數(shù)學(xué)建模集訓(xùn)答案

生成一個(gè)10個(gè)數(shù)據(jù)的隨機(jī)向量，繪制對(duì)應(yīng)的直方圖，并把畫出的圖形保存為jpg文件。程序r=rand(10);hist(r);結(jié)果2.用Lingo編程求解下列最小值問題，程序model:sets:in1/1..5/:a;in2/1..4/:b;endsetsdata:a=01234;b=2467;enddatamin=w-n-p;w=4*x1^3;p=2*x2;@for(in1:n=a*x1);x1+x2<=4;2*x1+x2<=5;@for(in2:-x1+b*x2>=2);end結(jié)果Globaloptimalsolutionfound.Objectivevalue:-8.000000Extendedsolversteps:0Totalsolveriterations:0VariableValueReducedCostW0.0000000.000000N0.0000000.000000P8.0000000.000000X10.0000001.000000X24.0000000.000000A(1)0.0000000.000000A(2)1.0000000.000000A(3)2.0000000.000000A(4)3.0000000.000000A(5)4.0000000.000000B(1)2.0000000.000000B(2)4.0000000.000000B(3)6.0000000.000000B(4)7.0000000.000000RowSlackorSurplusDualPrice1-8.000000-1.00000020.000000-1.00000030.0000001.00000040.0000000.00000050.0000001.00000060.0000000.00000070.0000000.00000080.0000000.00000090.0000002.000000101.0000000.000000116.0000000.0000001214.000000.0000001322.000000.0000001426.000000.000000用Lingo編程求解下列最小值問題，它的最小值為-83.已知經(jīng)管、汽車、信息、材化、計(jì)算機(jī)、土建、機(jī)械學(xué)院7個(gè)學(xué)院學(xué)生四門基礎(chǔ)課（數(shù)學(xué)，物理，英語，計(jì)算機(jī)）的平均成績(jī)見表10。試對(duì)學(xué)生成績(jī)進(jìn)行評(píng)價(jià)。表8基礎(chǔ)課平均成績(jī)表經(jīng)管汽車信息材化計(jì)算機(jī)土建機(jī)械數(shù)學(xué)62.0362.4878.5272.1274.1873.9566.83物理59.4763.7072.3873.2867.0768.3276.04英語68.1761.0475.1777.6867.7470.0976.87計(jì)算機(jī)72.4568.1774.6570.7770.4368.7373.181、現(xiàn)以7個(gè)學(xué)院都學(xué)習(xí)的四門基礎(chǔ)課成績(jī)?yōu)橐罁?jù),對(duì)7個(gè)學(xué)院成績(jī)好壞的相關(guān)程度分類。設(shè)7個(gè)學(xué)院組成一個(gè)分類集合:，分別代表經(jīng)管、汽車、信息、材化、計(jì)算機(jī)、土建、機(jī)械學(xué)院。每個(gè)學(xué)院成績(jī)均采用都學(xué)習(xí)的四門基礎(chǔ)課(工程數(shù)學(xué)、大學(xué)物理、高等數(shù)學(xué)、大學(xué)數(shù)學(xué))作為四項(xiàng)統(tǒng)計(jì)指標(biāo),即有:這里表示為第個(gè)學(xué)院的第門基礎(chǔ)課指標(biāo)，這四項(xiàng)成績(jī)指標(biāo)為:工程數(shù)學(xué)平均成績(jī)(),大學(xué)物理平均成績(jī)(),高等數(shù)學(xué)平均成績(jī)(),大學(xué)英語平均成績(jī)()。各專業(yè)成績(jī)指標(biāo)值見表1。表17個(gè)學(xué)院四門功課成績(jī)指標(biāo)學(xué)院（指標(biāo)/分）經(jīng)管汽車信息材化計(jì)算機(jī)土建機(jī)械62.0362.4878.5272.1274.1873.9566.8359.4763.7072.3873.2867.0768.3276.0468.1761.0475.1777.6867.7470.0976.8772.4568.1774.6570.7770.4368.7373.182、數(shù)據(jù)表準(zhǔn)化采用極差變換式中:是第個(gè)學(xué)院第門基礎(chǔ)課平均成績(jī)的原始數(shù)據(jù),和分別為不同學(xué)院的同一門基礎(chǔ)課平均成績(jī)的最大值和最小值。