計(jì)量地理實(shí)驗(yàn)報(bào)告

PAGEPAGE2計(jì)量地理學(xué)實(shí)驗(yàn)報(bào)告班級：地理092學(xué)號：2009011134組別：姓名：鄭德欣山東建筑大學(xué)土木工程學(xué)院二零一一年十一月實(shí)驗(yàn)須知實(shí)驗(yàn)是配合課堂教學(xué)的一個(gè)重要教學(xué)環(huán)節(jié)，同時(shí)也是培養(yǎng)學(xué)生掌握實(shí)驗(yàn)的基本技能和進(jìn)行基本訓(xùn)練的一個(gè)主要手段，為了保證實(shí)驗(yàn)的順利進(jìn)行，必須注意下列事項(xiàng)：1、實(shí)驗(yàn)之前，希望同學(xué)們要預(yù)習(xí)實(shí)驗(yàn)指導(dǎo)書，了解本次實(shí)驗(yàn)的目的，原理和要求：2、嚴(yán)格按操作步驟認(rèn)真操作，實(shí)驗(yàn)報(bào)告要客觀、詳細(xì)記錄實(shí)驗(yàn)步驟，實(shí)驗(yàn)成果等。3、愛護(hù)實(shí)驗(yàn)儀器，非本次實(shí)驗(yàn)用的儀器或雖是本次實(shí)驗(yàn)所用的儀器，但在老師沒有講解之前都不得隨便亂動，以免損壞儀器；4、實(shí)驗(yàn)中不慎損壞儀器或丟失儀器中的附件，均應(yīng)主動地告訴老師，按照有關(guān)規(guī)定處理；目錄實(shí)驗(yàn)一地理數(shù)據(jù)統(tǒng)計(jì)處理………1實(shí)驗(yàn)二統(tǒng)計(jì)分析方法……………3實(shí)驗(yàn)三線性規(guī)劃方法……………4實(shí)驗(yàn)四決策分析方法…………5實(shí)驗(yàn)一地理數(shù)據(jù)統(tǒng)計(jì)處理一、實(shí)驗(yàn)?zāi)康?.熟悉matlab的基本操作。2．掌握matlab的矩陣運(yùn)算。3．掌握matlab計(jì)算地理數(shù)據(jù)一般水平的各個(gè)指標(biāo)、離散水平的各個(gè)指標(biāo)、偏離程度的各個(gè)指標(biāo)4．掌握matlab的基本統(tǒng)計(jì)作圖。二、實(shí)驗(yàn)內(nèi)容1.熟悉matlab環(huán)境，并進(jìn)行基本的矩陣運(yùn)算。2.計(jì)算平均值、分組平均值、中位數(shù)、分組中位數(shù)、眾數(shù)。3.計(jì)算極差、離差、離差平方和、方差與標(biāo)準(zhǔn)差、變異系數(shù)。4.計(jì)算標(biāo)準(zhǔn)偏度系數(shù)、標(biāo)準(zhǔn)峰度系數(shù)。5．進(jìn)行統(tǒng)計(jì)作圖。三、實(shí)驗(yàn)方法與步驟打開matlab，重點(diǎn)熟悉命令窗口、工作空間窗口、歷史命令窗口、當(dāng)前工作目錄窗口的使用。運(yùn)用help命令查詢基本的矩陣運(yùn)算函數(shù)，明確各個(gè)參數(shù)的含義，以及函數(shù)的使用和輸出的結(jié)果，并代入數(shù)據(jù)進(jìn)行運(yùn)算。3.運(yùn)用help命令查詢平均值、中位數(shù)、眾數(shù)的計(jì)算函數(shù)的使用方法，并將Excel表格中的數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)，進(jìn)行計(jì)算并分析。4.運(yùn)用help命令查詢極差、離差、離差平方和、方差與標(biāo)準(zhǔn)差的計(jì)算函數(shù)的使用方法，并將Excel表格中的數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)，進(jìn)行計(jì)算并分析。5.運(yùn)用已有函數(shù)，計(jì)算分組平均值、分組中位數(shù)、變異系數(shù)。6.運(yùn)用help命令查詢計(jì)算標(biāo)準(zhǔn)偏度系數(shù)、標(biāo)準(zhǔn)峰度系數(shù)的計(jì)算函數(shù)的使用方法，并將Excel表格中的數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)，進(jìn)行計(jì)算并分析。7.運(yùn)用matlab函數(shù)進(jìn)行統(tǒng)計(jì)作圖。四、結(jié)果分析1.TABULATE（頻數(shù)/頻率/眾數(shù)）TABULATEFrequencytable.TABLE=TABULATE(X)takesavectorXandreturnsamatrix,TABLE.ThefirstcolumnofTABLEcontainstheuniquevaluesofX.Thesecondisthenumberofinstancesofeachvalue.Thelastcolumncontainsthepercentageofeachvalue.x=[2:0.1:6]x=Columns1through62.00002.10002.20002.30002.40002.5000Columns7through122.60002.70002.80002.90003.00003.1000Columns13through183.20003.30003.40003.50003.60003.7000Columns19through243.80003.90004.00004.10004.20004.3