fr.cnes.sirius.patrius.math.linear

Class DiagonalMatrix

java.lang.Object

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

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

fr.cnes.sirius.patrius.math.linear.DiagonalMatrix

All Implemented Interfaces:

AnyMatrix, RealMatrix, SymmetricMatrix, Serializable

public class DiagonalMatrix
extends AbstractRealMatrix
implements SymmetricMatrix, Serializable

Implementation of a diagonal matrix.
Caveat: This implementation is minimal; it is currently solely aimed at solving issue MATH-924. In particular many methods just throw MathUnsupportedOperationException.

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

Version:

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

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
DiagonalMatrix(double[] d) Creates a matrix using the input array as the underlying data.
DiagonalMatrix(double[] d, boolean copyArray) Creates a matrix using the input array as the underlying data.
DiagonalMatrix(int dimension) Creates a matrix with the supplied dimension.

Method Summary

Modifier and Type	Method and Description
DiagonalMatrix	add(DiagonalMatrix m) Compute the sum of this and m.
RealMatrix	add(RealMatrix m) Returns the sum of this and m.
SymmetricMatrix	add(SymmetricMatrix m) Adds a SymmetricMatrix to this matrix.
void	addToEntry(int row, int column, double increment) Adds (in place) the specified value to the specified entry of this matrix.
DiagonalMatrix	copy() Returns a (deep) copy of this.
void	copySubMatrix(int[] selectedRows, int[] selectedColumns, double[][] destination) Copy a submatrix.
void	copySubMatrix(int startRow, int endRow, int startColumn, int endColumn, double[][] destination) Copy a submatrix.
DiagonalMatrix	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 iff object is a RealMatrix instance with the same dimensions as this and all corresponding matrix entries are equal.
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.
double[][]	getData() Returns matrix entries as a two-dimensional array.
double[]	getDataRef() Gets a reference to the underlying data array.
double	getEntry(int row, int column) Get the entry in the specified row and column.
double	getFrobeniusNorm() Returns the Frobenius norm of the matrix.
DiagonalMatrix	getInverse() Optimized method for DiagonalMatrix matrix.
DiagonalMatrix	getInverse(Decomposition decomposition) Optimized method for DiagonalMatrix matrix.
double	getNorm() Returns the maximum absolute row sum norm of the matrix.
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.
RealMatrix	getSubMatrix(int[] selectedRows, int[] selectedColumns) Gets a submatrix.
RealMatrix	getSubMatrix(int startRow, int endRow, int startColumn, int endColumn) Gets a submatrix.
int	hashCode() Computes a hashcode for the diagonal matrix.
boolean	isAntisymmetric(double zeroDiagonalThreshold) 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	isSingular() Returns whether this diagonal matrix is singular, i.e. any diagonal entry is equal to 0 within the Precision.DOUBLE_COMPARISON_EPSILON threshold.
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
DiagonalMatrix	multiply(DiagonalMatrix m) Returns the result of postmultiplying this × m.
DiagonalMatrix	multiply(DiagonalMatrix m, boolean toTranspose) Returns the result of postmultiplying this × m (independently from the toTranspose parameter value as we use diagonal matrix).
DiagonalMatrix	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 isTranspose = false) or this × mT (if isTranspose = 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.
DiagonalMatrix	permutation(int[] index) Permute the rows/columns of this matrix according to a new specified index order list.
DiagonalMatrix	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.
RealVector	preMultiply(RealVector v) Returns the (row) vector result of premultiplying this by the vector v.
SymmetricMatrix	quadraticMultiplication(RealMatrix m) Gets the result of the quadratic multiplication M×S×MT, where S is this matrix and M is the provided matrix.
SymmetricMatrix	quadraticMultiplication(RealMatrix m, boolean isTranspose) Gets the result of the quadratic multiplication M×S×MT, where S is this matrix and M or MT is the provided matrix.
SymmetricMatrix	scalarAdd(double d) Returns the result of adding d to each entry of this.
DiagonalMatrix	scalarMultiply(double d) Returns the result of multiplying each entry of this by d.
void	setEntry(int row, int column, double value) Set the entry in the specified row and column.
void	setSubMatrix(double[][] subMatrix, int row, int column) The method systematically throws a MathUnsupportedOperationException as this operation is not safe when we deal with a DiagonalMatrix.
DiagonalMatrix	subtract(DiagonalMatrix m) Returns this minus m.
RealMatrix	subtract(RealMatrix m) Returns this minus m.
SymmetricMatrix	subtract(SymmetricMatrix m) Subtracts a SymmetricMatrix from this matrix.
DiagonalMatrix	transpose() 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	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.AbstractRealMatrix

concatenateDiagonally, concatenateHorizontally, concatenateVertically, equals, getColumn, getColumnVector, getDefaultDecomposition, getRow, getRowVector, getTrace, isSymmetric, operate, preMultiply, setColumn, setColumnMatrix, setColumnVector, setDefaultDecomposition, setRow, setRowMatrix, setRowVector, toString, toString, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder

