feat: menambahkan special matriks (#353)

* feat: menambahkan special matriks

* fix: memperbaiki test

* fix: memperbaiki test

Author: Ateng-labrador

matrix/matriks_special.py

@@ -0,0 +1,150 @@
+# https://en.wikipedia.org/wiki/Hankel_matrix
+# https://en.wikipedia.org/wiki/Toeplitz_matrix
+# https://en.wikipedia.org/wiki/Pascal_matrix
+# https://id.wikipedia.org/wiki/Matriks_identitas
+from typing import Union
+
+
+def faktorial(n) -> int:
+    """
+    >>> faktorial(5)
+    120
+    """
+    if n < 0:
+        raise ValueError("nilai harus positif")
+    if n == 0:
+        return 1
+    else:
+        f = 1
+        for i in range(1, n + 1):
+            f *= i
+        return f
+
+
+def kombinasi(n: int, r: int) -> int:
+    """
+    >>> kombinasi(5, 2)
+    10.0
+    """
+    if n < 0 or r < 0:
+        raise ValueError("Nilai Harus Positif")
+    if r > n:
+        return 0
+    else:
+        penyebut = faktorial(n)
+        pembilang = faktorial(r) * faktorial(n - r)
+        C = penyebut / pembilang
+        return C
+
+
+def identity(n: int = 2) -> list[list[Union[int]]]:
+    """
+    Membuat matriks identitas
+
+    >>> identity(3)
+    [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
+    """
+    A = []
+    for i in range(n):
+        row = []
+        for j in range(n):
+            if j == i:
+                row.append(1)
+            else:
+                row.append(0)
+        A.append(row)
+    return A
+
+
+def hankel(A, b=1) -> list[list[Union[int, float]]]:
+    """
+    Membuat matriks hankel
+
+    >>> hankel(3)
+    [[1, 2, 3], [2, 3, 4], [3, 4, 5]]
+    """
+    res = []
+    for i in range(b, A + 1):
+        row = []
+        for j in range(b, A + 1):
+            row.append(i + j - 1)
+        res.append(row)
+    return res
+
+
+def toeplite(A, b=1) -> list[list[Union[int, float]]]:
+    """
+    Membuat matriks hankel
+
+    >>> toeplite(3)
+    [[0, -1, -2], [1, 0, -1], [2, 1, 0]]
+    """
+    res = []
+    for i in range(b, A + 1):
+        row = []
+        for j in range(b, A + 1):
+            row.append(i - j)
+        res.append(row)
+    return res
+
+
+def hilbert(A, b=1) -> list[list[Union[int, float]]]:
+    """
+    Membuat matriks hilbert
+
+    >>> hilbert(2)
+    [[1.0, 0.5], [0.5, 0.3333333333333333]]
+    """
+    res = []
+    for i in range(b, A + 1):
+        row = []
+        for j in range(b, A + 1):
+            row.append(1 / (i + j - 1))
+        res.append(row)
+    return res
+
+
+def pascal(n, kind="simetri") -> list[list[Union[int, float]]]:
+    """
+    Membuat matriks pascal dengan beberapa tipe
+
+    >>> pascal(3)
+    [[1.0, 1.0, 1.0], [1.0, 2.0, 3.0], [1.0, 3.0, 6.0]]
+    >>> pascal(3, kind = 'lower')
+    [[1.0, 0, 0], [1.0, 1.0, 0], [1.0, 2.0, 1.0]]
+    """
+    L_n = []
+    for i in range(n):
+        colum = []
+        for j in range(n):
+            x = kombinasi(i, j)
+            colum.append(x)
+        L_n.append(colum)
+
+    r, c = len(L_n), len(L_n[0])
+    t = [[0] * r for _ in range(c)]
+    for i in range(r):
+        for j in range(c):
+            t[j][i] = L_n[i][j]
+
+    res = [[0 for _ in range(len(L_n))] for _ in range(len(L_n))]
+    x = len(L_n)
+    y = len(t)
+    y1 = len(t[0])
+    for i in range(x):
+        for j in range(y1):
+            for k in range(y):
+                res[i][j] += L_n[i][k] * t[k][j]
+
+    if kind.lower() == "lower":
+        return L_n
+    elif kind.lower() == "upper":
+        return t
+    else:
+        return res
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()