fr.cnes.sirius.patrius.math.linear

Interface SymmetricMatrix

All Superinterfaces:

AnyMatrix, RealMatrix, Serializable

All Known Subinterfaces:

SymmetricPositiveMatrix

All Known Implementing Classes:

ArrayRowSymmetricMatrix, ArrayRowSymmetricPositiveMatrix, DecomposedSymmetricPositiveMatrix, DiagonalMatrix

public interface SymmetricMatrix
extends RealMatrix

Interface for symmetric matrices.

Author:

Pierre Seimandi (GMV)

Method Summary

Modifier and Type	Method and Description
SymmetricMatrix	add(SymmetricMatrix m) Returns the result of adding the symmetric matrix m to this matrix.
SymmetricMatrix	copy() Returns a deep copy of this matrix.
SymmetricMatrix	createMatrix(int rowDimension, int columnDimension) Creates a new matrix of the same type as this matrix.
double[]	getDiagonal() Gets the diagonal vector from this matrix.
SymmetricMatrix	getInverse() Gets the inverse (or pseudo-inverse) of this matrix using the default decomposition.
SymmetricMatrix	getInverse(Function<RealMatrix,Decomposition> decompositionBuilder) Gets the inverse (or pseudo-inverse) of this matrix using the given decomposition algorithm.
SymmetricMatrix	getSubMatrix(int[] indices) Extracts the submatrix corresponding to the specified indices.
SymmetricMatrix	getSubMatrix(int startIndex, int endIndex) Extracts the submatrix corresponding to the specified indices.
SymmetricMatrix	power(int p) Returns the the result of multiplying this matrix with itself p times.
SymmetricMatrix	quadraticMultiplication(RealMatrix m) Returns the result of the quadratic multiplication M×this×MT, where M is the provided matrix.
SymmetricMatrix	quadraticMultiplication(RealMatrix m, boolean isTranspose) Returns the result of the quadratic multiplication M×this×MT, where M or MT is the provided matrix.
SymmetricMatrix	scalarAdd(double d) Returns the result of adding a scalar d to the entries of this matrix.
SymmetricMatrix	scalarMultiply(double d) Returns the result of multiplying the entries of this matrix by the scalar d.
SymmetricMatrix	subtract(SymmetricMatrix m) Returns the result of subtracting the symmetric matrix m from this matrix.
SymmetricMatrix	transpose() Returns the transpose of this matrix.
SymmetricMatrix	transpose(boolean forceCopy) Returns the transpose of this matrix.

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

add, addToEntry, concatenateDiagonally, concatenateDiagonally, concatenateDiagonally, concatenateHorizontally, concatenateHorizontally, concatenateVertically, concatenateVertically, copySubMatrix, copySubMatrix, copySubMatrix, copySubMatrix, equals, getColumn, getColumnMatrix, getColumnVector, getData, getData, getDefaultDecomposition, getEntry, getFrobeniusNorm, getMax, getMin, getNorm, getRow, getRowMatrix, getRowVector, getSubMatrix, getSubMatrix, getTrace, isAntisymmetric, isDiagonal, isInvertible, isOrthogonal, isSymmetric, isSymmetric, isSymmetric, multiply, multiply, multiply, multiplyEntry, operate, operate, preMultiply, preMultiply, preMultiply, setColumn, setColumnMatrix, setColumnVector, setDefaultDecomposition, setEntry, setRow, setRowMatrix, setRowVector, setSubMatrix, subtract, toString, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInRowOrder, walkInRowOrder, walkInRowOrder, walkInRowOrder

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

getColumnDimension, getRowDimension, isSquare

Method Detail

add

SymmetricMatrix add(SymmetricMatrix m)

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

Parameters:

m - the matrix to be added

Returns:

the matrix resulting from the addition this+m

Throws:

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

subtract

SymmetricMatrix subtract(SymmetricMatrix m)

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

Parameters:

m - the matrix to be subtracted

Returns:

the matrix resulting from the subtraction this-m

Throws:

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

scalarAdd

SymmetricMatrix scalarAdd(double d)

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

Specified by:

scalarAdd in interface RealMatrix

Parameters:

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

Returns:

the matrix resulting from the addition this+d

scalarMultiply

SymmetricMatrix scalarMultiply(double d)

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

Specified by:

scalarMultiply in interface RealMatrix

Parameters:

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

Returns:

the matrix resulting from the product this×d

quadraticMultiplication

SymmetricMatrix quadraticMultiplication(RealMatrix m)

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

Parameters:

m - the matrix M

Returns:

the matrix resulting from the quadratic multiplication M×this ×M^T

quadraticMultiplication

SymmetricMatrix quadraticMultiplication(RealMatrix m,
                                        boolean isTranspose)

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

Parameters:

m - the matrix M or the matrix M^T

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

Returns:

the matrix resulting from the quadratic multiplication M×this ×M^T

getSubMatrix

SymmetricMatrix getSubMatrix(int startIndex,
                             int endIndex)

Extracts the submatrix corresponding to the specified indices.