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

concatenateDiagonally, concatenateHorizontally, concatenateVertically, equals, getColumn, getColumnVector, getDefaultDecomposition, getRow, getRowVector, getTrace, isSymmetric, operate, preMultiply, setColumn, setColumnMatrix, setColumnVector, setDefaultDecomposition, setRow, setRowMatrix, setRowVector, toString, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder

Constructor Detail

DiagonalMatrix

public DiagonalMatrix(int dimension)

Creates a matrix with the supplied dimension.

Parameters:

dimension - Number of rows and columns in the new matrix.

Throws:

NotStrictlyPositiveException - if the dimension is not positive.

DiagonalMatrix

public DiagonalMatrix(double[] d)

Creates a matrix using the input array as the underlying data.
The input array is copied, not referenced.

Parameters:

d - Data for the new matrix.

Throws:

NullArgumentException - if d is null.

DiagonalMatrix

public DiagonalMatrix(double[] d,
                      boolean copyArray)

Creates a matrix using the input array as the underlying data.
If an array is created specially in order to be embedded in a this instance and not used directly, the copyArray may be set to false. This will prevent the copying and improve performance as no new array will be built and no data will be copied.

Parameters:

d - Data for new matrix.

copyArray - if true, the input array will be copied, otherwise it will be referenced.

Throws:

NullArgumentException - if d is null.

Method Detail

createMatrix

public DiagonalMatrix 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

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 the instance

Throws:

DimensionMismatchException - if the requested dimensions are not equal.

add

public RealMatrix add(RealMatrix m)

Returns the sum of this and m.

Specified by:

add in interface RealMatrix

Overrides:

add in class AbstractRealMatrix

Parameters:

m - matrix to be added

Returns:

this + m

add

public SymmetricMatrix add(SymmetricMatrix m)

Adds a SymmetricMatrix to this matrix.

Specified by:

add in interface SymmetricMatrix

Parameters:

m - the matrix to add

Returns:

the matrix resulting from this addition

add

public DiagonalMatrix add(DiagonalMatrix m)

Compute the sum of this and m.

Parameters:

m - Matrix to be added.

Returns:

this + m.

Throws:

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

subtract

public RealMatrix subtract(RealMatrix m)

Returns this minus m.

Specified by:

subtract in interface RealMatrix

Overrides:

subtract in class AbstractRealMatrix

Parameters:

m - matrix to be subtracted

Returns:

this - m

subtract

public SymmetricMatrix subtract(SymmetricMatrix m)

Subtracts a SymmetricMatrix from this matrix.

Specified by:

subtract in interface SymmetricMatrix

Parameters:

m - the matrix to subtract

Returns:

the matrix resulting from this subtraction

subtract

public DiagonalMatrix subtract(DiagonalMatrix m)

Returns this minus m.

Parameters:

m - Matrix to be subtracted.

Returns:

this - m

Throws:

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

scalarAdd

public SymmetricMatrix scalarAdd(double d)

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

Returns a ArrayRowSymmetricMatrix since the matrix is symmetric.

Specified by:

scalarAdd in interface RealMatrix

Specified by:

scalarAdd in interface SymmetricMatrix

Overrides:

scalarAdd in class AbstractRealMatrix

Parameters:

d - value to be added to each entry

Returns:

d + this

multiply

public RealMatrix multiply(RealMatrix m)

Returns the result of postmultiplying this by m.

Specified by:

multiply in interface RealMatrix

Overrides:

multiply in class AbstractRealMatrix

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 isTranspose = false) or this × m^T (if isTranspose = true)

Specified by:

multiply in interface RealMatrix

Overrides:

multiply in class AbstractRealMatrix

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

Overrides:

multiply in class AbstractRealMatrix

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 DiagonalMatrix multiply(DiagonalMatrix m)

Returns the result of postmultiplying this × m. Optimized method for diagonal matrix.

Parameters:

m - matrix to postmultiply by

Returns:

this * m

Throws:

DimensionMismatchException - if matrices are not multiplication compatible

multiply

public DiagonalMatrix multiply(DiagonalMatrix m,
                               boolean toTranspose)

Returns the result of postmultiplying 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

Returns:

this * m or @return this * m.transposed

Throws:

DimensionMismatchException - if matrices are not multiplication compatible

multiply

public DiagonalMatrix 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.

