Merge branch 'master' into tabs-to-spaces

Author: poyea

.coveragerc

@@ -0,0 +1,4 @@
+[report]
+sort = Cover
+omit =
+    .env/*

.github/workflows/autoblack.yml

@@ -0,0 +1,24 @@
+# GitHub Action that uses Black to reformat Python code (if needed) when doing a git push.
+# If all Python code in the repo is complient with Black then this Action does nothing.
+# Otherwise, Black is run and its changes are committed to the repo.
+# https://github.com/cclauss/autoblack
+
+name: autoblack_push
+on: [push]
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v1
+      - uses: actions/setup-python@v1
+      - run: pip install black
+      - run: black --check .
+      - name: If needed, commit black changes to a new pull request
+        if: failure()
+        run: |
+          black .
+          git config --global user.name github-actions
+          git config --global user.email '${GITHUB_ACTOR}@users.noreply.github.com'          
+          git remote set-url origin https://x-access-token:${{ secrets.GITHUB_TOKEN }}@github.com/$GITHUB_REPOSITORY
+          git commit -am "fixup! Format Python code with psf/black push"
+          git push --force origin HEAD:$GITHUB_REF

.github/workflows/directory_writer.yml

@@ -0,0 +1,20 @@
+# The objective of this GitHub Action is to update the DIRECTORY.md file (if needed)
+# when doing a git push
+name: directory_writer
+on: [push]
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v1
+      - uses: actions/setup-python@v1
+        with:
+          python-version: 3.x
+      - name: Update DIRECTORY.md
+        run: |
+          scripts/build_directory_md.py 2>&1 | tee DIRECTORY.md
+          git config --global user.name github-actions
+          git config --global user.email '${GITHUB_ACTOR}@users.noreply.github.com'
+          git remote set-url origin https://x-access-token:${{ secrets.GITHUB_TOKEN }}@github.com/$GITHUB_REPOSITORY
+          git commit -am "updating DIRECTORY.md" ||  true
+          git push --force origin HEAD:$GITHUB_REF || true

.travis.yml

@@ -5,11 +5,10 @@ before_install: pip install --upgrade pip setuptools
 install: pip install -r requirements.txt
 before_script:
   - black --check . || true
-  - flake8 . --count --select=E9,F4,F63,F7,F82 --show-source --statistics
+  - flake8 . --count --select=E101,E9,F4,F63,F7,F82,W191 --show-source --statistics
 script:
   - scripts/validate_filenames.py  # no uppercase, no spaces, in a directory
   - mypy --ignore-missing-imports .
-  - pytest . --doctest-modules
+  - pytest --doctest-modules --cov-report=term-missing:skip-covered --cov=. .
 after_success:
-  - scripts/build_directory_md.py > DIRECTORY.md
-  - cat DIRECTORY.md
+  - scripts/build_directory_md.py 2>&1 | tee DIRECTORY.md

DIRECTORY.md

@@ -0,0 +1,9 @@
+# Travis CI test are failing
+### How do I find out what is wrong with my pull request?
+1. In your PR look for the failing test and click the `Details` link: ![Travis_CI_fail_1.png](images/Travis_CI_fail_1.png)
+2. On the next page, click `The build failed` link: ![Travis_CI_fail_2.png](images/Travis_CI_fail_2.png)
+3. Now scroll down and look for `red` text describing the error(s) in the test log.
+
+Pull requests will __not__ be merged if the Travis CI tests are failing.
+
+If anything is unclear, please read through [CONTRIBUTING.md](CONTRIBUTING.md) and attempt to run the failing tests on your computer before asking for assistance.

