"Fundamentals of Algorithm design and analysis" 16, Gauss elimination element method

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Package Cn.xf.algorithm.ch06changerule;import Java.util.arraylist;import Java.util.list;import org.junit.Test; Import cn.xf.util.genericpair;/** * Function: Gaussian elimination method, that is, multivariate data matrix, and then each row of the other rows of data to eliminate to 0, and then find a solution of a meta, and then can be based on this data to hand out other meta solution * @author Xiaofeng * @date July 1, 2017 * @fileName Gaussianeliminationmethod.java * */public class Gaussianeliminationmethod {/** * This is defective if datas.get (i). get (i) is 0, then an error occurs * @param datas */public void Forwardelimination (list<list<double>> Datas) {if (datas.size () <= 0) {return;} Equation elimination data for (int i = 0; i < datas.size (); ++i) {//Traverse all lines, in this line, to remove the first item's parameter for (int j = i + 1; j < Datas.size (); ++j) {//Times The line after the calendar begins traversing for (int k = Datas.get (j). Size ()-1; k >= i;--k) {//When the last step forward, traverse forward and then remove the coefficients of the corresponding column I of each row by double value = Datas.get (j) . Get (k)-Datas.get (i). Get (k) * Datas.get (J). Get (i)/Datas.get (i). get (i);d Atas.get (j). Set (k, value);}}} /** * This idea is to start with the largest line of each column as the base row, and then do Gaussian elimination * @param datas */public void Betterforwardelimination (list<list<double >> datas) {if (datas.sizE () <= 0) {return;} First, traverse the diagonal data, because the data before the diagonal is merged into 0//traverse all the columns, the elimination of the element for (int column = 0; column < Datas.get (0). Size (); ++column) {//A variable is stored, The highest absolute value in this column is worth the line int maxvaluerow = column;//traverse all subsequent rows, comparing the absolute size for (int afterrow = Maxvaluerow; Afterrow < Datas.size (); + + Afterrow) {if (Math.Abs (Datas.get (Afterrow). Get (column)) > Math.Abs (Datas.get (Maxvaluerow). Get (column))) {// The absolute value of the line, assigned to him maxvaluerow = Afterrow;}} The current datum row and other rows are exchanged for (int swapcolumn = column; Swapcolumn < datas.get (0). Size (); ++swapcolumn) {if (column >= DATAS.S Ize ()) {break;} It is best to exchange Genericpair<integer with the current Datum line, integer> first = new Genericpair<integer, integer> (); First.setfirst (column); First.setsecond (Swapcolumn); Genericpair<integer, integer> second = new Genericpair<integer, integer> (); Second.setfirst (MaxValueRow); Second.setsecond (swapcolumn); Swap (datas, first, second);} Traverse each line, divided by the base after the interchange, starting at the following line, I, I------------------------------------------------------------------------------------------------------------------for (int afterrowr = column + 1; afterrowr < Datas.size (); ++afterrowr) {Double temp = datas.get (AFTERROWR). Get (column)/datas.get (column), or//with this divisor, exclude the data for this column of all rows after the interchange for (int rowchu = column; Rowchu < Datas.get ( AFTERROWR). Size (); ++rowchu) {//per row of data minus, base row and temp multiplier double resultvalue = Datas.get (AFTERROWR). Get (Rowchu)-datas.get (column). Get (Rowchu ) * Temp;datas.get (AFTERROWR). Set (Rowchu, Resultvalue);}}} public static void Swap (list<list<double>> datas, Genericpair<integer, integer> first, Genericpair <integer, integer> second) {if (datas.size () <= 0) {return;} Double temp = Datas.get (First.getfirst ()). Get (First.getsecond ());d Atas.get (First.getfirst ()). Set (First.getsecond ( ), Datas.get (Second.getfirst ()). Get (Second.getsecond ()));d Atas.get (Second.getfirst ()). Set (Second.getsecond (), temp);} @Testpublic void Test () {list<list<double>> datas = new arraylist<list<double>> (); list<double> data1 = new Arraylist<doubLe> ();d Ata1.add (2d);d Ata1.add ( -1d);d ata1.add (1d);d ata1.add (1d);d atas.add (data1); list<double> data2 = new arraylist<double> ();d ata2.add (4d);d ata2.add (1d);d Ata2.add ( -1d);d Ata2.add (5d); Datas.add (DATA2); list<double> data3 = new arraylist<double> ();d ata3.add (1d);d ata3.add (1d);d ata3.add (1d);d ata3.add (0d); Datas.add (DATA3);//Gaussian elimination Gaussianeliminationmethod gem = new Gaussianeliminationmethod (); Gem.forwardelimination ( datas);//gem.betterforwardelimination (datas); for (list<double> Data:datas) {System.out.println ( Data.tostring ());}}}

　　

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"Fundamentals of Algorithm design and analysis" 16, Gauss elimination element method