fr.cnes.sirius.patrius.math.linear

Class BlockRealMatrix

java.lang.Object

fr.cnes.sirius.patrius.math.linear.RealLinearOperator

fr.cnes.sirius.patrius.math.linear.AbstractRealMatrix

fr.cnes.sirius.patrius.math.linear.BlockRealMatrix

All Implemented Interfaces:

AnyMatrix, RealMatrix, Serializable

public class BlockRealMatrix
extends AbstractRealMatrix

Cache-friendly implementation of RealMatrix using a flat arrays to store square blocks of the matrix.

This implementation is specially designed to be cache-friendly. Square blocks are stored as small arrays and allow efficient traversal of data both in row major direction and columns major direction, one block at a time. This greatly increases performances for algorithms that use crossed directions loops like multiplication or transposition.

The size of square blocks is a static parameter. It may be tuned according to the cache size of the target computer processor. As a rule of thumbs, it should be the largest value that allows three blocks to be simultaneously cached (this is necessary for example for matrix multiplication). The default value is to use 52x52 blocks which is well suited for processors with 64k L1 cache (one block holds 2704 values or 21632 bytes). This value could be lowered to 36x36 for processors with 32k L1 cache.

The regular blocks represent BLOCK_SIZE x BLOCK_SIZE squares. Blocks at right hand side and bottom side which may be smaller to fit matrix dimensions. The square blocks are flattened in row major order in single dimension arrays which are therefore BLOCK_SIZE² elements long for regular blocks. The blocks are themselves organized in row major order.

As an example, for a block size of 52x52, a 100x60 matrix would be stored in 4 blocks. Block 0 would be a double[2704] array holding the upper left 52x52 square, block 1 would be a double[416] array holding the upper right 52x8 rectangle, block 2 would be a double[2496] array holding the lower left 48x52 rectangle and block 3 would be a double[384] array holding the lower right 48x8 rectangle.

The layout complexity overhead versus simple mapping of matrices to java arrays is negligible for small matrices (about 1%). The gain from cache efficiency leads to up to 3-fold improvements for matrices of moderate to large size.

Since:

2.0

Version:

$Id: BlockRealMatrix.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static int	BLOCK_SIZE Block size.

Constructor Summary

Constructors

Constructor and Description
BlockRealMatrix(double[][] rawData) Create a new dense matrix copying entries from raw layout data.
BlockRealMatrix(int rowsIn, int columnsIn) Create a new matrix with the supplied row and column dimensions.
BlockRealMatrix(int rowsIn, int columnsIn, double[][] blockData, boolean copyArray) Create a new dense matrix copying entries from block layout data.

