net.mumie.mathletfactory.math.number.numeric

Class EchelonForm

java.lang.Object

net.mumie.mathletfactory.math.number.numeric.EchelonForm

Deprecated.

use class MatrixUtils instead

public final class EchelonForm
extends java.lang.Object

This class calculates the echelon form of a given number matrix by using the gauss algorithm for linear equation systems.

Author:

Paehler

Document status:

finished

Constructor Summary

Constructors

Constructor and Description
EchelonForm() Deprecated.

Method Summary

Methods

Modifier and Type	Method and Description
static void	debug(MNumber[] a, int m, int n) Deprecated. For debugging purposes: output the matrix values
protected static int[]	echForm(boolean rowOrColumn, MNumber[] inputMatrix, int n, int m, MNumber[] productOfElmntMatrices, MNumber[] outputMatrix) Deprecated. This private method converts a an arbitrary matrix into the echelon form. rowOrColumn is a flag indicating the row or column echelon forms.
protected static MNumber	elemMatrix(int type, MNumber alpha, int first, int second, int i, int j) Deprecated. This private method returns elements of an elementary matrix.
protected static int[]	findAbsMax(MNumber[] inputMatrix, int col, int row, int n, int m, boolean rowOrColumn) Deprecated. This private method searches the absolute maximum element in the first nonzero column (row) of a submatrix whose upper left element is given by the indices row and col. a is the initial input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively.
static NumberMatrix	getEFMatrix(NumberMatrix matrix) Deprecated. Returns the echelon form of a NumberMatrix.
protected static MNumber	getElement(MNumber[] a, int n, int m, int i, int j, boolean rowOrColumn) Deprecated. This private method gets an element of a matrix. a is a matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. i and j represent the indices of the element to be returned.
protected static MNumber	getElementRef(MNumber[] a, int n, int m, int i, int j, boolean rowOrColumn) Deprecated. This private method gets an element of a matrix. a is a matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. i and j represent the indices of the element to be returned.
static NumberMatrix	getREFMatrix(NumberMatrix matrix) Deprecated. Returns the reduced echelon form of a NumberMatrix.
protected static void	setElementRef(MNumber[] a, int n, int m, int i, int j, MNumber elem, boolean rowOrColumn) Deprecated. This private method sets an element of a matrix to the specified value. a is a matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix.
protected static void	swapElements(MNumber[] a, int n, int m, int i1, int j1, int i2, int j2, boolean rowOrColumn) Deprecated. This private method gets an element of a matrix. a is a matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. i1,j1 and i2,j2 represent the indices of the elements to be swapped respectively.
static void	toColumnEchelonForm(MNumber[] inputMatrix, int m, int n, MNumber[] productOfElmntMatrices, MNumber[] outputMatrix) Deprecated. This method converts an arbitrary matrix into column echelon form.
static void	toReducedColumnEchelonForm(MNumber[] inputMatrix, int m, int n, MNumber[] productOfElmntMatrices, MNumber[] outputMatrix) Deprecated. This method converts an arbitrary matrix into reduced column echelon form. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively.
protected static void	toReducedEchelonForm(boolean rowOrColumn, MNumber[] inputMatrix, int n, int m, MNumber[] productOfElmntMatrices, MNumber[] outputMatrix) Deprecated. This private method converts a matrix in the echelon form to the reduced echelon form. rowOrColumn is a flag indicating the row or column echelon forms. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix.
static void	toReducedRowEchelonForm(MNumber[] inputMatrix, int m, int n, MNumber[] productOfElmntMatrices, MNumber[] outputMatrix) Deprecated. This method converts an arbitrary matrix into reduced row echelon form. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix.
static void	toRowEchelonForm(MNumber[] inputMatrix, int m, int n, MNumber[] productOfElmntMatrices, MNumber[] outputMatrix) Deprecated. This method converts an arbitrary matrix into row echelon form.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

EchelonForm

public EchelonForm()

Deprecated.

Method Detail

getREFMatrix

public static NumberMatrix getREFMatrix(NumberMatrix matrix)

Deprecated.

Returns the reduced echelon form of a NumberMatrix.

getEFMatrix

public static NumberMatrix getEFMatrix(NumberMatrix matrix)

Deprecated.

Returns the echelon form of a NumberMatrix.

toRowEchelonForm

public static void toRowEchelonForm(MNumber[] inputMatrix,
                    int m,
                    int n,
                    MNumber[] productOfElmntMatrices,
                    MNumber[] outputMatrix)
                             throws java.lang.Exception

Deprecated.

This method converts an arbitrary matrix into row echelon form. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. If the absolute value of an element of the input matrix is less or equal than the absolute value of eps the element is considered to be zero. After returning p holds the product of the elementary matrices used to transform the input matrix into row echelon form and e holds the matrix in row echelon form. Note that the user is him-/herself responsible for allocating corresponding arrays for e and p.

Throws:

java.lang.Exception

toColumnEchelonForm

public static void toColumnEchelonForm(MNumber[] inputMatrix,
                       int m,
                       int n,
                       MNumber[] productOfElmntMatrices,
                       MNumber[] outputMatrix)
                                throws java.lang.Exception

Deprecated.

This method converts an arbitrary matrix into column echelon form. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. If the absolute value of an element of the input matrix is less or equal than the absolute value of eps the element is considered to be zero. After returning p holds the product of the elementary matrices used to transform the input matrix into column echelon form and e holds the matrix in column echelon form. Note that the user is him-/herself responsible for allocating corresponding arrays for e and p.

