fr.cnes.sirius.patrius.math.linear

Class AbstractRealMatrix

java.lang.Object

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

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

All Implemented Interfaces:

AnyMatrix, RealMatrix, Serializable

Direct Known Subclasses:

Array2DRowRealMatrix, ArrayRowSymmetricMatrix, BlockRealMatrix, DecomposedSymmetricPositiveMatrix, DiagonalMatrix

public abstract class AbstractRealMatrix
extends RealLinearOperator
implements RealMatrix

Basic implementation of RealMatrix methods regardless of the underlying storage.

All the methods implemented here use getEntry(int, int) to access matrix elements. Derived class can provide faster implementations.

This class is up-to-date with commons-math 3.6.1.

Since:

2.0

Version:

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

See Also:

Serialized Form

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	AbstractRealMatrix() Creates a matrix with no data.
protected	AbstractRealMatrix(int rowDimension, int columnDimension) Create a new RealMatrix with the supplied row and column dimensions.

Method Summary

Modifier and Type	Method and Description
RealMatrix	add(RealMatrix m) Returns the sum of this and m.
void	addToEntry(int row, int column, double increment) Adds (in place) the specified value to the specified entry of this matrix.
RealMatrix	concatenateDiagonally(RealMatrix matrix, boolean lowerRightMatrix) Concatenate this and matrix vertically.
RealMatrix	concatenateHorizontally(RealMatrix matrix) Concatenate this and matrix horizontally.
RealMatrix	concatenateHorizontally(RealMatrix matrix, boolean rightMatrix) Concatenate this and matrix horizontally.
RealMatrix	concatenateVertically(RealMatrix matrix) Concatenate this and matrix vertically.
RealMatrix	concatenateVertically(RealMatrix matrix, boolean lowerMatrix) Concatenate this and matrix vertically.
abstract RealMatrix	copy() Returns a (deep) copy of this.
void	copySubMatrix(int[] selectedRows, int[] selectedColumns, double[][] destination) Copy a submatrix.
void	copySubMatrix(int[] selectedRows, int[] selectedColumns, double[][] destination, int startRowDest, int startColumnDest) Copy a submatrix.
void	copySubMatrix(int startRow, int endRow, int startColumn, int endColumn, double[][] destination) Copy a submatrix.
void	copySubMatrix(int startRow, int endRow, int startColumn, int endColumn, double[][] destination, int startRowDest, int startColumnDest) Copy a submatrix.
abstract RealMatrix	createMatrix(int rowDimension, int columnDimension) Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
boolean	equals(Object object) Returns true if object is a RealMatrix instance with the same dimensions as this and all corresponding matrix entries are strictly equal (0. thresholds).
boolean	equals(Object object, double relativeThreshold, double absoluteThreshold) Returns true if object is a RealMatrix instance with the same dimensions as this and all corresponding matrix entries are equal.
double[]	getColumn(int column) Get the entries at the given column index as an array.
abstract int	getColumnDimension() Returns the number of columns of this matrix.
RealMatrix	getColumnMatrix(int column) Get the entries at the given column index as a column matrix.
RealVector	getColumnVector(int column) Get the entries at the given column index as a vector.
double[][]	getData() Returns matrix entries as a two-dimensional array.
double[][]	getData(boolean forceCopy) Returns matrix entries as a two-dimensional array.
Function<RealMatrix,Decomposition>	getDefaultDecomposition() Returns default decomposition builder (used by #RealMatrix.getInverse() method).
abstract double	getEntry(int row, int column) Get the entry in the specified row and column.
double	getFrobeniusNorm() Returns the Frobenius norm of the matrix.
RealMatrix	getInverse() Get the inverse (or pseudo-inverse) of the decomposed matrix using the default decomposition.
RealMatrix	getInverse(Function<RealMatrix,Decomposition> decompositionBuilder) Get the inverse (or pseudo-inverse) matrix computed with the given decomposition algorithm.
double	getMax() Returns the maximum value of the matrix.
double	getMin() Returns the minimum value of the matrix.
double	getNorm() Returns the maximum absolute row sum norm of the matrix.
double[]	getRow(int row) Get the entries at the given row index.
abstract int	getRowDimension() Returns the number of rows of this matrix.
RealMatrix	getRowMatrix(int row) Get the entries at the given row index as a row matrix.
RealVector	getRowVector(int row) Returns the entries in row number row as a vector.
RealMatrix	getSubMatrix(int[] selectedRows, int[] selectedColumns) Gets a submatrix.
RealMatrix	getSubMatrix(int startRow, int endRow, int startColumn, int endColumn) Gets a submatrix.
double	getTrace() Returns the trace of the matrix (the sum of the elements on the main diagonal).
int	hashCode() Computes a hashcode for the matrix.
boolean	isAntisymmetric(double relativeThreshold, double absoluteThreshold) Checks if this is a antisymmetric matrix
boolean	isDiagonal(double threshold) Given a threshold, is this a diagonal matrix?
boolean	isInvertible(double threshold) Given a threshold, is this an invertible matrix?