Method Summary

Modifier and Type	Method and Description
BlockRealMatrix	add(BlockRealMatrix m) Compute the sum of this matrix and m.
BlockRealMatrix	add(RealMatrix m) Returns the result of adding the matrix m to this matrix.
void	addToEntry(int row, int column, double increment) Adds (in place) a given value to the specified entry of this matrix.
BlockRealMatrix	copy() Returns a deep copy of this matrix.
static double[][]	createBlocksLayout(int rows, int columns) Create a data array in blocks layout.
BlockRealMatrix	createMatrix(int rowDimension, int columnDimension) Creates a new matrix of the same type as this matrix.
double[]	getColumn(int column) Gets the entries of a given column.
int	getColumnDimension() Returns the dimension of the domain of this operator.
BlockRealMatrix	getColumnMatrix(int column) Gets the entries of a given column as a column matrix.
RealVector	getColumnVector(int column) Gets the entries of a given column as a vector.
double[][]	getData() Returns a 2D array containing the entries of the matrix.
double	getEntry(int row, int column) Gets the entry at the specified row and column.
double	getFrobeniusNorm() Returns the Frobenius norm of the matrix.
double	getNorm() Returns the maximum absolute row sum norm of the matrix.
double[]	getRow(int row) Gets the entries of a given row.
int	getRowDimension() Returns the dimension of the codomain of this operator.
BlockRealMatrix	getRowMatrix(int row) Gets the entries of a given row as a row matrix.
RealVector	getRowVector(int row) Gets the entries of a given row as a vector.
BlockRealMatrix	getSubMatrix(int startRow, int endRow, int startColumn, int endColumn) Gets a submatrix.
BlockRealMatrix	multiply(BlockRealMatrix m) Returns the result of postmultiplying this by m.
BlockRealMatrix	multiply(BlockRealMatrix m, boolean toTranspose) Returns the result of postmultiplying this × m (if toTranspose = false) or this × mT (if toTranspose = true)
BlockRealMatrix	multiply(BlockRealMatrix m, boolean toTranspose, double d) Returns the result of postmultiplying d × this × m (if toTranspose = false ) or d × this × mT (if toTranspose = true)
RealMatrix	multiply(RealMatrix m, boolean toTranspose, double d) Returns the result of postmultiplying this matrix by the matrix m or its transpose mT, then by the scalar d.
void	multiplyEntry(int row, int column, double factor) Multiplies (in place) the specified entry of this matrix by a given value.
double[]	operate(double[] v) Returns the result of postmultiplying this matrix by the vector v.
double[]	preMultiply(double[] v) Returns the result of premultiplying this matrix by the vector v.
BlockRealMatrix	scalarAdd(double d) Returns the result of adding a scalar d to the entries of this matrix.
BlockRealMatrix	scalarMultiply(double d) Returns the result of multiplying the entries of this matrix by the scalar d.
void	setColumn(int column, double[] array) Replaces the entries of a given column with the entries of the specified data array.
void	setColumnMatrix(int column, BlockRealMatrix matrix) Sets the entries in column number column as a column matrix.
void	setColumnMatrix(int column, RealMatrix matrix) Replaces the entries of a given column with the entries of the specified column matrix.
void	setColumnVector(int column, RealVector vector) Replaces the entries of a given column with the entries of the specified vector.
void	setEntry(int row, int column, double value) Sets the entry at the specified row and column to a new value.
void	setRow(int row, double[] array) Replaces the entries of a given row with the entries of the specified data array.
void	setRowMatrix(int row, BlockRealMatrix matrix) Sets the entries in row number row as a row matrix.
void	setRowMatrix(int row, RealMatrix matrix) Replaces the entries of a given row with the entries of the specified row matrix.
void	setRowVector(int row, RealVector vector) Replaces the entries of a given row with the entries of the specified vector.
void	setSubMatrix(double[][] subMatrix, int row, int column) Replaces part of the matrix with a given submatrix, starting at the specified row and column.
BlockRealMatrix	subtract(BlockRealMatrix m) Subtract m from this matrix.
BlockRealMatrix	subtract(RealMatrix m) Returns the result of subtracting the matrix m from this matrix.
static double[][]	toBlocksLayout(double[][] rawData) Convert a data array from raw layout to blocks layout.
BlockRealMatrix	transpose() Returns the transpose of this matrix.
double	walkInOptimizedOrder(RealMatrixChangingVisitor visitor) Visits (and possibly change) all matrix entries using the fastest possible order.
double	walkInOptimizedOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visits (and possibly change) some matrix entries using the fastest possible order.
double	walkInOptimizedOrder(RealMatrixPreservingVisitor visitor) Visits (but don't change) all matrix entries using the fastest possible order.
double	walkInOptimizedOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visits (but don't change) some matrix entries using the fastest possible order.
double	walkInRowOrder(RealMatrixChangingVisitor visitor) Visits (and possibly change) all matrix entries in row order.
double	walkInRowOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visits (and possibly change) some matrix entries in row order.
double	walkInRowOrder(RealMatrixPreservingVisitor visitor) Visits (but don't change) all matrix entries in row order.
double	walkInRowOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visits (but don't change) some matrix entries in row order.

Methods inherited from class fr.cnes.sirius.patrius.math.linear.AbstractRealMatrix

checkDestinationArray, checkSquare, concatenateDiagonally, concatenateDiagonally, concatenateDiagonally, concatenateHorizontally, concatenateHorizontally, concatenateVertically, concatenateVertically, copySubMatrix, copySubMatrix, copySubMatrix, copySubMatrix, equals, equals, getAbs, getData, getDefaultDecomposition, getDiagonal, getInverse, getInverse, getMax, getMin, getSubMatrix, getTrace, hashCode, isAntisymmetric, isDiagonal, isInvertible, isOrthogonal, isSquare, isSymmetric, isSymmetric, isSymmetric, multiply, multiply, multiply, operate, power, preMultiply, preMultiply, setDefaultDecomposition, toString, toString, transpose, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder

Methods inherited from class fr.cnes.sirius.patrius.math.linear.RealLinearOperator

isTransposable, operateTranspose

Methods inherited from class java.lang.Object

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

Methods inherited from interface fr.cnes.sirius.patrius.math.linear.RealMatrix

getMax, getMin

Field Detail

BLOCK_SIZE

public static final int BLOCK_SIZE

Block size.

