fr.cnes.sirius.patrius.math.linear

Class ArrayRowSymmetricPositiveMatrix

java.lang.Object

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

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

fr.cnes.sirius.patrius.math.linear.ArrayRowSymmetricMatrix

fr.cnes.sirius.patrius.math.linear.ArrayRowSymmetricPositiveMatrix

All Implemented Interfaces:

AnyMatrix, RealMatrix, SymmetricMatrix, SymmetricPositiveMatrix, Serializable

public class ArrayRowSymmetricPositiveMatrix
extends ArrayRowSymmetricMatrix
implements SymmetricPositiveMatrix

Symmetric positive semi-definite matrix defined by its lower triangular part.

This implementation stores the elements of the lower triangular part of a symmetric matrix. These elements are stored in a 1D array, row after row. For example, for a 3 by 3 matrix we have:
(1) = s_1,1;
(2) = s_2,1; (3) = s_2,2;
(4) = s_3,1; (5) = s_3,2; (6) = s_3,3;

The elements actually stored depends on the type of symmetry specified at construction: LOWER or UPPER implies the symmetry is enforced by keeping only the lower or upper triangular part of the matrix, while MEAN enforces the symmetry by computing the mean of the lower and upper elements. The symmetry of the provided matrix is not checked by default, meaning that the symmetry is enforced regardless of the inputs. However, such a check can be triggered by setting the default absolute or relative symmetry threshold to a non-null value, or by specifying any of these thresholds at construction. Note that the default values for these symmetry thresholds are shared with ArrayRowSymmetricMatrix.

In contrast, the positivity of the symmetrized matrix is always checked by default. This check can be disabled by setting the absolute and relative positivity thresholds to null, either by changing the default values or by overriding them at construction. A symmetric matrix is considered to be positive semi-definite if all its pivots are strictly positive, or if the pivot and the associated row/column are equal to zero. Possible numerical errors are taken into account by adding a small value (which depends on the specified tolerances) to the diagonal elements of the matrix. The relative tolerance is relative to the maximum row sum norm of the matrix.

Important:
Since it might induce a loss of positivity or definiteness, modifying any element of the matrix is forbidden.

Author:

Pierre Seimandi (GMV)

See Also:

ArrayRowSymmetricMatrix, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class fr.cnes.sirius.patrius.math.linear.ArrayRowSymmetricMatrix

ArrayRowSymmetricMatrix.SymmetryType

Constructor Summary

Constructors

Modifier	Constructor and Description
	ArrayRowSymmetricPositiveMatrix(ArrayRowSymmetricMatrix.SymmetryType symmetryType, double[][] dataIn) Builds a new ArrayRowSymmetricPositiveMatrix from the provided data, using the default symmetry and positivity thresholds.
	ArrayRowSymmetricPositiveMatrix(ArrayRowSymmetricMatrix.SymmetryType symmetryType, double[][] dataIn, Double absoluteSymmetryThreshold, Double relativeSymmetryThreshold, Double absolutePositivityThreshold, Double relativePositivityThreshold) Builds a new ArrayRowSymmetricPositiveMatrix from the provided data, using the specified symmetry and positivity thresholds.
	ArrayRowSymmetricPositiveMatrix(ArrayRowSymmetricMatrix.SymmetryType symmetryType, RealMatrix matrix) Builds a new ArrayRowSymmetricPositiveMatrix from the provided matrix, using the default symmetry and positivity thresholds.
	ArrayRowSymmetricPositiveMatrix(ArrayRowSymmetricMatrix.SymmetryType symmetryType, RealMatrix matrix, Double absoluteSymmetryThreshold, Double relativeSymmetryThreshold, Double absolutePositivityThreshold, Double relativePositivityThreshold) Builds a new ArrayRowSymmetricPositiveMatrix from the provided matrix, using the specified symmetry and positivity thresholds.
protected	ArrayRowSymmetricPositiveMatrix(double[] dataIn, boolean copyArray) Builds a new ArrayRowSymmetricPositiveMatrix by specifying the lower triangular part of the matrix directly.
	ArrayRowSymmetricPositiveMatrix(int n) Builds a new ArrayRowSymmetricPositiveMatrix of dimension n (filled with zero).

