
        return F.sigmoid(x)

An overview of the network architecture:

Pytorch tutorial deeplearning with python and pytorch mnist tutorial

SUMMARY – Pytorch tutorial :

Here is a summary of my pytorch tutorial : sheet that I created to allow you to choose the right activation function and the right cost function more quickly according to your problem to be solved.

Pytorch tutorial deeplearning with python and pytorch mnist tutorial

Pytorch tutorial : THE 5 BEST DEEP LEARNING LINKS

https://atcold.github.io/pytorch-Deep-Learning/ : Dree courses Yann LeCun

https://pytorch.org/ : Official web site PyToch

https://machinelearningmastery.com : Advanced on deep learning

https://www.fun-mooc.fr/courses/course-v1:CNAM+01031+session03/about : Free MOOC

https://dataanalyticspost.com/

Pytorch tutorial – internal links

http://128mots.com/index.php/en/category/non-classe-en/

http://128mots.com/index.php/category/python/

http://128mots.com/index.php/2020/10/09/bcewithlogitsloss-pytorch/

PyTorch how to load a pre-trained model?

There are several approaches to recording (serializing) and loading (deserialize) patterns for inference in PyTorch.

For example you may need to load a model that is already trained and back up that comes from the internet. More recently I answered this question on a discussion forum https://discuss.pytorch.org/t/i-want-to-do-machine-learning-with-android/98753. I take advantage of this article to give some details.

SAVE AND LOAD OF A PRE-TRAINED MODE with load_state_dict

In PyTorch you can save a model by storing in its file its state_dict these are Python dictionaries, they can be easily recorded, updated, modified and restored, adding great modularity to PyTorch models and optimizers.

In my example:

ESPNet is backed up with this method

https://github.com/sacmehta/ESPNet/tree/master/pretrained/encoder

I managed to load the encoder model using the ESPNet class that makes a load_state_dict

import torch
model = ESPNet(20,encoderFile="espnet_p_2_q_8.pth", p=2, q=8)
example = torch.rand(1, 3, 224, 224)
traced_script_module = torch.jit.trace(model, example)
traced_script_module.save("model.pt")

The exit is

Encode loaded!

Note that ESPNet uses the default GPU and that an adaptation in Model.py in https://github.com/sacmehta/ESPNet/tree/master/train was required by replacing:

self.encoder.load_state_dict(torch.load(encoderFile)

By:

self.encoder.load_state_dict(torch.load(encoderFile,map_location='cpu'))

Otherwise if you don’t make this adjustment don’t have the ability to launch on a GPU you’ll get the following error:

RuntimeError: Attempting to deserialize object on a CUDA device but torch.cuda.is_available() is False. If you are running on a CPU-only machine, please use torch.load with map_location-torch.device ('cpu') to map your storages to the CPU.
PYTORCH TORCHSCRIPT

BACKUP AND LOAD BY PYTORCH SCRIPT

https://pytorch.org/docs/stable/jit.html

TorchScript is a way to create models that can be made that can be optimized from the PyTorch code.

Any TorchScript program can be saved from a Python process and loaded into a process where there is no Python dependency.

The code below allows you to save the pre-trained ESPNet model that was backed up by the classic torch.save method via the use of TorchScript.

import torch


model = ESPNet(20,encoderFile="espnet_p_2_q_8.pth", p=2, q=8)
example = torch.rand(1, 3, 224, 224)
traced_script_module = torch.jit.trace(model, example)
#Exemple de save avec TorchScript
torch.jit.save(traced_script_module, "scriptmodel.pth")

An example for loader via TorchScript below:

import torch
model = torch.jit.load("scriptmodel.pth")

RESOURCES ON THE SUBJECT

https://pytorch.org/docs/stable/jit.html

https://pytorch.org/tutorials/beginner/Intro_to_TorchScript_tutorial.html

https://stackoverflow.com/questions/53900396/what-are-torch-scripts-in-pytorch

BCEWithLogitsLoss Pytorch with python

BCEWithLogitsLoss Here are some additional explanations on using Binary Cross-Entropy Loss with Pytorch in python.

BCEWithLogitsLoss Here are some additional explanations on using Binary Cross-Entropy Loss with Pytorch in python.

Introduction

I have been asked recently on How to find the code BCEWithLogitsLoss (https://discuss.pytorch.org/t/implementation-of-binary-cross-entropy/98715/2) for a function called in PYTORCH with the function handle_torch_function it takes me some time to understand it, and i will share it with you if it helps:

The question was about BCEWithLogitsLoss = BCELoss + sigmoid() ? My answer can be apply if you want to analyse the code of all the functions that figures in the ret dictionnary from https://github.com/pytorch/pytorch/blob/master/torch/overrides.py

BCEWithLogitsLoss is a combination of BCELOSS + a Sigmoid layer i. This is more numerically stable than using a plain Sigmoid followed by a BCELoss as, by combining the operations into one layer, it takes advantage of the log-sum-exp trick for numerical stability see : https://en.wikipedia.org/wiki/LogSumExp

BCEWithLogitsLoss in details

  1. The code of the BCEWithLogitsLoss Class can be found in https://github.com/pytorch/pytorch/blob/master/torch/nn/modules/loss.py
    def forward(self, input: Tensor, target: Tensor) -> Tensor:
        return F.binary_cross_entropy_with_logits(input, target,
                                                  self.weight,
                                                  pos_weight=self.pos_weight,
                                                  reduction=self.reduction)
BCEWithLogitLoss PYTORCH