Overrides:

multiply in class AbstractRealMatrix

Parameters:

m - matrix to postmultiply by

toTranspose - no used value for diagonal matrix

d - value to multiply all entries by

Returns:

d × this × m or d × this × m.transposed

Throws:

DimensionMismatchException - if matrices are not multiplication compatible

scalarMultiply

public DiagonalMatrix scalarMultiply(double d)

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

Specified by:

scalarMultiply in interface RealMatrix

Specified by:

scalarMultiply in interface SymmetricMatrix

Overrides:

scalarMultiply in class AbstractRealMatrix

Parameters:

d - value to multiply all entries by

Returns:

d * this

getInverse

public DiagonalMatrix getInverse()

Optimized method for DiagonalMatrix matrix.

Specified by:

getInverse in interface RealMatrix

Specified by:

getInverse in interface SymmetricMatrix

Overrides:

getInverse in class AbstractRealMatrix

Returns:

inverse matrix

Throws:

SingularMatrixException - if the decomposed matrix is singular.

getInverse

public DiagonalMatrix getInverse(Decomposition decomposition)

Optimized method for DiagonalMatrix matrix. The input Decomposition isn't used.

Specified by:

getInverse in interface RealMatrix

Specified by:

getInverse in interface SymmetricMatrix

Overrides:

getInverse in class AbstractRealMatrix

Parameters:

decomposition - decomposed matrix

Returns:

inverse matrix

Throws:

SingularMatrixException - if the decomposed matrix is singular.

isSingular

public boolean isSingular()

Returns whether this diagonal matrix is singular, i.e. any diagonal entry is equal to 0 within the Precision.DOUBLE_COMPARISON_EPSILON threshold.

Returns:

true if the matrix is singular, false otherwise

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

Overrides:

isOrthogonal in class AbstractRealMatrix

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

Overrides:

isDiagonal in class AbstractRealMatrix

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

isSquare

public boolean isSquare()

Is this a square matrix?

Specified by:

isSquare in interface AnyMatrix

Overrides:

isSquare in class AbstractRealMatrix

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

Overrides:

isSymmetric in class AbstractRealMatrix

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

Overrides:

isSymmetric in class AbstractRealMatrix

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

isAntisymmetric

public boolean isAntisymmetric(double zeroDiagonalThreshold)

Checks if this is a antisymmetric matrix

Specified by:

isAntisymmetric in interface RealMatrix

Overrides:

isAntisymmetric in class AbstractRealMatrix

Parameters:

zeroDiagonalThreshold - the threshold used in comparisons to zero for the diagonal values

Returns:

true if this is a antisymmetric matrix

transpose

public DiagonalMatrix transpose()

Returns the transpose of this matrix.

Specified by:

transpose in interface RealMatrix

Specified by:

transpose in interface SymmetricMatrix

Overrides:

transpose in class AbstractRealMatrix

Returns:

transpose matrix

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

Overrides:

isInvertible in class AbstractRealMatrix

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

getData

public double[][] getData()

Returns matrix entries as a two-dimensional array.

Specified by:

getData in interface RealMatrix

Overrides:

getData in class AbstractRealMatrix

Returns:

2-dimensional array of entries

getDataRef

public double[] getDataRef()

Gets a reference to the underlying data array.

Returns:

1-dimensional array of entries.

setSubMatrix

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

The method systematically throws a MathUnsupportedOperationException as this operation is not safe when we deal with a DiagonalMatrix.

Specified by:

setSubMatrix in interface RealMatrix

Overrides:

setSubMatrix in class AbstractRealMatrix

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

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

getEntry

public 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

Specified by:

getEntry in class AbstractRealMatrix

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 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

Specified by:

setEntry in class AbstractRealMatrix

Parameters:

row - Row index of entry to be set.

column - Column index of entry to be set.

value - the new value of the entry.

Throws:

MathUnsupportedOperationException - if row != column.

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

Overrides:

addToEntry in class AbstractRealMatrix

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.

Throws:

MathUnsupportedOperationException - if row != column.

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

Overrides:

multiplyEntry in class AbstractRealMatrix

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.

Throws:

MathUnsupportedOperationException - if row != column.

power

public DiagonalMatrix 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

Specified by:

power in interface SymmetricMatrix

Overrides:

power in class AbstractRealMatrix

Parameters:

p - raise this to power p

Returns:

this^p

getRowDimension

public int getRowDimension()

Returns the number of rows of this matrix.

Specified by:

getRowDimension in interface AnyMatrix

Specified by:

getRowDimension in class AbstractRealMatrix

Returns:

the number of rows.

getColumnDimension

public int getColumnDimension()

Returns the number of columns of this matrix.

