Create a Simultaneous Equation Solver Algorithm

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+ "githubPullRequests.ignoredPullRequestBranches": [
+ "master"
+ ]
+}

maths/simultaneous_linear_equation_solver.py

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+"""
+https://en.wikipedia.org/wiki/Augmented_matrix
+
+This algorithm solves simultaneous linear equations of the form
+λa + λb + λc + λd + ... = γ as [λ, λ, λ, λ, ..., γ]
+Where λ & γ are individual coefficients, the no. of equations = no. of coefficients - 1
+
+Note in order to work there must exist 1 equation where all instances of λ and γ != 0
+"""
+
+
+def simplify(current_set: list[list]) -> list[list]:
+ """
+ >>> simplify([[1, 2, 3], [4, 5, 6]])
+ [[1.0, 2.0, 3.0], [0.0, 0.75, 1.5]]
+ >>> simplify([[5, 2, 5], [5, 1, 10]])
+ [[1.0, 0.4, 1.0], [0.0, 0.2, -1.0]]
+ """
+ # Divide each row by magnitude of first term --> creates 'unit' matrix
+ duplicate_set = current_set.copy()
+ for row_index, row in enumerate(duplicate_set):
+ magnitude = row[0]
+ for column_index, column in enumerate(row):
+ if magnitude == 0:
+ current_set[row_index][column_index] = column
+ continue
+ current_set[row_index][column_index] = column / magnitude
+ # Subtract to cancel term
+ first_row = current_set[0]
+ final_set = [first_row]
+ current_set = current_set[1::]
+ for row in current_set:
+ temp_row = []
+ # If first term is 0, it is already in form we want, so we preserve it
+ if row[0] == 0:
+ final_set.append(row)
+ continue
+ for column_index in range(len(row)):
+ temp_row.append(first_row[column_index] - row[column_index])
+ final_set.append(temp_row)
+ # Create next recursion iteration set
+ if len(final_set[0]) != 3:
+ current_first_row = final_set[0]
+ current_first_column = []
+ next_iteration = []
+ for row in final_set[1::]:
+ current_first_column.append(row[0])
+ next_iteration.append(row[1::])
+ resultant = simplify(next_iteration)
+ for i in range(len(resultant)):
+ resultant[i].insert(0, current_first_column[i])
+ resultant.insert(0, current_first_row)
+ final_set = resultant
+ return final_set
+
+
+def solve_simultaneous(equations: list[list]) -> list:
+ """
+ >>> solve_simultaneous([[1, 2, 3],[4, 5, 6]])
+ [-1.0, 2.0]
+ >>> solve_simultaneous([[0, -3, 1, 7],[3, 2, -1, 11],[5, 1, -2, 12]])
+ [6.4, 1.2, 10.6]
+ >>> solve_simultaneous([])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],[1, 2]])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],["a", 7, 8]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires lists of integers
+ >>> solve_simultaneous([[0, 2, 3],[4, 0, 6]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires at least 1 full equation
+ """
+ if len(equations) == 0:
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ _length = len(equations) + 1
+ if any(len(item) != _length for item in equations):
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ for row in equations:
+ if any(not isinstance(column, (int, float)) for column in row):
+ raise ValueError("solve_simultaneous() requires lists of integers")
+ if len(equations) == 1:
+ return [equations[0][-1] / equations[0][0]]
+ data_set = equations.copy()
+ if any(0 in row for row in data_set):
+ temp_data = data_set.copy()
+ full_row = []
+ for row_index, row in enumerate(temp_data):
+ if 0 not in row:
+ full_row = data_set.pop(row_index)
+ break
+ if not full_row:
+ raise ValueError("solve_simultaneous() requires at least 1 full equation")
+ data_set.insert(0, full_row)
+ useable_form = data_set.copy()
+ simplified = simplify(useable_form)
+ simplified = simplified[::-1]
+ solutions: list = []
+ for row in simplified:
+ current_solution = row[-1]
+ if not solutions:
+ if row[-2] == 0:
+ solutions.append(0)
+ continue
+ solutions.append(current_solution / row[-2])
+ continue
+ temp_row = row.copy()[: len(row) - 1 :]
+ while temp_row[0] == 0:
+ temp_row.pop(0)
+ if len(temp_row) == 0:
+ solutions.append(0)
+ continue
+ temp_row = temp_row[1::]
+ temp_row = temp_row[::-1]
+ for column_index, column in enumerate(temp_row):
+ current_solution -= column * solutions[column_index]
+ solutions.append(current_solution)
+ final = []
+ for item in solutions:
+ final.append(float(round(item, 5)))
+ return final[::-1]
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+ eq = [
+ [2, 1, 1, 1, 1, 4],
+ [1, 2, 1, 1, 1, 5],
+ [1, 1, 2, 1, 1, 6],
+ [1, 1, 1, 2, 1, 7],
+ [1, 1, 1, 1, 2, 8],
+ ]
+ print(solve_simultaneous(eq))
+ print(solve_simultaneous([[4, 2]]))