Method Summary

Modifier and Type	Method and Description
ArrayRowSymmetricMatrix	add(SymmetricMatrix m) Returns the result of adding the symmetric matrix m to this matrix.
ArrayRowSymmetricPositiveMatrix	add(SymmetricPositiveMatrix m) Returns the result of adding the symmetric positive semi-definite matrix m to this matrix.
void	addToEntry(int row, int column, double increment) Adds (in place) a given value to the specified entry of this matrix.
protected static void	checkPositiveSemiDefinite(SymmetricMatrix symmetricMatrix, double tolerance) Ensures a symmetric matrix is positive semi-definite and throws an exception if that's not the case.
ArrayRowSymmetricPositiveMatrix	copy() Returns a deep copy of this matrix.
static ArrayRowSymmetricPositiveMatrix	createIdentityMatrix(int dim) Creates an identity matrix of the specified dimension.
ArrayRowSymmetricPositiveMatrix	createMatrix(int rowDimension, int columnDimension) Creates a new matrix of the same type as this matrix.
boolean	equals(Object object) Returns true if the provided object is a RealMatrix instance with the same dimensions as this matrix, whose entries are strictly equal to the entries of this matrix (no absolute or relative tolerance is taken into account when comparing the entries).
static Double	getDefaultAbsolutePositivityThreshold() Gets the default absolute positivity threshold, above which a value is considered to be strictly positive.
static Double	getDefaultRelativePositivityThreshold() Gets the default relative positivity threshold, above which a value is considered to be numerically significant when compared to another value.
protected static double	getEffectiveTolerance(Double absoluteTolerance, Double relativeTolerance, double maxValue) Gets the effective tolerance from a given absolute and relative tolerance.
ArrayRowSymmetricPositiveMatrix	getInverse() Gets the inverse (or pseudo-inverse) of this matrix using the default decomposition.
ArrayRowSymmetricPositiveMatrix	getInverse(Function<RealMatrix,Decomposition> decompositionBuilder) Gets the inverse (or pseudo-inverse) of this matrix using the given decomposition algorithm.
ArrayRowSymmetricPositiveMatrix	getSubMatrix(int[] index) Extracts the submatrix corresponding to the specified indices.
RealMatrix	getSubMatrix(int[] selectedRows, int[] selectedColumns) Gets a submatrix.
ArrayRowSymmetricPositiveMatrix	getSubMatrix(int startIndex, int endIndex) Extracts the submatrix corresponding to the specified indices.
RealMatrix	getSubMatrix(int startRow, int endRow, int startColumn, int endColumn) Gets a submatrix.
int	hashCode() Computes a hash code for the matrix.
boolean	isPositiveSemiDefinite(double absoluteTolerance) Determines if this matrix is positive semi-definite or not.
static boolean	isPositiveSemiDefinite(SymmetricMatrix symmetricMatrix, double absoluteTolerance) Determines if a symmetric matrix is positive semi-definite or not.
void	multiplyEntry(int row, int column, double factor) Multiplies (in place) the specified entry of this matrix by a given value.
ArrayRowSymmetricPositiveMatrix	positiveScalarAdd(double d) Returns the result of adding a positive scalar d to the entries of this matrix.
ArrayRowSymmetricPositiveMatrix	positiveScalarMultiply(double d) Returns the result of multiplying the entries of this matrix by a positive scalar d.
ArrayRowSymmetricPositiveMatrix	power(int p) Returns the the result of multiplying this matrix with itself p times.
ArrayRowSymmetricPositiveMatrix	quadraticMultiplication(RealMatrix m) Returns the result of the quadratic multiplication M×this×MT, where M is the provided matrix.
ArrayRowSymmetricPositiveMatrix	quadraticMultiplication(RealMatrix m, boolean isTranspose) Returns the result of the quadratic multiplication M×this×MT, where M or MT is the provided matrix.
ArrayRowSymmetricMatrix	scalarAdd(double d) Returns the result of adding a scalar d to the entries of this matrix.
ArrayRowSymmetricMatrix	scalarMultiply(double d) Returns the result of multiplying the entries of this matrix by the scalar d.
void	setColumn(int column, double[] array) Replaces the entries of a given column with the entries of the specified data array.
void	setColumnMatrix(int column, RealMatrix matrix) Replaces the entries of a given column with the entries of the specified column matrix.
void	setColumnVector(int column, RealVector vector) Replaces the entries of a given column with the entries of the specified vector.
static void	setDefaultAbsolutePositivityThreshold(Double threshold) Sets the default absolute positivity threshold, above which a value is considered to be positive.
static void	setDefaultRelativePositivityThreshold(Double threshold) Sets the default relative positivity threshold, above which a value is considered to be numerically significant when compared to another value.
void	setEntry(int row, int column, double value) Sets the entry at the specified row and column to a new value.
void	setRow(int row, double[] array) Replaces the entries of a given row with the entries of the specified data array.
void	setRowMatrix(int row, RealMatrix matrix) Replaces the entries of a given row with the entries of the specified row matrix.
void	setRowVector(int row, RealVector vector) Replaces the entries of a given row with the entries of the specified vector.
void	setSubMatrix(double[][] subMatrix, int row, int column) Replaces part of the matrix with a given submatrix, starting at the specified row and column.
ArrayRowSymmetricPositiveMatrix	transpose() Returns the transpose of this matrix.
ArrayRowSymmetricPositiveMatrix	transpose(boolean forceCopy) Returns the transpose of this matrix.
double	walkInColumnOrder(RealMatrixChangingVisitor visitor) Visits (and possibly change) all matrix entries in column order.
double	walkInColumnOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visits (and possibly change) some matrix entries in column order.
double	walkInOptimizedOrder(RealMatrixChangingVisitor visitor) Visits (and possibly change) all matrix entries using the fastest possible order.
double	walkInOptimizedOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visits (and possibly change) some matrix entries using the fastest possible order.
double	walkInRowOrder(RealMatrixChangingVisitor visitor) Visits (and possibly change) all matrix entries in row order.
double	walkInRowOrder(RealMatrixChangingVisitor visitor, int startRow, int endRow, int startColumn, int endColumn) Visits (and possibly change) some matrix entries in row order.

