fr.cnes.sirius.patrius.math.linear

Class SymmetricMatrix

java.lang.Object

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

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

fr.cnes.sirius.patrius.math.linear.SymmetricMatrix

All Implemented Interfaces:

AnyMatrix, RealMatrix, Serializable

public class SymmetricMatrix
extends AbstractRealMatrix
implements Serializable

Implementation of a symmetric matrix.
Operation are optimized to take advantage of symmetric properties of this kind of matrix.

Version:

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

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	SymmetricMatrix.SYMMETRIC Enumerate to fill in a symmetric matrix only by its lower/upper part.

Constructor Summary

Constructors

Constructor and Description
SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn, int nIn, int ldIn) Creates a matrix with the supplied dimensions.
SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn, int nIn, int ldIn, double[] dIn) Creates a matrix given the supplied dimensions and data array.
SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn, int nIn, int ldIn, double[][] d) Creates a matrix given the supplied dimensions and data array 2D.
SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn, int nIn, int ldIn, double[] d, boolean copyArray) Creates a matrix given the supplied dimensions and data array.
SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn, int nIn, int ldIn, RealMatrix m) Creates a symmetric matrix using a real matrix.

Method Summary

Methods

Modifier and Type	Method and Description
SymmetricMatrix	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) Compute 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.
SymmetricMatrix	copy() Returns a (deep) copy of this.
static SymmetricMatrix	createDiagonalMatrixWithArray(int dim, int lda, double[] coeff) Creates an instance of SymmetricMatrix which is diagonal of input element.
SymmetricMatrix	createMatrix(int lda, int dim) Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
int	getColumnDimension() Returns the number of columns of this matrix.
double	getEntry(int row, int column) Get the entry in the specified row and column.
int	getRowDimension() Returns the number of rows of this matrix.
boolean	isSymmetric() Checks if this is a symmetric matrix
RealMatrix	multiply(DiagonalMatrix m) Returns the result of postmultiplying this by m.
RealMatrix	multiply(RealMatrix m) Returns the result of postmultiplying this by m.
RealMatrix	multiply(SymmetricMatrix m) Returns the result of postmultiplying this by m.
void	multiplyEntry(int row, int column, double factor) Multiplies (in place) the specified entry of this matrix by the specified value.
static SymmetricMatrix	newByCopy(SymmetricMatrix.SYMMETRIC uplo, int n, int ld, SymmetricMatrix.SYMMETRIC uploMat, RealMatrix mat) Create a symmetric matrix by copy of a triangle of a matrix.
static SymmetricMatrix	newByCopyAndSymmetrize(SymmetricMatrix.SYMMETRIC uplo, int n, int ld, RealMatrix mat) Create a symmetric matrix by computation of the mean of the 2 triangles of a matrix.
static SymmetricMatrix	newByCopyOfPackedStorage(SymmetricMatrix.SYMMETRIC uplo, int n, int ld, double[] d) Creates a symmetric matrix using one of the triangles stored in 'packed' storage.
SymmetricMatrix	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) Replace the submatrix starting at row, column using data in the input subMatrix array.
void	setSubMatrixWithMatrix(RealMatrix subMatrix, int row, int column) Method setSubMatrix using a RealMatrix for subMatrix instead of an array
SymmetricMatrix	subtract(DiagonalMatrix m) Compute this minus m.
RealMatrix	subtract(RealMatrix m) Returns this minus m.
SymmetricMatrix	subtract(SymmetricMatrix m) Compute this minus m.
static void	symmetricMatrixOperation(double alpha, SymmetricMatrix symA, RealMatrix matB, double beta, RealMatrix matC) Performs the matrix-matrix operations C := alpha*A*B + beta*C where alpha and beta are scalars, A is a symmetric matrix and B and C are n by n matrices.
RealMatrix	transpose() Returns the transpose of this matrix.