See Also:

Constant Field Values

Constructor Detail

BlockRealMatrix

public BlockRealMatrix(int rowsIn,
                       int columnsIn)

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

Parameters:

rowsIn - the number of rows in the new matrix

columnsIn - the number of columns in the new matrix

Throws:

NotStrictlyPositiveException - if row or column dimension is not positive.

BlockRealMatrix

public BlockRealMatrix(double[][] rawData)

Create a new dense matrix copying entries from raw layout data.

The input array must already be in raw layout.

Calling this constructor is equivalent to call:

 matrix = new BlockRealMatrix(rawData.length, rawData[0].length,
     toBlocksLayout(rawData), false);
 

Parameters:

rawData - data for new matrix, in raw layout

Throws:

DimensionMismatchException - if the shape of blockData is inconsistent with block layout.

NotStrictlyPositiveException - if row or column dimension is not positive.

See Also:

BlockRealMatrix(int, int, double[][], boolean)

BlockRealMatrix

public BlockRealMatrix(int rowsIn,
                       int columnsIn,
                       double[][] blockData,
                       boolean copyArray)

Create a new dense matrix copying entries from block layout data.

The input array must already be in blocks layout.

Parameters:

rowsIn - Number of rows in the new matrix.

columnsIn - Number of columns in the new matrix.

blockData - data for new matrix

copyArray - Whether the input array will be copied or referenced.

Throws:

DimensionMismatchException - if the shape of blockData is inconsistent with block layout.

NotStrictlyPositiveException - if row or column dimension is not positive.

See Also:

createBlocksLayout(int, int), toBlocksLayout(double[][]), BlockRealMatrix(double[][])

Method Detail

toBlocksLayout

public static double[][] toBlocksLayout(double[][] rawData)

Convert a data array from raw layout to blocks layout.

Raw layout is the straightforward layout where element at row i and column j is in array element rawData[i][j]. Blocks layout is the layout used in BlockRealMatrix instances, where the matrix is split in square blocks (except at right and bottom side where blocks may be rectangular to fit matrix size) and each block is stored in a flattened one-dimensional array.

This method creates an array in blocks layout from an input array in raw layout. It can be used to provide the array argument of the BlockRealMatrix(int, int, double[][], boolean) constructor.

Parameters:

rawData - Data array in raw layout.

Returns:

a new data array containing the same entries but in blocks layout.

Throws:

DimensionMismatchException - if rawData is not rectangular.

See Also:

createBlocksLayout(int, int), BlockRealMatrix(int, int, double[][], boolean)

createBlocksLayout

public static double[][] createBlocksLayout(int rows,
                                            int columns)

Create a data array in blocks layout.

This method can be used to create the array argument of the BlockRealMatrix(int, int, double[][], boolean) constructor.

Parameters:

rows - Number of rows in the new matrix.

columns - Number of columns in the new matrix.

Returns:

a new data array in blocks layout.

See Also:

toBlocksLayout(double[][]), BlockRealMatrix(int, int, double[][], boolean)

createMatrix

public BlockRealMatrix createMatrix(int rowDimension,
                                    int columnDimension)

Creates a new matrix of the same type as this matrix.

The returned matrix is filled with zeros. Its size is determined by the specified row and column dimensions, which must both be strictly positive. Additional constraints on the dimensions may apply depending on the implementation (for example, symmetric matrices must be square, which implies that the row and column dimensions must be equal).

Specified by:

createMatrix in interface RealMatrix

Specified by:

createMatrix in class AbstractRealMatrix

Parameters:

rowDimension - the number of rows in the new matrix

columnDimension - the number of columns in the new matrix

Returns:

a new matrix of the same type as this matrix

copy

public BlockRealMatrix copy()

Returns a deep copy of this matrix.