boolean	isOrthogonal(double thresholdNorm, double thresholdOrthogonality) Given a threshold, is this an orthogonal matrix?
boolean	isPositiveDefinite() Test the positivity of a matrix.
boolean	isSquare() Is this a square matrix?
boolean	isSymmetric() Checks if this is a symmetric matrix
boolean	isSymmetric(double relativeSymmetryThreshold) Checks if this is a symmetric matrix
boolean	isSymmetric(double relativeSymmetryThreshold, double absoluteSymmetryThreshold) Checks if this is a symmetric matrix
RealMatrix	multiply(DiagonalMatrix m, boolean toTranspose, double d) Returns the result of postmultiplying d × this × m (independently from the toTranspose parameter value as we use diagonal matrix).
RealMatrix	multiply(RealMatrix m) Returns the result of postmultiplying this by m.
RealMatrix	multiply(RealMatrix m, boolean toTranspose) Returns the result of postmultiplying this × m (if toTranspose = false) or this × mT (if toTranspose = true)
RealMatrix	multiply(RealMatrix m, boolean toTranspose, double d) Returns the result of postmultiplying d × this × m (if toTranspose = false ) or d × this × mT (if toTranspose = true)
void	multiplyEntry(int row, int column, double factor) Multiplies (in place) the specified entry of this matrix by the specified value.
double[]	operate(double[] v) Returns the result of multiplying this by the vector v.
RealVector	operate(RealVector v) Returns the result of multiplying this by the vector x.
RealMatrix	power(int p) Returns the result of multiplying this with itself p times.
double[]	preMultiply(double[] v) Returns the (row) vector result of premultiplying this by the vector v.
RealMatrix	preMultiply(RealMatrix m) Returns the result of premultiplying this by m.
RealVector	preMultiply(RealVector v) Returns the (row) vector result of premultiplying this by the vector v.
RealMatrix	scalarAdd(double d) Returns the result of adding d to each entry of this.
RealMatrix	scalarMultiply(double d) Returns the result of multiplying each entry of this by d.
void	setColumn(int column, double[] array) Sets the specified column of this matrix to the entries of the specified array.
void	setColumnMatrix(int column, RealMatrix matrix) Sets the specified column of this matrix to the entries of the specified column matrix.
void	setColumnVector(int column, RealVector vector) Sets the specified column of this matrix to the entries of the specified vector.
void	setDefaultDecomposition(Function<RealMatrix,Decomposition> defaultDecompositionBuilder) Sets the default decomposition builder which will be used by the getInverse() method to compute the matrix inverse.
abstract void	setEntry(int row, int column, double value) Set the entry in the specified row and column.
void	setRow(int row, double[] array) Sets the specified row of this matrix to the entries of the specified array.
void	setRowMatrix(int row, RealMatrix matrix) Sets the specified row of this matrix to the entries of the specified row matrix.
void	setRowVector(int row, RealVector vector) Sets the specified row of this matrix to the entries of the specified vector.
void	setSubMatrix(double[][] subMatrix, int row, int column) Replace the submatrix starting at row, column using data in the input subMatrix array.
RealMatrix	subtract(RealMatrix m) Returns this minus m.
String	toString() Get a string representation for this matrix.
String	toString(RealMatrixFormat realMatrixFormat) Get a string representation for this matrix.
RealMatrix	transpose() Returns the transpose of this matrix.
RealMatrix	transpose(boolean forceCopy) Returns the transpose of this matrix.
double	walkInColumnOrder(RealMatrixChangingVisitor visitor) Visit (and possibly change) all matrix entries in column order.
double	walkInColumnOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visit (and possibly change) some matrix entries in column order.
double	walkInColumnOrder(RealMatrixPreservingVisitor visitor) Visit (but don't change) all matrix entries in column order.
double	walkInColumnOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visit (but don't change) some matrix entries in column order.
double	walkInOptimizedOrder(RealMatrixChangingVisitor visitor) Visit (and possibly change) all matrix entries using the fastest possible order.
double	walkInOptimizedOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visit (and possibly change) some matrix entries using the fastest possible order.
double	walkInOptimizedOrder(RealMatrixPreservingVisitor visitor) Visit (but don't change) all matrix entries using the fastest possible order.
double	walkInOptimizedOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visit (but don't change) some matrix entries using the fastest possible order.
double	walkInRowOrder(RealMatrixChangingVisitor visitor) Visit (and possibly change) all matrix entries in row order.
double	walkInRowOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visit (and possibly change) some matrix entries in row order.
double	walkInRowOrder(RealMatrixPreservingVisitor visitor) Visit (but don't change) all matrix entries in row order.
double	walkInRowOrder(RealMatrixPreservingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visit (but don't change) some matrix entries in row order.