000Columns25through304.40004.50004.60004.70004.80004.9000Columns31through365.00005.10005.20005.30005.40005.5000Columns37through415.60005.70005.80005.90006.0000>>table=tabulate(x)table=2.00001.00002.43902.10001.00002.43902.20001.00002.43902.30001.00002.43902.40001.00002.43902.50001.00002.43902.60001.00002.43902.70001.00002.43902.80001.00002.43902.90001.00002.43903.00001.00002.43903.10001.00002.43903.20001.00002.43903.30001.00002.43903.40001.00002.43903.50001.00002.43903.60001.00002.43903.70001.00002.43903.80001.00002.43903.90001.00002.43904.00001.00002.43904.10001.00002.43904.20001.00002.43904.30001.00002.43904.40001.00002.43904.50001.00002.43904.60001.00002.43904.70001.00002.43904.80001.00002.43904.90001.00002.43905.00001.00002.43905.10001.00002.43905.20001.00002.43905.30001.00002.43905.40001.00002.43905.50001.00002.43905.60001.00002.43905.70001.00002.43905.80001.00002.43905.90001.00002.43906.00001.00002.43902.MEAN（平均值）MEANAverageormeanvalue.Forvectors,MEAN(X)isthemeanvalueoftheelementsinX.Formatrices,MEAN(X)isarowvectorcontainingthemeanvalueofeachcolumn.ForN-Darrays,MEAN(X)isthemeanvalueoftheelementsalongthefirstnon-singletondimensionofX.>>mean(x)ans=43.MEDIAN（中位數(shù)）MEDIANMedianvalue.Forvectors,MEDIAN(X)isthemedianvalueoftheelementsinX.Formatrices,MEDIAN(X)isarowvectorcontainingthemedianvalueofeachcolumn.ForN-Darrays,MEDIAN(X)isthemedianvalueoftheelementsalongthefirstnon-singletondimensionofX.>>median(x)ans=44.RANGE（極差）RANGESamplerange.Y=RANGE(X)returnstherangeofthevaluesinX.Foravectorinput,Yisthedifferencebetweenthemaximumandminimumvalues.Foramatrixinput,Yisavectorcontainingtherangeforeachcolumn.ForN-Darrays,RANGEoperatesalongthefirstnon-singletondimension.>>Y=range(x)Y=45.VARVariance.（方差）VARVariance.Forvectors,Y=VAR(X)returnsthevarianceofthevaluesinX.Formatrices,YisarowvectorcontainingthevarianceofeachcolumnofX.ForN-Darrays,VARoperatesalongthefirstnon-singletondimensionofX.>>y=var(x)y=1.43506.STDStandarddeviation.（標(biāo)準(zhǔn)差）STDStandarddeviation.Forvectors,Y=STD(X)returnsthestandarddeviation.Formatrices,Yisarowvectorcontainingthestandarddeviationofeachcolumn.ForN-Darrays,STDoperatesalongthefirstnon-singletondimensionofX.>>M=std(x)M=1.19797.SKEWNESSSkewness.（偏度系數(shù)）SKEWNESSSkewness.S=SKEWNESS(X)returnsthesampleskewnessofthevaluesinX.Foravectorinput,SisthethirdcentralmomentofX,dividedbythecubeofitsstandarddeviation.Foramatrixinput,SisarowvectorcontainingthesampleskewnessofeachcolumnofX.ForN-Darrays,SKEWNESSoperatesalongthefirstnon-singletondimension.