Specified by:

copy in interface RealMatrix

Specified by:

copy in class AbstractRealMatrix

Returns:

a deep copy of this matrix

add

public BlockRealMatrix add(RealMatrix m)

Returns the result of adding the matrix m to this matrix.

Specified by:

add in interface RealMatrix

Overrides:

add in class AbstractRealMatrix

Parameters:

m - the matrix to be added

Returns:

the matrix resulting from the addition this+m

add

public BlockRealMatrix add(BlockRealMatrix m)

Compute the sum of this matrix and m.

Parameters:

m - Matrix to be added.

Returns:

this + m.

Throws:

MatrixDimensionMismatchException - if m is not the same size as this matrix.

subtract

public BlockRealMatrix subtract(RealMatrix m)

Returns the result of subtracting the matrix m from this matrix.

Specified by:

subtract in interface RealMatrix

Overrides:

subtract in class AbstractRealMatrix

Parameters:

m - the matrix to be subtracted

Returns:

the matrix resulting from the subtraction this-m

subtract

public BlockRealMatrix subtract(BlockRealMatrix m)

Subtract m from this matrix.

Parameters:

m - Matrix to be subtracted.

Returns:

this - m.

Throws:

MatrixDimensionMismatchException - if m is not the same size as this matrix.

scalarAdd

public BlockRealMatrix scalarAdd(double d)

Returns the result of adding a scalar d to the entries of this matrix.

Specified by:

scalarAdd in interface RealMatrix

Overrides:

scalarAdd in class AbstractRealMatrix

Parameters:

d - the scalar value to be added to the entries of this matrix

Returns:

the matrix resulting from the addition this+d

scalarMultiply

public BlockRealMatrix scalarMultiply(double d)

Returns the result of multiplying the entries of this matrix by the scalar d.

Specified by:

scalarMultiply in interface RealMatrix

Overrides:

scalarMultiply in class AbstractRealMatrix

Parameters:

d - the scalar value by which to multiply the entries of this matrix by

Returns:

the matrix resulting from the product this×d

multiply

public RealMatrix multiply(RealMatrix m,
                           boolean toTranspose,
                           double d)

Returns the result of postmultiplying this matrix by the matrix m or its transpose m^T, then by the scalar d.

Specified by:

multiply in interface RealMatrix

Overrides:

multiply in class AbstractRealMatrix

Parameters:

m - the matrix by which to multiply this matrix by

toTranspose - whether to compute the product this×m×d ( toTranspose=false), or the product this×m ^T×d (toTranspose=true)

d - the scalar by which to multiply the resulting matrix by

Returns:

the matrix resulting from the product this×m×d or this×m^T×d

multiply

public BlockRealMatrix multiply(BlockRealMatrix m)

Returns the result of postmultiplying this by m.

Parameters:

m - matrix to postmultiply by

Returns:

this * m

Throws:

DimensionMismatchException - if matrices are not multiplication compatible

multiply

public BlockRealMatrix multiply(BlockRealMatrix m,
                                boolean toTranspose)

Returns the result of postmultiplying this × m (if toTranspose = false) or this × m^T (if toTranspose = true)

Parameters:

m - matrix to postmultiply by

toTranspose - indication value, true if we expect the m matrix to be transposed

Returns:

this × m or this × m^T

Throws:

DimensionMismatchException - if matrices are not multiplication compatible

multiply

public BlockRealMatrix multiply(BlockRealMatrix m,
                                boolean toTranspose,
                                double d)

Returns the result of postmultiplying d × this × m (if toTranspose = false ) or d × this × m^T (if toTranspose = true)

Parameters:

m - matrix to postmultiply by

toTranspose - indication value, true if we expect the m matrix to be transposed

d - value to multiply all entries by

Returns:

d × this × m or d × this × m^T

Throws:

DimensionMismatchException - if matrices are not multiplication compatible

getData

public double[][] getData()

Returns a 2D array containing the entries of the matrix.

Specified by:

getData in interface RealMatrix

Overrides:

getData in class AbstractRealMatrix

Returns:

a 2D array containing the entries of the matrix

getNorm

public double getNorm()

Returns the maximum absolute row sum norm of the matrix.

Specified by:

getNorm in interface RealMatrix

Overrides:

getNorm in class AbstractRealMatrix

Returns:

the maximum absolute row sum norm of the matrix

getFrobeniusNorm

public double getFrobeniusNorm()

Returns the Frobenius norm of the matrix.

