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/*
* Matrix.java
*
* Created on 22 mars 2007, 16:01
*
*/
package org.umh.math.linear;
/**
* This class models a Matrix object that will be able to
* @author Absil Romain
*/
public class Matrix
{
/**
* The rowspace of the matrix (i.e. the set of its rows view as a set of row
* vectors.
*/
protected Vector[] rowSpace;
/**
* The number of columns of the matrix.
*/
protected int n;
/**
* The number of rows of the matrix.
*/
protected int m;
/**
* Conctructs a new num matrix with m columns and n rows.
* @param m the number of rows of the matrix.
* @param n the number of columns of the matrix.
**/
public Matrix(int m, int n)
{
this.rowSpace = new Vector[m];
for (int i = 0; i < rowSpace.length; i++)
rowSpace[i] = new Vector(n);
this.n = m;
this.m = n;
}
/**
* Constructs a new matrix with the given 2D array.
* @param cofs the coefficients of the matrix.
**/
public Matrix(double[][] cofs)
{
this.n = cofs[0].length;
this.m = cofs.length;
this.rowSpace = new Vector[m];
for (int i = 0; i < m; i++)
rowSpace[i] = new Vector(cofs[i]);
}
/**
* Construcs a new matrix with the rows are the given vectors.
* @param vectors the rows of the matrix.
**/
public Matrix(Vector ... vectors)
{
this.m = vectors.length;
this.n = vectors[0].size();
rowSpace = new Vector[m];
rowSpace[0] = vectors[0];
for (int i = 1; i < m; i++)
{
if(vectors[i].size() != n)
throw new IllegalArgumentException(
"All vectors must be the same dimension");
rowSpace[i] = vectors[i];
}
}
/**
* Returns the line space of the matrix.
* @return the line space of the matrix.
**/
public Vector[] getRowSpace()
{
return rowSpace;
}
/**
* Returns the number of rows of the current matrix.
* @return the number of rows of the current matrix.
**/
public int getRowsNumber()
{
return m;
}
/**
* Returns the number of columns of the current matrix.
* @return the number of columns of the current matrix.
**/
public int getColumnsNumber()
{
return n;
}
/**
* Returns the element (i,j) of the current matrix.
* @param i the row of the element to return.
* @param j the column of the element to return.
* @return the element (i,j) of the current matrix.
**/
public double get(int i, int j)
{
return rowSpace[i].getComp(j);
}
/**
* Returns the row indexed by the given number of the current matrix.
* @return the row indexed by the given number of the current matrix.
* @param i the index of the row you want to be returned.
*/
public Vector getRow(int i)
{
return rowSpace[i];
}
/**
* Returns the column indexed by the given number of the current matrix.
* @return the column indexed by the given number of the current matrix.
* @param i the index of the columns you want to be returned.
*/
public Vector getColumn(int i)
{
Vector vector = new Vector(m);
for (int j = 0; j < m; j++)
vector.setComp(j,rowSpace[j].getComp(i));
return vector;
}
/**
* Sets the element (i,j) to the given value.
* @param i the row of the element to set.
* @param j the column of the element to set.
* @param value the element to set.
**/
public void set(int i, int j, double value)
{
rowSpace[i].setComp(j,value);
}
/**
* Sets the line of the given matrix to the given vector.
* @param i the line to set.
* @param vector the nex value of the line.
**/
public void setRow(int i, Vector vector)
{
rowSpace[i] = vector;
}
/**
* Sets the column of the given matrix to the given vector.
* @param i the column to set.
* @param vector the nex value of the column.
**/
public void setColumn(int i, Vector vector)
{
for (int j = 0; j < m; j++)
rowSpace[j].setComp(i,vector.getComp(j));
}
/**
* Extracts a submatrix from the current matrix at the elements (l,c) and the rank (height, width).
* @param l the index of the row you want the matrix to be extracted.
* @param c the index of the column you want the matrix to be extracted
* @param height the height of the extracted matrix
* @param width the width of the extracted matrix
* @return a submatrix from the current matrix at the elements (l,c) and the rank (height, width).
