Python LU 分解
LU decomposition in Python
''' a = LUdecomp(a). LU decomposition: [L][U] = [a]. The returned matrix [a] = [L\U] contains [U] in the upper triangle and the nondiagonal terms of [L] in the lower triangle. x = LUsolve(a,b). Solves [L][U]{x} = b, where [a] = [L\U] is the matrix returned from LUdecomp. ''' from numpy import dot def LUdecomp(a): n = len(a) for k in range(0,n-1): for i in range(k+1,n): if abs(a[i,k]) > 1.0e-9: lam = a [i,k]/a[k,k] a[i,k+1:n] = a[i,k+1:n] - lam*a[k,k+1:n] a[i,k] = lam return a def LUsolve(a,b): n = len(a) for k in range(1,n): b[k] = b[k] - dot(a[k,0:k],b[0:k]) b[n-1] = b[n-1]/a[n-1,n-1] for k in range(n-2,-1,-1): b[k] = (b[k] - dot(a[k,k+1:n],b[k+1:n]))/a[k,k] return b