Python code for linear gauss deletion

LZW_decompress.py

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+"""
+    One of the several implementations of Lempel–Ziv–Welch decompression algorithm
+    https://en.wikipedia.org/wiki/Lempel%E2%80%93Ziv%E2%80%93Welch
+"""
+
+import math
+import sys
+
+
+def read_file_binary(file_path: str) -> str:
+    """
+    Reads given file as bytes and returns them as a long string
+    """
+    result = ""
+    try:
+        with open(file_path, "rb") as binary_file:
+            data = binary_file.read()
+        for dat in data:
+            curr_byte = f"{dat:08b}"
+            result += curr_byte
+        return result
+    except OSError:
+        print("File not accessible")
+        sys.exit()
+
+
+def decompress_data(data_bits: str) -> str:
+    """
+    Decompresses given data_bits using Lempel–Ziv–Welch compression algorithm
+    and returns the result as a string
+    """
+    lexicon = {"0": "0", "1": "1"}
+    result, curr_string = "", ""
+    index = len(lexicon)
+
+    for i in range(len(data_bits)):
+        curr_string += data_bits[i]
+        if curr_string not in lexicon:
+            continue
+
+        last_match_id = lexicon[curr_string]
+        result += last_match_id
+        lexicon[curr_string] = last_match_id + "0"
+
+        if math.log2(index).is_integer():
+            newLex = {}
+            for curr_key in list(lexicon):
+                newLex["0" + curr_key] = lexicon.pop(curr_key)
+            lexicon = newLex
+
+        lexicon[bin(index)[2:]] = last_match_id + "1"
+        index += 1
+        curr_string = ""
+    return result
+
+
+def write_file_binary(file_path: str, to_write: str) -> None:
+    """
+    Writes given to_write string (should only consist of 0's and 1's) as bytes in the
+    file
+    """
+    byte_length = 8
+    try:
+        with open(file_path, "wb") as opened_file:
+            result_byte_array = [
+                to_write[i : i + byte_length]
+                for i in range(0, len(to_write), byte_length)
+            ]
+
+            if len(result_byte_array[-1]) % byte_length == 0:
+                result_byte_array.append("10000000")
+            else:
+                result_byte_array[-1] += "1" + "0" * (
+                    byte_length - len(result_byte_array[-1]) - 1
+                )
+
+            for elem in result_byte_array[:-1]:
+                opened_file.write(int(elem, 2).to_bytes(1, byteorder="big"))
+    except OSError:
+        print("File not accessible")
+        sys.exit()
+
+
+def remove_prefix(data_bits: str) -> str:
+    """
+    Removes size prefix, that compressed file should have
+    Returns the result
+    """
+    counter = 0
+    for letter in data_bits:
+        if letter == "1":
+            break
+        counter += 1
+
+    data_bits = data_bits[counter:]
+    data_bits = data_bits[counter + 1 :]
+    return data_bits
+
+
+def compress(source_path: str, destination_path: str) -> None:
+    """
+    Reads source file, decompresses it and writes the result in destination file
+    """
+    data_bits = read_file_binary(source_path)
+    data_bits = remove_prefix(data_bits)
+    decompressed = decompress_data(data_bits)
+    write_file_binary(destination_path, decompressed)
+
+
+if __name__ == "__main__":
+    compress(sys.argv[1], sys.argv[2])

cellular_automata/gauss_deletion.py

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+"""
+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.ndarray) -> np.ndarray:
+    """
+    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.ndarray) -> np.ndarray:
+    """
+    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 np.array((), dtype=float)
+
+    # 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()