dev.nm.algebra.linear.matrix.doubles.operation

Class ElementaryOperation

java.lang.Object

dev.nm.algebra.linear.matrix.doubles.operation.ElementaryOperation

All Implemented Interfaces:

MatrixAccess, MatrixTable, Table

public class ElementaryOperation
extends Object
implements MatrixTable

There are three elementary row operations which are equivalent to left multiplying an elementary matrix. They are row switching, row multiplication, and row addition. By applying these operations to an identity matrix, I, the resultant matrix, T, is a transformation matrix, such that left multiplying T with a matrix A, i.e., T * A, is equivalent to applying the same sequence of operations to A. Similarly, the three elementary column operations are: column switching, column multiplication, and column addition. Column operations correspond to right multiplying a transformation matrix.

See Also:

Wikipedia: Elementary matrix

Constructor Summary

Constructors

Constructor and Description
ElementaryOperation(int dim) Construct a transformation matrix of elementary operations.
ElementaryOperation(int nRows, int nCols) Construct a transformation matrix of elementary operations.
ElementaryOperation(Matrix A) Transform A by elementary operations.

Method Summary

Modifier and Type	Method and Description
ElementaryOperation	addColumn(int j1, int j2, double c) Column addition: \[ A[, j_{1}] = A[, j_{1}] + c \cdot A[, j_{2}] \]
ElementaryOperation	addRow(int i1, int i2, double c) Row addition: \[ A[i_{1}, ] = A[i_{1}, ] + c \cdot A[i_{2}, ] \]
double	get(int i, int j) Get the matrix entry at [i,j].
int	nCols() Gets the number of columns.
int	nRows() Gets the number of rows.
ElementaryOperation	scaleColumn(int j, double c) Scale a column: \[ A[, j] = c \cdot A[, j] \]
ElementaryOperation	scaleRow(int i, double c) Scale a row: \[ A[i, ] = c \cdot A[i, ] \]
void	set(int i, int j, double value) Deprecated.
ElementaryOperation	swapColumn(int j1, int j2) Swap columns: \[ \begin{gathered} A[, j_{1}] = A[, j_{2}] \\ A[, j_{2}] = A[, j_{1}] \end{gathered} \]
ElementaryOperation	swapRow(int i1, int i2) Swap rows: \[ \begin{gathered} A[i_{1}, ] = A[i_{2}, ] \\ A[i_{2}, ] = A[i_{1}, ] \end{gathered} \]
Matrix	T() Get the transformed matrix T.
String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

ElementaryOperation

public ElementaryOperation(int dim)

Construct a transformation matrix of elementary operations. The initial transformation matrix T is an identity matrix.

Parameters:

dim - the dimension of T

ElementaryOperation

public ElementaryOperation(int nRows,
                           int nCols)

Construct a transformation matrix of elementary operations. The initial transformation matrix T is an identity matrix, if it is square. Otherwise, the rightmost columns are padded with zeros.

Parameters:

nRows - the number of rows of T

nCols - the number of columns of T

ElementaryOperation

public ElementaryOperation(Matrix A)

Transform A by elementary operations.

Parameters:

A - a matrix

Method Detail

nRows

public int nRows()

Description copied from interface: Table

Gets the number of rows. Rows count from 1.

Specified by:

nRows in interface Table

Returns:

the number of rows

nCols

public int nCols()

Description copied from interface: Table

Gets the number of columns. Columns count from 1.

Specified by:

nCols in interface Table

Returns:

the number of columns

get

public double get(int i,
                  int j)

Description copied from interface: MatrixAccess

Get the matrix entry at [i,j].

Specified by:

get in interface MatrixAccess

Parameters:

i - the row index

j - the column index

Returns:

A[i,j]

T

public Matrix T()

Get the transformed matrix T.

Returns:

T

swapRow

public ElementaryOperation swapRow(int i1,
                                   int i2)

Swap rows: \[ \begin{gathered} A[i_{1}, ] = A[i_{2}, ] \\ A[i_{2}, ] = A[i_{1}, ] \end{gathered} \]

Parameters:

i1 - becoming row \(i_{2}\)

i2 - becoming row \(i_{1}\)

Returns:

the modified self

scaleRow

public ElementaryOperation scaleRow(int i,
                                    double c)

Scale a row: \[ A[i, ] = c \cdot A[i, ] \]

Parameters:

i - the row to be scaled

c - the scaling factor

Returns:

the modified self

addRow

public ElementaryOperation addRow(int i1,
                                  int i2,
                                  double c)

Row addition: \[ A[i_{1}, ] = A[i_{1}, ] + c \cdot A[i_{2}, ] \]

Parameters:

i1 - addend; the row to add to; the row is modified afterward

i2 - the row to add with

c - the scaling factor for row \(i_{2}\)

Returns:

the modified self

swapColumn

public ElementaryOperation swapColumn(int j1,
                                      int j2)

Swap columns: \[ \begin{gathered} A[, j_{1}] = A[, j_{2}] \\ A[, j_{2}] = A[, j_{1}] \end{gathered} \]

Parameters:

j1 - becoming column \(j_{2}\)

j2 - becoming column \(j_{1}\)

Returns:

the modified self

scaleColumn

public ElementaryOperation scaleColumn(int j,
                                       double c)

Scale a column: \[ A[, j] = c \cdot A[, j] \]

Parameters:

j - the column to be scaled

c - the scaling factor

Returns:

the modified self

addColumn

public ElementaryOperation addColumn(int j1,
                                     int j2,
                                     double c)

Column addition: \[ A[, j_{1}] = A[, j_{1}] + c \cdot A[, j_{2}] \]

Parameters:

j1 - addend; the column to add to; the column is modified afterward

j2 - the column to add with

c - the scaling factor for col2

Returns:

the modified self

toString

public String toString()

Overrides:

toString in class Object

set

@Deprecated
public void set(int i,
                            int j,
                            double value)
                     throws MatrixAccessException

Deprecated.

Description copied from interface: MatrixAccess

Set the matrix entry at [i,j] to a value. This is the only method that may change a matrix.

Specified by:

set in interface MatrixAccess

Parameters:

i - the row index

j - the column index

value - the value to set A[i,j] to

Throws:

MatrixAccessException - if i or j is out of range