The reason that has all diagonal entries set to 1 is that this means the LU decomposition is unique.The LU decomposition provides an efficient means of solving linear equations.If the LU decomposition exists then it is unique.The LU decomposition may not exist for a matrix.The properties of the LU decomposition are: is a lower-triangular matrix with all diagonal entries equal to 1.The LU decomposition of a matrix is the pair of matrices and such that: Zeros ( n ) for i in range ( n - 1, - 1, - 1 ): tmp = b for j in range ( i + 1, n ): tmp -= U * x x = tmp / U return x LU decomposition Import numpy as np def back_sub ( U, b ): """x = back_sub(U, b) is the solution to U x = bī must be a vector of the same leading dimension as U
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