Data commit

Task/LU-decomposition/Python/lu-decomposition.py

@@ -0,0 +1,42 @@
+from pprint import pprint
+
+def matrixMul(A, B):
+    TB = zip(*B)
+    return [[sum(ea*eb for ea,eb in zip(a,b)) for b in TB] for a in A]
+
+def pivotize(m):
+    """Creates the pivoting matrix for m."""
+    n = len(m)
+    ID = [[float(i == j) for i in xrange(n)] for j in xrange(n)]
+    for j in xrange(n):
+        row = max(xrange(j, n), key=lambda i: abs(m[i][j]))
+        if j != row:
+            ID[j], ID[row] = ID[row], ID[j]
+    return ID
+
+def lu(A):
+    """Decomposes a nxn matrix A by PA=LU and returns L, U and P."""
+    n = len(A)
+    L = [[0.0] * n for i in xrange(n)]
+    U = [[0.0] * n for i in xrange(n)]
+    P = pivotize(A)
+    A2 = matrixMul(P, A)
+    for j in xrange(n):
+        L[j][j] = 1.0
+        for i in xrange(j+1):
+            s1 = sum(U[k][j] * L[i][k] for k in xrange(i))
+            U[i][j] = A2[i][j] - s1
+        for i in xrange(j, n):
+            s2 = sum(U[k][j] * L[i][k] for k in xrange(j))
+            L[i][j] = (A2[i][j] - s2) / U[j][j]
+    return (L, U, P)
+
+a = [[1, 3, 5], [2, 4, 7], [1, 1, 0]]
+for part in lu(a):
+    pprint(part, width=19)
+    print
+print
+b = [[11,9,24,2],[1,5,2,6],[3,17,18,1],[2,5,7,1]]
+for part in lu(b):
+    pprint(part)
+    print