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

Constructor Detail

AbstractRealMatrix

protected AbstractRealMatrix()

Creates a matrix with no data.

AbstractRealMatrix

protected AbstractRealMatrix(int rowDimension,
                             int columnDimension)

Create a new RealMatrix 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

Throws:

NotStrictlyPositiveException - if row or column dimension is not positive

Method Detail

add

public RealMatrix add(RealMatrix m)

Returns the sum of this and m.

Specified by:

add in interface RealMatrix

Parameters:

m - matrix to be added

Returns:

this + m

subtract

public RealMatrix subtract(RealMatrix m)

Returns this minus m.

Specified by:

subtract in interface RealMatrix

Parameters:

m - matrix to be subtracted

Returns:

this - m

scalarAdd

public RealMatrix scalarAdd(double d)

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

Specified by:

scalarAdd in interface RealMatrix

Parameters:

d - value to be added to each entry

Returns:

d + this

scalarMultiply

public RealMatrix scalarMultiply(double d)

Returns the result of multiplying each entry of this by d.

Specified by:

scalarMultiply in interface RealMatrix

Parameters:

d - value to multiply all entries by

Returns:

d * this

multiply

public RealMatrix multiply(RealMatrix m)

Returns the result of postmultiplying this by m.

Specified by:

multiply in interface RealMatrix

Parameters:

m - matrix to postmultiply by

Returns:

this * m

multiply

public RealMatrix multiply(RealMatrix m,
                           boolean toTranspose)

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

Specified by:

multiply in interface RealMatrix

Parameters:

m - matrix to postmultiply by

toTranspose - if true, assumes the provided matrix is M^T, otherwise assumes it is M

Returns:

this × m or this × m^T

multiply

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

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

Specified by:

multiply in interface RealMatrix

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

multiply

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

Returns the result of postmultiplying d × this × m (independently from the toTranspose parameter value as we use diagonal matrix). Optimized method for diagonal matrix.

Parameters:

m - matrix to postmultiply by

toTranspose - no used value for diagonal matrix

d - value to multiply all entries by

Returns:

d × this × m

Throws:

DimensionMismatchException - if matrices are not multiplication compatible

preMultiply

public RealMatrix preMultiply(RealMatrix m)

Returns the result of premultiplying this by m.

Specified by:

preMultiply in interface RealMatrix

Parameters:

m - matrix to premultiply by

Returns:

m * this

power

public RealMatrix power(int p)

Returns the result of multiplying this with itself p times. Depending on the underlying storage, instability for high powers might occur.

Specified by:

power in interface RealMatrix

Parameters:

p - raise this to power p

Returns:

this^p

getData

public double[][] getData()

Returns matrix entries as a two-dimensional array. Data is a copy of internal data.