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+ "githubPullRequests.ignoredPullRequestBranches": [
+ "master"
+ ]
+}

maths/simultaneous_linear_equation_solver.py

@@ -0,0 +1,142 @@
+"""
+https://en.wikipedia.org/wiki/Augmented_matrix
+
+This algorithm solves simultaneous linear equations of the form
+λa + λb + λc + λd + ... = γ as [λ, λ, λ, λ, ..., γ]
+Where λ & γ are individual coefficients, the no. of equations = no. of coefficients - 1
+
+Note in order to work there must exist 1 equation where all instances of λ and γ != 0
+"""
+
+
+def simplify(current_set: list[list]) -> list[list]:
+ """
+ >>> simplify([[1, 2, 3], [4, 5, 6]])
+ [[1.0, 2.0, 3.0], [0.0, 0.75, 1.5]]
+ >>> simplify([[5, 2, 5], [5, 1, 10]])
+ [[1.0, 0.4, 1.0], [0.0, 0.2, -1.0]]
+ """
+ # Divide each row by magnitude of first term --> creates 'unit' matrix
+ duplicate_set = current_set.copy()
+ for row_index, row in enumerate(duplicate_set):
+ magnitude = row[0]
+ for column_index, column in enumerate(row):
+ if magnitude == 0:
+ current_set[row_index][column_index] = column
+ continue
+ current_set[row_index][column_index] = column / magnitude
+ # Subtract to cancel term
+ first_row = current_set[0]
+ final_set = [first_row]
+ current_set = current_set[1::]
+ for row in current_set:
+ temp_row = []
+ # If first term is 0, it is already in form we want, so we preserve it
+ if row[0] == 0:
+ final_set.append(row)
+ continue
+ for column_index in range(len(row)):
+ temp_row.append(first_row[column_index] - row[column_index])
+ final_set.append(temp_row)
+ # Create next recursion iteration set
+ if len(final_set[0]) != 3:
+ current_first_row = final_set[0]
+ current_first_column = []
+ next_iteration = []
+ for row in final_set[1::]:
+ current_first_column.append(row[0])
+ next_iteration.append(row[1::])
+ resultant = simplify(next_iteration)
+ for i in range(len(resultant)):
+ resultant[i].insert(0, current_first_column[i])
+ resultant.insert(0, current_first_row)
+ final_set = resultant
+ return final_set
+
+
+def solve_simultaneous(equations: list[list]) -> list:
+ """
+ >>> solve_simultaneous([[1, 2, 3],[4, 5, 6]])
+ [-1.0, 2.0]
+ >>> solve_simultaneous([[0, -3, 1, 7],[3, 2, -1, 11],[5, 1, -2, 12]])
+ [6.4, 1.2, 10.6]
+ >>> solve_simultaneous([])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],[1, 2]])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],["a", 7, 8]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires lists of integers
+ >>> solve_simultaneous([[0, 2, 3],[4, 0, 6]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires at least 1 full equation
+ """
+ if len(equations) == 0:
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ _length = len(equations) + 1
+ if any(len(item) != _length for item in equations):
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ for row in equations:
+ if any(not isinstance(column, (int, float)) for column in row):
+ raise ValueError("solve_simultaneous() requires lists of integers")
+ if len(equations) == 1:
+ return [equations[0][-1] / equations[0][0]]
+ data_set = equations.copy()
+ if any(0 in row for row in data_set):
+ temp_data = data_set.copy()
+ full_row = []
+ for row_index, row in enumerate(temp_data):
+ if 0 not in row:
+ full_row = data_set.pop(row_index)
+ break
+ if not full_row:
+ raise ValueError("solve_simultaneous() requires at least 1 full equation")
+ data_set.insert(0, full_row)
+ useable_form = data_set.copy()
+ simplified = simplify(useable_form)
+ simplified = simplified[::-1]
+ solutions: list = []
+ for row in simplified:
+ current_solution = row[-1]
+ if not solutions:
+ if row[-2] == 0:
+ solutions.append(0)
+ continue
+ solutions.append(current_solution / row[-2])
+ continue
+ temp_row = row.copy()[: len(row) - 1 :]
+ while temp_row[0] == 0:
+ temp_row.pop(0)
+ if len(temp_row) == 0:
+ solutions.append(0)
+ continue
+ temp_row = temp_row[1::]
+ temp_row = temp_row[::-1]
+ for column_index, column in enumerate(temp_row):
+ current_solution -= column * solutions[column_index]
+ solutions.append(current_solution)
+ final = []
+ for item in solutions:
+ final.append(float(round(item, 5)))
+ return final[::-1]
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+ eq = [
+ [2, 1, 1, 1, 1, 4],
+ [1, 2, 1, 1, 1, 5],
+ [1, 1, 2, 1, 1, 6],
+ [1, 1, 1, 2, 1, 7],
+ [1, 1, 1, 1, 2, 8],
+ ]
+ print(solve_simultaneous(eq))
+ print(solve_simultaneous([[4, 2]]))