*/
public Vector[] subMatrix(int l, int c, int height, int width)
{
Vector[] matrix = new Vector[height];
for(int i = 0; i < height; i++)
{
Vector v = new Vector(width);
for(int j = 0; j < width; j++)
v.setComp(j,get(l+i,c+j));
matrix[i] = v;
}
return matrix;
}
/**
* Returns true if the given object and the current matrix are equals,
* returns false otherwise.
* @param other the object you want to know if it is equals to the current matrix.
* @return true if the given object and the current matrix are equals,
* returns false otherwise.
*/
public boolean equals(Object other)
{
if(!(other instanceof Matrix))
return false;
Matrix matrix = (Matrix)other;
for (int i = 0; i < m; i++)
if(!rowSpace[i].equals(matrix.getRow(i)))
return false;
return true;
}
/**
* Returns a copy of the current matrix.
* @return a copy of the current matrix.
*/
public Matrix clone()
{
return new Matrix(rowSpace);
}
/**
* Returns the String representation of the current matrix.
* @return the String representation of the current matrix.
**/
public String toString()
{
String s = "";
for(int i = 0 ; i < m ; i++)
for(int j = 0 ; j < n ; j++)
{
s += get(i,j) + "\t";
if(j == n-1)
s += "\n";
}
return s;
}
/**
* Adds the given matrix to the current matrix and return the result of
* the addition.
* @param matrix the matrix to add.
* @return the result of the addition of the current matrix to the given other matrix.
*/
public Matrix add(Matrix matrix)
{
if(n != matrix.getRowsNumber() || m != matrix.getColumnsNumber())
throw new IllegalArgumentException();
Matrix added = clone();
for (int i = 0; i < m; i++)
added.setRow(i,matrix.getRow(i).add(matrix.getRow(i)));
return added;
}
/**
* Returns the opposite of the current matrix for additive law.
* @return the opposite of the current matrix for additive law.
*/
public Matrix getOpposite()
{
Vector[] oppositeRows = new Vector[m];
for (int i = 0; i < oppositeRows.length; i++)
oppositeRows[i] = rowSpace[i].getOpposite();
return new Matrix(oppositeRows);
}
/**
* Substracts the given matrix to the current matrix.
* @param matrix the matrix to substract
* @return the result of the substraction of the current matrix and the given other matrix.
*/
public Matrix substract(Matrix matrix)
{
if(n != matrix.getRowsNumber() || m != matrix.getColumnsNumber())
throw new IllegalArgumentException();
Matrix added = clone();
for (int i = 0; i < m; i++)
added.setRow(i,matrix.getRow(i).substract(matrix.getRow(i)));
return added;
}
/**
* Multiplies the current matrix by the given scalar, i.e. by a real number.
* @param scalar the number you want the current matrix to be multiplied by.
* @return the result of the multiplication of the current matrix by the given scalar.
*/
public Matrix multByScal(double scalar)
{
Matrix added = clone();
for (int i = 0; i < m; i++)
added.setRow(i,added.getRow(i).multByScal(scalar));
return added;
}
/**
* Multiplies the current matrix by another matrix.
* @param matrix the matrix you want multiply the current matrix by.
* @return the result of the multiplication of the current matrix by the given other matrix.
*/
public Matrix multiply(Matrix matrix)
{
Matrix mult = clone();
for (int i = 0; i < m; i++)
for (int j = 0; j < n; j++)
mult.set(i,j,mult.getRow(i).multiply(matrix.getColumn(j)));
return mult;
}
/**
* Sets the upper part of the matrix triangular and return the factor by
* wich the determinant must be multiplied in case of suare matrix.
* @return the number by wich the determinant of the matrix must be
* multiplied by after the triangularisation.
