勒让德多项式的 Matlab 代码优化

Question

我知道 Matlab 具有用于确定相关 Legendre 函数的内置函数。我想计算勒让德多项式，这是这些多项式的特例。我为此任务编写了自己的代码，并与 Matlab 内置函数进行了比较。这是比较代码:

function op
t1 = zeros(1,100);
t2 = zeros(1,100);
P1 = zeros(1,10);
for m = 1:100
tic;
% It is neccessary a for loop for the first ten terms (m =1,...,10) of 
% Legendre polynomial with legendre matlab built-in function
for i = 1:10
    A = legendre(i,0);% legendre function determines the associated 
    % Legendre functions
    P1(i) = A(1,1);% Legendre polynomials are the first row of A
end
t1(m) = toc;
tic;
% My own function determines the first ten terms at a time
P2 = legendrep2(0,10);
t2(m) = toc;
end
% Mean time using the Matlab built-in legendre functions
t1_mean = mean(t1),
% Mean time using my own custom legendre polynomial function
t2_mean = mean(t2),

function [Pl] = legendrep2(gamma,fin_suma)
Pl = zeros(1,fin_suma);
Pl(1) = gamma;
Pl(2) = 0.5*(3*gamma*Pl(1)-1);
    for j =3:fin_suma;
        Pl(j) = ((2*j-1)*gamma*Pl(j-1)-(j-1)*Pl(j-2))/j;
    end
end
end

这些是我的结果:

t1_mean =
     0.001621042906210
t2_mean =
      7.536710452587590e-006

所以，我想知道是否有可能进一步改进我的代码(legendrep2 函数)。

Answer 1

尝试使用 Matlab 分析器找出瓶颈在哪里:

Menu -> Desktop -> Profiler

这将帮助您集中注意力。