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+ "githubPullRequests.ignoredPullRequestBranches": [
+ "master"
+ ]
+}

maths/simultaneous_linear_equation_solver.py

@@ -0,0 +1,142 @@
+"""
+https://en.wikipedia.org/wiki/Augmented_matrix
+
+This algorithm solves simultaneous linear equations of the form
+λa + λb + λc + λd + ... = γ as [λ, λ, λ, λ, ..., γ]
+Where λ & γ are individual coefficients, the no. of equations = no. of coefficients - 1
+
+Note in order to work there must exist 1 equation where all instances of λ and γ != 0
+"""
+
+
+def simplify(current_set: list[list]) -> list[list]:
+ """
+ >>> simplify([[1, 2, 3], [4, 5, 6]])
+ [[1.0, 2.0, 3.0], [0.0, 0.75, 1.5]]
+ >>> simplify([[5, 2, 5], [5, 1, 10]])
+ [[1.0, 0.4, 1.0], [0.0, 0.2, -1.0]]
+ """
+ # Divide each row by magnitude of first term --> creates 'unit' matrix
+ duplicate_set = current_set.copy()
+ for row_index, row in enumerate(duplicate_set):
+ magnitude = row[0]
+ for column_index, column in enumerate(row):
+ if magnitude == 0:
+ current_set[row_index][column_index] = column
+ continue
+ current_set[row_index][column_index] = column / magnitude
+ # Subtract to cancel term
+ first_row = current_set[0]
+ final_set = [first_row]
+ current_set = current_set[1::]
+ for row in current_set:
+ temp_row = []
+ # If first term is 0, it is already in form we want, so we preserve it
+ if row[0] == 0:
+ final_set.append(row)
+ continue
+ for column_index in range(len(row)):
+ temp_row.append(first_row[column_index] - row[column_index])
+ final_set.append(temp_row)
+ # Create next recursion iteration set
+ if len(final_set[0]) != 3:
+ current_first_row = final_set[0]
+ current_first_column = []
+ next_iteration = []
+ for row in final_set[1::]:
+ current_first_column.append(row[0])
+ next_iteration.append(row[1::])
+ resultant = simplify(next_iteration)
+ for i in range(len(resultant)):
+ resultant[i].insert(0, current_first_column[i])
+ resultant.insert(0, current_first_row)
+ final_set = resultant
+ return final_set
+
+
+def solve_simultaneous(equations: list[list]) -> list:
+ """
+ >>> solve_simultaneous([[1, 2, 3],[4, 5, 6]])
+ [-1.0, 2.0]
+ >>> solve_simultaneous([[0, -3, 1, 7],[3, 2, -1, 11],[5, 1, -2, 12]])
+ [6.4, 1.2, 10.6]
+ >>> solve_simultaneous([])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],[1, 2]])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],["a", 7, 8]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires lists of integers
+ >>> solve_simultaneous([[0, 2, 3],[4, 0, 6]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires at least 1 full equation
+ """
+ if len(equations) == 0:
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ _length = len(equations) + 1
+ if any(len(item) != _length for item in equations):
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ for row in equations:
+ if any(not isinstance(column, (int, float)) for column in row):
+ raise ValueError("solve_simultaneous() requires lists of integers")
+ if len(equations) == 1:
+ return [equations[0][-1] / equations[0][0]]
+ data_set = equations.copy()
+ if any(0 in row for row in data_set):
+ temp_data = data_set.copy()
+ full_row = []
+ for row_index, row in enumerate(temp_data):
+ if 0 not in row:
+ full_row = data_set.pop(row_index)
+ break
+ if not full_row:
+ raise ValueError("solve_simultaneous() requires at least 1 full equation")
+ data_set.insert(0, full_row)
+ useable_form = data_set.copy()
+ simplified = simplify(useable_form)
+ simplified = simplified[::-1]
+ solutions: list = []
+ for row in simplified:
+ current_solution = row[-1]
+ if not solutions:
+ if row[-2] == 0:
+ solutions.append(0)
+ continue
+ solutions.append(current_solution / row[-2])
+ continue
+ temp_row = row.copy()[: len(row) - 1 :]
+ while temp_row[0] == 0:
+ temp_row.pop(0)
+ if len(temp_row) == 0:
+ solutions.append(0)
+ continue
+ temp_row = temp_row[1::]
+ temp_row = temp_row[::-1]
+ for column_index, column in enumerate(temp_row):
+ current_solution -= column * solutions[column_index]
+ solutions.append(current_solution)
+ final = []
+ for item in solutions:
+ final.append(float(round(item, 5)))
+ return final[::-1]
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+ eq = [
+ [2, 1, 1, 1, 1, 4],
+ [1, 2, 1, 1, 1, 5],
+ [1, 1, 2, 1, 1, 6],
+ [1, 1, 1, 2, 1, 7],
+ [1, 1, 1, 1, 2, 8],
+ ]
+ print(solve_simultaneous(eq))
+ print(solve_simultaneous([[4, 2]]))