Specified by:

getFrobeniusNorm in interface RealMatrix

Overrides:

getFrobeniusNorm in class AbstractRealMatrix

Returns:

the Frobenius norm of the matrix

getSubMatrix

public BlockRealMatrix getSubMatrix(int startRow,
                                    int endRow,
                                    int startColumn,
                                    int endColumn)

Gets a submatrix.

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

Specified by:

getSubMatrix in interface RealMatrix

Overrides:

getSubMatrix in class AbstractRealMatrix

Parameters:

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the final column index (inclusive)

Returns:

the submatrix containing the data of the specified rows and columns

setSubMatrix

public void setSubMatrix(double[][] subMatrix,
                         int row,
                         int column)

Replaces part of the matrix with a given submatrix, starting at the specified row and column.

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

Usage example:

 // Initial matrix
 matrix = [a00, a10, a20]
          [a10, a11, a21]
          [a20, a21, a22]
 // Submatrix
 subMatrix = [b00, b01]
             [b10, b11]
            
 // Replace part of the initial matrix 
 matrix.setSubMatrix(subMatrix, 1, 1) =>[a00, a10, a20]
                                        [a10, b00, b01]
                                        [a20, b10, b11]
 

Specified by:

setSubMatrix in interface RealMatrix

Overrides:

setSubMatrix in class AbstractRealMatrix

Parameters:

subMatrix - the array containing the submatrix replacement data

row - the row coordinate of the top, left element to be replaced

column - the column coordinate of the top, left element to be replaced

getRowMatrix

public BlockRealMatrix getRowMatrix(int row)

Gets the entries of a given row as a row matrix.

Row indices start at 0.

Specified by:

getRowMatrix in interface RealMatrix

Overrides:

getRowMatrix in class AbstractRealMatrix

Parameters:

row - the index of the row to be fetched

Returns:

the extracted row matrix

setRowMatrix

public void setRowMatrix(int row,
                         RealMatrix matrix)

Replaces the entries of a given row with the entries of the specified row matrix.

Row indices start at 0.
The provided matrix must have one row and the same number of columns as this matrix.

Specified by:

setRowMatrix in interface RealMatrix

Overrides:

setRowMatrix in class AbstractRealMatrix

Parameters:

row - the index of the row to be replaced

matrix - the row matrix to be copied

setRowMatrix

public void setRowMatrix(int row,
                         BlockRealMatrix matrix)

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

Parameters:

row - the row to be set

matrix - row matrix (must have one row and the same number of columns as the instance)

Throws:

OutOfRangeException - if the specified row index is invalid.

MatrixDimensionMismatchException - if the matrix dimensions do not match one instance row.

getColumnMatrix

public BlockRealMatrix getColumnMatrix(int column)

Gets the entries of a given column as a column matrix.

Column indices start at 0.

Specified by:

getColumnMatrix in interface RealMatrix

Overrides:

getColumnMatrix in class AbstractRealMatrix

Parameters:

column - the index of the column to be fetched

Returns:

the extracted column matrix

setColumnMatrix

public void setColumnMatrix(int column,
                            RealMatrix matrix)

Replaces the entries of a given column with the entries of the specified column matrix.

Column indices start at 0.
The provided matrix must have one column and the same number of rows as this matrix.

Specified by:

setColumnMatrix in interface RealMatrix

Overrides:

setColumnMatrix in class AbstractRealMatrix

Parameters:

column - the index of the column to be replaced

matrix - the column matrix to be copied

setColumnMatrix

public void setColumnMatrix(int column,
                            BlockRealMatrix matrix)

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

Parameters:

column - the column to be set

matrix - column matrix (must have one column and the same number of rows as the instance)

Throws:

OutOfRangeException - if the specified column index is invalid.

MatrixDimensionMismatchException - if the matrix dimensions do not match one instance column.

getRowVector

public RealVector getRowVector(int row)

Gets the entries of a given row as a vector.

Row indices start at 0.

Specified by:

getRowVector in interface RealMatrix

Overrides:

getRowVector in class AbstractRealMatrix

Parameters:

row - the index of the row to be fetched

Returns:

the extracted row vector

setRowVector

public void setRowVector(int row,
                         RealVector vector)

Replaces the entries of a given row with the entries of the specified vector.