為第個(gè)學(xué)院第門基礎(chǔ)課平均成績(jī)指標(biāo)的標(biāo)準(zhǔn)化數(shù)值。當(dāng)時(shí),當(dāng)時(shí),。按上述公式計(jì)算得到7個(gè)學(xué)院四門基礎(chǔ)課成績(jī)指標(biāo)的標(biāo)準(zhǔn)化數(shù)值見表2。表2平均成績(jī)指標(biāo)值的標(biāo)準(zhǔn)化數(shù)值學(xué)院（指標(biāo)/分）經(jīng)管汽車信息材化計(jì)算機(jī)土建機(jī)械00.027310.61190.73680.72290.291100.25530.77910.83850.45870.534110.428500.849210.39660.54390.95130.6605010.40120.34880.08640.77313、用最大最小法建立相似矩陣計(jì)算模糊相似矩陣,根據(jù)標(biāo)準(zhǔn)化數(shù)值建立各學(xué)院之間四門基礎(chǔ)課成績(jī)指標(biāo)的相似關(guān)系矩陣。采用最大最小法來計(jì)算,其計(jì)算公式其中:是表示第個(gè)學(xué)院與第個(gè)學(xué)院在四門基礎(chǔ)課成績(jī)指標(biāo)上相似程度的量。將表2中標(biāo)準(zhǔn)化數(shù)值代入公式(2),可計(jì)算得到7個(gè)學(xué)院四門基礎(chǔ)課成績(jī)指標(biāo)的相似關(guān)系矩陣。4、改造相似關(guān)系為等價(jià)關(guān)系進(jìn)行聚類分析可知,全部元素分為一類:{u1,u2,u3,u4,u5,u6,u7}。從以上分類可以得到如下聚類分析當(dāng)0.77<K≤1時(shí),將U分為7類:{經(jīng)管},{汽車},{土建},{計(jì)算機(jī)},{信息},{材化},{機(jī)械}。當(dāng)0.73<K≤0.77時(shí),將U分為6類:{經(jīng)管},{汽車},{信息,材化},{計(jì)算機(jī)},{土建},{機(jī)械}。當(dāng)0.69<K≤0.73時(shí),將U分為5類:{經(jīng)管},{汽車},{信息,材化},{計(jì)算機(jī)},{土建,機(jī)械}。當(dāng)0.61<K≤0.69時(shí),將U分為4類:{經(jīng)管},{汽車},{信息,材化},{計(jì)算機(jī),土建,機(jī)械}。當(dāng)0.36<K≤0.61時(shí),將U分為3類:{經(jīng)管},{汽車},{信息,計(jì)算機(jī),土建,材化,機(jī)械}。當(dāng)0.15<K≤0.36時(shí),將U分為2類:{汽車}{經(jīng)管,土建,計(jì)算機(jī),信息,材化,機(jī)械}。當(dāng)0<K≤0.15時(shí),將U分為1類:{經(jīng)管,汽車,土建,計(jì)算機(jī),信息,材化,機(jī)械}。按不同的置信水平對(duì)7個(gè)學(xué)院進(jìn)行模糊聚類,將會(huì)得到不同的分類結(jié)果,聚類如圖對(duì)所得聚類結(jié)果進(jìn)行分析:在上面分類結(jié)果中,按0.77<K≤1進(jìn)行分類,由于過分強(qiáng)調(diào)7個(gè)學(xué)院在四門基礎(chǔ)課成績(jī)指標(biāo)上的差異,而沒有注意到各指標(biāo)的相互影響關(guān)系,沒有真正起到分類的作用,因而不可取。按0.36<K≤0.61和0.15<K≤0.36以及0<K≤0.15分類又完全忽視了7個(gè)學(xué)院在成績(jī)上所表現(xiàn)出的各種差異分類太粗。本例的模糊聚類按0.73<K≤0.77、0.69<K≤0.73、0.61<K≤0.69分類比較不僅將具有相同特征的學(xué)院歸并到了一塊,而且還將不同特征的學(xué)院區(qū)分開來。學(xué)院成績(jī)的分類利于學(xué)院成績(jī)的比較、排隊(duì)。通過對(duì)02級(jí)七個(gè)學(xué)院四門基礎(chǔ)課成績(jī)所做的分析,可以了解到信息、材化這兩個(gè)學(xué)院的學(xué)生成績(jī)較高;土建、機(jī)械、計(jì)算機(jī)這三個(gè)學(xué)院比較接近,成績(jī)一般;經(jīng)營(yíng)、汽車學(xué)院的學(xué)生成績(jī)稍差一些。