>>S=skewness(x)S=-7.8465e-0178.KURTOSISKurtosis（峰度系數(shù)）.KURTOSISKurtosis.K=KURTOSIS(X)returnsthesamplekurtosisofthevaluesinX.Foravectorinput,KisthefourthcentralmomentofX,dividedbyfourthpowerofitsstandarddeviation.Foramatrixinput,KisarowvectorcontainingthesamplekurtosisofeachcolumnofX.ForN-Darrays,KURTOSISoperatesalongthefirstnon-singletondimension.>>K=kurtosis(x)K=1.7986實(shí)驗(yàn)二統(tǒng)計(jì)分析方法一、實(shí)驗(yàn)?zāi)康?.掌握相關(guān)分析的計(jì)算方法和計(jì)算函數(shù)。2．掌握回歸分析的計(jì)算方法和計(jì)算函數(shù)。3．掌握時(shí)間序列分析的方法和編程。4．掌握系統(tǒng)聚類分析的計(jì)算方法和計(jì)算函數(shù)。5．掌握主成分分析的計(jì)算方法和計(jì)算函數(shù)。6．掌握馬爾可夫預(yù)測的方法和編程。7．掌握趨勢面分析的計(jì)算方法和計(jì)算函數(shù)。8．掌握各種統(tǒng)計(jì)分析方法的結(jié)果檢驗(yàn)。二、實(shí)驗(yàn)內(nèi)容1.運(yùn)用corrcoef函數(shù)進(jìn)行相關(guān)分析，并分析計(jì)算結(jié)果。2．運(yùn)用regress函數(shù)進(jìn)行回歸分析，并進(jìn)行檢驗(yàn)。3．運(yùn)用matlab編程實(shí)現(xiàn)移動平均、滑動平均、二次指數(shù)平滑、線性自回歸。4．運(yùn)用zscore、pdist、linkage、dendrogram等函數(shù)進(jìn)行系統(tǒng)聚類分析，并分析計(jì)算結(jié)果。5．運(yùn)用princomp函數(shù)進(jìn)行主成分分析，并分析計(jì)算結(jié)果。6．運(yùn)用matlab編程實(shí)現(xiàn)馬爾可夫預(yù)測方法。7．運(yùn)用regress函數(shù)進(jìn)行趨勢面分析，并進(jìn)行檢驗(yàn)。三、實(shí)驗(yàn)方法與步驟（一）相關(guān)分析1.運(yùn)用help命令查詢corrcoef函數(shù)的使用方法。2.將Excel變量數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)矩陣A，調(diào)用命令：R=corrcoef(A)，計(jì)算各變量之間的相關(guān)系數(shù)矩陣。3.分析計(jì)算結(jié)果。（二）回歸分析1.運(yùn)用help命令查詢r(jià)egress函數(shù)的使用方法。2.將Excel變量數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)矩陣A。3.作出散點(diǎn)圖。4．運(yùn)用[b,bint,r,rint,stats]=regress(y,x)進(jìn)行計(jì)算，其中b是回歸方程中的參數(shù)估計(jì)值，bint是b的置信區(qū)間，r和rint分別表示殘差及殘差對應(yīng)的置信區(qū)間。stats包含三個(gè)數(shù)字，分別是相關(guān)系數(shù)，F(xiàn)統(tǒng)計(jì)量及對應(yīng)的概率p值。5.進(jìn)行檢驗(yàn)并分析計(jì)算結(jié)果。（三）時(shí)間序列分析1.將Excel變量數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)矩陣。2．編程計(jì)算移動平均、滑動平均、二次指數(shù)平滑、線性自回歸。3．分析計(jì)算結(jié)果。（四）系統(tǒng)聚類分析1.將Excel變量數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)矩陣。2．進(jìn)行標(biāo)準(zhǔn)化處理。3．計(jì)算距離。4．用linkage進(jìn)行聚類分析。5．做出聚類譜系圖。（五）主成分分析1.運(yùn)用help命令查詢primcomp函數(shù)的使用方法。2.將Excel變量數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)矩陣。3.運(yùn)用[pc,score,latent,t2]=princomp(X)進(jìn)行計(jì)算，其中①pc主分量fi的系數(shù)，也叫因子系數(shù)；注意：pcTpc=單位陣。②score是主分量下的得分值；得分矩陣與數(shù)據(jù)矩陣X的階數(shù)是一致的。③latent是score對應(yīng)列的方差向量，即A的特征值；容易計(jì)算方差所占的百分比。④t2表示檢驗(yàn)的t2-統(tǒng)計(jì)量（方差分析要用）4.分析計(jì)算結(jié)果。（六）馬爾可夫預(yù)測1.將Excel變量數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)矩陣。