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+ "githubPullRequests.ignoredPullRequestBranches": [
+ "master"
+ ]
+}

maths/simultaneous_linear_equation_solver.py

@@ -0,0 +1,142 @@
+"""
+https://en.wikipedia.org/wiki/Augmented_matrix
+
+This algorithm solves simultaneous linear equations of the form
+λa + λb + λc + λd + ... = γ as [λ, λ, λ, λ, ..., γ]
+Where λ & γ are individual coefficients, the no. of equations = no. of coefficients - 1
+
+Note in order to work there must exist 1 equation where all instances of λ and γ != 0
+"""
+
+
+def simplify(current_set: list[list]) -> list[list]:
+ """
+ >>> simplify([[1, 2, 3], [4, 5, 6]])
+ [[1.0, 2.0, 3.0], [0.0, 0.75, 1.5]]
+ >>> simplify([[5, 2, 5], [5, 1, 10]])
+ [[1.0, 0.4, 1.0], [0.0, 0.2, -1.0]]
+ """
+ # Divide each row by magnitude of first term --> creates 'unit' matrix
+ duplicate_set = current_set.copy()
+ for row_index, row in enumerate(duplicate_set):
+ magnitude = row[0]
+ for column_index, column in enumerate(row):
+ if magnitude == 0:
+ current_set[row_index][column_index] = column
+ continue
+ current_set[row_index][column_index] = column / magnitude
+ # Subtract to cancel term
+ first_row = current_set[0]
+ final_set = [first_row]
+ current_set = current_set[1::]
+ for row in current_set:
+ temp_row = []
+ # If first term is 0, it is already in form we want, so we preserve it
+ if row[0] == 0:
+ final_set.append(row)
+ continue
+ for column_index in range(len(row)):
+ temp_row.append(first_row[column_index] - row[column_index])
+ final_set.append(temp_row)
+ # Create next recursion iteration set
+ if len(final_set[0]) != 3:
+ current_first_row = final_set[0]
+ current_first_column = []
+ next_iteration = []
+ for row in final_set[1::]:
+ current_first_column.append(row[0])
+ next_iteration.append(row[1::])
+ resultant = simplify(next_iteration)
+ for i in range(len(resultant)):
+ resultant[i].insert(0, current_first_column[i])
+ resultant.insert(0, current_first_row)
+ final_set = resultant
+ return final_set
+
+
+def solve_simultaneous(equations: list[list]) -> list:
+ """
+ >>> solve_simultaneous([[1, 2, 3],[4, 5, 6]])
+ [-1.0, 2.0]
+ >>> solve_simultaneous([[0, -3, 1, 7],[3, 2, -1, 11],[5, 1, -2, 12]])
+ [6.4, 1.2, 10.6]
+ >>> solve_simultaneous([])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],[1, 2]])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],["a", 7, 8]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires lists of integers
+ >>> solve_simultaneous([[0, 2, 3],[4, 0, 6]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires at least 1 full equation
+ """
+ if len(equations) == 0:
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ _length = len(equations) + 1
+ if any(len(item) != _length for item in equations):
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ for row in equations:
+ if any(not isinstance(column, (int, float)) for column in row):
+ raise ValueError("solve_simultaneous() requires lists of integers")
+ if len(equations) == 1:
+ return [equations[0][-1] / equations[0][0]]
+ data_set = equations.copy()
+ if any(0 in row for row in data_set):
+ temp_data = data_set.copy()
+ full_row = []
+ for row_index, row in enumerate(temp_data):
+ if 0 not in row:
+ full_row = data_set.pop(row_index)
+ break
+ if not full_row:
+ raise ValueError("solve_simultaneous() requires at least 1 full equation")
+ data_set.insert(0, full_row)
+ useable_form = data_set.copy()
+ simplified = simplify(useable_form)
+ simplified = simplified[::-1]
+ solutions: list = []
+ for row in simplified:
+ current_solution = row[-1]
+ if not solutions:
+ if row[-2] == 0:
+ solutions.append(0)
+ continue
+ solutions.append(current_solution / row[-2])
+ continue
+ temp_row = row.copy()[: len(row) - 1 :]
+ while temp_row[0] == 0:
+ temp_row.pop(0)
+ if len(temp_row) == 0:
+ solutions.append(0)
+ continue
+ temp_row = temp_row[1::]
+ temp_row = temp_row[::-1]
+ for column_index, column in enumerate(temp_row):
+ current_solution -= column * solutions[column_index]
+ solutions.append(current_solution)
+ final = []
+ for item in solutions:
+ final.append(float(round(item, 5)))
+ return final[::-1]
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+ eq = [
+ [2, 1, 1, 1, 1, 4],
+ [1, 2, 1, 1, 1, 5],
+ [1, 1, 2, 1, 1, 6],
+ [1, 1, 1, 2, 1, 7],
+ [1, 1, 1, 1, 2, 8],
+ ]
+ print(solve_simultaneous(eq))
+ print(solve_simultaneous([[4, 2]]))