MATLAB代碼functionY=bzh1(X)[a,b]=size(X);C=max(X);D=min(X);Y=zeros(a,b);fori=1:aforj=1:bY(i,j)=(X(i,j)-D(j))/(C(j)-D(j));%平移極差變化進(jìn)行數(shù)據(jù)標(biāo)準(zhǔn)化endfprintf('標(biāo)準(zhǔn)化矩陣如下：Y=\n');disp(Y)endY=bzh1(X)functionR=biaod2(Y,c)[a,b]=size(Y);Z=zeros(a);R=zeros(a);fori=1:aforj=1:afork=1:bZ(i,j)=abs(Y(i,k)-Y(j,k))+Z(i,j);R(i,j)=1-c*Z(i,j);%絕對(duì)值減數(shù)法--歐氏距離求模糊相似矩陣endendendfprintf('模糊相似矩陣如下：R=\n');disp(R)endR=biaod2(Y,0.1)functionB=cd3(R)a=size(R);B=zeros(a);flag=0;whileflag==0fori=1:aforj=1:afork=1:aB(i,j)=max(min(R(i,k),R(k,j)),B(i,j))%R與R內(nèi)積，先取小再取大endendendifB==Rflag=1;elseR=B;%循環(huán)計(jì)算R傳遞閉包endendB=cd3(R)function[Dk]=jjz4(B)L=unique(B)';a=size(B);D=zeros(a);form=length(L):-1:1k=L(m);fori=1:aforj=1:aifB(i,j)>=kD(i,j)=1;elseD(i,j)=0;%求?截距陣，當(dāng)bij≥?時(shí)，bij(?)=1；當(dāng)bij＜?時(shí)，bij(?)=0endendendfprintf('當(dāng)分類系數(shù)k=：\n');disp(L(m));fprintf('所得截距陣為：\n');disp(D);end[Dk]=jjz4(B)4.利用表4中的數(shù)據(jù)，求解下列問題（1）求關(guān)于的線性回歸方程，計(jì)算的估計(jì)值。程序[x1,x2]=[23.73005.490022.34004.320028.84005.040027.67004.720020.83005.350022.27004.270027.57005.250028.01004.620024.79004.420028.96005.300025.77004.870023.17005.800028.57005.220023.52005.180021.86004.860028.95005.180024.53004.880027.65005.020027.29005.550029.07005.260032.47005.180029.65005.080022.11004.900022.43004.6500]y=[15.020012.620014.860013.980015.910012.470015.800014.320013.760015.180014.200017.070015.400015.940014.330015.110013.810015.580015.850015.280016.400015.020015.730014.7500]x=[ones(24,1),x1,x2][b,bi,r,ri,s]=regress(y,x,0.05)結(jié)果b=2.26550.01732.4355計(jì)算的估計(jì)值分別為2.2655，0.0173，2.4355。分別利用Matlab的命令lsqcurvefit和nlinfit擬合非線性函數(shù)表4已知數(shù)據(jù)資料序號(hào)yx1x2序號(hào)yx1x2115.0223.735.491415.9423.525.18212.6222.344.321514.3321.864.86314.8628.845.041615.1128.955.18413.9827.674.721713.8124.534.88515.9120.835.351815.5827.655.02612.4722.274.271915.8527.295.55715.8027.575.252015.2829.075.26814.3228.014.622116.4032.475.18913.7624.794.422215.0229.655.081015.1828.965.302315.7322.114.901114.2025.774.