2．編程進(jìn)行馬爾可夫預(yù)測。3．分析計(jì)算結(jié)果。（七）趨勢面分析1.將Excel變量數(shù)據(jù)轉(zhuǎn)化成matlab數(shù)據(jù)矩陣。2．進(jìn)行矩陣計(jì)算和變換，化為二次、三次趨勢面分析的原始數(shù)據(jù)矩陣。3．運(yùn)用regress進(jìn)行計(jì)算。4．檢驗(yàn)計(jì)算結(jié)果。5．作出趨勢面圖：首先準(zhǔn)備數(shù)據(jù)；然后運(yùn)用meshgrid進(jìn)行變換；最后用mesh或surf等函數(shù)做圖。四、結(jié)果分析（一）相關(guān)分析CORRCOEFCorrelationcoefficients.R=CORRCOEF(X)calculatesamatrixRofcorrelationcoefficientsforanarrayX,inwhicheachrowisanobservationandeachcolumnisavariable.表格轉(zhuǎn)置：>>q=[3.80 4.00 5.80 8.00 11.30 14.40 16.50 16.20 13.80 10.80 6.70 4.70]q=Columns1through83.80004.00005.80008.000011.300014.400016.500016.2000Columns9through1213.800010.80006.70004.7000>>j=[77.70 51.20 60.10 54.10 55.40 56.80 45.00 55.30 67.50 73.30 76.60 79.60]j=Columns1through877.700051.200060.100054.100055.400056.800045.000055.3000Columns9through1267.500073.300076.600079.6000>>h=[q',j']h=3.800077.70004.000051.20005.800060.10008.000054.100011.300055.400014.400056.800016.500045.000016.200055.300013.800067.500010.800073.30006.700076.60004.700079.6000>>r=corrcoef(h)r=1.0000-0.4895-0.48951.0000>>[R,P]=CORRCOEF(h)Warning:FunctioncallCORRCOEFinvokesinexactmatchD:\matlab7\toolbox\matlab\datafun\corrcoef.m.R=1.0000-0.4895-0.48951.0000P=1.00000.10630.10631.0000因?yàn)閜=0.1063〉0.05所以不滿足條件（二）回歸分析REGRESSMultiplelinearregressionusingleastsquares.B=REGRESS(Y,X)returnsthevectorBofregressioncoefficientsinthelinearmodelY=X*B.Xisann-by-pdesignmatrix,withrowscorrespondingtoobservationsandcolumnstopredictorvariables.Yisann-by-1vectorofresponseobservations.>>y=[48.25193.72413.94……786.75584.89574.00]y=48.2500193.7200413.9400……786.7500584.8900574.0000>>x1=[40.5036.6035.53……34.2135.4336.14]x1=40.500036.600035.5300……34.210035.430036.1400>>x2=[1170.801707.201908.80……3362.701221.201111.70]x2=1.0e+003*1.17081.70721.9088……3.36271.22121.1117>>[B,BINT,R,RINT,STATS]=REGRESS(y,[ones(53,1)x1x2])Warning:FunctioncallREGRESSinvokesinexactmatchD:\matlab7\toolbox\stats\regress.m.B=1.0e+003*3.2951-0.08120.0000BINT=1.0e+003*2.88253.7078-0.0920-0.0704-0.00000.0001R=-1.7426-192.2752-66.2118……146.7975121.5216172.2303RINT=-179.3270175.8418-367.0625-17.4879-247.9691115.5456…………-16.8142310.4091-56.2909299.3340-1.9993346.4599STATS=1.0e+003*0.00080.119308.3189R2f值（三）多元非線性回歸（趨勢面分析）>>z=[27.638.4……44.9]z=27.600038.4000……44.9000>>x=[01.1……3.65]x=01.1000……3.6500>>y=[10.6……2.55]y=1.00000.6000……2.5500>>[B,BINT,R,RINT,STATS]=REGRESS(z,[ones(12,1)xyx.^2x.*yy.