The F oject is imported from functionnal.py here : https://github.com/pytorch/pytorch/blob/master/torch/nn/functional.py

You will find the function called

def binary_cross_entropy_with_logits(input, target, weight=None, size_average=None,
                                     reduce=None, reduction='mean', pos_weight=None):

It calls the handle_torch_function in https://github.com/pytorch/pytorch/blob/master/torch/overrides.py
You will find an entry of the function binary_cross_entropy_with_logits in the ret dictionnary wich contain every function that can be overriden in pytorch.
This is the Python implementation of torch_function
More info in https://github.com/pytorch/pytorch/issues/24015

Then the code called is in the C++ File
https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/native/Loss.cpp

Tensor binary_cross_entropy_with_logits(const Tensor& input, const Tensor& target, const Tensor& weight, const Tensor& pos_weight, int64_t 
...
BCEWithLogitLoss PYTORCH

LIENS DE RESSOURCES :

https://pytorch.org/docs/stable/generated/torch.nn.BCEWithLogitsLoss.html

https://discuss.pytorch.org/t/bceloss-vs-bcewithlogitsloss/33586

https://stackoverflow.com/questions/59246416/the-output-of-numerical-calculation-of-bcewithlogitsloss-for-pytorch-example

https://www.semicolonworld.com/question/61244/implementing-bcewithlogitsloss-from-pytorch-in-keras

http://128mots.com/index.php/en/category/non-classe-en/

Mastering IBM COBOL Language – Part 1 – FREE TRAINING

This article follows my introduction to the COBOL language. I advise you to reread the first part that deals with the general principles of COBOL. Here: http://128mots.com/index.php/2020/10/07/ibm-cobol/ and English http://128mots.com/index.php/en/2020/10/07/ibm-cobol-3/ (IBM COBOL FREE TRAINING)

Here we discuss the general concepts of the structure of a COBOL program.

DATA DIVISION

All the data that will be used by the program is located in the Data Division. This is where all the memory allowances required by the program are taken care of. This division is optional.

FILE MANAGEMENT:

IBM COBOL TRAINING FREE

FILE SECTION describes data sent or from the system, especially files.

The SYNtax in COBOL is the following

DATA DIVISION.
FILE SECTION.
 FD/SD NameOfFile[RECORD CONTAINS intgr CHARACTERS] 
	[BLOCK CONTAINS intgr RECORDS] 
[DATA RECORD IS NameOfRecord].
	[RECORDING MODE IS {F/V/U/S}]

FD describes the files and SD the sorting files.

FILE IN INPUT

In FILE-CONTROL the statement will be:

           SELECT FMASTER ASSIGN FMASTER
                  FILE STATUS W-STATUS-FMASTER.

If the input file is indexed:
           SELECT FMASTER ASSIGN FMASTER
                  ORGANIZATION IS INDEXED
                  RECORD KEY IS FMASTER-KEY
                  FILE STATUS W-STATUS-FMASTER.

In this case at the file-SECTION level we will have:

      FMAITRE as an appetizer  
       FD FMAITRE.
       01 ENR-FMAITRE.
      Statements from the registration areas

At the JCL level the statement will be of the form:
ENTREE DD DSN-SAMPLE. INPUTF,DISP-SHR
IBM COBOL TRAINING FREE

FILE OUT

The JCL statement will then be:

OUTFILE DD DSN-SAMPLE. OUTPUTF,DISP(,CATLG,DELETE),
LRECL-150,RECFM-FB

RECFM specifies the characteristics of records with fixed length (F), variable length (V), variable length ASCII (D) or indefinite length (U). Records that are said to be blocked are described as FB, VB or DB.

OPENING AND CLOSING FILE IN PROCEDURE DIVISION

COBOL uses PROCEDURE DIVISION mechanisms to perform writing, closing and file openings.

Entry file opening:

OPEN INPUT FICENT

Opening the output file:

OPEN OUTPUT FICSOR

File closure:

CLOSE FICENT
CLOSE FICSOR

File playback:

READ ACTENR
AT END MOVE 'O' TO LAST-RECORD
END-READ

File writing

WRITE SOR-ENR
IBM COBOL TRAINING FREE

EXTERNAL LINKS TO RESOURCES (IBM COBOL FREE TRAINING)

Below are some links that I found interesting that also deal with file management with COBOL.

Example of IBM file management: https://www.ibm.com/support/knowledgecenter/en/SS6SGM_5.1.0/com.ibm.cobol51.aix.doc/PGandLR/ref/rpfio13e.html

REFM Format: https://www.ibm.com/support/knowledgecenter/en/SSLTBW_2.2.0/com.ibm.zos.v2r2.idad400/d4037.htm

Tutorialspoint an article on file management https://www.tutorialspoint.com/cobol/cobol_file_handling.htm

COURSERA COBOL with VSCODE: https://www.coursera.org/lecture/cobol-programming-vscode/file-handling-YVlcf

MEDIUM an interesting article for COBOL beginners: https://medium.com/@yvanscher/7-cobol-examples-with-explanations-ae1784b4d576

Also on his blog: http://yvanscher.com/2018-08-01_7-cobol-examples-with-explanations–ae1784b4d576.html

Many example COBOL free tutorials and sample code: http://www.csis.ul.ie/cobol/examples/default.htm

GITHUB Awesome-cobol https://github.com/mickaelandrieu/awesome-cobol you

IBM COBOL FREE TRAINING