Throws:

java.lang.Exception

toReducedRowEchelonForm

public static void toReducedRowEchelonForm(MNumber[] inputMatrix,
                           int m,
                           int n,
                           MNumber[] productOfElmntMatrices,
                           MNumber[] outputMatrix)
                                    throws java.lang.Exception

Deprecated.

This method converts an arbitrary matrix into reduced row echelon form. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. If the absolute value of an element of the input matrix is less or equal than the absolute value of eps the element is considered to be zero. After returning p holds the product of the elementary matrices used to transform the input matrix into reduced row echelon form and e holds the matrix in reduced row echelon form. Note that the user is him-/herself responsible for allocating corresponding arrays for e and p.

Throws:

java.lang.Exception

toReducedColumnEchelonForm

public static void toReducedColumnEchelonForm(MNumber[] inputMatrix,
                              int m,
                              int n,
                              MNumber[] productOfElmntMatrices,
                              MNumber[] outputMatrix)
                                       throws java.lang.Exception

Deprecated.

This method converts an arbitrary matrix into reduced column echelon form. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. If the absolute value of an element of the input matrix is less or equal than the absolute value of eps the element is considered to be zero. After returning p holds the product of the elementary matrices used to transform the input matrix into reduced column echelon form and e holds the matrix in reduced row echelon form. Note that the user is him-/herself responsible for allocating corresponding arrays for e and p.

Throws:

java.lang.Exception

toReducedEchelonForm

protected static void toReducedEchelonForm(boolean rowOrColumn,
                        MNumber[] inputMatrix,
                        int n,
                        int m,
                        MNumber[] productOfElmntMatrices,
                        MNumber[] outputMatrix)
                                    throws java.lang.Exception

Deprecated.

This private method converts a matrix in the echelon form to the reduced echelon form. rowOrColumn is a flag indicating the row or column echelon forms. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. After returning p holds the product of the elementary matrices used to transform the input matrix into the reduced echelon form and e holds the matrix in reduced echelon form. Note that the user is him-/herself responsible for allocating corresponding arrays for e and p.

Throws:

java.lang.Exception

echForm

protected static int[] echForm(boolean rowOrColumn,
            MNumber[] inputMatrix,
            int n,
            int m,
            MNumber[] productOfElmntMatrices,
            MNumber[] outputMatrix)
                        throws java.lang.Exception

Deprecated.

This private method converts a an arbitrary matrix into the echelon form. rowOrColumn is a flag indicating the row or column echelon forms. The Gauss elimination method is used here. a is the input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. After returning p holds the product of the elementary matrices used to transform the input matrix into the echelon form and e holds the matrix in the echelon form. The method returns an array of pivot positions. Note that the user is him-/herself responsible for allocating corresponding arrays for e and p.

Throws:

java.lang.Exception

findAbsMax

protected static int[] findAbsMax(MNumber[] inputMatrix,
               int col,
               int row,
               int n,
               int m,
               boolean rowOrColumn)

Deprecated.

This private method searches the absolute maximum element in the first nonzero column (row) of a submatrix whose upper left element is given by the indices row and col. a is the initial input matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. If the absolute value of an element of the input matrix is less or equal than the absolute value of eps the element is considered to be zero. the parameter typ indicates whether the columns or the rows should be searched. The method returns an array of two elements holding the row and column of the maximum element. If all the elements in the submatrix were zero, the method returns null.

elemMatrix

protected static MNumber elemMatrix(int type,
                 MNumber alpha,
                 int first,
                 int second,
                 int i,
                 int j)

Deprecated.

This private method returns elements of an elementary matrix. The parameter type indicates the type of the elementary matrix. The parameter alf is used for certain elementary matrices such as the scaling elementary matrix e.g. Parameters first and second indicate which rows should be swapped in the elementary matrix which performs the row exchange. Parameters i and j indicate the row and column of the element of the matrix we are interested in.

setElementRef

protected static void setElementRef(MNumber[] a,
                 int n,
                 int m,
                 int i,
                 int j,
                 MNumber elem,
                 boolean rowOrColumn)

Deprecated.

This private method sets an element of a matrix to the specified value. a is a matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. i and j represent the indices of the element to be set. Parameter elem is the new element. If the absolute value of the element is less or equal than the absolute value of eps the element is considered to be zero. the parameter typ indicates wheather the matrix should be considered as transposed.

getElementRef

protected static MNumber getElementRef(MNumber[] a,
                    int n,
                    int m,
                    int i,
                    int j,
                    boolean rowOrColumn)

Deprecated.

This private method gets an element of a matrix. a is a matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. i and j represent the indices of the element to be returned. If the absolute value of the element is less or equal than the absolute value of eps the element is considered to be zero. the parameter rowOrColumn indicates wheather the matrix should be considered as transposed.

getElement

protected static MNumber getElement(MNumber[] a,
                 int n,
                 int m,
                 int i,
                 int j,
                 boolean rowOrColumn)

Deprecated.

This private method gets an element of a matrix. a is a matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. i and j represent the indices of the element to be returned. If the absolute value of the element is less or equal than the absolute value of eps the element is considered to be zero. the parameter rowOrColumn indicates wheather the matrix should be considered as transposed.

swapElements

protected static void swapElements(MNumber[] a,
                int n,
                int m,
                int i1,
                int j1,
                int i2,
                int j2,
                boolean rowOrColumn)

Deprecated.

This private method gets an element of a matrix. a is a matrix represented as an array of MMNumbers, where the rows of the matrix are stored successively. m and n are the dimensions of the matrix. i1,j1 and i2,j2 represent the indices of the elements to be swapped respectively. The parameter rowOrColumns indicates whether the matrix should be considered as transposed.

debug

public static void debug(MNumber[] a,
         int m,
         int n)

Deprecated.

For debugging purposes: output the matrix values