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

copySubMatrix, copySubMatrix, equals, getColumn, getColumnMatrix, getColumnVector, getData, getFrobeniusNorm, getNorm, getRow, getRowMatrix, getRowVector, getSubMatrix, getSubMatrix, getTrace, hashCode, isAntisymmetric, isDiagonal, isInvertible, isOrthogonal, isSquare, isSymmetric, operate, operate, power, preMultiply, preMultiply, preMultiply, scalarAdd, setColumn, setColumnMatrix, setColumnVector, setRow, setRowMatrix, setRowVector, toString, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInRowOrder, walkInRowOrder, walkInRowOrder, walkInRowOrder

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

SymmetricMatrix

public SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn,
               int nIn,
               int ldIn)

Creates a matrix with the supplied dimensions.

Parameters:

uploIn - the triangle that will be used

nIn - the dimension of the matrix

ldIn - the leading dimension of the matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

SymmetricMatrix

public SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn,
               int nIn,
               int ldIn,
               double[] d,
               boolean copyArray)

Creates a matrix given the supplied dimensions and data array.

Parameters:

uploIn - the triangle that will be used

nIn - the dimension of the matrix

ldIn - the leading dimension of the matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

d - the array to be viewed as a conventional full storage symmetric matrix

copyArray - if the array must be copied

SymmetricMatrix

public SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn,
               int nIn,
               int ldIn,
               double[] dIn)

Creates a matrix given the supplied dimensions and data array.

Parameters:

uploIn - the triangle that will be used

nIn - the dimension of the matrix

ldIn - the leading dimension of the matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

dIn - the array to be viewed as a conventional full storage symmetric matrix

Throws:

NonSquareMatrixException - if matrix is not square

SymmetricMatrix

public SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn,
               int nIn,
               int ldIn,
               double[][] d)

Creates a matrix given the supplied dimensions and data array 2D. If data array has no symmetric elements, symmetrization is performed by calling the method newByCopy(SYMMETRIC, int, int, SYMMETRIC, RealMatrix).

Parameters:

uploIn - the triangle that will be used

nIn - the dimension of the matrix

ldIn - the leading dimension of the created matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

d - data for the new matrix

Throws:

NonSquareMatrixException - if matrix is not square

SymmetricMatrix

public SymmetricMatrix(SymmetricMatrix.SYMMETRIC uploIn,
               int nIn,
               int ldIn,
               RealMatrix m)

Creates a symmetric matrix using a real matrix.

Parameters:

uploIn - the triangle that will be used

nIn - the dimension of the matrix

ldIn - the leading dimension of the created matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

m - the real matrix to be used

Throws:

NonSquareMatrixException - if matrix is not square

Method Detail

newByCopy

public static SymmetricMatrix newByCopy(SymmetricMatrix.SYMMETRIC uplo,
                        int n,
                        int ld,
                        SymmetricMatrix.SYMMETRIC uploMat,
                        RealMatrix mat)

Create a symmetric matrix by copy of a triangle of a matrix.

Parameters:

uplo - the triangle to use

n - the dimension of the created matrix

ld - the leading dimension of the created matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

uploMat - the triangle to use from the input matrix

mat - the matrix from which the data are extracted

Returns:

The symmetric matrix according to the input triangle

Throws:

NonSquareMatrixException - if matrix is not square

newByCopyAndSymmetrize

public static SymmetricMatrix newByCopyAndSymmetrize(SymmetricMatrix.SYMMETRIC uplo,
                                     int n,
                                     int ld,
                                     RealMatrix mat)

Create a symmetric matrix by computation of the mean of the 2 triangles of a matrix.

Parameters:

uplo - the triangle to use

n - the dimension of the created matrix

ld - the leading dimension of the created matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

mat - the matrix from which the data are extracted

Returns:

The symmetric matrix based on the mean of the 2 triangles

newByCopyOfPackedStorage

public static SymmetricMatrix newByCopyOfPackedStorage(SymmetricMatrix.SYMMETRIC uplo,
                                       int n,
                                       int ld,
                                       double[] d)

Creates a symmetric matrix using one of the triangles stored in 'packed' storage. The size of the packed storage form can be higher than the number of elements really used to construct the matrix.

Parameters:

uplo - lower/upper known part of the matrix

n - the dimension of the created matrix

ld - the leading dimension of the created matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

d - data in 'packed storage'

Returns:

The symmetric matrix according to the packed storage

Throws:

NonSquareMatrixException - if matrix is not square

createMatrix

public SymmetricMatrix createMatrix(int lda,
                           int dim)

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:

lda - the number of rows in the new matrix

dim - the number of columns in the new matrix

Returns:

a new matrix of the same type as the instance

createDiagonalMatrixWithArray

public static SymmetricMatrix createDiagonalMatrixWithArray(int dim,
                                            int lda,
                                            double[] coeff)

Creates an instance of SymmetricMatrix which is diagonal of input element.