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+ "githubPullRequests.ignoredPullRequestBranches": [
+ "master"
+ ]
+}

maths/simultaneous_linear_equation_solver.py

@@ -0,0 +1,142 @@
+"""
+https://en.wikipedia.org/wiki/Augmented_matrix
+
+This algorithm solves simultaneous linear equations of the form
+λa + λb + λc + λd + ... = γ as [λ, λ, λ, λ, ..., γ]
+Where λ & γ are individual coefficients, the no. of equations = no. of coefficients - 1
+
+Note in order to work there must exist 1 equation where all instances of λ and γ != 0
+"""
+
+
+def simplify(current_set: list[list]) -> list[list]:
+ """
+ >>> simplify([[1, 2, 3], [4, 5, 6]])
+ [[1.0, 2.0, 3.0], [0.0, 0.75, 1.5]]
+ >>> simplify([[5, 2, 5], [5, 1, 10]])
+ [[1.0, 0.4, 1.0], [0.0, 0.2, -1.0]]
+ """
+ # Divide each row by magnitude of first term --> creates 'unit' matrix
+ duplicate_set = current_set.copy()
+ for row_index, row in enumerate(duplicate_set):
+ magnitude = row[0]
+ for column_index, column in enumerate(row):
+ if magnitude == 0:
+ current_set[row_index][column_index] = column
+ continue
+ current_set[row_index][column_index] = column / magnitude
+ # Subtract to cancel term
+ first_row = current_set[0]
+ final_set = [first_row]
+ current_set = current_set[1::]
+ for row in current_set:
+ temp_row = []
+ # If first term is 0, it is already in form we want, so we preserve it
+ if row[0] == 0:
+ final_set.append(row)
+ continue
+ for column_index in range(len(row)):
+ temp_row.append(first_row[column_index] - row[column_index])
+ final_set.append(temp_row)
+ # Create next recursion iteration set
+ if len(final_set[0]) != 3:
+ current_first_row = final_set[0]
+ current_first_column = []
+ next_iteration = []
+ for row in final_set[1::]:
+ current_first_column.append(row[0])
+ next_iteration.append(row[1::])
+ resultant = simplify(next_iteration)
+ for i in range(len(resultant)):
+ resultant[i].insert(0, current_first_column[i])
+ resultant.insert(0, current_first_row)
+ final_set = resultant
+ return final_set
+
+
+def solve_simultaneous(equations: list[list]) -> list:
+ """
+ >>> solve_simultaneous([[1, 2, 3],[4, 5, 6]])
+ [-1.0, 2.0]
+ >>> solve_simultaneous([[0, -3, 1, 7],[3, 2, -1, 11],[5, 1, -2, 12]])
+ [6.4, 1.2, 10.6]
+ >>> solve_simultaneous([])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],[1, 2]])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],["a", 7, 8]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires lists of integers
+ >>> solve_simultaneous([[0, 2, 3],[4, 0, 6]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires at least 1 full equation
+ """
+ if len(equations) == 0:
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ _length = len(equations) + 1
+ if any(len(item) != _length for item in equations):
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ for row in equations:
+ if any(not isinstance(column, (int, float)) for column in row):
+ raise ValueError("solve_simultaneous() requires lists of integers")
+ if len(equations) == 1:
+ return [equations[0][-1] / equations[0][0]]
+ data_set = equations.copy()
+ if any(0 in row for row in data_set):
+ temp_data = data_set.copy()
+ full_row = []
+ for row_index, row in enumerate(temp_data):
+ if 0 not in row:
+ full_row = data_set.pop(row_index)
+ break
+ if not full_row:
+ raise ValueError("solve_simultaneous() requires at least 1 full equation")
+ data_set.insert(0, full_row)
+ useable_form = data_set.copy()
+ simplified = simplify(useable_form)
+ simplified = simplified[::-1]
+ solutions: list = []
+ for row in simplified:
+ current_solution = row[-1]
+ if not solutions:
+ if row[-2] == 0:
+ solutions.append(0)
+ continue
+ solutions.append(current_solution / row[-2])
+ continue
+ temp_row = row.copy()[: len(row) - 1 :]
+ while temp_row[0] == 0:
+ temp_row.pop(0)
+ if len(temp_row) == 0:
+ solutions.append(0)
+ continue
+ temp_row = temp_row[1::]
+ temp_row = temp_row[::-1]
+ for column_index, column in enumerate(temp_row):
+ current_solution -= column * solutions[column_index]
+ solutions.append(current_solution)
+ final = []
+ for item in solutions:
+ final.append(float(round(item, 5)))
+ return final[::-1]
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+ eq = [
+ [2, 1, 1, 1, 1, 4],
+ [1, 2, 1, 1, 1, 5],
+ [1, 1, 2, 1, 1, 6],
+ [1, 1, 1, 2, 1, 7],
+ [1, 1, 1, 1, 2, 8],
+ ]
+ print(solve_simultaneous(eq))
+ print(solve_simultaneous([[4, 2]]))

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+ "githubPullRequests.ignoredPullRequestBranches": [
+ "master"
+ ]
+}

