feat: menambahkan algoritma taylor

implementation/linear_algebra/LU_decomposition.py

@@ -0,0 +1,41 @@
+# https://en.wikipedia.org/wiki/LU_decomposition#Algorithms
+
+
+def LU(A) -> tuple:
+    """
+    >>> A = [[2, 3, 1], [4, 7, 7], [-2, 4, 5]]
+    >>> L, U = LU(A)
+    >>> L
+    [[1, 0, 0], [2.0, 1, 0], [-1.0, 7.0, 1]]
+    >>> U
+    [[2, 3, 1], [0.0, 1.0, 5.0], [0.0, 0.0, -29.0]]
+    """
+    n = len(A)
+    L = [[1 if i == j else 0 for j in range(n)] for i in range(n)]
+    U = [[A[i][j] for j in range(n)] for i in range(n)]
+
+    for k in range(n - 1):
+        if U[k][k] == 0:
+            raise ValueError("Faktorisasi LU tidak ada")
+        for i in range(k + 1, n):
+            L[i][k] = U[i][k] / U[k][k]
+            for j in range(k, n):
+                U[i][j] -= L[i][k] * U[k][j]
+    return L, U
+
+
+def main(args=None):
+    import doctest
+
+    doctest.testmod()
+    A = [[2, 3, 1], [4, 7, 7], [-2, 4, 5]]
+    L, U = LU(A)
+    for row in L:
+        print(row)
+    print("\n")
+    for row in U:
+        print(row)
+
+
+if __name__ == "__main__":
+    main()

math/deret_taylor.py

@@ -0,0 +1,129 @@
+# macam macam deret taylor
+# https://en.wikipedia.org/wiki/Taylor_series
+import math
+
+
+def faktorial(n : int = 2) -> int:
+    """
+    Fungsi untuk kalkulasi faktorial
+
+    parameter :
+    n = bilangan bulat
+
+    return :
+    hasil = hasil dari operasi faktorial
+    """
+    if n == 1 or n == 0:
+        return 1
+    if n > 1:
+        return n * faktorial(n - 1)
+
+
+def sin(x : float) -> float:
+    """
+    Fungsi untuk kalkulasi dari deret sin.
+    Input dari fungsi ini dikonvergensi menjadi
+    radian.
+
+    >>> sin(0)
+    0.0
+    >>> sin(45)
+    0.7071067811865475
+    """
+    result = 0.0
+    interable = 10
+    radian = x * math.pi / 180
+    for i in range(interable + 1):
+        numerator = math.pow(radian, (1 + i * 2)) * math.pow(-1, i)
+        detector = faktorial((1 + 2 * i))
+        result = result + (numerator / detector)
+    return float(result)
+
+
+def cos(x : float) -> float:
+    """
+    Fungsi untuk kalkulasi dari deret cosinus.
+    Input dari fungsi ini dikonvergensi menjadi
+    radian.
+
+    >>> cos(0)
+    1.0
+    >>> cos(45)
+    0.7071067811865475
+    """
+    result = 0.0
+    interable = 10
+    radian = x * math.pi / 180
+    for i in range(interable):
+        numerator = math.pow(radian, 2 * i) * math.pow(-1, i)
+        detector = faktorial(2 * i)
+        result = result + (numerator / detector)
+    return float(result)
+
+
+def euler(x: int = 1) -> float:
+    """
+    Fungsi untuk kalkulasi dari deret
+    taylor euler e^x
+
+    >>> euler(1)
+    2.7182815255731922
+    >>> euler(2)
+    7.3887125220458545
+    """
+    result = 0.0
+    interable = 10
+    for i in range(interable):
+        numerator = math.pow(x, (i))
+        detector = faktorial(i)
+        result = result + (numerator / detector)
+    return float(result)
+
+
+def ln(x : float) -> float:
+    """
+    Fungsi untuk melakukan kalkulasi deret taylor
+    ln(x + 1).Dengan batas -1 < x <= 1.
+
+
+    >>> ln(0.5)
+    0.4054346478174603
+    >>> ln(1)
+    0.6456349206349207
+    """
+    if x > -1 and x <= 1:
+        result = 0.0
+        interable = 10
+        for i in range(1, interable + 1):
+            numerator = math.pow(x, i) * math.pow(-1, i + 1)
+            detector = i
+            result = result + (numerator / detector)
+        return float(result)
+    else :
+        return ValueError("Angka tidak valid")
+
+
+def main(args=None):
+    import doctest
+
+    doctest.testmod()
+
+    # test untuk fungsi cos
+    print(cos(0))
+    print(cos(45))
+
+    # test untuk fungsi sin
+    print(sin(0))
+    print(sin(45))
+
+    # test untuk fungsi euler
+    print(euler(1))
+    print(euler(2))
+
+    # test untuk fungsi ln(1 + x)
+    print(ln(0.5))
+    print(ln(1))
+
+
+if __name__ == "__main__":
+    main()