計量地理實驗報告

PAGEPAGE2計量地理學實驗報告班級：地理092學號：2009011134組別：姓名：鄭德欣山東建筑大學土木工程學院二零一一年十一月實驗須知實驗是配合課堂教學的一個重要教學環(huán)節(jié)，同時也是培養(yǎng)學生掌握實驗的基本技能和進行基本訓練的一個主要手段，為了保證實驗的順利進行，必須注意下列事項：1、實驗之前，希望同學們要預習實驗指導書，了解本次實驗的目的，原理和要求：2、嚴格按操作步驟認真操作，實驗報告要客觀、詳細記錄實驗步驟，實驗成果等。3、愛護實驗儀器，非本次實驗用的儀器或雖是本次實驗所用的儀器，但在老師沒有講解之前都不得隨便亂動，以免損壞儀器；4、實驗中不慎損壞儀器或丟失儀器中的附件，均應主動地告訴老師，按照有關規(guī)定處理；目錄實驗一地理數(shù)據(jù)統(tǒng)計處理………1實驗二統(tǒng)計分析方法……………3實驗三線性規(guī)劃方法……………4實驗四決策分析方法…………5實驗一地理數(shù)據(jù)統(tǒng)計處理一、實驗目的1.熟悉matlab的基本操作。2．掌握matlab的矩陣運算。3．掌握matlab計算地理數(shù)據(jù)一般水平的各個指標、離散水平的各個指標、偏離程度的各個指標4．掌握matlab的基本統(tǒng)計作圖。二、實驗內容1.熟悉matlab環(huán)境，并進行基本的矩陣運算。2.計算平均值、分組平均值、中位數(shù)、分組中位數(shù)、眾數(shù)。3.計算極差、離差、離差平方和、方差與標準差、變異系數(shù)。4.計算標準偏度系數(shù)、標準峰度系數(shù)。5．進行統(tǒng)計作圖。三、實驗方法與步驟打開matlab，重點熟悉命令窗口、工作空間窗口、歷史命令窗口、當前工作目錄窗口的使用。運用help命令查詢基本的矩陣運算函數(shù)，明確各個參數(shù)的含義，以及函數(shù)的使用和輸出的結果，并代入數(shù)據(jù)進行運算。3.運用help命令查詢平均值、中位數(shù)、眾數(shù)的計算函數(shù)的使用方法，并將Excel表格中的數(shù)據(jù)轉化成matlab數(shù)據(jù)，進行計算并分析。4.運用help命令查詢極差、離差、離差平方和、方差與標準差的計算函數(shù)的使用方法，并將Excel表格中的數(shù)據(jù)轉化成matlab數(shù)據(jù)，進行計算并分析。5.運用已有函數(shù)，計算分組平均值、分組中位數(shù)、變異系數(shù)。6.運用help命令查詢計算標準偏度系數(shù)、標準峰度系數(shù)的計算函數(shù)的使用方法，并將Excel表格中的數(shù)據(jù)轉化成matlab數(shù)據(jù)，進行計算并分析。7.運用matlab函數(shù)進行統(tǒng)計作圖。四、結果分析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.（標準差）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實驗二統(tǒng)計分析方法一、實驗目的1.掌握相關分析的計算方法和計算函數(shù)。2．掌握回歸分析的計算方法和計算函數(shù)。3．掌握時間序列分析的方法和編程。4．掌握系統(tǒng)聚類分析的計算方法和計算函數(shù)。5．掌握主成分分析的計算方法和計算函數(shù)。6．掌握馬爾可夫預測的方法和編程。7．掌握趨勢面分析的計算方法和計算函數(shù)。8．掌握各種統(tǒng)計分析方法的結果檢驗。二、實驗內容1.運用corrcoef函數(shù)進行相關分析，并分析計算結果。2．運用regress函數(shù)進行回歸分析，并進行檢驗。3．運用matlab編程實現(xiàn)移動平均、滑動平均、二次指數(shù)平滑、線性自回歸。4．運用zscore、pdist、linkage、dendrogram等函數(shù)進行系統(tǒng)聚類分析，并分析計算結果。5．運用princomp函數(shù)進行主成分分析，并分析計算結果。6．運用matlab編程實現(xiàn)馬爾可夫預測方法。7．運用regress函數(shù)進行趨勢面分析，并進行檢驗。三、實驗方法與步驟（一）相關分析1.運用help命令查詢corrcoef函數(shù)的使用方法。2.將Excel變量數(shù)據(jù)轉化成matlab數(shù)據(jù)矩陣A，調用命令：R=corrcoef(A)，計算各變量之間的相關系數(shù)矩陣。3.分析計算結果。（二）回歸分析1.運用help命令查詢regress函數(shù)的使用方法。2.將Excel變量數(shù)據(jù)轉化成matlab數(shù)據(jù)矩陣A。3.作出散點圖。4．運用[b,bint,r,rint,stats]=regress(y,x)進行計算，其中b是回歸方程中的參數(shù)估計值，bint是b的置信區(qū)間，r和rint分別表示殘差及殘差對應的置信區(qū)間。stats包含三個數(shù)字，分別是相關系數(shù)，F(xiàn)統(tǒng)計量及對應的概率p值。5.進行檢驗并分析計算結果。（三）時間序列分析1.將Excel變量數(shù)據(jù)轉化成matlab數(shù)據(jù)矩陣。2．編程計算移動平均、滑動平均、二次指數(shù)平滑、線性自回歸。3．分析計算結果。（四）系統(tǒng)聚類分析1.將Excel變量數(shù)據(jù)轉化成matlab數(shù)據(jù)矩陣。2．進行標準化處理。3．計算距離。4．用linkage進行聚類分析。5．做出聚類譜系圖。（五）主成分分析1.運用help命令查詢primcomp函數(shù)的使用方法。2.將Excel變量數(shù)據(jù)轉化成matlab數(shù)據(jù)矩陣。3.運用[pc,score,latent,t2]=princomp(X)進行計算，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對應列的方差向量，即A的特征值；容易計算方差所占的百分比。④t2表示檢驗的t2-統(tǒng)計量（方差分析要用）4.分析計算結果。（六）馬爾可夫預測1.將Excel變量數(shù)據(jù)轉化成matlab數(shù)據(jù)矩陣。2．編程進行馬爾可夫預測。3．分析計算結果。（七）趨勢面分析1.將Excel變量數(shù)據(jù)轉化成matlab數(shù)據(jù)矩陣。2．進行矩陣計算和變換，化為二次、三次趨勢面分析的原始數(shù)據(jù)矩陣。3．運用regress進行計算。4．檢驗計算結果。5．作出趨勢面圖：首先準備數(shù)據(jù)；然后運用meshgrid進行變換；最后用mesh或surf等函數(shù)做圖。四、結果分析（一）相關分析CORRCOEFCorrelationcoefficients.R=CORRCOEF(X)calculatesamatrixRofcorrelationcoefficientsforanarrayX,inwhicheachrowisanobservationandeachcolumnisavariable.表格轉置：>>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因為p=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)行這個方程得到Z對應的值，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)得到標準差標準化的數(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)

實驗三線性規(guī)劃方法一、實驗目的1.熟悉matlab優(yōu)化工具箱。2．掌握線性規(guī)劃方法。二、實驗內容1.練習matlab優(yōu)化工具箱的相關函數(shù)。2.運用linprog進行線性規(guī)劃。三、實驗方法與步驟1.運用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.運用linprog進行計算四、結果分析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