Specified by:

getData in interface RealMatrix

Returns:

2-dimensional array of entries

getData

public double[][] getData(boolean forceCopy)

Returns matrix entries as a two-dimensional array.

Specified by:

getData in interface RealMatrix

Parameters:

forceCopy - true if we want to copy the array, false if we only pass it as a reference (if existing like for instance Array2DRowRealMatrix)

Returns:

2-dimensional array of entries

getNorm

public double getNorm()

Returns the maximum absolute row sum norm of the matrix.

Specified by:

getNorm in interface RealMatrix

Returns:

norm

getFrobeniusNorm

public double getFrobeniusNorm()

Returns the Frobenius norm of the matrix.

Specified by:

getFrobeniusNorm in interface RealMatrix

Returns:

norm

getMax

public double getMax()

Returns the maximum value of the matrix.

Specified by:

getMax in interface RealMatrix

Returns:

maximum

getMin

public double getMin()

Returns the minimum value of the matrix.

Specified by:

getMin in interface RealMatrix

Returns:

minimum

getSubMatrix

public RealMatrix 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

Parameters:

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - Final column index (inclusive)

Returns:

The subMatrix containing the data of the specified rows and columns.

getSubMatrix

public RealMatrix getSubMatrix(int[] selectedRows,
                               int[] selectedColumns)

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

Specified by:

getSubMatrix in interface RealMatrix

Parameters:

selectedRows - Array of row indices.

selectedColumns - Array of column indices.

Returns:

The subMatrix containing the data in the specified rows and columns

copySubMatrix

public void copySubMatrix(int startRow,
                          int endRow,
                          int startColumn,
                          int endColumn,
                          double[][] destination)

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

Specified by:

copySubMatrix in interface RealMatrix

Parameters:

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - Final column index (inclusive)

destination - The arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)

copySubMatrix

public void copySubMatrix(int startRow,
                          int endRow,
                          int startColumn,
                          int endColumn,
                          double[][] destination,
                          int startRowDest,
                          int startColumnDest)

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

Specified by:

copySubMatrix in interface RealMatrix

Parameters:

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - Final column index (inclusive)

destination - The arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)

startRowDest - Initial row index of the destination array

startColumnDest - Initial column index of the destination array

copySubMatrix

public void copySubMatrix(int[] selectedRows,
                          int[] selectedColumns,
                          double[][] destination)

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

Specified by:

copySubMatrix in interface RealMatrix

Parameters:

selectedRows - Array of row indices.

selectedColumns - Array of column indices.

destination - The arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)

copySubMatrix

public void copySubMatrix(int[] selectedRows,
                          int[] selectedColumns,
                          double[][] destination,
                          int startRowDest,
                          int startColumnDest)

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

Specified by:

copySubMatrix in interface RealMatrix

Parameters:

selectedRows - Array of row indices.

selectedColumns - Array of column indices.

destination - The arrays where the submatrix data should be copied (if larger than rows/columns counts, only the upper-left part will be used)

startRowDest - Initial row index of the destination array

startColumnDest - Initial column index of the destination array

setSubMatrix

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

Replace the submatrix starting at row, column using data in the input subMatrix array. Indexes are 0-based.

Example:
Starting with

 1  2  3  4
 5  6  7  8
 9  0  1  2
 

and subMatrix = {{3, 4} {5,6}}, invoking setSubMatrix(subMatrix,1,1)) will result in

 1  2  3  4
 5  3  4  8
 9  5  6  2
 

Specified by:

setSubMatrix in interface RealMatrix

Parameters:

subMatrix - array containing the submatrix replacement data

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

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

getRowMatrix

public RealMatrix getRowMatrix(int row)

Get the entries at the given row index as a row matrix. Row indices start at 0.

Specified by:

getRowMatrix in interface RealMatrix

Parameters:

row - Row to be fetched.

Returns:

row Matrix.

setRowMatrix

public void setRowMatrix(int row,
                         RealMatrix matrix)

Sets the specified row of this matrix to the entries of the specified row matrix. Row indices start at 0.