872414.7522.434.651217.0723.175.801315.4028.575.22lsqcurvefit擬合非線性函數(shù)程序xdata=[23.73,5.49;22.344.32;28.84,5.04;27.67,4.72;20.83,5.35;22.27,4.27;27.57,5.25;28.01,4.62;24.79,4.42;28.96,5.30;25.77,4.87;23.17,5.80;28.57,5.22;23.52,5.18;21.86,4.86;28.95,5.18;24.53,4.88;27.65,5.02;27.29,5.55;29.07,5.26;32.47,5.18;29.65,5.08;22.11,4.90;22.43,4.65]ydata=[15.02,12.62,14.86,13.98,15.91,12.47,15.8,14.32,13.76,15.18,14.2,17.07,15.4,15.94,14.33,15.11,13.81,15.58,15.85,15.28,16.4,15.02,15.73,14.75];c0=[1:3];f=@(c,xdata)exp(c(1).*xdata(:,1)).*sin(c(2).*xdata(:,2))+c(3).*xdata(:,1).*cos(xdata(:,2));[c,resnorm]=lsqcurvefit(f,x0,xdata,ydata')結(jié)果c=0.11811.83251.3808nlinfit擬合非線性函數(shù)程序functionyy=fn(beta,x)a=beta(1)b=beta(2)c=beta(3)x1=x(:,1);x2=x(:,2);yy=exp(beta(1)*x1).*sin(beta(2)*x2)+beta(3)*x1.*cos(x2);x=[23.73005.490022.34004.320028.84005.040027.67004.720020.83005.350022.27004.270027.57005.250028.01004.620024.79004.420028.96005.300025.77004.870023.17005.800028.57005.220023.52005.180021.86004.860028.95005.180024.53004.880027.65005.020027.29005.550029.07005.260032.47005.180029.65005.080022.11004.900022.43004.6500]y=[15.020012.620014.860013.980015.910012.470015.800014.320013.760015.180014.200017.070015.400015.940014.330015.110013.810015.580015.850015.280016.400015.020015.730014.7500]beta0=[1,1,1]';[beta,r,j]=nlinfit(x,y,@fn,beta0)beta=0.1496,0.6039,1.1878生成一個(gè)10個(gè)數(shù)據(jù)的隨機(jī)向量，繪制對(duì)應(yīng)的直方圖，并把畫出的圖形保存為jpg文件。程序r=rand(1，10);hist(r);圖形2.用Lingo編程求解下列最小值問題，程序model:sets:in1/1..5/:a;in2/1..4/:b;endsetsdata:a=01234;b=2467;enddatamin=w-n-p;w=4*x1^3;p=2*x2;@for(in1:n=a*x1);x1+x2<=4;2*x1+x2<=5;@for(in2:-x1+b*x2>=2);End結(jié)果Globaloptimalsolutionfound.Objectivevalue:-8.000000Extendedsolversteps:0Totalsolveriterations:0VariableValueReducedCostW0.0000000.000000N0.0000000.000000P8.0000000.000000X10.0000001.000000X24.0000000.000000A(1)0.0000000.000000A(2)1.0000000.000000A(3)2.0000000.000000A(4)3.0000000.000000A(5)4.0000000.000000B(1)2.0000000.000000B(2)4.0000000.000000B(3)6.0000000.000000B(4)7.0000000.0000003.