fr.cnes.sirius.patrius.math.linear

Class DecomposedSymmetricPositiveMatrix

java.lang.Object

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

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

fr.cnes.sirius.patrius.math.linear.DecomposedSymmetricPositiveMatrix

All Implemented Interfaces:

AnyMatrix, RealMatrix, SymmetricMatrix, SymmetricPositiveMatrix, Serializable

public class DecomposedSymmetricPositiveMatrix
extends AbstractRealMatrix
implements SymmetricPositiveMatrix

Stores a symmetric positive semi-definite matrix as A = B×B^T.

The matrix A is symmetric positive semi-definite by definition for any matrix B. Although the matrix A is always a NxN matrix, this is not necessarily the case for the matrix B: any NxM matrix multiplied by its transpose will yield a NxN matrix.

The decomposition matrix B is not unique and building it is left to the user. Typically, this matrix is computed through a Cholesky decomposition A = L×L^T, where L is a lower-triangular matrix. The matrix yielded by this decomposition is unique for positive definite matrices, but is not for positive semi-definite matrices (the implementation CholeskyDecomposition does not even support the latter). It can also be obtained through a LDL decomposition (A = L×D×L^T), or through an eigen decomposition (A = V×D×V^T).

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
DecomposedSymmetricPositiveMatrix(double[][] dataBT) Builds a new DecomposedSymmetricPositiveMatrix by specifying the data of a matrix BT which satisfies A = B×BT.
DecomposedSymmetricPositiveMatrix(int dimension) Builds a new NxN SymmetricPositiveMatrix (filled with zero).
DecomposedSymmetricPositiveMatrix(RealMatrix matrixBTran) Builds a new SymmetricPositiveMatrix by specifying a matrix BT which satisfies A = B×BT.

Method Summary

Modifier and Type	Method and Description
DecomposedSymmetricPositiveMatrix	add(DecomposedSymmetricPositiveMatrix m) Adds another SymmetricPositiveMatrix to this matrix.
DecomposedSymmetricPositiveMatrix	add(DecomposedSymmetricPositiveMatrix m, boolean resize) Adds another SymmetricPositiveMatrix to this matrix.
RealMatrix	add(RealMatrix m) Returns the sum of this and m.
SymmetricMatrix	add(SymmetricMatrix m) Adds a SymmetricMatrix to this matrix.
SymmetricPositiveMatrix	add(SymmetricPositiveMatrix m) Adds a SymmetricPositiveMatrix to this matrix.
DecomposedSymmetricPositiveMatrix	copy() Returns a (deep) copy of this.
DecomposedSymmetricPositiveMatrix	createMatrix(int rowDimension, int columnDimension) Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
DecomposedSymmetricPositiveMatrix	extractSubSymmetricMatrix(int[] index) Extract a sub-part of the matrix providing a subset of indices.
RealMatrix	getB() Gets the matrix B of the decomposition A = B×BT of this matrix.
RealMatrix	getBT() Gets the matrix BT of the decomposition A = B×BT of this matrix.
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	getEntry(int row, int column) Get the entry in the specified row and column.
DecomposedSymmetricPositiveMatrix	getInverse() Get the inverse of the decomposed matrix given as input.
DecomposedSymmetricPositiveMatrix	getInverse(Function<RealMatrix,Decomposition> decompositionBuilder) Get the inverse of the decomposed matrix given as input.
RealMatrix	getResizedB() Gets the matrix B after reducing or extending it to match this matrix's dimensions.
RealMatrix	getResizedBT() Gets the matrix BT after reducing or extending it to match this matrix's dimensions.
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	getTransparentDimension() Gets this matrix's transparent dimension (i.e. the number of columns of the matrix B).
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)
RealMatrix	multiply(SymmetricMatrix m, boolean toTranspose, double d) Returns the result of postmultiplying d × this × m (independently from the toTranspose parameter value as we use diagonal matrix).
DecomposedSymmetricPositiveMatrix	positiveScalarAdd(double d) Adds a positive scalar to each entry of this matrix.
DecomposedSymmetricPositiveMatrix	positiveScalarMultiply(double d) Multiplies each entry of this matrix by a positive scalar.
DecomposedSymmetricPositiveMatrix	power(int p) Returns the result of multiplying this with itself p times.
DecomposedSymmetricPositiveMatrix	quadraticMultiplication(RealMatrix m) Gets the result of the quadratic multiplication M×S×MT, where S is this matrix and M is the provided matrix.
DecomposedSymmetricPositiveMatrix	quadraticMultiplication(RealMatrix m, boolean toTranspose) Gets the result of the quadratic multiplication M×S×MT, where S is this matrix and M or MT is the provided matrix.
DecomposedSymmetricPositiveMatrix	resizeB() Reduces or extends the matrix B to ensure it is a NxN matrix.
SymmetricMatrix	scalarAdd(double d) Returns the result of adding d to each entry of this.
SymmetricMatrix	scalarMultiply(double d) Returns the result of multiplying each entry of this by d.
void	setEntry(int row, int column, double value) The method systematically throws a MathUnsupportedOperationException as this operation is not safe when we deal with a SymmetricPositiveMatrix.
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 SymmetricPositiveMatrix.
RealMatrix	subtract(RealMatrix m) Returns this minus m.
SymmetricMatrix	subtract(SymmetricMatrix m) Subtracts a SymmetricMatrix from this matrix.
SymmetricMatrix	toSymmetricMatrix() Gets the matrix A resulting of the decomposition A = B×BT of this matrix.
DecomposedSymmetricPositiveMatrix	transpose() Returns the transpose of this matrix.
DecomposedSymmetricPositiveMatrix	transpose(boolean forceCopy) Returns the transpose of this matrix.