maths/simultaneous_linear_equation_solver.py

@@ -0,0 +1,142 @@
+"""
+https://en.wikipedia.org/wiki/Augmented_matrix
+
+This algorithm solves simultaneous linear equations of the form
+λa + λb + λc + λd + ... = γ as [λ, λ, λ, λ, ..., γ]
+Where λ & γ are individual coefficients, the no. of equations = no. of coefficients - 1
+
+Note in order to work there must exist 1 equation where all instances of λ and γ != 0
+"""
+
+
+def simplify(current_set: list[list]) -> list[list]:
+ """
+ >>> simplify([[1, 2, 3], [4, 5, 6]])
+ [[1.0, 2.0, 3.0], [0.0, 0.75, 1.5]]
+ >>> simplify([[5, 2, 5], [5, 1, 10]])
+ [[1.0, 0.4, 1.0], [0.0, 0.2, -1.0]]
+ """
+ # Divide each row by magnitude of first term --> creates 'unit' matrix
+ duplicate_set = current_set.copy()
+ for row_index, row in enumerate(duplicate_set):
+ magnitude = row[0]
+ for column_index, column in enumerate(row):
+ if magnitude == 0:
+ current_set[row_index][column_index] = column
+ continue
+ current_set[row_index][column_index] = column / magnitude
+ # Subtract to cancel term
+ first_row = current_set[0]
+ final_set = [first_row]
+ current_set = current_set[1::]
+ for row in current_set:
+ temp_row = []
+ # If first term is 0, it is already in form we want, so we preserve it
+ if row[0] == 0:
+ final_set.append(row)
+ continue
+ for column_index in range(len(row)):
+ temp_row.append(first_row[column_index] - row[column_index])
+ final_set.append(temp_row)
+ # Create next recursion iteration set
+ if len(final_set[0]) != 3:
+ current_first_row = final_set[0]
+ current_first_column = []
+ next_iteration = []
+ for row in final_set[1::]:
+ current_first_column.append(row[0])
+ next_iteration.append(row[1::])
+ resultant = simplify(next_iteration)
+ for i in range(len(resultant)):
+ resultant[i].insert(0, current_first_column[i])
+ resultant.insert(0, current_first_row)
+ final_set = resultant
+ return final_set
+
+
+def solve_simultaneous(equations: list[list]) -> list:
+ """
+ >>> solve_simultaneous([[1, 2, 3],[4, 5, 6]])
+ [-1.0, 2.0]
+ >>> solve_simultaneous([[0, -3, 1, 7],[3, 2, -1, 11],[5, 1, -2, 12]])
+ [6.4, 1.2, 10.6]
+ >>> solve_simultaneous([])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],[1, 2]])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],["a", 7, 8]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires lists of integers
+ >>> solve_simultaneous([[0, 2, 3],[4, 0, 6]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires at least 1 full equation
+ """
+ if len(equations) == 0:
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ _length = len(equations) + 1
+ if any(len(item) != _length for item in equations):
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ for row in equations:
+ if any(not isinstance(column, (int, float)) for column in row):
+ raise ValueError("solve_simultaneous() requires lists of integers")
+ if len(equations) == 1:
+ return [equations[0][-1] / equations[0][0]]
+ data_set = equations.copy()
+ if any(0 in row for row in data_set):
+ temp_data = data_set.copy()
+ full_row = []
+ for row_index, row in enumerate(temp_data):
+ if 0 not in row:
+ full_row = data_set.pop(row_index)
+ break
+ if not full_row:
+ raise ValueError("solve_simultaneous() requires at least 1 full equation")
+ data_set.insert(0, full_row)
+ useable_form = data_set.copy()
+ simplified = simplify(useable_form)
+ simplified = simplified[::-1]
+ solutions: list = []
+ for row in simplified:
+ current_solution = row[-1]
+ if not solutions:
+ if row[-2] == 0:
+ solutions.append(0)
+ continue
+ solutions.append(current_solution / row[-2])
+ continue
+ temp_row = row.copy()[: len(row) - 1 :]
+ while temp_row[0] == 0:
+ temp_row.pop(0)
+ if len(temp_row) == 0:
+ solutions.append(0)
+ continue
+ temp_row = temp_row[1::]
+ temp_row = temp_row[::-1]
+ for column_index, column in enumerate(temp_row):
+ current_solution -= column * solutions[column_index]
+ solutions.append(current_solution)
+ final = []
+ for item in solutions:
+ final.append(float(round(item, 5)))
+ return final[::-1]
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+ eq = [
+ [2, 1, 1, 1, 1, 4],
+ [1, 2, 1, 1, 1, 5],
+ [1, 1, 2, 1, 1, 6],
+ [1, 1, 1, 2, 1, 7],
+ [1, 1, 1, 1, 2, 8],
+ ]
+ print(solve_simultaneous(eq))
+ print(solve_simultaneous([[4, 2]]))

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+ "githubPullRequests.ignoredPullRequestBranches": [
+ "master"
+ ]
+}

