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glazio

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1. ¹«Ê½
ÉøÁ÷¹«Ê½Îªy=A*(x-xc)^p
ÆäÖÐxΪ×Ô±äÁ¿£¬yΪÒò±äÁ¿£¬A¡¢xcºÍp¾ùΪ³£Êý¡£

2. Êý¾Ý
ΪÁ˲âÊÔÄ£Ä⣬É趨A=18.5£¬xc=0.095£¬p=-2.3£¬µÃµ½ÒÔÏÂÊý¾Ý

x                y
------------------------------
0.1001        3.5E+06
0.1002        3.3E+06
0.11        2.9E+05
0.12        9.0E+04
0.15        1.5E+04
0.2        3.3E+03
0.3        7.1E+02
0.4        2.8E+02
0.5        1.5E+02
0.6        8.9E+01

3. ÎÒµÄorigin£¨Pro V8.5£©ÄâºÏ¹ý³Ì
ѡȡNonlinear Curve Fit£¬CategoryѡȡPower£¬FunctionѡȡPower1£¬¸Ã·½³ÌÐÎʽΪy=A|x-xc|^p¡£
ÔÚ²ÎÊýboundsÖÐÉ趨p<0£¬0
¿¼Âǵ½yÖµ±ä¶¯½Ï´ó£¬ÓÖÔÚNLCF-Settings-Data SelectionÖн«yÖµÈ¨ÖØÉèΪ¡°Variance~y^2¡±ºó£¬ÏÔʾChi-SquareΪ1.42513£¬ÏÖÔÚÖ´ÐС°1 Iteration¡±£¬µ«ÏµÍ³ÈÔÈ»ÏÔʾ¡°Fit did not converge - reason unknown.¡±



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[ Last edited by glazio on 2011-11-25 at 09:33 ]
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dbb627

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glazio(½ð±Ò+10): dbb627°æÖ÷²»À¢ÊÇmatlabÉñÈË£¬ËùÓÐÎÊÌâ¶¼µÃµ½»Ø´ð£¬·Ç³£¸Ðл£¡ 2011-11-30 08:57:21
cenwanglai(¼ÆËãÇ¿Ìû+1): ÄãµÄ»Ø¸´¶¼Í¦ºÃ¡£²»¹ýÎÒ²»ÊìϤ£¬Ã»ÓÐ×Ðϸ¿´Ã÷°×¡£¾ÍÕâÀï¸øÒ»¸öEPI°É~ 2011-12-22 20:09:16
ÒýÓûØÌû:
13Â¥: Originally posted by glazio at 2011-11-29 22:38:41:
Äã¸øµÄÌû×ÓÀïµÄÇé¿öºÃÏñ²¢²»ÊÇÎÒ˵µÄ¹²Ïí²ÎÊýÄâºÏ¡£ÏÂÃæ¾Ù¸öÀý×Ó˵Ã÷һϡ£

¼ÙÈç˵ÔÚÊý¾ÝͼÖÐÓÐÁ½×éʵÑéÊý¾Ý¼¯Y1ºÍY2£¬¿ÉÒÔÓÃij¸öº¬ÓÐÈý¸ö²ÎÊýa£¬b£¬cµÄ·½³Ìy=f(x)ÃèÊö¡£ÆÕͨµÄÄâºÏÒ»°ãÊÇÓÃF(x)¶ÔÊý¾Ý¼¯Y1ºÍY2 ...

Õâ¸öûÓÐÎÊÌâ
matlab¿ÉÒÔ×öµÄ
¼ûÏÂÃæµÄÀý×Ó
CODE:
x=rand(1,7);
y1=2*x+3*sin(x)+6*x.^2;
y2=2*x+3*cos(x)+2*x.^2;%²ÎÊý 2 3 6 2Ç°Ãæ2 3¹²ÓÃ
F=@(p,x)[p(1)*x+p(2)*sin(x)+p(3)*x.^2;p(1)*x+p(2)*cos(x)+p(4)*x.^2];
p = lsqcurvefit(F, [1 1 1 1], x,[y1;y2])

Local minimum found.

