org.apache.commons.math.linear
Class BigMatrixImpl

java.lang.Object
  org.apache.commons.math.linear.BigMatrixImpl

All Implemented Interfaces:

BigMatrix, Serializable

public class BigMatrixImpl

extends Object

implements BigMatrix, Serializable

Implementation for BigMatrix using a BigDecimal[][] array to store entries and LU decompostion to support linear system solution and inverse.

The LU decompostion is performed as needed, to support the following operations:

• solve
• isSingular
• getDeterminant
• inverse

Usage notes:

• The LU decomposition is stored and reused on subsequent calls. If matrix data are modified using any of the public setXxx methods, the saved decomposition is discarded. If data are modified via references to the underlying array obtained using getDataRef(), then the stored LU decomposition will not be discarded. In this case, you need to explicitly invoke LUDecompose() to recompute the decomposition before using any of the methods above.
• As specified in the BigMatrix interface, matrix element indexing is 0-based -- e.g., getEntry(0, 0) returns the element in the first row, first column of the matrix.

Version:

$Revision: 1.10 $ $Date: 2004/11/07 20:19:22 $

See Also:

Serialized Form

Field Summary

(package private) static long	serialVersionUID Serialization id
protected static BigDecimal	TOO_SMALL Bound to determine effective singularity in LU decomposition

Constructor Summary

BigMatrixImpl()
Creates a matrix with no data

BigMatrixImpl(BigDecimal[] v)
Create a new (column) BigMatrix using v as the data for the unique column of the v.length x 1 matrix created.

BigMatrixImpl(BigDecimal[][] d)
Create a new BigMatrix using the data as the underlying data array.

BigMatrixImpl(double[][] d)
Create a new BigMatrix using the data as the underlying data array.

BigMatrixImpl(int rowDimension, int columnDimension)
Create a new BigMatrix with the supplied row and column dimensions.

BigMatrixImpl(String[][] d)
Create a new BigMatrix using the values represented by the strings in data as the underlying data array.

Method Summary

BigMatrix	add(BigMatrix m) Compute the sum of this and m.
BigMatrix	copy() Create a new BigMatrix which is a copy of this.
boolean	equals(Object object) Returns true iff object is a BigMatrixImpl instance with the same dimensions as this and all corresponding matrix entries are equal.
BigDecimal[]	getColumn(int col) Returns the entries in column number col as an array.
double[]	getColumnAsDoubleArray(int col) Returns the entries in column number col as an array of double values.
int	getColumnDimension() Returns the number of columns in the matrix.
BigMatrix	getColumnMatrix(int column) Returns the entries in column number column as a column matrix.
BigDecimal[][]	getData() Returns matrix entries as a two-dimensional array.
double[][]	getDataAsDoubleArray() Returns matrix entries as a two-dimensional array.
BigDecimal[][]	getDataRef() Returns a reference to the underlying data array.
BigDecimal	getDeterminant() Returns the determinant of this matrix.
BigDecimal	getEntry(int row, int column) Returns the entry in the specified row and column.
double	getEntryAsDouble(int row, int column) Returns the entry in the specified row and column as a double.
protected BigMatrix	getIdentity(int dimension) Returns dimension x dimension identity matrix.
protected BigMatrix	getLUMatrix() Returns the LU decomposition as a BigMatrix.
BigDecimal	getNorm() Returns the maximum absolute row sum norm of the matrix.
protected int[]	getPermutation() Returns the permutation associated with the lu decomposition.
int	getRoundingMode() Gets the rounding mode for division operations The default is BigDecimal.ROUND_HALF_UP
BigDecimal[]	getRow(int row) Returns the entries in row number row as an array.
double[]	getRowAsDoubleArray(int row) Returns the entries in row number row as an array of double values.
int	getRowDimension() Returns the number of rows in the matrix.
BigMatrix	getRowMatrix(int row) Returns the entries in row number row as a row matrix.
int	getScale() Sets the scale for division operations.
BigMatrix	getSubMatrix(int[] selectedRows, int[] selectedColumns) Gets a submatrix.
BigMatrix	getSubMatrix(int startRow, int endRow, int startColumn, int endColumn) Gets a submatrix.
BigDecimal	getTrace() Returns the trace of the matrix (the sum of the elements on the main diagonal).
int	hashCode() Computes a hashcode for the matrix.
BigMatrix	inverse() Returns the inverse matrix if this matrix is invertible.
boolean	isSingular() Is this a singular matrix?
boolean	isSquare() Is this a square matrix?
void	luDecompose() Computes a new LU decompostion for this matrix, storing the result for use by other methods.
BigMatrix	multiply(BigMatrix m) Returns the result of postmultiplying this by m.
BigDecimal[]	operate(BigDecimal[] v) Returns the result of multiplying this by the vector v.
BigDecimal[]	operate(double[] v) Returns the result of multiplying this by the vector v.
BigDecimal[]	preMultiply(BigDecimal[] v) Returns the (row) vector result of premultiplying this by the vector v.
BigMatrix	preMultiply(BigMatrix m) Returns the result premultiplying this by m.
BigMatrix	scalarAdd(BigDecimal d) Returns the result of adding d to each entry of this.
BigMatrix	scalarMultiply(BigDecimal d) Returns the result multiplying each entry of this by d
void	setRoundingMode(int roundingMode) Sets the rounding mode for decimal divisions.
void	setScale(int scale) Sets the scale for division operations.
BigDecimal[]	solve(BigDecimal[] b) Returns a matrix of (column) solution vectors for linear systems with coefficient matrix = this and constant vectors = columns of b.
BigMatrix	solve(BigMatrix b) Returns a matrix of (column) solution vectors for linear systems with coefficient matrix = this and constant vectors = columns of b.
BigDecimal[]	solve(double[] b) Returns a matrix of (column) solution vectors for linear systems with coefficient matrix = this and constant vectors = columns of b.
BigMatrix	subtract(BigMatrix m) Compute this minus m.
String	toString()
BigMatrix	transpose() Returns the transpose matrix.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