maths/simultaneous_linear_equation_solver.py

@@ -0,0 +1,142 @@
+"""
+https://en.wikipedia.org/wiki/Augmented_matrix
+
+This algorithm solves simultaneous linear equations of the form
+λa + λb + λc + λd + ... = γ as [λ, λ, λ, λ, ..., γ]
+Where λ & γ are individual coefficients, the no. of equations = no. of coefficients - 1
+
+Note in order to work there must exist 1 equation where all instances of λ and γ != 0
+"""
+
+
+def simplify(current_set: list[list]) -> list[list]:
+ """
+ >>> simplify([[1, 2, 3], [4, 5, 6]])
+ [[1.0, 2.0, 3.0], [0.0, 0.75, 1.5]]
+ >>> simplify([[5, 2, 5], [5, 1, 10]])
+ [[1.0, 0.4, 1.0], [0.0, 0.2, -1.0]]
+ """
+ # Divide each row by magnitude of first term --> creates 'unit' matrix
+ duplicate_set = current_set.copy()
+ for row_index, row in enumerate(duplicate_set):
+ magnitude = row[0]
+ for column_index, column in enumerate(row):
+ if magnitude == 0:
+ current_set[row_index][column_index] = column
+ continue
+ current_set[row_index][column_index] = column / magnitude
+ # Subtract to cancel term
+ first_row = current_set[0]
+ final_set = [first_row]
+ current_set = current_set[1::]
+ for row in current_set:
+ temp_row = []
+ # If first term is 0, it is already in form we want, so we preserve it
+ if row[0] == 0:
+ final_set.append(row)
+ continue
+ for column_index in range(len(row)):
+ temp_row.append(first_row[column_index] - row[column_index])
+ final_set.append(temp_row)
+ # Create next recursion iteration set
+ if len(final_set[0]) != 3:
+ current_first_row = final_set[0]
+ current_first_column = []
+ next_iteration = []
+ for row in final_set[1::]:
+ current_first_column.append(row[0])
+ next_iteration.append(row[1::])
+ resultant = simplify(next_iteration)
+ for i in range(len(resultant)):
+ resultant[i].insert(0, current_first_column[i])
+ resultant.insert(0, current_first_row)
+ final_set = resultant
+ return final_set
+
+
+def solve_simultaneous(equations: list[list]) -> list:
+ """
+ >>> solve_simultaneous([[1, 2, 3],[4, 5, 6]])
+ [-1.0, 2.0]
+ >>> solve_simultaneous([[0, -3, 1, 7],[3, 2, -1, 11],[5, 1, -2, 12]])
+ [6.4, 1.2, 10.6]
+ >>> solve_simultaneous([])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],[1, 2]])