Optimization completed because the size of the gradient is less than
the default value of the function tolerance.




p =

    2.0000    3.0000    6.0000    2.0000
The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
14Â¥2011-11-30 00:26:50
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
ÆÕͨ»ØÌû

seaharrier

Ìú¸Ëľ³æ (ÖªÃû×÷¼Ò)

µÛ¹ú¿Õ¾üÖн«

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

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¿ÉÒԲο¼Ò»Ï¿´¿´ÊÇ·ñ¿ÉÐС£
Patienceisbitter,butitsfruitissweet.
2Â¥2011-11-25 13:02:45
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dbb627

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¡¾´ð°¸¡¿Ó¦Öú»ØÌû

¡ï ¡ï ¡ï
cenwanglai(½ð±Ò+3): ~~ 2011-12-22 20:07:18
origin²»³£Óã¬matlab¿ÉÒÔÄâºÏ³ö½ÏºÃµÄ½á¹û
´úÂëÈçÏÂ
CODE:
A=[0.1001       3.5e06
0.1002       3.3e06
0.11         2.9e05
0.12        9.0e04
0.15        1.5e04
0.2        3.3e03
0.3        7.1e02
0.4        2.8e02
0.5        1.5e02
0.6        8.9e01];
x=A(:,1);y=A(:,2);
st_ = [18.5 0.095 -2.3];
ft_ = fittype('A*(x-xc).^p','dependent',{'y'},'independent',{'x'},'coefficients',{'A', 'xc','p'});
[cf_,good]= fit(x,y,ft_ ,'Startpoint',st_)
h_ = plot(cf_,'fit',0.95);
legend off;  % turn off legend from plot method call
set(h_(1),'Color',[1 0 0],...
     'LineStyle','-', 'LineWidth',2,...
     'Marker','none', 'MarkerSize',6);
hold on,plot(x,y,'*')

cf_ =

     General model:
     cf_(x) = A*(x-xc).^p
     Coefficients (with 95% confidence bounds):
       A =       111.5  (11.4, 211.6)
       xc =     0.09683  (0.09604, 0.09762)
       p =      -1.809  (-2.04, -1.578)

good =

           sse: 3.8499e+008
       rsquare: 1.0000
           dfe: 7
    adjrsquare: 1.0000
          rmse: 7.4161e+003
The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
3Â¥2011-11-25 20:14:26
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dbb627

ÈÙÓþ°æÖ÷ (ÖøÃûдÊÖ)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

ͼÈçÏÂ


The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
4Â¥2011-11-25 20:18:15
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

glazio

Ìú³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
2Â¥: Originally posted by seaharrier at 2011-11-25 13:02:45:
ÎÒÒ²²»»á£¬
ÊÔÁËһϣ¬Ñ¡ÔñPower2¿ÉÒÔÄâºÏ£¬µ«ÊÇϵÊý¸úÄã¸øµÄ²»Ò»Ñù£¬
¿ÉÒԲο¼Ò»Ï¿´¿´ÊÇ·ñ¿ÉÐС£

ºÃµÄ£¬ÎÒÔÙÈ¥ÊÔÒ»ÏÂpowerÀàÀïÆäËûº¯ÊýµÄÄâºÏ£¬¿´¿´Äܲ»Äܽâ¾ö¡£Ð»Ð»ÄãµÄ½¨Òé¡£
5Â¥2011-11-25 20:40:31
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

glazio

Ìú³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
3Â¥: Originally posted by dbb627 at 2011-11-25 20:14:26:
origin²»³£Óã¬matlab¿ÉÒÔÄâºÏ³ö½ÏºÃµÄ½á¹û
´úÂëÈçÏÂ
[code]


A=[0.1001       3.5e06
0.1002       3.3e06
0.11         2.9e05
0.12        9.0e04
0.15        1.5e04
0.2        3.3e03
0.3     ...