Parameters:

dim - the dimension of the created matrix

lda - the leading dimension of the created matrix. ld is normaly equal to n. It can be set larger in some case for performance improvements

coeff - value of diagonals elements

Returns:

The diagonal matrix of diagonal value coeff

Throws:

NotStrictlyPositiveException - if n or ld are not positive

copy

public SymmetricMatrix copy()

Returns a (deep) copy of this.

Specified by:

copy in interface RealMatrix

Specified by:

copy in class AbstractRealMatrix

Returns:

matrix copy

transpose

public RealMatrix transpose()

Returns the transpose of this matrix.

Specified by:

transpose in interface RealMatrix

Overrides:

transpose in class AbstractRealMatrix

Returns:

transpose matrix

symmetricMatrixOperation

public static void symmetricMatrixOperation(double alpha,
                            SymmetricMatrix symA,
                            RealMatrix matB,
                            double beta,
                            RealMatrix matC)

Performs the matrix-matrix operations C := alpha*A*B + beta*C where alpha and beta are scalars, A is a symmetric matrix and B and C are n by n matrices. This general method aims to perform all elementary operations involving instances of SymmetricMatrix, DiagonalMatrix or RealMatrix

Parameters:

alpha - the first value to use in above linear combination

symA - the input symmetric matrix

matB - the input matrix, instance of RealMatrix

beta - the second value to use in above linear combination

matC - the input/output matrix, instance of RealMatrix

add

public SymmetricMatrix add(SymmetricMatrix m)

Compute the sum of this and m.

Parameters:

m - matrix to be added

Returns:

this + m

Throws:

DimensionMismatchException - if m is not the same size as this

add

public SymmetricMatrix add(DiagonalMatrix m)

Compute the sum of this and m.

Parameters:

m - Diagonal matrix to be added

Returns:

this + m

Throws:

IllegalArgumentException - if m is not the same size as this

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

subtract

public SymmetricMatrix subtract(SymmetricMatrix m)

Compute this minus m.

Parameters:

m - matrix to be subtracted

Returns:

this - m

Throws:

IllegalArgumentException - if m is not the same size as this

subtract

public SymmetricMatrix subtract(DiagonalMatrix m)

Compute this minus m.

Parameters:

m - Diagonal matrix to be added

Returns:

this + m

Throws:

IllegalArgumentException - 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

multiply

public RealMatrix multiply(SymmetricMatrix m)

Returns the result of postmultiplying this by m.

Parameters:

m - matrix to postmultiply by

Returns:

this*m

Throws:

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

multiply

public RealMatrix multiply(DiagonalMatrix m)

Returns the result of postmultiplying this by m.

Parameters:

m - Diagonal matrix to postmultiply by

Returns:

this*m

Throws:

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

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

scalarMultiply

public SymmetricMatrix scalarMultiply(double d)

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

Specified by:

scalarMultiply in interface RealMatrix

Overrides:

scalarMultiply in class AbstractRealMatrix

Parameters:

d - value to multiply all entries by

Returns:

d * this

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

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

setSubMatrixWithMatrix

public void setSubMatrixWithMatrix(RealMatrix subMatrix,
                          int row,
                          int column)

Method setSubMatrix using a RealMatrix for subMatrix instead of an array

Parameters:

subMatrix - matrix 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:

NoDataException - if subMatrix is empty.

OutOfRangeException - if subMatrix does not fit into this matrix from element in (row, column).

DimensionMismatchException - if subMatrix is not rectangular (not all rows have the same length) or empty.

NullArgumentException - if subMatrix is null.

Since:

3.1

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.

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.

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.

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.

isSymmetric

public boolean isSymmetric()

Checks if this is a symmetric matrix

Specified by:

isSymmetric in interface RealMatrix

Overrides:

isSymmetric in class AbstractRealMatrix

Returns:

true if this is a symmetric matrix