1.matlab里的解释
%CHOL Cholesky factorization. % R = CHOL(A) calculates the Cholesky factor of full or sparse A using % the diagonal and upper triangle of A, such that A = R'*R. A must be % positive definite, and the lower triangle is assumed to be the (complex % conjugate) transpose of the upper triangle. % % R = CHOL(A,TRIANGLE) specifies which triangle of A to use. For example, % if TRIANGLE is 'lower', then CHOL uses only the diagonal and lower % triangle of A to produce a lower triangular R such that A = R*R'. The % default value of TRIANGLE is 'upper'. Using the 'lower' option is % equivalent to calling CHOL with the 'upper' option and the transpose of % A, and then transposing the output matrix R. In the following syntaxes, % the output R is described only for the case when TRIANGLE is 'upper'. % % [R,FLAG] = CHOL(___) also returns the output FLAG indicating whether A % is positive definite. Use this syntax to suppress errors produced when % A is not positive definite. % * If A is positive definite, then FLAG is 0 and R is the same as above. % * If A is not positive definite, then FLAG is a positive integer. % - If A is full, then R is an upper triangular matrix of size % q = FLAG-1 such that R'*R = A(1:q,1:q). % - If A is sparse, then R is an upper triangular matrix of size % q-by-n such that the L-shaped region of the first q rows and % first q columns of R'*R agree with those of A. % % [R,FLAG,P] = CHOL(S), for sparse S, additionally returns a permutation % matrix P, which is a preordering of S obtained by AMD. The Cholesky % factor of P'*S*P tends to be sparser than that of S. % If FLAG = 0, then R is an upper triangular matrix such that R'*R = P'*S*P. % % [R,FLAG,p] = CHOL(___,OUTPUTFORM) specifies whether to return the % permutation information as a vector p or matrix P. With this syntax you % must specify a sparse input matrix S, and you optionally can specify % TRIANGLE. For example, if OUTPUTFORM is 'vector' and FLAG = 0, then % S(p,p) = R'*R. The default value of OUTPUTFORM is 'matrix' such that % P'*S*P = R'*R. % % See also CHOLUPDATE, ICHOL, LDL, LU. % Copyright 1984-2018 The MathWorks, Inc. % Built-in function. 讯享网
2.中文解释
chol函数的功能是对正定矩阵做cholesky分解，求出它的上三角阵。
讯享网clc;clear;close all; % chol函数说明 % R=chol(A) ,A = R'*R. A=[1,2,3; 2,8,8; 3,8,35]; A R=chol(A); R R'*R %上面程序的运行结果 A = 1 2 3 2 8 8 3 8 35 R = 1 2 3 0 2 1 0 0 5 ans = 1 2 3 2 8 8 3 8 35
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