Dbb627°æÖ÷µÄMatlabÄâºÏ´úÂëºÜÏêϸ£¬ÎÒÓÃÄãÄâºÏµÃµ½µÄ²ÎÊý[A, xc, p] = [111.5 0.09683 -1.809 ]´øÈ빫ʽy=A*(x-xc)^p¼ÆËã³öµÄ½á¹û(Fitted)£¬ºÍԭʼÊý¾Ý(Data)Ò»Æð×÷semilogͼÈçÏ¡£½«FittedºÍData¶Ô±È¿É¼û£¬¿ÉÄÜÔÚÄâºÏµÄ¹ý³ÌÖÐûÓвÉÓÃÈ¨ÖØw_i=1/y_i^2£¬ËùÒÔÄâºÏ¶ÔsseµÄ¿ØÖÆÖ»¼¯ÖÐÔڽϴóµÄy_iÊý¾Ý²¿·Ö£¬¶øÔÚ½ÏСµÄy_iÈ´Æ«À뿪ÁË¡£¶ÔÓÚÕâ¸öÎÊÌâÎÒÒÔǰ³¢ÊÔ½«¹«Ê½Á½±ßÈ¡¶ÔÊýºóÔÙ×öMatlabÄâºÏ£¬ÕâÑùµÄЧ¹ûµÄÈ·½ÏºÃ¡£ÁíÍâÎÒÏë¿ÉÒÔÒ²Ðí²ÉÈ¡È¨ÖØw_i=1/y_i^2µÄ·½·¨°É£¬µ«Ã»ÊÔ¹ý²»Çå³þ¡£

´ËǰÎÒÊÇÓÃMatlabµÄCftoolÄâºÏ£¨ÎªÁËÄâºÏ²Å´ÖdzµÄѧÁ˵ãMatlab£©£¬ÓÉÓÚÏÖÔÚÐèÒªÓÃÒ»¸ö·½³Ì¶Ô¶à×éÊý¾ÝÄâºÏ£¬Õâ¾ÍÐèÒª²ÉÓÃÄâºÏ²ÎÊý¹²ÏíµÄ·½·¨ÁË£¬¼´originËùÐû³ÆµÄGlobal Nonlinear Curve Fitting¡£

ÔÚ´ÎÏëÇë½ÌDbb627°æÖ÷£¬
1. ÎÒµÄÄ¿µÄÊǽâ¾öÄâºÏ²ÎÊý¹²ÏíµÄÎÊÌ⣬²ÅͶÈëOriginµÄ»³±§µÄ¡£ÇëÎÊMatlabĿǰÓнâ¾öÕâ¸öÎÊÌâµÄ·½°¸Ã´£¿Èç¹ûÓеϰÇëÌáʾһ¶þ¡£
2. ½ÓÏÂÀ´²ÉÓõķ½³Ì²»¿ÉÄÜÌ«¼òµ¥£¬ËùÒÔÖ±½ÓÈ¥¶ÔÊýÕâÌõ·²»ÄÜÒ»Ö±×ßµ½ºÚ¡£Òò´ËÈôÖ±½ÓÓÃMatlab¶Ôy=A*(x-xc)^pÔ­·½³ÌÄâºÏ¹ý³ÌÖУ¬²ÉÓÃÈ¨ÖØw_i=1/y_i^2¿ÉÒÔÓÐЧÌá¸ßÄâºÏ¾«¶Èô£¿MatlabÖ§³Ö£¨´úÂ뷽ʽ»òCftool·½Ê½£©ÕâÖÖÈ¨ÖØÂð£¿

Dbb627°æµÄMatlabÄâºÏ½á¹û

6Â¥2011-11-25 21:39:03
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dbb627

ÈÙÓþ°æÖ÷ (ÖøÃûдÊÖ)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

ÊÇ¿ÉÒÔ¸ÄÉÆµÄ
CODE:
A=[0.1001   3.5e06
0.1002      3.3e06
0.11        2.9e05
0.12        9.0e04
0.15        1.5e04
0.2        3.3e03
0.3        7.1e02
0.4        2.8e02
0.5        1.5e02
0.6        8.9e01];
x=A(:,1);y=A(:,2);
w=1./y;
opts=fitoptions('method','NonlinearLeastSquares','Weights',w.^2,'Lower',[-Inf 0  -Inf],'Upper',[Inf 1 0]);
opts.StartPoint= [10 0.095 -2.3];
ft_ = fittype('A*(x-xc).^p','dependent',{'y'},'independent',{'x'},'coefficients',{'A', 'xc','p'},'options',opts);
[cf_,good]= fit(x,y,ft_)
plot(x,log(cf_(x)),'or-',x, log(y), '* ');
legend('ÄâºÏͼ','ԭʼÊý¾Ý')