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

addToEntry, concatenateDiagonally, concatenateHorizontally, concatenateHorizontally, concatenateVertically, concatenateVertically, copySubMatrix, copySubMatrix, copySubMatrix, copySubMatrix, equals, equals, getColumn, getColumnVector, getData, getData, getDefaultDecomposition, getFrobeniusNorm, getMax, getMin, getNorm, getRow, getRowVector, getTrace, hashCode, isAntisymmetric, isDiagonal, isInvertible, isOrthogonal, isPositiveDefinite, isSquare, isSymmetric, isSymmetric, isSymmetric, multiply, multiplyEntry, operate, operate, preMultiply, preMultiply, preMultiply, setColumn, setColumnMatrix, setColumnVector, setDefaultDecomposition, setRow, setRowMatrix, setRowVector, toString, 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

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

addToEntry, concatenateDiagonally, concatenateHorizontally, concatenateHorizontally, concatenateVertically, concatenateVertically, copySubMatrix, copySubMatrix, copySubMatrix, copySubMatrix, equals, getColumn, getColumnVector, getData, getData, getDefaultDecomposition, getFrobeniusNorm, getMax, getMin, getNorm, getRow, getRowVector, getTrace, isAntisymmetric, isDiagonal, isInvertible, isOrthogonal, isPositiveDefinite, isSymmetric, isSymmetric, isSymmetric, multiplyEntry, operate, operate, preMultiply, preMultiply, preMultiply, setColumn, setColumnMatrix, setColumnVector, setDefaultDecomposition, setRow, setRowMatrix, setRowVector, toString, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInColumnOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInRowOrder, walkInRowOrder, walkInRowOrder, walkInRowOrder

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

isSquare

Constructor Detail

DecomposedSymmetricPositiveMatrix

public DecomposedSymmetricPositiveMatrix(int dimension)

Builds a new NxN SymmetricPositiveMatrix (filled with zero).

Parameters:

dimension - the dimension N of the matrix

DecomposedSymmetricPositiveMatrix

public DecomposedSymmetricPositiveMatrix(double[][] dataBT)

Builds a new DecomposedSymmetricPositiveMatrix by specifying the data of a matrix B^T which satisfies A = B×B^T.

Parameters:

dataBT - the data of the matrix B^T

DecomposedSymmetricPositiveMatrix

public DecomposedSymmetricPositiveMatrix(RealMatrix matrixBTran)

Builds a new SymmetricPositiveMatrix by specifying a matrix B^T which satisfies A = B×B^T.

Parameters:

matrixBTran - the matrix B^T

Method Detail

getB

public RealMatrix getB()

Gets the matrix B of the decomposition A = B×B^T of this matrix.

