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Reduced row echelon form: Difference between revisions
→{{header|Java}}: Basically, the original code had a floating point error. Apache Commons' Fraction classes allow us to avoid that whole issue.
(→{{header|Java}}: Removed extraneous statement. If there's some reason a code should not be copied, it should be explained more clearly. And the code should probably not be on RC.) |
(→{{header|Java}}: Basically, the original code had a floating point error. Apache Commons' Fraction classes allow us to avoid that whole issue.) |
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Line 1,199:
=={{header|Java}}==
''This requires Apache Commons 2.2+''
<lang java>import java.util.*;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
/* Matrix class
* Handles elementary Matrix operations:
* Interchange
* Multiply and Add
* Scale
* Reduced Row Echelon Form
* Maintainer: patnatali(AT)gmail(DOT)com
*/
class Matrix {
LinkedList<LinkedList<Fraction>> matrix;
int numRows;
int numCols;
static class Coordinate {
int row;
int col;
Coordinate(int r, int c) {
row = r;
col = c;
}
public String toString() {
return "(" + row + ", " + col + ")";
}
}
Matrix(double [][] m) {
numRows = m.length;
numCols = m[0].length;
matrix = new LinkedList<LinkedList<Fraction>>();
for (int i = 0; i < numRows; i++) {
matrix.add(new LinkedList<Fraction>());
for (int j = 0; j < numCols; j++) {
try {
matrix.get(i).add(new Fraction(m[i][j]));
} catch (FractionConversionException e) {
System.err.println("Fraction could not be converted from double by apache commons . . .");
}
}
}
}
public void Interchange(Coordinate a, Coordinate b) {
LinkedList<Fraction> temp = matrix.get(a.row);
matrix.set(a.row, matrix.get(b.row));
matrix.set(b.row, temp);
int t = a.row;
a.row = b.row;
b.row = t;
}
public void Scale(Coordinate x, Fraction d) {
LinkedList<Fraction> row = matrix.get(x.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).multiply(d));
}
}
public void MultiplyAndAdd(Coordinate to, Coordinate from, Fraction scalar) {
LinkedList<Fraction> row = matrix.get(to.row);
LinkedList<Fraction> rowMultiplied = matrix.get(from.row);
for (int i = 0; i < numCols; i++) {
row.set(i, row.get(i).add((rowMultiplied.get(i).multiply(scalar))));
}
}
public void RREF() {
Coordinate pivot = new Coordinate(0,0);
int submatrix = 0;
for (int x = 0; x < numCols; x++) {
pivot = new Coordinate(pivot.row, x);
//Step 1
//Begin with the leftmost nonzero column. This is a pivot column. The pivot position is at the top.
for (int i = x; i < numCols; i++) {
if (isColumnZeroes(pivot) == false) {
break;
} else {
pivot.col = i;
}
}
//Step 2
//Select a nonzero entry in the pivot column with the highest absolute value as a pivot.
pivot = findPivot(pivot);
if (getCoordinate(pivot).doubleValue() == 0.0) {
pivot.row++;
continue;
}
//If necessary, interchange rows to move this entry into the pivot position.
//move this row to the top of the submatrix
if (pivot.row != submatrix) {
Interchange(new Coordinate(submatrix, pivot.col), pivot);
}
//Force pivot to be 1
if (getCoordinate(pivot).doubleValue() != 1) {
/*
System.out.println(getCoordinate(pivot));
System.out.println(pivot);
System.out.println(matrix);
*/
Fraction scalar = getCoordinate(pivot).reciprocal();
Scale(pivot, scalar);
}
//Step 3
//Use row replacement operations to create zeroes in all positions below the pivot.
//belowPivot = belowPivot + (Pivot * -belowPivot)
for (int i = pivot.row; i < numRows; i++) {
if (i == pivot.row) {
continue;
}
Coordinate belowPivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(belowPivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(belowPivot, pivot, complement);
}
//Step 5
//Beginning with the rightmost pivot and working upward and to the left, create zeroes above each pivot.
//If a pivot is not 1, make it 1 by a scaling operation.
//Use row replacement operations to create zeroes in all positions above the pivot
for (int i = pivot.row; i >= 0; i--) {
if (i == pivot.row) {
if (getCoordinate(pivot).doubleValue() != 1.0) {
Scale(pivot, getCoordinate(pivot).reciprocal());
}
continue;
}
if (i == pivot.row) {
continue;
}
Coordinate abovePivot = new Coordinate(i, pivot.col);
Fraction complement = (getCoordinate(abovePivot).negate().divide(getCoordinate(pivot)));
MultiplyAndAdd(abovePivot, pivot, complement);
}
//Step 4
//Ignore the row containing the pivot position and cover all rows, if any, above it.
//Apply steps 1-3 to the remaining submatrix. Repeat until there are no more nonzero entries.
if ((pivot.row + 1) >= numRows || isRowZeroes(new Coordinate(pivot.row+1, pivot.col))) {
break;
}
submatrix++;
pivot.row++;
}
}
public boolean isColumnZeroes(Coordinate a) {
for (int i = 0; i < numRows; i++) {
if (matrix.get(i).get(a.col).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public boolean isRowZeroes(Coordinate a) {
for (int i = 0; i < numCols; i++) {
if (matrix.get(a.row).get(i).doubleValue() != 0.0) {
return false;
}
}
return true;
}
public Coordinate findPivot(Coordinate a) {
int first_row = a.row;
Coordinate pivot = new Coordinate(a.row, a.col);
Coordinate current = new Coordinate(a.row, a.col);
for (int i = a.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() == 1.0) {
Interchange(current, a);
}
}
current.row = a.row;
for (int i = current.row; i < (numRows - first_row); i++) {
current.row = i;
if (getCoordinate(current).doubleValue() != 0) {
pivot.row = i;
break;
}
}
return pivot;
}
public Fraction getCoordinate(Coordinate a) {
return matrix.get(a.row).get(a.col);
}
public String toString() {
return matrix.toString().replace("], ", "]\n");
}
public static void main (String[] args) {
double[][] matrix_1 = {
{1, 2, -1, -4},
{2, 3, -1, -11},
{-2, 0, -3, 22}
};
Matrix x = new Matrix(matrix_1);
System.out.println("before\n" + x.toString() + "\n");
x.RREF();
System.out.println("after\n" + x.toString() + "\n");
double matrix_2 [][] = {
{2, 0, -1, 0, 0},
{1, 0, 0, -1, 0},
{3, 0, 0, -2, -1},
{0, 1, 0, 0, -2},
{0, 1, -1, 0, 0}
};
Matrix y = new Matrix(matrix_2);
System.out.println("before\n" + y.toString() + "\n");
y.RREF();
System.out.println("after\n" + y.toString() + "\n");
double matrix_3 [][] = {
{1, 2, 3, 4, 3, 1},
{2, 4, 6, 2, 6, 2},
{3, 6, 18, 9, 9, -6},
{4, 8, 12, 10, 12, 4},
{5, 10, 24, 11, 15, -4}
};
Matrix z = new Matrix(matrix_3);
System.out.println("before\n" + z.toString() + "\n");
z.RREF();
System.out.println("after\n" + z.toString() + "\n");
double matrix_4 [][] = {
{0, 1},
{1, 2},
{0,5}
};
Matrix a = new Matrix(matrix_4);
System.out.println("before\n" + a.toString() + "\n");
a.RREF();
System.out.println("after\n" + a.toString() + "\n");
}
}</lang>
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