This method uses the same start/end indices to select the rows and columns to be extracted. These indices must be valid indices with respect to the dimensions of the matrix (valid indices range from 0 to n-1, with n the row/column dimension of the matrix). Calling this method is equivalent to calling RealMatrix.getSubMatrix(int, int, int, int) using the same start/end indices for the rows and columns. The extracted submatrix is guaranteed to be symmetric. It will also remain positive semi-definite if the initial matrix originally is.

Usage examples:

 // Initial matrix
 matrix = [a00, a10, a20]
          [a10, a11, a21]
          [a20, a21, a22]
 
 // Submatrix extraction
 matrix.getSubMatrix(1, 2) => [a11, a21]
                              [a21, a22]
 

Parameters:

startIndex - the initial row/column index

endIndex - the final row/column index (inclusive)

Returns:

the extracted submatrix

getSubMatrix

SymmetricMatrix getSubMatrix(int[] indices)

Extracts the submatrix corresponding to the specified indices.

This method uses a single index array to select the rows and columns to be extracted. All indices must be valid indices with respect to the dimensions of the matrix (valid indices range from 0 to n-1, with n the row/column dimension of the matrix). The provided index array is allowed to contain duplicates. Calling this method is equivalent to calling RealMatrix.getSubMatrix(int[], int[]) using the provided index array for the selected rows and columns. This method can be used to extract any submatrix and perform a symmetric reordering of its rows/columns. The extracted submatrix is guaranteed to be symmetric. It will also remain positive semi-definite if the initial matrix originally is.

Usage examples:

 // Initial matrix
 matrix = [a00, a10, a20]
          [a10, a11, a21]
          [a20, a21, a22]
 
 // Submatrix extraction
 matrix.getSubMatrix([1, 2]) => [a11, a21]
                                [a21, a22]
 
 // Rows/Columns permutation
 matrix.getSubMatrix([1, 2, 0]) => [a11, a21, a10]
                                   [a21, a22, a20]
                                   [a10, a20, a00]
 
 // Submatrix extraction (with duplicated indices)
 matrix.getSubMatrix([1, 2, 0, 1, 0]) 
      => [a11, a21, a10, a11, a10]
         [a21, a22, a20, a21, a20]
         [a10, a20, a00, a10, a00]
         [a11, a21, a10, a11, a10]
         [a10, a20, a00, a10, a00]
 

Parameters:

indices - the selected indices

Returns:

the extracted submatrix

getDiagonal

double[] getDiagonal()

Gets the diagonal vector from this matrix.

Specified by:

getDiagonal in interface RealMatrix

Returns:

the diagonal vector from this matrix

copy

SymmetricMatrix copy()

Returns a deep copy of this matrix.

Specified by:

copy in interface RealMatrix

Returns:

a deep copy of this matrix

transpose

SymmetricMatrix transpose()

Returns the transpose of this matrix.

Specified by:

transpose in interface RealMatrix

Returns:

the transpose of this matrix

transpose

SymmetricMatrix transpose(boolean forceCopy)

Returns the transpose of this matrix.

If forceCopy is true, the returned matrix is guaranteed to be a new instance, which can be modified without any risk of impacting the current instance. Otherwise, this method may simply return the current instance when the matrix is its own transpose (symmetric matrix).

Specified by:

transpose in interface RealMatrix

Parameters:

forceCopy - if true, the transpose of the matrix is systematically stored in a new matrix; otherwise the method may return the current instance when the matrix is its own transpose

Returns:

the transpose of this matrix

power

SymmetricMatrix power(int p)

Returns the the result of multiplying this matrix with itself p times.

The exponent p must be positive or equal to zero.
This operation is only supported for square matrices.
Depending on the underlying storage, numerical instabilities might occur for high powers.

Specified by:

power in interface RealMatrix

Parameters:

p - the exponent p to which this matrix is to be raised

Returns:

the matrix resulting from raising this matrix to the power of p

getInverse

SymmetricMatrix getInverse()

Gets the inverse (or pseudo-inverse) of this matrix using the default decomposition.

The default decomposition builder can be changed using the setDefaultDecomposition method.

Specified by:

getInverse in interface RealMatrix

Returns:

the inverse matrix

See Also:

RealMatrix.getDefaultDecomposition(), RealMatrix.setDefaultDecomposition(Function)

getInverse

SymmetricMatrix getInverse(Function<RealMatrix,Decomposition> decompositionBuilder)

Gets the inverse (or pseudo-inverse) of this matrix using the given decomposition algorithm.

The decomposition builder is a function capable of generating new instances of the decomposition algorithm to be used for the computation of the inverse matrix (like the QRDecomposition or the EigenDecomposition, for instance).

Specified by:

getInverse in interface RealMatrix

Parameters:

decompositionBuilder - the decomposition builder to use

Returns:

the inverse matrix

createMatrix

SymmetricMatrix createMatrix(int rowDimension,
                             int columnDimension)

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

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

Since the matrix build is a symmetric matrix, the row and column dimensions are expected to be equal.

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 this matrix