Returns:

the matrix B

getBT

public RealMatrix getBT()

Gets the matrix B^T of the decomposition A = B×B^T of this matrix.

Returns:

the matrix B^T

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.

getTransparentDimension

public int getTransparentDimension()

Gets this matrix's transparent dimension (i.e. the number of columns of the matrix B).

Returns:

this matrix's transparent dimension

toSymmetricMatrix

public SymmetricMatrix toSymmetricMatrix()

Gets the matrix A resulting of the decomposition A = B×B^T of this matrix.

Returns:

the matrix A

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)

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

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 - systematically, since this operation is not supported

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 SymmetricPositiveMatrix.

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

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 SymmetricPositiveMatrix add(SymmetricPositiveMatrix m)

Adds a SymmetricPositiveMatrix to this matrix.

Specified by:

add in interface SymmetricPositiveMatrix

Parameters:

m - the matrix to add

Returns:

the matrix resulting from this addition

add

public DecomposedSymmetricPositiveMatrix add(DecomposedSymmetricPositiveMatrix m)

Adds another SymmetricPositiveMatrix to this matrix.

Adding another SymmetricPositiveMatrix amounts to concatenating their B matrices horizontally. As a result, the number of column of the matrix B increases with each addition. The concatenated matrix B is automatically resized afterward to ensure it is a NxN matrix.

Parameters:

m - the matrix to add

Returns:

the sum of the two matrices

See Also:

add(DecomposedSymmetricPositiveMatrix, boolean), resizeB()

add

public DecomposedSymmetricPositiveMatrix add(DecomposedSymmetricPositiveMatrix m,
                                             boolean resize)

Adds another SymmetricPositiveMatrix to this matrix.

Adding another SymmetricPositiveMatrix amounts to concatenating their B matrices horizontally. As a result, the number of column of the matrix B increases with each addition. Setting resize to true triggers a reduction or an extension of the matrix B afterward to ensure it is a NxN matrix.

Parameters:

m - the matrix to add

resize - if true, the matrix B is resized afterward to ensure it is NxN

Returns:

the sum of the two matrices

See Also:

resizeB()

scalarAdd

public SymmetricMatrix scalarAdd(double d)

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

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

positiveScalarAdd

public DecomposedSymmetricPositiveMatrix positiveScalarAdd(double d)

Adds a positive scalar to each entry of this matrix.

The scalar addition is computed by doing a vertical concatenation between the matrix B^T and a row matrix composed by the square root of the scalar.

Specified by:

positiveScalarAdd in interface SymmetricPositiveMatrix

Parameters:

d - the scalar to add to each entry

Returns:

the matrix resulting from this addition

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

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 toTranspose = false) or this × m^T (if toTranspose = 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 RealMatrix multiply(SymmetricMatrix 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 symmetric 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

scalarMultiply

public SymmetricMatrix 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

positiveScalarMultiply

public DecomposedSymmetricPositiveMatrix positiveScalarMultiply(double d)

Multiplies each entry of this matrix by a positive scalar.

Specified by:

positiveScalarMultiply in interface SymmetricPositiveMatrix

Parameters:

d - the scalar by which each entry is multiplied

Returns:

the matrix resulting from this multiplication

Throws:

NotPositiveException - if the d is negative (unchecked)

quadraticMultiplication

public DecomposedSymmetricPositiveMatrix 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

Specified by:

quadraticMultiplication in interface SymmetricPositiveMatrix

Parameters:

m - the matrix M

Returns:

M×S×M^T

quadraticMultiplication

public DecomposedSymmetricPositiveMatrix quadraticMultiplication(RealMatrix m,
                                                                 boolean toTranspose)

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

Specified by:

quadraticMultiplication in interface SymmetricPositiveMatrix

Parameters:

m - the matrix M or the matrix M^T

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

Returns:

M×S×M^T

power

public DecomposedSymmetricPositiveMatrix 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

Specified by:

power in interface SymmetricPositiveMatrix

Overrides:

power in class AbstractRealMatrix

Parameters:

p - raise this to power p

Returns:

this^p

Throws:

NotPositiveException - if p is negative

resizeB

public DecomposedSymmetricPositiveMatrix resizeB()

Reduces or extends the matrix B to ensure it is a NxN matrix.