Specified by:

setRowMatrix in interface RealMatrix

Parameters:

row - Row to be set.

matrix - Row matrix to be copied (must have one row and the same number of columns as the instance).

getColumnMatrix

public RealMatrix getColumnMatrix(int column)

Get the entries at the given column index as a column matrix. Column indices start at 0.

Specified by:

getColumnMatrix in interface RealMatrix

Parameters:

column - Column to be fetched.

Returns:

column Matrix.

setColumnMatrix

public void setColumnMatrix(int column,
                            RealMatrix matrix)

Sets the specified column of this matrix to the entries of the specified column matrix. Column indices start at 0.

Specified by:

setColumnMatrix in interface RealMatrix

Parameters:

column - Column to be set.

matrix - Column matrix to be copied (must have one column and the same number of rows as the instance).

getRowVector

public RealVector getRowVector(int row)

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

Specified by:

getRowVector in interface RealMatrix

Parameters:

row - Row to be fetched.

Returns:

a row vector.

setRowVector

public void setRowVector(int row,
                         RealVector vector)

Sets the specified row of this matrix to the entries of the specified vector. Row indices start at 0.

Specified by:

setRowVector in interface RealMatrix

Parameters:

row - Row to be set.

vector - row vector to be copied (must have the same number of column as the instance).

getColumnVector

public RealVector getColumnVector(int column)

Get the entries at the given column index as a vector. Column indices start at 0.

Specified by:

getColumnVector in interface RealMatrix

Parameters:

column - Column to be fetched.

Returns:

a column vector.

setColumnVector

public void setColumnVector(int column,
                            RealVector vector)

Sets the specified column of this matrix to the entries of the specified vector. Column indices start at 0.

Specified by:

setColumnVector in interface RealMatrix

Parameters:

column - Column to be set.

vector - column vector to be copied (must have the same number of rows as the instance).

getRow

public double[] getRow(int row)

Get the entries at the given row index. Row indices start at 0.

Specified by:

getRow in interface RealMatrix

Parameters:

row - Row to be fetched.

Returns:

the array of entries in the row.

setRow

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

Sets the specified row of this matrix to the entries of the specified array. Row indices start at 0.

Specified by:

setRow in interface RealMatrix

Parameters:

row - Row to be set.

array - Row matrix to be copied (must have the same number of columns as the instance)

getColumn

public double[] getColumn(int column)

Get the entries at the given column index as an array. Column indices start at 0.

Specified by:

getColumn in interface RealMatrix

Parameters:

column - Column to be fetched.

Returns:

the array of entries in the column.

setColumn

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

Sets the specified column of this matrix to the entries of the specified array. Column indices start at 0.

Specified by:

setColumn in interface RealMatrix

Parameters:

column - Column to be set.

array - Column array to be copied (must have the same number of rows as the instance).

addToEntry

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

Adds (in place) the specified value to the specified entry of this matrix. Row and column indices start at 0.

Specified by:

addToEntry in interface RealMatrix

Parameters:

row - Row index of the entry to be modified.

column - Column index of the entry to be modified.

increment - 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 the specified value. Row and column indices start at 0.

Specified by:

multiplyEntry in interface RealMatrix

Parameters:

row - Row index of the entry to be modified.

column - Column index of the entry to be modified.

factor - Multiplication factor for the matrix entry.

transpose

public RealMatrix transpose()

Returns the transpose of this matrix.

Specified by:

transpose in interface RealMatrix

Returns:

transpose matrix

transpose

public RealMatrix transpose(boolean forceCopy)

Returns the transpose of this matrix.

Specified by:

transpose in interface RealMatrix

Parameters:

forceCopy - true if we want to return a copy of the matrix, false otherwise

Returns:

transpose matrix

concatenateHorizontally

public RealMatrix concatenateHorizontally(RealMatrix matrix)

Concatenate this and matrix horizontally.

Specified by:

concatenateHorizontally in interface RealMatrix

Parameters:

matrix - Matrix to concatenate

Returns:

the concatenated matrix

concatenateHorizontally

public RealMatrix concatenateHorizontally(RealMatrix matrix,
                                          boolean rightMatrix)

Concatenate this and matrix horizontally.

