(原创)利用克拉默法则求解多元一次方程组.doc

(原创)利用克拉默法则求解多元一次方程组packagezouyf.matrix;/*/*authorzouyf2008-4-7本程序利用克拉默法则求解多元一次方程组*/publicclassGetMatrix.privatedoublesavequot;/保存变量系数privatedoubleconstquot;/保存常量系数privatedoublesaveResult;/保存解的集合publicGetMatrix(doublequot).intcount=quot.length;savequot=newdoublecountcount;constquot=newdoublecount;saveResult=newdoublecount;inti=0,j=0;for(i=0;icount;i+).for(j=0;jcount;j+).savequotij=quotij;constquoti=quoticount;saveResulti=0;privatedoublegetMatrixResult(doubleinput)/递归的方法求得某个行列式的值.if(input.length=2)/递归出口，为二阶行列式时，直接返回.returninput00*input11-input01*input10;else.doubletemp=newdoubleinput.length;/存放第一列的系数值doubletempinput=newdoubleinput.length-1input.length-1;doubleresult=0;for(inti=0;iinput.length;i+).tempi=inputi0;intm=0,n=0;for(intk=0;kinput.length;k+).if(k!=i).for(m=0;minput.length-1;m+).tempinputnm=inputkm+1;/删除当前变量系数所在的行和列，得到减少一阶的新的行列式n+;if(i%2=0)/递归调用，利用代数余子式与相应系数变量的乘积之和得到多阶行列式的值.result=result+tempi*getMatrixResult(tempinput);else.result=result-tempi*getMatrixResult(tempinput);returnresult;privatedoublegetReplaceMatrix(inti)/用常数系数替换相应的变量系数,得到新的行列式.doubletempresult=newdoublesavequot.lengthsavequot.length;for(intm=0;msavequot.length;m+).for(intn=0;nsavequot.length;n+).if(i!=m).tempresultnm=savequotnm;else.tempresultni=constquotn;/用常量系数替换当前变量系数returntempresult;publicdoublegetResult().doublebasic=0;basic=getMatrixResult(savequot);/得到变量系数行列式的值if(Math.abs(basic)0.00001)/得到行列式的值为零时，表示此方程组没有唯一解.System.out.println(itdosenothavethequeueresult!);returnsaveResult;doubletemp=newdoublesaveResult.lengthsaveResult.length;for(inti=0;isaveResult.length;i+).temp=getReplaceMatrix(i);saveResulti=getMatrixResult(temp)/basic;/依次计算得到每一个变量的解returnsaveResult;publicstaticvoidmain(Stringargs)./*/*测试方程组*2a+b-5c+d=8*a-3b-6d=9*2b-c+2d=-5*a+4b-7c+6d=0*/doubletest=.2,1,-5,1,8,.1,-3,0,-6,9,.0,2,-1,2,-5,.1,4,-7,6,0;GetMatrixgm=newGetMatrix(test);doubleuu=newdoubletest.length;/返回结果集uu=gm.getResult();for(inti=0;iuu.length;i+).System.out.println(uui+,);C+版#include stdafx.h#include #include #include /本程序利用克拉默法则求解多元一次方程组using namespace std;class GetMatrixpublic:GetMatrix(vector vector quot);double getMatrixResult(vector vector input);vector vector getReplaceMatrix(int i);vector getResult();private:vector vector savequot;vector constquot;vector saveResult;GetMatrix:GetMatrix(vector vector quot)int count = quot.size();savequot.resize(count);for (int i=0;icount;i+)savequoti.resize(count);constquot.resize(count);saveResult.resize(count);int i = 0, j = 0;for (i = 0; i count; i+)for (j = 0; j count; j+)savequotij = quotij;constquoti = quoticount;saveResulti = 0;double GetMatrix:getMatrixResult(vector vector input)/ 递归的方法求得某个行列式的值if (input.size() = 2)/递归出口，为二阶行列式时，直接返回return input00 * input11 - input01 * input10; elseint iLength=input.size();vector temp(iLength);vector vector tempinput(iLength-1,vector(iLength-1);double result = 0;for (int i = 0; i iLength; i+)tempi = inputi0;int m = 0, n = 0;for (int k = 0; k iLength; k+)if (k != i)for (m = 0; m iLength - 1; m+)tempinputnm = inputkm + 1;/删除当前变量系数所在的行和列，得到减少一阶的新的行列式n+;if (i % 2 = 0)/ 递归调用，利用代数余子式与相应系数变量的乘积之和得到多阶行列式的值result = result + tempi * getMatrixResult(tempinput);elseresult = result - tempi * getMatrixResult(tempinput);return result;vector vector GetMatrix:getReplaceMatrix(int i)/ 用常数系数替换相应的变量系数,得到新的行列式vector vector tempresult(savequot);for (int m = 0; m savequot.size(); m+)for (int n = 0; n savequot.size(); n+)if (i != m)tempresultnm = savequotnm; elsetempresultni = constquotn;/ 用常量系数替换当前变量系数return tempresult;vector GetMatrix:getResult()double basic = 0;basic = getMatrixResult(savequot);/得到变量系数行列式的值if (abs(basic) 0.00001)/得到行列式的值为零时，表示此方程组没有唯一解coutit dose not have the queue result!endl;return saveResult;int iLength=saveResult.size();vector vector temp(iLength,vector(iLength);for (int i = 0; i iLength; i+)temp = getReplaceMatrix(i);saveResulti = getMatrixResult(temp) / basic;/依次计算得到每一个变量的解return saveResult;int _tmain(int argc, _TCHAR* argv)/* 测试方程组* 2a+b-5c+d=8 * a-3b-6d=9 * 2b-c+2d=-5 * a+4b-7c+6d=0*/*double test145 = 2, 1, -5, 1, 8 , 1, -3, 0, -6, 9 , 0, 2, -1, 2, -5 , 1, 4, -7, 6, 0 ;*/* 测试方程组* 4a+b=3 * 8a+b=6*/double test123 = 4, 1 ,3, 8, 1,6 ;vector vector t