serialVersionUID

static final long serialVersionUID

Serialization id

See Also:

Constant Field Values

TOO_SMALL

protected static BigDecimal TOO_SMALL

Bound to determine effective singularity in LU decomposition

Constructor Detail

BigMatrixImpl

public BigMatrixImpl()

Creates a matrix with no data

BigMatrixImpl

public BigMatrixImpl(int rowDimension,
                     int columnDimension)

Create a new BigMatrix with the supplied row and column dimensions.

Parameters:

rowDimension - the number of rows in the new matrix

columnDimension - the number of columns in the new matrix

BigMatrixImpl

public BigMatrixImpl(BigDecimal[][] d)

Create a new BigMatrix using the data as the underlying data array.

The input array is copied, not referenced.

Parameters:

d - data for new matrix

Throws:

IllegalArgumentException - if d is not rectangular (not all rows have the same length) or empty

NullPointerException - if d is null

BigMatrixImpl

public BigMatrixImpl(double[][] d)

Create a new BigMatrix using the data as the underlying data array.

The input array is copied, not referenced.

Parameters:

d - data for new matrix

Throws:

IllegalArgumentException - if d is not rectangular (not all rows have the same length) or empty

NullPointerException - if d is null

BigMatrixImpl

public BigMatrixImpl(String[][] d)

Create a new BigMatrix using the values represented by the strings in data as the underlying data array.

Parameters:

d - data for new matrix

Throws:

IllegalArgumentException - if d is not rectangular (not all rows have the same length) or empty

NullPointerException - if d is null

BigMatrixImpl

public BigMatrixImpl(BigDecimal[] v)

Create a new (column) BigMatrix using v as the data for the unique column of the v.length x 1 matrix created.

The input array is copied, not referenced.

Parameters:

v - column vector holding data for new matrix

Method Detail

copy

public BigMatrix copy()

Create a new BigMatrix which is a copy of this.

Specified by:

copy in interface BigMatrix

Returns:

the cloned matrix

add

public BigMatrix add(BigMatrix m)
              throws IllegalArgumentException

Compute the sum of this and m.

Specified by:

add in interface BigMatrix

Parameters:

m - matrix to be added

Returns:

this + m

Throws:

IllegalArgumentException - if m is not the same size as this

subtract

public BigMatrix subtract(BigMatrix m)
                   throws IllegalArgumentException

Compute this minus m.

Specified by:

subtract in interface BigMatrix

Parameters:

m - matrix to be subtracted

Returns:

this + m

Throws:

IllegalArgumentException - if m is not the same size as *this

scalarAdd

public BigMatrix scalarAdd(BigDecimal d)

Returns the result of adding d to each entry of this.

Specified by:

scalarAdd in interface BigMatrix

Parameters:

d - value to be added to each entry

Returns:

d + this

scalarMultiply

public BigMatrix scalarMultiply(BigDecimal d)

Returns the result multiplying each entry of this by d

Specified by:

scalarMultiply in interface BigMatrix

Parameters:

d - value to multiply all entries by

Returns:

d * this

multiply

public BigMatrix multiply(BigMatrix m)
                   throws IllegalArgumentException

Returns the result of postmultiplying this by m.