*/
public double setTriangularSup()
{
int rowIndex = 0;
int columnIndex = 0;
double factor = 1; //factor to return
while(columnIndex < n && rowIndex < m)
{
//if the pivot = 0, swap line
if(get(rowIndex,columnIndex) == 0)
{
int index = indexofFirstDownNonNullPivot(columnIndex);
if(index != -1) //pivot !=0 found
{
swapRow(rowIndex,index);
factor *= -1;
}
else //if no pivot != 0, nothing to do
{
columnIndex++;
factor = 0; //det = 0
continue; //don't make the rest of the loop
}
}
//make null all the elements abose the pivot
// L_i <- L_i - k * L_{pivot != 0} and k choosen to make the
// element i,columnIndex null
double pivot = get(rowIndex, columnIndex);
for(int i = rowIndex + 1; i < m ; i++)
setRow(i,rowSpace[i].substract(
rowSpace[rowIndex].multByScal(get(i,columnIndex)
/ pivot)));
//increment line and column index to continue the algorithm
rowIndex++;
columnIndex++;
}
return factor;
}
public double setTriangularSup(Vector independant)
{
int rowIndex = 0;
int columnIndex = 0;
double factor = 1; //factor to return
while(columnIndex < n && rowIndex < m)
{
//if the pivot = 0, swap line
if(get(rowIndex,columnIndex) == 0)
{
int index = indexofFirstDownNonNullPivot(columnIndex);
if(index != -1) //pivot !=0 found
{
swapRow(rowIndex,index);
factor *= -1;
}
else //if no pivot != 0, nothing to do
{
columnIndex++;
factor = 0; //det = 0
continue; //don't make the rest of the loop
}
}
//make null all the elements abose the pivot
// L_i <- L_i - k * L_{pivot != 0} and k choosen to make the
// element i,columnIndex null
double pivot = get(rowIndex, columnIndex);
for(int i = rowIndex + 1; i < m ; i++)
{
if(independant != null)
independant.setComp(i, independant.getComp(i) -
independant.getComp(rowIndex) *
get(i,columnIndex) / pivot);
setRow(i,rowSpace[i].substract(
rowSpace[rowIndex].multByScal(get(i,columnIndex)
/ pivot)));
}
//increment line and column index to continue the algorithm
rowIndex++;
columnIndex++;
}
return factor;
}
/**
* Sets the lower part of the matrix triangular and return the factor by
* wich the determinant must be multiplied in case of suare matrix.
* @return the number by wich the determinant of the matrix must be multiplied by after the triangularisation.
*/
public double setTriangularInf()
{
int rowIndex = n - 1;
int columnIndex = m - 1;
double factor = 1;
while(rowIndex >= 0 && columnIndex >= 0)
{
//if the pivot = 0, swap line
if(get(rowIndex,columnIndex) == 0)
{
int index = indexofFirstUpNonNullPivot(columnIndex);
if(index != -1) //pivot !=0 found
{
swapRow(rowIndex,index);
factor *= -1;
}
else //if no pivot != 0, nothing to do
{
columnIndex--;
factor = 0; //det = 0
continue; //don't make the rest of the loop
}
}
//make null all the elements abose the pivot
// L_i <- L_i - k * L_{pivot != 0} and k choosen to make the
// element i,columnIndex null
double pivot = get(rowIndex, columnIndex);
for(int i = rowIndex - 1; i >= 0 ; i--)
setRow(i,rowSpace[i].substract(
rowSpace[rowIndex].multByScal(get(i,columnIndex)
/ pivot)));
//increment line and column index to continue the algorithm
rowIndex--;
columnIndex--;
}
return factor;
}
// swaps the line i and the line j
private void swapRow(int i, int j)
{
Vector v = rowSpace[i];
rowSpace[i] = rowSpace[j];
rowSpace[j] = v;
}
//returns the index of the first no null pivot of the matrix at the
//given column, returns -1 if no non null pivots at the given column
private int indexofFirstDownNonNullPivot(int column)
{
Vector vector = getColumn(column);
for (int i = 0; i < m; i++)
if(vector.getComp(i) == 0)
return i;
return -1;
}
private int indexofFirstUpNonNullPivot(int column)
{
Vector vector = getColumn(column);
for (int i = m - 1; i >= 0; i--)
if(vector.getComp(i) == 0)
return i;
return -1;
}
} |
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