已知經(jīng)管、汽車、信息、材化、計(jì)算機(jī)、土建、機(jī)械學(xué)院7個(gè)學(xué)院學(xué)生四門基礎(chǔ)課（數(shù)學(xué)，物理，英語，計(jì)算機(jī)）的平均成績(jī)見表10。試對(duì)學(xué)生成績(jī)進(jìn)行評(píng)價(jià)。表基礎(chǔ)課平均成績(jī)表經(jīng)管汽車信息材化計(jì)算機(jī)土建機(jī)械數(shù)學(xué)62.0362.4878.5272.1274.1873.9566.83物理59.4763.7072.3873.2867.0768.3276.04英語68.1761.0475.1777.6867.7470.0976.87計(jì)算機(jī)72.4568.1774.6570.7770.4368.7373.18現(xiàn)以7個(gè)學(xué)院都學(xué)習(xí)的四門基礎(chǔ)課成績(jī)?yōu)橐罁?jù),對(duì)7個(gè)學(xué)院成績(jī)好壞的相關(guān)程度分類。設(shè)7個(gè)學(xué)院組成一個(gè)分類集合:，分別代表經(jīng)管、汽車、信息、材化、計(jì)算機(jī)、土建、機(jī)械學(xué)院。每個(gè)學(xué)院成績(jī)均采用都學(xué)習(xí)的四門基礎(chǔ)課(工程數(shù)學(xué)、大學(xué)物理、高等數(shù)學(xué)、大學(xué)數(shù)學(xué))作為四項(xiàng)統(tǒng)計(jì)指標(biāo),即有:這里表示為第個(gè)學(xué)院的第門基礎(chǔ)課指標(biāo)這四項(xiàng)成績(jī)指標(biāo)為:工程數(shù)學(xué)平均成績(jī)(),大學(xué)物理平均成績(jī)(),高等數(shù)學(xué)平均成績(jī)(),大學(xué)英語平均成績(jī)()。各專業(yè)成績(jī)指標(biāo)值見表1。表17個(gè)學(xué)院四門功課成績(jī)指標(biāo)學(xué)院（指標(biāo)/分）經(jīng)管汽車信息材化計(jì)算機(jī)土建機(jī)械62.0362.4878.5272.1274.1873.9566.8359.4763.7072.3873.2867.0768.3276.0468.1761.0475.1777.6867.7470.0976.8772.4568.1774.6570.7770.4368.7373.18步驟一數(shù)據(jù)規(guī)格化采用極差變換是第個(gè)學(xué)院第門基礎(chǔ)課平均成績(jī)的原始數(shù)據(jù)，和分別為不同學(xué)院的同一門基礎(chǔ)課平均成績(jī)的最大值和最小值。為第個(gè)學(xué)院第門基礎(chǔ)課平均成績(jī)指標(biāo)的標(biāo)準(zhǔn)化數(shù)值。當(dāng)時(shí),當(dāng)時(shí)，。按上述公式利用MATLAB編程（程序1），計(jì)算得到7個(gè)學(xué)院四門基礎(chǔ)課成績(jī)指標(biāo)的標(biāo)準(zhǔn)化數(shù)值見表2。表27個(gè)學(xué)院四門課標(biāo)準(zhǔn)化值學(xué)院（指標(biāo)/分）經(jīng)管汽車信息材化計(jì)算機(jī)土建機(jī)械00.027310.61190.73680.72290.291100.25530.77910.83850.45870.534110.428500.849210.39660.54390.95130.6605010.40120.34880.08640.7731步驟二用最大最小法建立相似矩陣計(jì)算模糊相似矩陣,根據(jù)標(biāo)準(zhǔn)化數(shù)值建立各學(xué)院之間四門基礎(chǔ)課成績(jī)指標(biāo)的相似關(guān)系矩陣。采用最大最小法來計(jì)算,其計(jì)算公式是表示第個(gè)學(xué)院與第個(gè)學(xué)院在四門基礎(chǔ)課成績(jī)指標(biāo)上相似程度的量。根據(jù)計(jì)算公式,通過MATLAB編寫程序（程序2），可計(jì)算得到7個(gè)學(xué)院四門基礎(chǔ)課成績(jī)指標(biāo)的相似關(guān)系矩陣。步驟三利用平方自合成方法求傳遞閉包矩陣滿足自反性和對(duì)稱性,但不具有傳遞性,為求等價(jià)矩陣,要對(duì)進(jìn)行改造,只需求其傳遞閉包。利用MATLAB編寫程序（程序3），由程序可得最后得到，故傳遞閉包為，即模糊等價(jià)關(guān)系矩陣。采用等價(jià)關(guān)系矩陣可對(duì)7個(gè)學(xué)院進(jìn)行聚類分析。