Specified by:

multiply in interface BigMatrix

Parameters:

m - matrix to postmultiply by

Returns:

this*m

Throws:

IllegalArgumentException - if columnDimension(this) != rowDimension(m)

preMultiply

public BigMatrix preMultiply(BigMatrix m)
                      throws IllegalArgumentException

Returns the result premultiplying this by m.

Specified by:

preMultiply in interface BigMatrix

Parameters:

m - matrix to premultiply by

Returns:

m * this

Throws:

IllegalArgumentException - if rowDimension(this) != columnDimension(m)

getData

public BigDecimal[][] getData()

Returns matrix entries as a two-dimensional array.

Makes a fresh copy of the underlying data.

Specified by:

getData in interface BigMatrix

Returns:

2-dimensional array of entries

getDataAsDoubleArray

public double[][] getDataAsDoubleArray()

Returns matrix entries as a two-dimensional array.

Makes a fresh copy of the underlying data converted to double values.

Specified by:

getDataAsDoubleArray in interface BigMatrix

Returns:

2-dimensional array of entries

getDataRef

public BigDecimal[][] getDataRef()

Returns a reference to the underlying data array.

Does not make a fresh copy of the underlying data.

Returns:

2-dimensional array of entries

getRoundingMode

public int getRoundingMode()

Gets the rounding mode for division operations The default is BigDecimal.ROUND_HALF_UP

Specified by:

getRoundingMode in interface BigMatrix

Returns:

the rounding mode.

See Also:

BigDecimal

setRoundingMode

public void setRoundingMode(int roundingMode)

Sets the rounding mode for decimal divisions.

Parameters:

roundingMode -

See Also:

BigDecimal

getScale

public int getScale()

Sets the scale for division operations. The default is 64

Returns:

the scale

See Also:

BigDecimal

setScale

public void setScale(int scale)

Sets the scale for division operations.

Parameters:

scale -

See Also:

BigDecimal

getNorm

public BigDecimal getNorm()

Returns the maximum absolute row sum norm of the matrix.

Specified by:

getNorm in interface BigMatrix

Returns:

norm

getSubMatrix

public BigMatrix getSubMatrix(int startRow,
                              int endRow,
                              int startColumn,
                              int endColumn)
                       throws MatrixIndexException

Gets a submatrix. Rows and columns are indicated counting from 0 to n-1.

Specified by:

getSubMatrix in interface BigMatrix

Parameters:

startRow - Initial row index

endRow - Final row index

startColumn - Initial column index

endColumn - Final column index

Returns:

The subMatrix containing the data of the specified rows and columns

Throws:

MatrixIndexException - if row or column selections are not valid

getSubMatrix

public BigMatrix getSubMatrix(int[] selectedRows,
                              int[] selectedColumns)
                       throws MatrixIndexException

Gets a submatrix. Rows and columns are indicated counting from 0 to n-1.

Specified by:

getSubMatrix in interface BigMatrix

Parameters:

selectedRows - Array of row indices must be non-empty

selectedColumns - Array of column indices must be non-empty

Returns:

The subMatrix containing the data in the specified rows and columns

Throws:

MatrixIndexException - if supplied row or column index arrays are not valid

getRowMatrix

public BigMatrix getRowMatrix(int row)
                       throws MatrixIndexException

Returns the entries in row number row as a row matrix. Row indices start at 0.

Specified by:

getRowMatrix in interface BigMatrix

Parameters:

row - the row to be fetched

Returns:

row matrix

Throws:

MatrixIndexException - if the specified row index is invalid

getColumnMatrix

public BigMatrix getColumnMatrix(int column)
                          throws MatrixIndexException

Returns the entries in column number column as a column matrix. Column indices start at 0.

Specified by:

getColumnMatrix in interface BigMatrix

Parameters:

column - the column to be fetched

Returns:

column matrix

Throws:

MatrixIndexException - if the specified column index is invalid

getRow

public BigDecimal[] getRow(int row)
                    throws MatrixIndexException

Returns the entries in row number row as an array.

Row indices start at 0. A MatrixIndexException is thrown unless 0 <= row < rowDimension.