Specified by:

getColumnDimension in interface AnyMatrix

Specified by:

getColumnDimension in class AbstractRealMatrix

Returns:

the number of columns.

operate

public double[] operate(double[] v)

Returns the result of multiplying this by the vector v.

Specified by:

operate in interface RealMatrix

Overrides:

operate in class AbstractRealMatrix

Parameters:

v - the vector to operate on

Returns:

this * v

preMultiply

public double[] preMultiply(double[] v)

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

Specified by:

preMultiply in interface RealMatrix

Overrides:

preMultiply in class AbstractRealMatrix

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

Overrides:

preMultiply in class AbstractRealMatrix

Parameters:

v - the row vector to premultiply by

Returns:

v * this

quadraticMultiplication

public SymmetricMatrix quadraticMultiplication(RealMatrix m)

Gets the result of the quadratic multiplication M×S×M^T, where S is this matrix and M is the provided matrix.

Specified by:

quadraticMultiplication in interface SymmetricMatrix

Parameters:

m - the matrix M

Returns:

M×S×M^T

quadraticMultiplication

public SymmetricMatrix quadraticMultiplication(RealMatrix m,
                                               boolean isTranspose)

Gets the result of the quadratic multiplication M×S×M^T, where S is this matrix and M or M^T is the provided matrix.

Specified by:

quadraticMultiplication in interface SymmetricMatrix

Parameters:

m - the matrix M or the matrix M^T

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

Returns:

M×S×M^T

permutation

public DiagonalMatrix permutation(int[] index)

Permute the rows/columns of this matrix according to a new specified index order list.

The index list must be the same dimension as the matrix and each index must be represented.

 Usage example :
        1        2        3                            2       3        1
   1 [lambda1,      mu,   gamma]                 2 [lambda2,    beta,      mu]
   2 [     mu, lambda2,    beta] --> {2,3,1} --> 3 [   beta, lambda3,   gamma]
   3 [  gamma,    beta, lambda3]                 1 [     mu,   gamma, lambda1]
 

Specified by:

permutation in interface SymmetricMatrix

Parameters:

index - Index list of the expected permutation

Returns:

permuted matrix

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

Overrides:

getRowMatrix in class AbstractRealMatrix

Parameters:

row - Row to be fetched.

Returns:

row Matrix.

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

Overrides:

getColumnMatrix in class AbstractRealMatrix

Parameters:

column - Column to be fetched.

Returns:

column Matrix.

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

Overrides:

copySubMatrix in class AbstractRealMatrix

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[] 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

Overrides:

copySubMatrix in class AbstractRealMatrix

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)

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

Overrides:

walkInRowOrder in class AbstractRealMatrix

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

Overrides:

walkInRowOrder in class AbstractRealMatrix

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

Overrides:

walkInRowOrder in class AbstractRealMatrix

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

Overrides:

walkInRowOrder in class AbstractRealMatrix

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

Overrides:

walkInColumnOrder in class AbstractRealMatrix

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

Overrides:

walkInColumnOrder in class AbstractRealMatrix

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

Overrides:

walkInColumnOrder in class AbstractRealMatrix

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

Overrides:

walkInColumnOrder in class AbstractRealMatrix

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)

copy

public DiagonalMatrix copy()

Returns a (deep) copy of this.

Specified by:

copy in interface RealMatrix

Specified by:

copy in interface SymmetricMatrix

Specified by:

copy in class AbstractRealMatrix

Returns:

matrix copy

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:

norm

getFrobeniusNorm

public double getFrobeniusNorm()

Returns the Frobenius norm of the matrix.

Specified by:

getFrobeniusNorm in interface RealMatrix

Overrides:

getFrobeniusNorm in class AbstractRealMatrix

Returns:

norm

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.

Note that if the selected rows and columns are not the same, the returned matrix will be a regular matrix.

Specified by:

getSubMatrix in interface RealMatrix

Overrides:

getSubMatrix in class AbstractRealMatrix

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.

Note that if the selected rows and columns are not the same, the returned matrix will be a regular matrix.

Specified by:

getSubMatrix in interface RealMatrix

Overrides:

getSubMatrix in class AbstractRealMatrix

Parameters:

selectedRows - Array of row indices.

selectedColumns - Array of column indices.

Returns:

The subMatrix containing the data in the specified rows and columns

equals

public boolean equals(Object object)

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

Overrides:

equals in class AbstractRealMatrix

Parameters:

object - the object to test equality against.

Returns:

true if object equals this

hashCode

public int hashCode()

Computes a hashcode for the diagonal matrix.

Overrides:

hashCode in class AbstractRealMatrix

Returns:

hashcode for diagonal matrix