Travis_CI_tests_are_failing.md

@@ -0,0 +1,83 @@
+"""
+Gaussian elimination method for solving a system of linear equations.
+Gaussian elimination - https://en.wikipedia.org/wiki/Gaussian_elimination
+"""
+
+
+import numpy as np
+
+
+def retroactive_resolution(coefficients: np.matrix, vector: np.array) -> np.array:
+    """
+    This function performs a retroactive linear system resolution
+        for triangular matrix
+
+    Examples:
+        2x1 + 2x2 - 1x3 = 5         2x1 + 2x2 = -1
+        0x1 - 2x2 - 1x3 = -7        0x1 - 2x2 = -1
+        0x1 + 0x2 + 5x3 = 15
+    >>> gaussian_elimination([[2, 2, -1], [0, -2, -1], [0, 0, 5]], [[5], [-7], [15]])
+    array([[2.],
+           [2.],
+           [3.]])
+    >>> gaussian_elimination([[2, 2], [0, -2]], [[-1], [-1]])
+    array([[-1. ],
+           [ 0.5]])
+    """
+
+    rows, columns = np.shape(coefficients)
+
+    x = np.zeros((rows, 1), dtype=float)
+    for row in reversed(range(rows)):
+        sum = 0
+        for col in range(row + 1, columns):
+            sum += coefficients[row, col] * x[col]
+
+        x[row, 0] = (vector[row] - sum) / coefficients[row, row]
+
+    return x
+
+
+def gaussian_elimination(coefficients: np.matrix, vector: np.array) -> np.array:
+    """
+    This function performs Gaussian elimination method
+
+    Examples:
+        1x1 - 4x2 - 2x3 = -2        1x1 + 2x2 = 5
+        5x1 + 2x2 - 2x3 = -3        5x1 + 2x2 = 5
+        1x1 - 1x2 + 0x3 = 4
+    >>> gaussian_elimination([[1, -4, -2], [5, 2, -2], [1, -1, 0]], [[-2], [-3], [4]])
+    array([[ 2.3 ],
+           [-1.7 ],
+           [ 5.55]])
+    >>> gaussian_elimination([[1, 2], [5, 2]], [[5], [5]])
+    array([[0. ],
+           [2.5]])
+    """
+    # coefficients must to be a square matrix so we need to check first
+    rows, columns = np.shape(coefficients)
+    if rows != columns:
+        return []
+
+    # augmented matrix
+    augmented_mat = np.concatenate((coefficients, vector), axis=1)
+    augmented_mat = augmented_mat.astype("float64")
+
+    # scale the matrix leaving it triangular
+    for row in range(rows - 1):
+        pivot = augmented_mat[row, row]
+        for col in range(row + 1, columns):
+            factor = augmented_mat[col, row] / pivot
+            augmented_mat[col, :] -= factor * augmented_mat[row, :]
+
+    x = retroactive_resolution(
+        augmented_mat[:, 0:columns], augmented_mat[:, columns : columns + 1]
+    )
+
+    return x
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

arithmetic_analysis/gaussian_elimination.py

@@ -0,0 +1,28 @@
+# Implementing Secant method in Python
+# Author: dimgrichr
+
+
+from math import exp
+
+
+def f(x):
+    """
+    >>> f(5)
+    39.98652410600183
+    """
+    return 8 * x - 2 * exp(-x)
+
+
+def SecantMethod(lower_bound, upper_bound, repeats):
+    """
+    >>> SecantMethod(1, 3, 2)
+    0.2139409276214589
+    """
+    x0 = lower_bound
+    x1 = upper_bound
+    for i in range(0, repeats):
+        x0, x1 = x1, x1 - (f(x1) * (x1 - x0)) / (f(x1) - f(x0))
+    return x1
+
+
+print(f"The solution is: {SecantMethod(1, 3, 2)}")

arithmetic_analysis/secant_method.py

@@ -1,9 +1,9 @@
 # -*- coding: utf-8 -*-
 
 """
-	In this problem, we want to determine all possible combinations of k
-	numbers out of 1 ... n. We use backtracking to solve this problem.
-	Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!)))
+        In this problem, we want to determine all possible combinations of k
+        numbers out of 1 ... n. We use backtracking to solve this problem.
+        Time complexity: O(C(n,k)) which is O(n choose k) = O((n!/(k! * (n - k)!)))
 """
 
 

backtracking/all_combinations.py

@@ -1,9 +1,9 @@
 """
-	In this problem, we want to determine all possible permutations
-	of the given sequence. We use backtracking to solve this problem.
+        In this problem, we want to determine all possible permutations
+        of the given sequence. We use backtracking to solve this problem.
 