If the matrix B has more columns than rows, this method replaces the current matrix B by the matrix R resulting from the QR decomposition of B^T, after truncating it to its first N rows (where N is the dimension of this matrix). If it has less columns than rows, it simply adds new columns filled with zero.

Returns:

this matrix

getResizedB

public RealMatrix getResizedB()

Gets the matrix B after reducing or extending it to match this matrix's dimensions.

If the matrix B has more columns than rows, this method returns the transpose of the matrix R resulting from the QR decomposition of B^T, after truncating it to its first N rows (where N is the dimension of this matrix). If the matrix B has less columns than rows, this methods simply adds columns filled with zero to match its row dimensions.

Returns:

the resized matrix B

getResizedBT

public RealMatrix getResizedBT()

Gets the matrix B^T after reducing or extending it to match this matrix's dimensions.

If the matrix B has more columns than rows, this method returns the matrix R resulting from the QR decomposition of B^T, after truncating it to its first N rows (where N is the dimension of this matrix). If the matrix B has less columns than rows, this methods simply adds columns filled with zero to match its row dimensions.

Returns:

the resized matrix B^T

createMatrix

public DecomposedSymmetricPositiveMatrix 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 row and column dimensions are not the same (unchecked)

copy

public DecomposedSymmetricPositiveMatrix copy()

Returns a (deep) copy of this.

Specified by:

copy in interface RealMatrix

Specified by:

copy in interface SymmetricMatrix

Specified by:

copy in interface SymmetricPositiveMatrix

Specified by:

copy in class AbstractRealMatrix

Returns:

matrix copy

transpose

public DecomposedSymmetricPositiveMatrix transpose()

Returns the transpose of this matrix..

Specified by:

transpose in interface RealMatrix

Specified by:

transpose in interface SymmetricMatrix

Specified by:

transpose in interface SymmetricPositiveMatrix

Overrides:

transpose in class AbstractRealMatrix

Returns:

transpose matrix

transpose

public DecomposedSymmetricPositiveMatrix transpose(boolean forceCopy)

Returns the transpose of this matrix..

Specified by:

transpose in interface RealMatrix

Overrides:

transpose in class AbstractRealMatrix

Parameters:

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

Returns:

transpose matrix

extractSubSymmetricMatrix

public DecomposedSymmetricPositiveMatrix extractSubSymmetricMatrix(int[] index)

Extract a sub-part of the matrix providing a subset of indices. It also allows to permute the rows/columns.

 Usage example (with permutation):
        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]
 

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

Specified by:

extractSubSymmetricMatrix in interface SymmetricMatrix

Parameters:

index - Index list

Returns:

extracted matrix

getInverse

public DecomposedSymmetricPositiveMatrix getInverse()

Get the inverse of the decomposed matrix given as input.

The default decomposition is used.

The inverse DecomposedSymmetricPositiveMatrix matrix is calculated like : If A₁ = B₁ × B₁^T and A₂ = B₂ × B₂^T = A₁^-1, then we have B₂^T = B₁^-1.

Specified by:

getInverse in interface RealMatrix

Specified by:

getInverse in interface SymmetricMatrix

Specified by:

getInverse in interface SymmetricPositiveMatrix

Overrides:

getInverse in class AbstractRealMatrix

Returns:

inverse matrix

Throws:

SingularMatrixException - if the decomposed matrix is singular.

getInverse

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

Get the inverse of the decomposed matrix given as input.

Warning: The decomposition should be instantiated without providing any matrix (avoids useless operations).

The inverse DecomposedSymmetricPositiveMatrix matrix is calculated like : If A₁ = B₁ × B₁^T and A₂ = B₂ × B₂^T = A₁^-1, then we have B₂^T = B₁^-1. The inverse of B₁ is computed using the provided decomposition.

Specified by:

getInverse in interface RealMatrix

Specified by:

getInverse in interface SymmetricMatrix

Specified by:

getInverse in interface SymmetricPositiveMatrix

Overrides:

getInverse in class AbstractRealMatrix

Parameters:

decompositionBuilder - The decomposition algorithm

Returns:

inverse matrix

Throws:

SingularMatrixException - if the decomposed matrix is singular.

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 the returned matrix is 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 returned matrix is 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

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.