^2])B=5.998017.438229.7874-3.58830.3569-8.0695BINT=-18.528830.52480.760834.11557.440352.1346-7.22960.0530-3.58284.2966-13.1699-2.9691R=-0.11592.3589-1.7605-1.51332.31581.3295-1.45740.71832.5279-8.91778.2646-3.7500RINT=-9.16438.9324-9.980114.6978-11.75358.2324-13.027010.0005-6.880311.5119-7.29879.9577-14.333011.4181-10.463311.8998-5.898910.9546-16.4202-1.41511.302715.2265-10.04202.5420STATS=0.83866.23590.022731.5030R^2F值P值做趨勢面的三維圖首先對模型方程的xy賦值x=[0:0.2:4] X=X'Y=[1:0.2:5]Y=Y’Z=5.998+17.438*X+29.787*Y-3.558*X.^2+0.357*X.*Y-8.07*Y.^2在matlab中執(zhí)行這個(gè)方程得到Z對應(yīng)的值，然后做三維圖所用的函數(shù)方法是：方法一helpmeshgridMESHGRIDXandYarraysfor3-Dplots.[X,Y]=MESHGRID(x,y)transformsthedomainspecifiedbyvectorsxandyintoarraysXandYthatcanbeusedfortheevaluationoffunctionsoftwovariablesand3-Dsurfaceplots.TherowsoftheoutputarrayXarecopiesofthevectorxandthecolumnsoftheoutputarrayYarecopiesofthevectory.[X,Y]=MESHGRID(x)isanabbreviationfor[X,Y]=MESHGRID(x,x).[X,Y,Z]=MESHGRID(x,y,z)produces3-Darraysthatcanbeusedtoevaluatefunctionsofthreevariablesand3-Dvolumetricplots.由mesh(X,Y,Z)得方法2surf(X,Y,Z)（四）系統(tǒng)聚類分析1.>>x=[363.912141.503100.695143.739131.41268.33795.41662.90186.62491.39476.91251.27468.83177.30176.94899.265118.505141.473137.761117.612122.781]2.回車后得到一個(gè)21*9矩陣3.>>helpzscoreZSCOREStandardizedzscore.Z=ZSCORE(X)returnsacentered,scaledversionofX,knownastheZscoresofX.Foravectorinput,Z=(X-MEAN(X))./STD(X).Foramatrixinput,ZisarowvectorcontainingtheZscoresofeachcolumnofX.ForN-Darrays,ZSCOREoperatesalongthefirstnon-singletondimension.4.輸入>>z=zscore(x)得到標(biāo)準(zhǔn)差標(biāo)準(zhǔn)化的數(shù)據(jù)5.>>helppdist6.>>y=pdist(z)7.>>helplinkage8.>>z=linkage(y)z=9.000010.00000.457412.000013.00000.800617.000019.00000.933916.000024.00000.956522.000023.00000.972218.000025.00000.985215.000026.00001.048327.000028.00001.12897.000029.00001.181320.000030.00001.40676.00008.00001.480431.000032.00001.804121.000033.00001.93652.00005.00002.068711.000034.00002.14443.000014.00002.48414.000035.00002.674236.000037.00002.721338.000039.00002.88551.000040.00005.67949.>>helpdendrogram10.>>dendrogram(z)

實(shí)驗(yàn)三線性規(guī)劃方法一、實(shí)驗(yàn)?zāi)康?.熟悉matlab優(yōu)化工具箱。2．掌握線性規(guī)劃方法。二、實(shí)驗(yàn)內(nèi)容1.練習(xí)matlab優(yōu)化工具箱的相關(guān)函數(shù)。2.運(yùn)用linprog進(jìn)行線性規(guī)劃。三、實(shí)驗(yàn)方法與步驟1.運(yùn)用help命令查詢linprog函數(shù)的使用方法。2.建立線性規(guī)劃模型。3.