-	Time complexity: O(n! * n),
-	where n denotes the length of the given sequence.
+        Time complexity: O(n! * n),
+        where n denotes the length of the given sequence.
 """
 
 
@@ -13,10 +13,10 @@ def generate_all_permutations(sequence):
 
 def create_state_space_tree(sequence, current_sequence, index, index_used):
     """
-	Creates a state space tree to iterate through each branch using DFS.
-	We know that each state has exactly len(sequence) - index children.
-	It terminates when it reaches the end of the given sequence.
-	"""
+        Creates a state space tree to iterate through each branch using DFS.
+        We know that each state has exactly len(sequence) - index children.
+        It terminates when it reaches the end of the given sequence.
+        """
 
     if index == len(sequence):
         print(current_sequence)
@@ -32,7 +32,7 @@ def create_state_space_tree(sequence, current_sequence, index, index_used):
 
 
 """
-remove the comment to take an input from the user 
+remove the comment to take an input from the user
 
 print("Enter the elements")
 sequence = list(map(int, input().split()))

backtracking/all_permutations.py

@@ -1,9 +1,9 @@
 """
-	In this problem, we want to determine all possible subsequences
-	of the given sequence. We use backtracking to solve this problem.
+        In this problem, we want to determine all possible subsequences
+        of the given sequence. We use backtracking to solve this problem.
 
-	Time complexity: O(2^n),
-	where n denotes the length of the given sequence.
+        Time complexity: O(2^n),
+        where n denotes the length of the given sequence.
 """
 
 
@@ -13,10 +13,10 @@ def generate_all_subsequences(sequence):
 
 def create_state_space_tree(sequence, current_subsequence, index):
     """
-	Creates a state space tree to iterate through each branch using DFS.
-	We know that each state has exactly two children.
-	It terminates when it reaches the end of the given sequence.
-	"""
+        Creates a state space tree to iterate through each branch using DFS.
+        We know that each state has exactly two children.
+        It terminates when it reaches the end of the given sequence.
+        """
 
     if index == len(sequence):
         print(current_subsequence)
@@ -29,7 +29,7 @@ def create_state_space_tree(sequence, current_subsequence, index):
 
 
 """
-remove the comment to take an input from the user 
+remove the comment to take an input from the user
 
 print("Enter the elements")
 sequence = list(map(int, input().split()))

backtracking/all_subsequences.py

@@ -1,9 +1,9 @@
 """
-	The sum-of-subsetsproblem states that a set of non-negative integers, and a value M, 
-	determine all possible subsets of the given set whose summation sum equal to given M.
+        The sum-of-subsetsproblem states that a set of non-negative integers, and a value M,
+        determine all possible subsets of the given set whose summation sum equal to given M.
 
-	Summation of the chosen numbers must be equal to given number M and one number can 
-	be used only once.
+        Summation of the chosen numbers must be equal to given number M and one number can
+        be used only once.
 """
 
 
@@ -18,12 +18,12 @@ def generate_sum_of_subsets_soln(nums, max_sum):
 
 def create_state_space_tree(nums, max_sum, num_index, path, result, remaining_nums_sum):
     """
-	Creates a state space tree to iterate through each branch using DFS.
-	It terminates the branching of a node when any of the two conditions 
-	given below satisfy.
-	This algorithm follows depth-fist-search and backtracks when the node is not branchable.
+        Creates a state space tree to iterate through each branch using DFS.
+        It terminates the branching of a node when any of the two conditions
+        given below satisfy.
+        This algorithm follows depth-fist-search and backtracks when the node is not branchable.
 
-	"""
+        """
     if sum(path) > max_sum or (remaining_nums_sum + sum(path)) < max_sum:
         return
     if sum(path) == max_sum:
@@ -41,7 +41,7 @@ def create_state_space_tree(nums, max_sum, num_index, path, result, remaining_nu
 
 
 """
-remove the comment to take an input from the user 
+remove the comment to take an input from the user
 
 print("Enter the elements")
 nums = list(map(int, input().split()))