+ Traceback (most recent call last):
+ ...
+ IndexError: solve_simultaneous() requires n lists of length n+1
+ >>> solve_simultaneous([[1, 2, 3],["a", 7, 8]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires lists of integers
+ >>> solve_simultaneous([[0, 2, 3],[4, 0, 6]])
+ Traceback (most recent call last):
+ ...
+ ValueError: solve_simultaneous() requires at least 1 full equation
+ """
+ if len(equations) == 0:
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ _length = len(equations) + 1
+ if any(len(item) != _length for item in equations):
+ raise IndexError("solve_simultaneous() requires n lists of length n+1")
+ for row in equations:
+ if any(not isinstance(column, (int, float)) for column in row):
+ raise ValueError("solve_simultaneous() requires lists of integers")
+ if len(equations) == 1:
+ return [equations[0][-1] / equations[0][0]]
+ data_set = equations.copy()
+ if any(0 in row for row in data_set):
+ temp_data = data_set.copy()
+ full_row = []
+ for row_index, row in enumerate(temp_data):
+ if 0 not in row:
+ full_row = data_set.pop(row_index)
+ break
+ if not full_row:
+ raise ValueError("solve_simultaneous() requires at least 1 full equation")
+ data_set.insert(0, full_row)
+ useable_form = data_set.copy()
+ simplified = simplify(useable_form)
+ simplified = simplified[::-1]
+ solutions: list = []
+ for row in simplified:
+ current_solution = row[-1]
+ if not solutions:
+ if row[-2] == 0:
+ solutions.append(0)
+ continue
+ solutions.append(current_solution / row[-2])
+ continue
+ temp_row = row.copy()[: len(row) - 1 :]
+ while temp_row[0] == 0:
+ temp_row.pop(0)
+ if len(temp_row) == 0:
+ solutions.append(0)
+ continue
+ temp_row = temp_row[1::]
+ temp_row = temp_row[::-1]
+ for column_index, column in enumerate(temp_row):
+ current_solution -= column * solutions[column_index]
+ solutions.append(current_solution)
+ final = []
+ for item in solutions:
+ final.append(float(round(item, 5)))
+ return final[::-1]
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+ eq = [
+ [2, 1, 1, 1, 1, 4],
+ [1, 2, 1, 1, 1, 5],
+ [1, 1, 2, 1, 1, 6],
+ [1, 1, 1, 2, 1, 7],
+ [1, 1, 1, 1, 2, 8],
+ ]
+ print(solve_simultaneous(eq))
+ print(solve_simultaneous([[4, 2]]))