Row indices start at 0.
The size of the provided vector must match the column dimension of this matrix.

Specified by:

setRowVector in interface RealMatrix

Overrides:

setRowVector in class AbstractRealMatrix

Parameters:

row - the index of the row to be replaced

vector - the row vector to be copied

getColumnVector

public RealVector getColumnVector(int column)

Gets the entries of a given column as a vector.

Column indices start at 0.

Specified by:

getColumnVector in interface RealMatrix

Overrides:

getColumnVector in class AbstractRealMatrix

Parameters:

column - the index of the column to be fetched

Returns:

the extracted column vector

setColumnVector

public void setColumnVector(int column,
                            RealVector vector)

Replaces the entries of a given column with the entries of the specified vector.

Column indices start at 0.
The size of the provided vector must match the row dimension of this matrix.

Specified by:

setColumnVector in interface RealMatrix

Overrides:

setColumnVector in class AbstractRealMatrix

Parameters:

column - the index of the column to be replaced

vector - the column vector to be copied

getRow

public double[] getRow(int row)

Gets the entries of a given row.

Row indices start at 0.

Specified by:

getRow in interface RealMatrix

Overrides:

getRow in class AbstractRealMatrix

Parameters:

row - the index of the row to be fetched

Returns:

the extracted row data

setRow

public void setRow(int row,
                   double[] array)

Replaces the entries of a given row with the entries of the specified data array.

Row indices start at 0.
The size of the provided data array must match the column dimension of this matrix.

Specified by:

setRow in interface RealMatrix

Overrides:

setRow in class AbstractRealMatrix

Parameters:

row - the index of the row to be replaced

array - the row data array to be copied

getColumn

public double[] getColumn(int column)

Gets the entries of a given column.

Column indices start at 0.

Specified by:

getColumn in interface RealMatrix

Overrides:

getColumn in class AbstractRealMatrix

Parameters:

column - the index of the column to be fetched

Returns:

the extracted column data

setColumn

public void setColumn(int column,
                      double[] array)

Replaces the entries of a given column with the entries of the specified data array.

Column indices start at 0.
The size of the provided data array must match the row dimension of this matrix.

Specified by:

setColumn in interface RealMatrix

Overrides:

setColumn in class AbstractRealMatrix

Parameters:

column - the index of the column to be replaced

array - the column data array to be copied

getEntry

public double getEntry(int row,
                       int column)

Gets the entry at the specified row and column.

Row and column indices start at 0.

Specified by:

getEntry in interface RealMatrix

Specified by:

getEntry in class AbstractRealMatrix

Parameters:

row - the row index of entry to be fetched

column - the column index of entry to be fetched

Returns:

the matrix entry at the specified row and column

setEntry

public void setEntry(int row,
                     int column,
                     double value)

Sets the entry at the specified row and column to a new value.

Row and column indices start at 0.

Specified by:

setEntry in interface RealMatrix

Specified by:

setEntry in class AbstractRealMatrix

Parameters:

row - the row index of entry to be set

column - the column index of entry to be set

value - the new value of the entry

addToEntry

public void addToEntry(int row,
                       int column,
                       double increment)

Adds (in place) a given value to the specified entry of this matrix.

Row and column indices start at 0.

Specified by:

addToEntry in interface RealMatrix

Overrides:

addToEntry in class AbstractRealMatrix

Parameters:

row - the row index of the entry to be modified

column - the column index of the entry to be modified

increment - the value to add to the matrix entry

multiplyEntry

public void multiplyEntry(int row,
                          int column,
                          double factor)

Multiplies (in place) the specified entry of this matrix by a given value.

Row and column indices start at 0.

Specified by:

multiplyEntry in interface RealMatrix

Overrides:

multiplyEntry in class AbstractRealMatrix

Parameters:

row - the row index of the entry to be modified

column - the column index of the entry to be modified

factor - the multiplication factor for the matrix entry

transpose

public BlockRealMatrix transpose()

Returns the transpose of this matrix.

Specified by:

transpose in interface RealMatrix

Overrides:

transpose in class AbstractRealMatrix

Returns:

the transpose of this matrix

getRowDimension

public int getRowDimension()

Returns the dimension of the codomain of this operator.

