feat: menambahkan algoritma LDLT

implementation/linear_algebra/LDLT_decomposition.py

@@ -0,0 +1,52 @@
+# https://en.wikipedia.org/wiki/Cholesky_decomposition#LDL_decomposition
+
+
+def transpose(x: list[list[int]]) -> list[list[int]]:
+    """
+    >>> transpose([[1, 2], [3, 4]])
+    [[1, 3], [2, 4]]
+    """
+    x = [[x[j][i] for j in range(len(x))] for i in range(len(x[0]))]
+    return x
+
+
+def LDLT_decomposition(x: list[list[int]]) -> list[list[int]]:
+    """
+    >>> L, D, Lt = LDLT_decomposition([[2, 4, 6], [4, 9, 14], [6, 14, 19]])
+    >>> L
+    [[1, 0, 0], [2.0, 1, 0], [3.0, 2.0, 1]]
+    >>> D
+    [2.0, 1.0, -3.0]
+    >>> Lt
+    [[1, 2.0, 3.0], [0, 1, 2.0], [0, 0, 1]]
+    """
+    if transpose(x) == x:
+        n = len(x)
+        L = [[0 for _ in range(len(x))] for _ in range(len(x))]
+        d = [0 for _ in range(len(x))]
+        for i in range(n):
+            sum_val = 0.0
+            for k in range(i):
+                sum_val += (L[i][k] ** 2) * d[k]
+            d[i] = x[i][i] - sum_val
+
+            for j in range(i + 1, n):
+                sum_val = 0.0
+                for k in range(i):
+                    sum_val += L[j][k] * L[i][k] * d[k]
+                L[j][i] = (x[j][i] - sum_val) / d[i]
+            L[i][i] = 1
+        Lt = transpose(L)
+        return L, d, Lt
+    else:
+        return ValueError("Matriks tidak simetri")
+
+
+def main(args=None):
+    import doctest
+
+    doctest.testmod()
+
+
+if __name__ == "__main__":
+    main()