离散点的三种积分方法

sigma665

1. u11_diff1=[-2.45201999620600e-11,-2.48250167183622e-11,-2.51007358917776e-11,-2.53394809061095e-11,-2.55318209608212e-11,-2.56664735613173e-11,-2.57299543117095e-11,-2.57061652072925e-11,-2.55759107158193e-11,-2.53163373659719e-11,-2.49002863080025e-11,-2.42955586583647e-11,-2.34640982271767e-11,-2.23610999901153e-11,-2.09340802800899e-11,-1.91219605931146e-11,-1.68542545215205e-11,-1.40505026465634e-11,-1.06201583513189e-11,-6.46322106523632e-12,-1.47200958997967e-12,4.46542446668152e-12,1.14596467192481e-11,1.96113043123626e-11,2.89990901319279e-11,3.96637551155679e-11,5.15880483213738e-11,6.46729547543299e-11,7.87111849739582e-11,9.33594688846403e-11,1.08111812132548e-10,1.22276849460840e-10,1.34964794283387e-10,1.45094967566822e-10,1.51444909273165e-10,1.52774264661495e-10,1.48058499572933e-10,1.36833062663733e-10,1.19556598056066e-10,9.77887436243853e-11,7.39705351919348e-11,5.07991711499344e-11,3.04856103100565e-11,1.42779545981162e-11,2.41957231848944e-12,-5.57957587064350e-12,-1.05961240755479e-11,-1.37676962078628e-11,-1.47901266615879e-11,-1.44238739430232e-11,-1.41962547121365e-11,-1.39198010987821e-11,-1.35849609711397e-11,-1.31859377313266e-11,-1.27165816828024e-11,-1.21705722502716e-11,-1.15415221608610e-11,-1.08231106707057e-11,-1.00092486810625e-11,-9.09427685632744e-12,-8.07319587030308e-12,-6.94192528954289e-12,-5.69758438998606e-12,-4.33878456440758e-12,-2.86591923355580e-12,-1.28143380278431e-12,4.09944175802256e-13,2.20103518337328e-12,4.08211719855967e-12,6.04092902704988e-12,8.06277487918258e-12,1.01307279460397e-11,1.22259195990620e-11,1.43278896282002e-11,1.64149633324322e-11,1.84646149980143e-11,2.04537758114532e-11,2.23590485971953e-11,2.41568025378204e-11,2.58231385184906e-11,2.73337401646698e-11,2.86636573232270e-11,2.97871078353309e-11,3.06774289924117e-11,3.13073578127846e-11,3.16498583133865e-11,3.16797227650062e-11,3.13761185757576e-11,3.07260922676372e-11,2.97287497921390e-11,2.83994318015006e-11,2.67728085658901e-11,2.49036433977237e-11,2.28642441510143e-11,2.07384203815561e-11,1.86128728194234e-11,1.77177662163107e-11,7.63703113724532e-12;];
   
2. dtt=[-1.35707362045903,-1.32850364950200,-1.29993367854497,-1.27136370758793,-1.24279373663090,-1.21422376567387,-1.18565379471684,-1.15708382375981,-1.12851385280277,-1.09994388184574,-1.07137391088871,-1.04280393993168,-1.01423396897464,-0.985663998017613,-0.957094027060580,-0.928524056103548,-0.899954085146516,-0.871384114189484,-0.842814143232452,-0.814244172275420,-0.785674201318387,-0.757104230361355,-0.728534259404323,-0.699964288447291,-0.671394317490259,-0.642824346533226,-0.614254375576194,-0.585684404619162,-0.557114433662130,-0.528544462705098,-0.499974491748066,-0.471404520791033,-0.442834549834001,-0.414264578876969,-0.385694607919937,-0.357124636962905,-0.328554666005872,-0.299984695048840,-0.271414724091808,-0.242844753134776,-0.214274782177744,-0.185704811220712,-0.157134840263679,-0.128564869306647,-0.0999948983496151,-0.0714249273925829,-0.0428549564355507,-0.0142849854785185,0.0142849854785136,0.0428549564355458,0.0714249273925780,0.0999948983496102,0.128564869306642,0.157134840263675,0.185704811220707,0.214274782177739,0.242844753134771,0.271414724091803,0.299984695048835,0.328554666005868,0.357124636962900,0.385694607919932,0.414264578876964,0.442834549833996,0.471404520791028,0.499974491748061,0.528544462705093,0.557114433662125,0.585684404619157,0.614254375576189,0.642824346533222,0.671394317490254,0.699964288447286,0.728534259404318,0.757104230361350,0.785674201318382,0.814244172275415,0.842814143232447,0.871384114189479,0.899954085146511,0.928524056103543,0.957094027060575,0.985663998017608,1.01423396897464,1.04280393993167,1.07137391088870,1.09994388184574,1.12851385280277,1.15708382375980,1.18565379471683,1.21422376567387,1.24279373663090,1.27136370758793,1.29993367854496,1.32850364950199,1.35707362045903,1.38564359141606,1.41421356237309;];
   
3. 
   
4. LL=2.828;
   
5. 
   
6. Q=trapz(dtt,u11_diff1);%梯形积分
   
7. 
   
8. f=inline('interp1(dtt,u11_diff1,t,''spline'')','t','dtt','u11_diff1');
   
9. QQ=quadl(f,-LL/2,LL/2,1e-8,[],dtt,u11_diff1);%插值积分
   
10. 
    
11. sp=csapi(dtt,u11_diff1);b=fnint(sp,1);xx=fnval(b,[-LL/2,LL/2]);
    
12. QQQ=xx(2)-xx(1);%样条积分
    
13. 
    

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>> Q
Q =
  5.4229e-011
>> QQ
QQ =
  2.2316e-011
>> QQQ
QQQ =
  5.2895e-011

第一和第三个相差不大
可是第2个怎么差这么大
主要还是对inline函数不了解，不知道为什么

附图

[ 本帖最后由 sigma665 于 2008-8-17 16:55 编辑 ]

sigma665

1. dtt=sort(rand(1,100));
   
2. u11_diff1=rand(1,100)*10;
   
3. 
   
4. Q=trapz(dtt,u11_diff1);%梯形积分
   
5. 
   
6. f=inline('interp1(dtt,u11_diff1,t,''spline'')','t','dtt','u11_diff1');
   
7. QQ=quadl(f0,1,1e-8,[],dtt,u11_diff1);%插值积分
   
8. 
   
9. sp=csapi(dtt,u11_diff1);b=fnint(sp,1);xx=fnval(b，[0,1]);
   
10. QQQ=xx(2)-xx(1);%样条积分

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但是，对于其他的数据，得到的结果却又相差不大
真奇怪

sigma665

知道了
把值乘1e11，就好了