Specified by:

getRowDimension in interface AnyMatrix

Specified by:

getRowDimension in class AbstractRealMatrix

Returns:

the number of rows of the underlying matrix

getColumnDimension

public int getColumnDimension()

Returns the dimension of the domain of this operator.

Specified by:

getColumnDimension in interface AnyMatrix

Specified by:

getColumnDimension in class AbstractRealMatrix

Returns:

the number of columns of the underlying matrix

operate

public double[] operate(double[] v)

Returns the result of postmultiplying this matrix by the vector v.

Specified by:

operate in interface RealMatrix

Overrides:

operate in class AbstractRealMatrix

Parameters:

v - the vector by which to multiply this matrix by

Returns:

the column vector resulting from the product this×v

preMultiply

public double[] preMultiply(double[] v)

Returns the result of premultiplying this matrix by the vector v.

Specified by:

preMultiply in interface RealMatrix

Overrides:

preMultiply in class AbstractRealMatrix

Parameters:

v - the row vector by which to premultiply this matrix by

Returns:

the row vector resulting from the product v×this

walkInRowOrder

public double walkInRowOrder(RealMatrixChangingVisitor visitor)

Visits (and possibly change) all matrix entries in row order.

Row order starts at upper left element, iterating through all elements of a row from left to right before going to the leftmost element of the next row.

Specified by:

walkInRowOrder in interface RealMatrix

Overrides:

walkInRowOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

See Also:

RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

walkInRowOrder

public double walkInRowOrder(RealMatrixPreservingVisitor visitor)

Visits (but don't change) all matrix entries in row order.

Row order starts at upper left element, iterating through all elements of a row from left to right before going to the leftmost element of the next row.

Specified by:

walkInRowOrder in interface RealMatrix

Overrides:

walkInRowOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

Returns:

the value returned by RealMatrixPreservingVisitor.end() at the end of the walk

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

walkInRowOrder

public double walkInRowOrder(RealMatrixChangingVisitor visitor,
                             int startRow,
                             int endRow,
                             int startColumn,
                             int endColumn)

Visits (and possibly change) some matrix entries in row order.

Row order starts at upper left element, iterating through all elements of a row from left to right before going to the leftmost element of the next row.

Specified by:

walkInRowOrder in interface RealMatrix

Overrides:

walkInRowOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the final column index

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

walkInRowOrder

public double walkInRowOrder(RealMatrixPreservingVisitor visitor,
                             int startRow,
                             int endRow,
                             int startColumn,
                             int endColumn)

Visits (but don't change) some matrix entries in row order.

Row order starts at upper left element, iterating through all elements of a row from left to right before going to the leftmost element of the next row.

Specified by:

walkInRowOrder in interface RealMatrix

Overrides:

walkInRowOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the final column index

Returns:

the value returned by RealMatrixPreservingVisitor.end() at the end of the walk

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

walkInOptimizedOrder

public double walkInOptimizedOrder(RealMatrixChangingVisitor visitor)

Visits (and possibly change) all matrix entries using the fastest possible order.

The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

Specified by:

walkInOptimizedOrder in interface RealMatrix

Overrides:

walkInOptimizedOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

walkInOptimizedOrder

public double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor)

Visits (but don't change) all matrix entries using the fastest possible order.

The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

Specified by:

walkInOptimizedOrder in interface RealMatrix

Overrides:

walkInOptimizedOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

Returns:

the value returned by RealMatrixPreservingVisitor.end() at the end of the walk

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

walkInOptimizedOrder

public double walkInOptimizedOrder(RealMatrixChangingVisitor visitor,
                                   int startRow,
                                   int endRow,
                                   int startColumn,
                                   int endColumn)

Visits (and possibly change) some matrix entries using the fastest possible order.

The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

Specified by:

walkInOptimizedOrder in interface RealMatrix

Overrides:

walkInOptimizedOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the final column index (inclusive)

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

walkInOptimizedOrder

public double walkInOptimizedOrder(RealMatrixPreservingVisitor visitor,
                                   int startRow,
                                   int endRow,
                                   int startColumn,
                                   int endColumn)

Visits (but don't change) some matrix entries using the fastest possible order.

The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

Specified by:

walkInOptimizedOrder in interface RealMatrix

Overrides:

walkInOptimizedOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the final column index (inclusive)

Returns:

the value returned by RealMatrixPreservingVisitor.end() at the end of the walk

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int)