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Krasic: ½ð±Ò+5, ¡ï¡ï¡ïºÜÓаïÖú, ·Ç³£¸Ðл!ÎÒÏëһϣ¬ÔÙ¼ÌÐøÇë½ÌÄ㣡 2012-05-22 11:04:38
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7Â¥: Originally posted by Krasic at 2012-05-20 09:18:42:
1£¬·Ç³£¸Ðл£¬ÎÒÊÇ·Ö±ðÓÃ^(-1)ºÍ^(-1/2)×öµÄÇóÄæºÍÇ󯽷½¸ù¡£ÊDz»ÏëºÍinvÓësqrtmµÈ¼Û£¿

2£¬»¹ÓУ¬Êµ¼ÊÉÏÎÒ²»¹ØÐÄÄÇô¸ß½×µÄ¾ØÕ󣬵ͽף¨5-10½×£©µÄʱºò£¬ÇóÄæºÍƽ·½¸ùµÄ¼ÆË㸴ÔÓ¶ÈÈçºÎ£¬Äܲ»ÄÜÇëÄã×ö¸öͼ·ÖÎöÒ»

²»Çå³þËã·¨µÄ¾ßÌåʵÏÖ£¬ËùÒÔºÜÄѸø³ö¶¨Á¿µÄ¸´ÔÓ¶È£¬´ÓͼÖпÉÒÔ¿´³ö£¬µ±n²»Ì«´óʱ£¬Æ½·½¸ùÊÇn^1.2, ¶øÇóÄæ´ó¸ÅÊÇn^0.6. Äã¿ÉÒÔÓÃÕâ¸öcode×Ô¼ºËã¡£

function [t1,t2,t3]=test2(t1,t2,t3)

if nargin == 0
    N = 30; M = 100;
    t1 = zeros(1,N);
    t2 = zeros(1,N);
    t3 = zeros(1,N);
    for n=1:N
        n
        for m=1:M
        A = rand(n);
        tic; inv(A); t1(n)=t1(n)+toc;
        tic; sqrtm(A); t2(n)=t2(n)+toc;
        tic; mpower(A,0.5); t3(n)=t3(n)+toc;
        end      
    end
end
t1 = t1/M; t2=t2/M; t3=t3/M;
n = 1:N;
loglog(n, t1, 'rx-', n, t2, 'bo-', n, t3, 'g+-')
legend('inv', 'sqrtm', 'mpower','Location','NorthWest');
hold on
p1=polyfit(log(n),log(t1),1);
p2=polyfit(log(n),log(t2),1);
p3=polyfit(log(n),log(t3),1);

f1 = @(x)(p1(1)*log(x)+p1(2));
f2 = @(x)(p2(1)*log(x)+p2(2));
f3 = @(x)(p3(1)*log(x)+p3(2));

X = [min(n)*1.1, max(n)/1.1];

line(X, exp(f1(X)-1));
text(X(1), exp(f1(X(1))-0.5), ['the slope is', num2str(p1(1))])
line(X, exp(f2(X)+1));
text(X(1), exp(f2(X(1))+0.5), ['the slope is', num2str(p2(1))])
line(X, exp(f3(X)-1));
text(X(1), exp(f3(X(1))-0.5), ['the slope is', num2str(p3(1))])
11Â¥2012-05-22 04:22:18
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