cf_ =

     General model:
     cf_(x) = A*(x-xc).^p
     Coefficients (with 95% confidence bounds):
       A =       18.46  (18.03, 18.88)
       xc =     0.09496  (0.09485, 0.09508)
       p =      -2.304  (-2.315, -2.292)

good =

           sse: 0.0010
       rsquare: 0.9999
           dfe: 7
    adjrsquare: 0.9998
          rmse: 0.0121
The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
7Â¥2011-11-25 23:22:39
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dbb627

ÈÙÓþ°æÖ÷ (ÖøÃûдÊÖ)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

cenwanglai: ~~ 2011-12-22 20:08:01
ÄâºÏ½á¹û¼ûͼ


The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
8Â¥2011-11-25 23:24:34
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

wypjyq

ľ³æ (ÕýʽдÊÖ)

ÒýÓûØÌû:
3Â¥: Originally posted by dbb627 at 2011-11-25 20:14:26:
origin²»³£Óã¬matlab¿ÉÒÔÄâºÏ³ö½ÏºÃµÄ½á¹û
´úÂëÈçÏÂ
[code]


A=[0.1001       3.5e06
0.1002       3.3e06
0.11         2.9e05
0.12        9.0e04
0.15        1.5e04
0.2        3.3e03
0.3     ...

°ßÖñ£¬ÎÊÏÂÄãÔÚÆ½Ê±×ö¼ÆËãµÄʱºòÔõôȷ¶¨²ÎÊýµÄ³õÖµ£¨st£©µÄ£¬ÎÒÿ´Î¶¼Òªµ÷ÊԺܾòÅÄÜÊÕÁ²µô¡£
9Â¥2011-11-26 22:08:31
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dbb627

ÈÙÓþ°æÖ÷ (ÖøÃûдÊÖ)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

Õâ¸öÒ»°ãÈç¹ûÕâ¸öʽ×ÓÓÐÃ÷ȷʵ¼ÊÒâÒ壬¾Í¸ù¾Ýʵ¼Ê¶¨·¶Î§£¬Èç¹ûûÓеϰ£¬¿´Äܲ»Äܱä³ÉÏßÐÔµÄÔÚÇó²ÎÊýµÄ·¶Î§£¬»¹Óиö·½·¨¾ÍÊÇÓÃÐ©Ëæ»úÈ«¾ÖÓÅ»¯Ë㷨ȷ¶¨³õÖµ£¬ÈçÒÅ´«Ëã·¨£¬ÍË»ðËã·¨µÈ
The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
10Â¥2011-11-26 23:35:39
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
Ïà¹Ø°æ¿éÌø×ª ÎÒÒª¶©ÔÄÂ¥Ö÷ glazio µÄÖ÷Ìâ¸üÐÂ
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[¿¼ÑÐ] 0832ʳƷ¿ÆÑ§Ó빤³Ìѧ˶282µ÷¼Á +6 ÓãÔÚË®ÖÐÓÎa 2026-04-02 9/450 2026-04-05 11:45 by flysky1234
[¿¼ÑÐ] ²ÄÁϹ¤³Ì302·ÖÇóµ÷¼Á +6 zyxÉϰ¶£¡ 2026-04-04 6/300 2026-04-05 07:57 by qlm5820
[¿¼ÑÐ] 11408 Ò»Ö¾Ô¸Î÷µç£¬277·ÖÇóµ÷¼Á +4 zhouzhen654 2026-04-03 4/200 2026-04-04 18:10 by Öí»á·É
[¿¼ÑÐ] 0856µ÷¼Á +8 ÇúÌýóÞ 2026-03-30 8/400 2026-04-04 08:46 by tianyyysss
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