Specified by:

getRow in interface BigMatrix

Parameters:

row - the row to be fetched

Returns:

array of entries in the row

Throws:

MatrixIndexException - if the specified row index is not valid

getRowAsDoubleArray

public double[] getRowAsDoubleArray(int row)
                             throws MatrixIndexException

Returns the entries in row number row as an array of double values.

Row indices start at 0. A MatrixIndexException is thrown unless 0 <= row < rowDimension.

Specified by:

getRowAsDoubleArray in interface BigMatrix

Parameters:

row - the row to be fetched

Returns:

array of entries in the row

Throws:

MatrixIndexException - if the specified row index is not valid

getColumn

public BigDecimal[] getColumn(int col)
                       throws MatrixIndexException

Returns the entries in column number col as an array.

Column indices start at 0. A MatrixIndexException is thrown unless 0 <= column < columnDimension.

Specified by:

getColumn in interface BigMatrix

Parameters:

col - the column to be fetched

Returns:

array of entries in the column

Throws:

MatrixIndexException - if the specified column index is not valid

getColumnAsDoubleArray

public double[] getColumnAsDoubleArray(int col)
                                throws MatrixIndexException

Returns the entries in column number col as an array of double values.

Column indices start at 0. A MatrixIndexException is thrown unless 0 <= column < columnDimension.

Specified by:

getColumnAsDoubleArray in interface BigMatrix

Parameters:

col - the column to be fetched

Returns:

array of entries in the column

Throws:

MatrixIndexException - if the specified column index is not valid

getEntry

public BigDecimal getEntry(int row,
                           int column)
                    throws MatrixIndexException

Returns the entry in the specified row and column.

Row and column indices start at 0 and must satisfy

• 0 <= row < rowDimension
• 0 <= column < columnDimension

otherwise a MatrixIndexException is thrown.

Specified by:

getEntry in interface BigMatrix

Parameters:

row - row location of entry to be fetched

column - column location of entry to be fetched

Returns:

matrix entry in row,column

Throws:

MatrixIndexException - if the row or column index is not valid

getEntryAsDouble

public double getEntryAsDouble(int row,
                               int column)
                        throws MatrixIndexException

Returns the entry in the specified row and column as a double.

Row and column indices start at 0 and must satisfy

• 0 <= row < rowDimension
• 0 <= column < columnDimension

otherwise a MatrixIndexException is thrown.

Specified by:

getEntryAsDouble in interface BigMatrix

Parameters:

row - row location of entry to be fetched

column - column location of entry to be fetched

Returns:

matrix entry in row,column

Throws:

MatrixIndexException - if the row or column index is not valid

transpose

public BigMatrix transpose()

Returns the transpose matrix.

Specified by:

transpose in interface BigMatrix

Returns:

transpose matrix

inverse

public BigMatrix inverse()
                  throws InvalidMatrixException

Returns the inverse matrix if this matrix is invertible.

Specified by:

inverse in interface BigMatrix

Returns:

inverse matrix

Throws:

InvalidMatrixException - if this is not invertible

getDeterminant

public BigDecimal getDeterminant()
                          throws InvalidMatrixException

Returns the determinant of this matrix.

Specified by:

getDeterminant in interface BigMatrix

Returns:

determinant

Throws:

InvalidMatrixException - if matrix is not square

isSquare

public boolean isSquare()

Is this a square matrix?

Specified by:

isSquare in interface BigMatrix

Returns:

true if the matrix is square (rowDimension = columnDimension)

isSingular

public boolean isSingular()

Is this a singular matrix?

Specified by:

isSingular in interface BigMatrix

Returns:

true if the matrix is singular

getRowDimension

public int getRowDimension()

Returns the number of rows in the matrix.

Specified by:

getRowDimension in interface BigMatrix

Returns:

rowDimension

getColumnDimension

public int getColumnDimension()

Returns the number of columns in the matrix.

Specified by:

getColumnDimension in interface BigMatrix

Returns:

columnDimension

getTrace

public BigDecimal getTrace()
                    throws IllegalArgumentException

Returns the trace of the matrix (the sum of the elements on the main diagonal).

Specified by:

getTrace in interface BigMatrix

Returns:

trace

Throws:

IllegalArgumentException - if this matrix is not square.

operate

public BigDecimal[] operate(BigDecimal[] v)
                     throws IllegalArgumentException

Returns the result of multiplying this by the vector v.

Specified by:

operate in interface BigMatrix

Parameters:

v - the vector to operate on

Returns:

this*v

Throws:

IllegalArgumentException - if columnDimension != v.size()

operate

public BigDecimal[] operate(double[] v)
                     throws IllegalArgumentException

Returns the result of multiplying this by the vector v.