• If rightMatrix is true : [Mout] = [this , matrix]
• If rightMatrix is false : [Mout] = [matrix , this]

Specified by:

concatenateHorizontally in interface RealMatrix

Parameters:

matrix - Matrix to concatenate

rightMatrix - Position indication of the matrix argument : right or left (true/false)

Returns:

the concatenated matrix

concatenateVertically

public RealMatrix concatenateVertically(RealMatrix matrix)

Concatenate this and matrix vertically.

Specified by:

concatenateVertically in interface RealMatrix

Parameters:

matrix - Matrix to concatenate

Returns:

the concatenated matrix

concatenateVertically

public RealMatrix concatenateVertically(RealMatrix matrix,
                                        boolean lowerMatrix)

Concatenate this and matrix vertically.

• If lowerMatrix is true : [Mout] = [this ; matrix]
• If lowerMatrix is false : [Mout] = [matrix ; this]

Specified by:

concatenateVertically in interface RealMatrix

Parameters:

matrix - Matrix to concatenate

lowerMatrix - Position indication of the matrix argument : bottom or top (true/false)

Returns:

the concatenated matrix

concatenateDiagonally

public RealMatrix concatenateDiagonally(RealMatrix matrix,
                                        boolean lowerRightMatrix)

Concatenate this and matrix vertically.

• If lowerRightMatrix is true : [Mout] = [this, 0, ..., 0 ; 0, ..., 0, matrix]
• If lowerRightMatrix is false : [Mout] = [matrix, 0, ..., 0; 0, ..., 0, this]

Specified by:

concatenateDiagonally in interface RealMatrix

Parameters:

matrix - Matrix to concatenate

lowerRightMatrix - Position indication of the matrix argument : bottom-right or top-left (true/false)

Returns:

the concatenated matrix

setDefaultDecomposition

public void setDefaultDecomposition(Function<RealMatrix,Decomposition> defaultDecompositionBuilder)

Sets the default decomposition builder which will be used by the getInverse() method to compute the matrix inverse.

Specified by:

setDefaultDecomposition in interface RealMatrix

Parameters:

defaultDecompositionBuilder - default decomposition builder

getDefaultDecomposition

public Function<RealMatrix,Decomposition> getDefaultDecomposition()

Returns default decomposition builder (used by #RealMatrix.getInverse() method). By default, without any user call to #setDefaultDecomposition(Function), a LUDecomposition.decompositionBuilder(1e-11) will be returned.

Specified by:

getDefaultDecomposition in interface RealMatrix

Returns:

default decomposition builder

getInverse

public RealMatrix getInverse()

Get the inverse (or pseudo-inverse) of the decomposed matrix using the default decomposition. The default decomposition builder can be changed using the setDefaultDecomposition(Function) method. Default decomposition is used. Default decomposition builder is set to LUDecomposition.decompositionBuilder(1e-11).

Specified by:

getInverse in interface RealMatrix

Returns:

inverse matrix

getInverse

public RealMatrix getInverse(Function<RealMatrix,Decomposition> decompositionBuilder)

Get the inverse (or pseudo-inverse) matrix computed with the given decomposition algorithm.

Specified by:

getInverse in interface RealMatrix

Parameters:

decompositionBuilder - function to construct the decomposition available in the Decomposition classes, for instance QRDecomposition.decompositionBuilder(double)

Returns:

inverse matrix

isSquare

public boolean isSquare()

Is this a square matrix?

Specified by:

isSquare in interface AnyMatrix

Returns:

true if the matrix is square (rowDimension = columnDimension)

isSymmetric

public boolean isSymmetric()

Checks if this is a symmetric matrix

Matrix is considered symmetric if no cross-term violates default absolute and relative thresholds ( both Precision.DOUBLE_COMPARISON_EPSILON).

Specified by:

isSymmetric in interface RealMatrix

Returns:

true if this is a symmetric matrix

isSymmetric

public boolean isSymmetric(double relativeSymmetryThreshold)

Checks if this is a symmetric matrix

Matrix is considered symmetric if no cross-term violates provided relative threshold and 0 absolute threshold.