模糊聚類程序data=[62.03,59.47,68.17,72.45;62.48,63.70,61.04,68.17;78.52,72.38,75.17,74.65;72.12,73.28,77.68,70.77;74.18,67.07,67.74,70.43;73.95,68.32,70.09,68.73;66.83,76.04,76.87,73.18];A=data;[NM]=size(A);fori=1:Nforj=1:NR(i,j)=abs(1-sum(abs(A(i,:)-A(j,:)))/sum(max([A(i,:);A(j,:)])));endendforj=1:7fori=1:7y(i,j)=0;fork=1:7mn(k)=min(R(i,k),R(k,j));endy(i,j)=max(mn);endendnumda=[10.90.950.850.80.750.550.7];fori=1:7TT(i)=i;endfori=1:length(numda)disp('當(dāng)分類系數(shù)是');disp(numda(i));a=numda(i);T=TT;disp('分類為');while1if~isempty(T)xi=T(1);endX=[];Q=[];while2forj=1:7if(y(xi,j)>=a)&isempty(intersect(X,j))X=union(X,j);Q(length(Q)+1)=j;endendifisempty(Q)disp(X);breakelsexi=Q(1);Q(1)=[];endendT=setdiff(T,X)ifisempty(T)breakendendend結(jié)果：當(dāng)分類系數(shù)是0.9000分類為1234567當(dāng)分類系數(shù)是0.9500分類為1234756當(dāng)分類系數(shù)是0.8500分類為1234567當(dāng)分類系數(shù)是0.8000分類為1234567當(dāng)分類系數(shù)是0.7500分類為1234567圖形程序1%數(shù)據(jù)規(guī)格化MATLAB程序a=[62.0362.4878.5272.1274.1873.9566.83;59.4763.7072.3873.2867.0768.3276.04;68.1761.0475.1777.6867.7470.0976.87;72.4568.1774.6570.7770.4368.7373.18];mu=max(a)fori=i:4forj=1:7r(i,j)=a(i,j)/mu(j);endendr程序2%采用最大最小法構(gòu)造相似矩陣b=r';fori=1:7forj=1:7R(i,j)=sum(min([r(i,:);b(:,j)']))/sum(max([r(i,:);b(:,j)']));endendR程序3%利用平方自合成方法求傳遞閉包functionrhat=hech(r);n=length(r);fori=1:nforj=1:nrhat(i,j)=max(min([r(i,:);r(:,j)']));endend4.利用表4中的數(shù)據(jù)，求解下列問題（1）求關(guān)于的線性回歸方程，計(jì)算的估計(jì)值。程序x1=[23.73,22.34,28.84,27.67,20.83,22.27,27.57,28.01,24.79,28.96,25.77,23.17,28.57,23.52,21.86,28.95,24.53,27.65,27.29,29.07,32.47,29.65,22.11,22.43];x2=[5.49,4.32,5.04,4.72,5.35,4.27,5.25,4.62,4.42,5.3,4.87,5.80,5.22,5.18,4.86,5.18,4.88,5.02,5.55,5.26,5.18,5.08,4.9,4.65];ydata=[15.02,12.62,14.86,13.98,15.91,12.47,15.8,14.32,13.76,15.18,14.2,17.07,15.4,15.94,14.33,15.11,13.81,15.58,15.85,15.28,16.4,15.02,15.73,14.75];x=[ones(24,1),x1,x2][b,bi,r,rint,s]=regress(y,x,0.05)結(jié)果b=2.26550.01732.4355得到關(guān)于的線性回歸方程：分別利用Matlab的命令lsqcurvefit和nlinfit擬合非線性函數(shù)表4已知數(shù)據(jù)資料序號(hào)yx1x2序號(hào)yx1x2115.0223.735.491415.9423.525.18212.6222.