Parameters:

v - the vector to operate on

Returns:

this*v

Throws:

IllegalArgumentException - if columnDimension != v.size()

preMultiply

public BigDecimal[] preMultiply(BigDecimal[] v)
                         throws IllegalArgumentException

Returns the (row) vector result of premultiplying this by the vector v.

Specified by:

preMultiply in interface BigMatrix

Parameters:

v - the row vector to premultiply by

Returns:

v*this

Throws:

IllegalArgumentException - if rowDimension != v.size()

solve

public BigDecimal[] solve(BigDecimal[] b)
                   throws IllegalArgumentException,
                          InvalidMatrixException

Returns a matrix of (column) solution vectors for linear systems with coefficient matrix = this and constant vectors = columns of b.

Specified by:

solve in interface BigMatrix

Parameters:

b - array of constants forming RHS of linear systems to to solve

Returns:

solution array

Throws:

IllegalArgumentException - if this.rowDimension != row dimension

InvalidMatrixException - if this matrix is not square or is singular

solve

public BigDecimal[] solve(double[] b)
                   throws IllegalArgumentException,
                          InvalidMatrixException

Returns a matrix of (column) solution vectors for linear systems with coefficient matrix = this and constant vectors = columns of b.

Parameters:

b - array of constants forming RHS of linear systems to to solve

Returns:

solution array

Throws:

IllegalArgumentException - if this.rowDimension != row dimension

InvalidMatrixException - if this matrix is not square or is singular

solve

public BigMatrix solve(BigMatrix b)
                throws IllegalArgumentException,
                       InvalidMatrixException

Returns a matrix of (column) solution vectors for linear systems with coefficient matrix = this and constant vectors = columns of b.

Specified by:

solve in interface BigMatrix

Parameters:

b - matrix of constant vectors forming RHS of linear systems to to solve

Returns:

matrix of solution vectors

Throws:

IllegalArgumentException - if this.rowDimension != row dimension

InvalidMatrixException - if this matrix is not square or is singular

luDecompose

public void luDecompose()
                 throws InvalidMatrixException

Computes a new LU decompostion for this matrix, storing the result for use by other methods.

Implementation Note:
Uses Crout's algortithm, with partial pivoting.

Usage Note:
This method should rarely be invoked directly. Its only use is to force recomputation of the LU decomposition when changes have been made to the underlying data using direct array references. Changes made using setXxx methods will trigger recomputation when needed automatically.

Throws:

InvalidMatrixException - if the matrix is non-square or singular.

toString

public String toString()

See Also:

Object.toString()

equals

public boolean equals(Object object)

Returns true iff object is a BigMatrixImpl instance with the same dimensions as this and all corresponding matrix entries are equal. BigDecimal.equals is used to compare corresponding entries.

Parameters:

object - the object to test equality against.

Returns:

true if object equals this

hashCode

public int hashCode()

Computes a hashcode for the matrix.

Returns:

hashcode for matrix

getIdentity

protected BigMatrix getIdentity(int dimension)

Returns dimension x dimension identity matrix.

Parameters:

dimension - dimension of identity matrix to generate

Returns:

identity matrix

getLUMatrix

protected BigMatrix getLUMatrix()
                         throws InvalidMatrixException

Returns the LU decomposition as a BigMatrix. Returns a fresh copy of the cached LU matrix if this has been computed; otherwise the composition is computed and cached for use by other methods. Since a copy is returned in either case, changes to the returned matrix do not affect the LU decomposition property.

The matrix returned is a compact representation of the LU decomposition. Elements below the main diagonal correspond to entries of the "L" matrix; elements on and above the main diagonal correspond to entries of the "U" matrix.

Example:

 
     Returned matrix                L                  U
         2  3  1                   1  0  0            2  3  1          
         5  4  6                   5  1  0            0  4  6
         1  7  8                   1  7  1            0  0  8          
 

The L and U matrices satisfy the matrix equation LU = permuteRows(this),
where permuteRows reorders the rows of the matrix to follow the order determined by the permutation property.

Returns:

LU decomposition matrix

Throws:

InvalidMatrixException - if the matrix is non-square or singular.

getPermutation

protected int[] getPermutation()

Returns the permutation associated with the lu decomposition. The entries of the array represent a permutation of the numbers 0, ... , nRows - 1.

Example: permutation = [1, 2, 0] means current 2nd row is first, current third row is second and current first row is last.

Returns a fresh copy of the array.

Returns:

the permutation