Specified by:

isSymmetric in interface RealMatrix

Parameters:

relativeSymmetryThreshold - relative threshold above which off-diagonal elements are considered too different and matrix not symmetric

Returns:

true if symmetric taking into account threshold

isSymmetric

public boolean isSymmetric(double relativeSymmetryThreshold,
                           double absoluteSymmetryThreshold)

Checks if this is a symmetric matrix

Matrix is considered symmetric if no cross-term violate both provided thresholds.

Specified by:

isSymmetric in interface RealMatrix

Parameters:

relativeSymmetryThreshold - relative threshold above which off-diagonal elements are considered too different and matrix not symmetric

absoluteSymmetryThreshold - absolute threshold above which off-diagonal elements are considered too different and matrix not symmetric

Returns:

true if symmetric taking into account threshold

isAntisymmetric

public boolean isAntisymmetric(double relativeThreshold,
                               double absoluteThreshold)

Checks if this is a antisymmetric matrix

Specified by:

isAntisymmetric in interface RealMatrix

Parameters:

relativeThreshold - the relative threshold to compare the elements out of the diagonal

absoluteThreshold - the absolute threshold used in comparisons to zero for the diagonal values

Returns:

true if antisymmetric taking into account threshold

getRowDimension

public abstract int getRowDimension()

Returns the number of rows of this matrix.

Specified by:

getRowDimension in interface AnyMatrix

Specified by:

getRowDimension in class RealLinearOperator

Returns:

the number of rows.

getColumnDimension

public abstract int getColumnDimension()

Returns the number of columns of this matrix.

Specified by:

getColumnDimension in interface AnyMatrix

Specified by:

getColumnDimension in class RealLinearOperator

Returns:

the number of columns.

getTrace

public double getTrace()

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

Specified by:

getTrace in interface RealMatrix

Returns:

the trace.

operate

public double[] operate(double[] v)

Returns the result of multiplying this by the vector v.

Specified by:

operate in interface RealMatrix

Parameters:

v - the vector to operate on

Returns:

this * v

operate

public RealVector operate(RealVector v)

Returns the result of multiplying this by the vector x.

Specified by:

operate in interface RealMatrix

Specified by:

operate in class RealLinearOperator

Parameters:

v - the vector to operate on

Returns:

the product of this instance with x

preMultiply

public double[] preMultiply(double[] v)

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

Specified by:

preMultiply in interface RealMatrix

Parameters:

v - the row vector to premultiply by

Returns:

v * this

preMultiply

public RealVector preMultiply(RealVector v)

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

Specified by:

preMultiply in interface RealMatrix

Parameters:

v - the row vector to premultiply by

Returns:

v * this

walkInRowOrder

public double walkInRowOrder(RealMatrixChangingVisitor visitor)

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

Row order starts at upper left and 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

Parameters:

visitor - 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)

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

Row order starts at upper left and 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

Parameters:

visitor - 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)

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

Row order starts at upper left and 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

Parameters:

visitor - visitor used to process all matrix entries

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - 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)

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

Row order starts at upper left and 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

Parameters:

visitor - visitor used to process all matrix entries

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - 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)

walkInColumnOrder

public double walkInColumnOrder(RealMatrixChangingVisitor visitor)

Visit (and possibly change) all matrix entries in column order.

Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.

Specified by:

walkInColumnOrder in interface RealMatrix

Parameters:

visitor - 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(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)

walkInColumnOrder

public double walkInColumnOrder(RealMatrixPreservingVisitor visitor)

Visit (but don't change) all matrix entries in column order.

Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.

Specified by:

walkInColumnOrder in interface RealMatrix

Parameters:

visitor - 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(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)

walkInColumnOrder

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

Visit (and possibly change) some matrix entries in column order.

Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.

Specified by:

walkInColumnOrder in interface RealMatrix

Parameters:

visitor - visitor used to process all matrix entries

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - 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(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), 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)

walkInColumnOrder

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

Visit (but don't change) some matrix entries in column order.

Column order starts at upper left and iterating through all elements of a column from top to bottom before going to the topmost element of the next column.

