packagecom.song.badmath;publicclassLeastSquares(/***由最小二乘法擬合最逼近二維曲線@paramxx散點坐標@paramyy散點坐標@return擬合的曲線系數(shù)，曲線次數(shù)為length-1*/publicstaticdouble[]leastSquares(doublex[],doubley[])(if(x.length!=y.length)returnnull;intm=1;doublec[]=leastSquares(x,y,m);doublebackError=leastSquaresError(x,y,c);System.out.print("m:"+m+"->ERROR:"+backError);while(true)(m++;doublebc[]=leastSquares(x,y,m);doubleerror=leastSquaresError(x,y,bc);if(error>=backError){System.out.println("=>final");break;}else{c=bc;backError=error;System.out.println("=>next");}System.out.print("m:"+m+"->ERROR:"+backError);}returnc;}publicstaticdouble[]leastSquares(doublex[],doubley[],doublemax_error){if(x.length!=y.length)returnnull;intm=1;doublec[]=leastSquares(x,y,m);doublebackError=leastSquaresError(x,y,c);System.out.print("m:"+m+"->ERROR:"+backError);while(true){m++;doublebc[]=leastSquares(x,y,m);doubleerror=leastSquaresError(x,y,bc);if(error>=backError||backError<max_error){System.out.println("=>final");break;}else{c=bc;backError=error;System.out.println("=>next");}System.out.print("m:"+m+"->ERROR:"+backError);}returnc;/***由最小二乘法擬合m次二維曲線@paramxx散點坐標@paramyy散點坐標@paramm曲線次數(shù)@return擬合的曲線系數(shù)*/publicstaticdouble[]leastSquares(doublex[],doubley[],intm)(if(x.length!=y.length)returnnull;doubleA[][]=newdouble[m+1][m+1];doubleB[]=newdouble[m+1];doublesx[]=newdouble[2*m+1];//sxTil=Sx八idoublesy[]=newdouble[m+1];//syTil=Sx八iydoublepx[][]=newdouble[x.length][2*m+1];//px[i][j]=x[i]八jdoublepxy[][]=newdouble[y.length][m+1];//pxy[i][j]=x[i]八j*y[i]//計算并存儲x[i]八jfor(inti=0;i<px.length;i++){px[i][0]=1;for(intj=1;j<px[i].length;j++)px[i][j]=px[i][j-1]*x[i];}//計算并存儲x[i]八j*y[i]for(inti=0;i<pxy.length;i++){for(intj=0;j<pxy[i].length;j++)pxy[i][j]=px[i][j]*y[i];}//計算Sx八ifor(inti=1;i<sx.length;i++){sx[i]=0;for(intj=0;j<px.length;j++){sx[i]+=px[j][i];}}sx[0]=x.length;//計算SxAiyfor(inti=0;i<sy.length;i++){sy[i]=0;for(intj=0;j<pxy.length;j++){sy[i]+=pxy[j][i];}}//計算矩陣Afor(inti=0;i<A.length;i++){for(intj=0;j<A[i].length;j++){A[i][j]=sx[i+j];}}//計算矩陣Bfor(inti=0;i<B.length;i++){B[i]=sy[i];returnMatrix.linearEquations(A,B);}publicstaticStringpolynomialToString(doublec[])(StringstrPolynomial="y=";for(inti=0;i<c.length;i++){if(i>0)(if(c[i]==1){strPolynomial+="+x八"+i;}else{strPolynomial+="+"+c[i]+"x八"+i;}}else{strPolynomial+=c[i];}}returnstrPolynomial;}publicstaticStringpolynomialToStringNoZero(doublec[]){StringstrPolynomial="y=";intj=0;for(inti=0;i<c.length;i++){if(c[i]==0)continue;if(j>0){if(c[i]==1){strPolynomial+="+x八"+i;}else{strPolynomial+="+"+c[i]+"x八"+i;}}elseif(i==0){strPolynomial+=c[i];}else{if(c[i]==1){strPolynomial+="x八"+i;}else{strPolynomial+=c[i]+"x八"+i;}}j++;}returnstrPolynomial;}publicstaticdoubleleastSquaresError(doublex[],doubley[],doublea[]){doublepx[][]=newdouble[x.length][a.length];//px[i][j]=x[i]八jfor(inti=0;i<px.length;i++){px[i][0]=1;for(intj=1;j<px[i].length;j++)px[i][j]=px[i][j-1]*x[i];}doubleerror=0;for(inti=0;i<x.length;i++){doublef=0;for(intj=0;j<a.length;j++){f+=px[i][j]*a[j];}doubledy=f-y[i];error+=dy*dy;}returnerror;}publicstaticvoidtest(){doublex[]={1,2,3};doubley[]={2.2f,6.2f