運(yùn)用linprog進(jìn)行計(jì)算四、結(jié)果分析LINPROGLinearprogramming.X=LINPROG(f,A,b)attemptstosolvethelinearprogrammingproblem:minf'*xsubjectto:A*x<=bxX=LINPROG(f,A,b,Aeq,beq)solvestheproblemabovewhileadditionallysatisfyingtheequalityconstraintsAeq*x=beq.X=LINPROG(f,A,b,Aeq,beq,LB,UB)definesasetoflowerandupperboundsonthedesignvariables,X,sothatthesolutionisintherangeLB<=X<=UB.UseemptymatricesforLBandUBifnoboundsexist.SetLB(i)=-InfifX(i)isunboundedbelow;setUB(i)=InfifX(i)isunboundedabove.X=LINPROG(f,A,b,Aeq,beq,LB,UB,X0)setsthestartingpointtoX0.Thisoptionisonlyavailablewiththeactive-setalgorithm.Thedefaultinteriorpointalgorithmwillignoreanynon-emptystartingpoint.X=LINPROG(f,A,b,Aeq,beq,LB,UB,X0,OPTIONS)minimizeswiththedefaultoptimizationparametersreplacedbyvaluesinthestructureOPTIONS,anargumentcreatedwiththeOPTIMSETfunction.SeeOPTIMSETfordetails.OptionsareDisplay,Diagnostics,TolFun,LargeScale,MaxIter.Currently,only'final'and'off'arevalidvaluesfortheparameterDisplaywhenLargeScaleis'off'('iter'isvalidwhenLargeScaleis'on').[X,FVAL]=LINPROG(f,A,b)returnsthevalueoftheobjectivefunctionatX:FVAL=f'*X.[X,FVAL,EXITFLAG]=LINPROG(f,A,b)returnsanEXITFLAGthatdescribestheexitconditionofLINPROG.PossiblevaluesofEXITFLAGandthecorrespondingexitconditionsare1LINPROGconvergedtoasolutionX.0Maximumnumberofiterationsreached.-2Nofeasiblepointfound.-3Problemisunbounded.-4NaNvalueencounteredduringexecutionofalgorithm.-5Bothprimalanddualproblemsareinfeasible.-7Searchdirectionbecametoosmall;nofurtherprogresscanbemade.[X,FVAL,EXITFLAG,OUTPUT]=LINPROG(f,A,b)returnsastructureOUTPUTwiththenumberofiterationstakeninOUTPUT.iterations,thetypeofalgorithmusedinOUTPUT.algorithm,thenumberofconjugategradientiterations(ifused)inOUTPUT.cgiterations,andtheexitmessageinOUTPUT.message.[X,FVAL,EXITFLAG,OUTPUT,LAMBDA]=LINPROG(f,A,b)returnsthesetofLagrangianmultipliersLAMBDA,atthesolution:LAMBDA.ineqlinforthelinearinequalitiesA,LAMBDA.eqlinforthelinearequalitiesAeq,LAMBDA.lowerforLB,andLAMBDA.upperforUB.>>A=1A=1>>A=[1321]A=1321>>A=[13;21]A=1321>>B=[12;9]B=129>>f=[-2-3]f=-2-3>>X=LINPROG(f,A,B)Warning:FunctioncallLINPROGinvokesinexactmatchD:\matlab7\toolbox\optim\linprog.m.Optimizationterminated.X=3.00003.0000>>[A,B,C]=LINPROG(f,A,B)Optimizationterminated.A=3.00003.0000B=-15.0000C=1>>a=[1100095009000000000;000800068006000000;000000140001200010000]a=Columns1through711000950090000000000800068006000000000014000Columns8through900001200010000>>a=-aa=Columns1through7-11000-9500-90000000000-8000-6800-60000000000-14000Columns8through90000-12000-10000>>b=[190000;130000;350000]b=190000130000350000>>b=-bb=-190000-13000