Specified by:

walkInColumnOrder in interface RealMatrix

Parameters:

visitor - visitor used to process all matrix entries

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - 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.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, 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)

Visit (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

Parameters:

visitor - 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)

Visit (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

Parameters:

visitor - 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)

Visit (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

Parameters:

visitor - visitor used to process all matrix entries

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - 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)

Visit (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

Parameters:

visitor - visitor used to process all matrix entries

startRow - Initial row index

endRow - Final row index (inclusive)

startColumn - Initial column index

endColumn - 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)

toString

public String toString()

Get a string representation for this matrix.

Default format is MatrixUtils.VISUAL_FORMAT.

Overrides:

toString in class Object

Returns:

a string representation for this matrix

toString

public String toString(RealMatrixFormat realMatrixFormat)

Get a string representation for this matrix.

Specified by:

toString in interface RealMatrix

Parameters:

realMatrixFormat - matrix format there exist predefined formats in MatrixUtils

Returns:

a string representation for this matrix

equals

public boolean equals(Object object)

Returns true if object is a RealMatrix instance with the same dimensions as this and all corresponding matrix entries are strictly equal (0. thresholds).

Overrides:

equals in class Object

Parameters:

object - the object to test equality against.

Returns:

true if object equals this

equals

public boolean equals(Object object,
                      double relativeThreshold,
                      double absoluteThreshold)

Returns true if object is a RealMatrix instance with the same dimensions as this and all corresponding matrix entries are equal.

Specified by:

equals in interface RealMatrix

Parameters:

object - the object to test equality against.

relativeThreshold - RelativeThreshold used for comparison

absoluteThreshold - AbsoluteThreshold used for comparison

Returns:

true if object equals this

hashCode

public int hashCode()

Computes a hashcode for the matrix.

Overrides:

hashCode in class Object

Returns:

hashcode for matrix

isOrthogonal

public boolean isOrthogonal(double thresholdNorm,
                            double thresholdOrthogonality)

Given a threshold, is this an orthogonal matrix? The method indicates if the matrix is orthogonal. To do so the method checks if the column vectors of the matrix form an orthonomal set.

Specified by:

isOrthogonal in interface RealMatrix

Parameters:

thresholdNorm - : allowed relative error with respect to the normality of the vectors

thresholdOrthogonality - : allowed absolute error with respect to the mutual orthogonality of the vectors

Returns:

true if the vectors form an orthonormal set taking into account an allowed error, false otherwise

isDiagonal

public boolean isDiagonal(double threshold)

Given a threshold, is this a diagonal matrix? The method indicates if the matrix is diagonal. To do so the method checks if the non diagonal elements are zero.

Specified by:

isDiagonal in interface RealMatrix

Parameters:

threshold - : allowed absolute error on non diagonal elements

Returns:

true if the non diagonal elements are zero taking into account a threshold, false otherwise

isInvertible

public boolean isInvertible(double threshold)

Given a threshold, is this an invertible matrix? The method indicates if the matrix is invertible. To do so the method checks the linear independence between the column vectors of the matrix.

Specified by:

isInvertible in interface RealMatrix

Parameters:

threshold - : allowed relative error on the column vectors independence

Returns:

true if the determinant is different to zero taking into account a threshold, false otherwise

isPositiveDefinite

public boolean isPositiveDefinite()

Test the positivity of a matrix.

Specified by:

isPositiveDefinite in interface RealMatrix

Returns:

true if the matrix is symmetric positive semidefinite false otherwise

createMatrix

public abstract RealMatrix createMatrix(int rowDimension,
                                        int columnDimension)

Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.

Specified by:

createMatrix in interface RealMatrix

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 the instance

copy

public abstract RealMatrix copy()

Returns a (deep) copy of this.

Specified by:

copy in interface RealMatrix

Returns:

matrix copy

getEntry

public abstract double getEntry(int row,
                                int column)

Get the entry in the specified row and column. Row and column indices start at 0.

Specified by:

getEntry in interface RealMatrix

Parameters:

row - Row index of entry to be fetched.

column - Column index of entry to be fetched.

Returns:

the matrix entry at (row, column).

setEntry

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

Set the entry in the specified row and column. Row and column indices start at 0.

Specified by:

setEntry in interface RealMatrix

Parameters:

row - Row index of entry to be set.

column - Column index of entry to be set.

value - the new value of the entry.