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

add, add, checkAbsoluteThreshold, checkDataArray, checkMatrix, checkRelativeThreshold, concatenateDiagonally, concatenateHorizontally, concatenateVertically, getColumnDimension, getColumnMatrix, getDataRef, getDefaultAbsoluteSymmetryThreshold, getDefaultRelativeSymmetryThreshold, getEntry, getRowDimension, getRowMatrix, isSquare, isSymmetric, isSymmetric, isSymmetric, multiply, multiply, setDefaultAbsoluteSymmetryThreshold, setDefaultRelativeSymmetryThreshold, subtract, subtract, subtract

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

checkDestinationArray, checkSquare, concatenateDiagonally, concatenateDiagonally, concatenateHorizontally, concatenateVertically, copySubMatrix, copySubMatrix, copySubMatrix, copySubMatrix, equals, getAbs, getColumn, getColumnVector, getData, getData, getDefaultDecomposition, getDiagonal, getFrobeniusNorm, getMax, getMin, getNorm, getRow, getRowVector, getTrace, isAntisymmetric, isDiagonal, isInvertible, isOrthogonal, multiply, multiply, operate, operate, preMultiply, preMultiply, preMultiply, setDefaultDecomposition, toString, toString, walkInColumnOrder, walkInColumnOrder, walkInOptimizedOrder, walkInOptimizedOrder, 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.SymmetricMatrix

getDiagonal, subtract

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

add, concatenateDiagonally, concatenateDiagonally, concatenateDiagonally, concatenateHorizontally, concatenateHorizontally, concatenateVertically, concatenateVertically, copySubMatrix, copySubMatrix, copySubMatrix, copySubMatrix, equals, getAbs, getColumn, getColumnMatrix, getColumnVector, getData, getData, getDefaultDecomposition, getEntry, getFrobeniusNorm, getMax, getMax, getMin, getMin, getNorm, getRow, getRowMatrix, getRowVector, getTrace, isAntisymmetric, isDiagonal, isInvertible, isOrthogonal, isSymmetric, isSymmetric, isSymmetric, multiply, multiply, multiply, operate, operate, preMultiply, preMultiply, preMultiply, setDefaultDecomposition, subtract, toString, walkInColumnOrder, walkInColumnOrder, walkInOptimizedOrder, walkInOptimizedOrder, walkInRowOrder, walkInRowOrder

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

getColumnDimension, getRowDimension, isSquare

Constructor Detail

ArrayRowSymmetricPositiveMatrix

public ArrayRowSymmetricPositiveMatrix(int n)

Builds a new ArrayRowSymmetricPositiveMatrix of dimension n (filled with zero).

Parameters:

n - the dimension of the matrix

ArrayRowSymmetricPositiveMatrix

public ArrayRowSymmetricPositiveMatrix(ArrayRowSymmetricMatrix.SymmetryType symmetryType,
                                       double[][] dataIn)

Builds a new ArrayRowSymmetricPositiveMatrix from the provided data, using the default symmetry and positivity thresholds.

Parameters:

symmetryType - the type of symmetry enforced at construction

dataIn - the data of the matrix (must be a NxN array)

See Also:

ArrayRowSymmetricMatrix.getDefaultRelativeSymmetryThreshold(), getDefaultAbsolutePositivityThreshold()

ArrayRowSymmetricPositiveMatrix

public ArrayRowSymmetricPositiveMatrix(ArrayRowSymmetricMatrix.SymmetryType symmetryType,
                                       double[][] dataIn,
                                       Double absoluteSymmetryThreshold,
                                       Double relativeSymmetryThreshold,
                                       Double absolutePositivityThreshold,
                                       Double relativePositivityThreshold)

Builds a new ArrayRowSymmetricPositiveMatrix from the provided data, using the specified symmetry and positivity thresholds.

The provided thresholds must either be null, or set to a positive value. Setting both the absolute and relative thresholds to null completely disables the associated symmetry or positivity check. Any null threshold is considered to be equal to zero if the associated check is not disabled.

Parameters:

symmetryType - the type of symmetry enforced at construction

dataIn - the data of the matrix (must be a NxN array)

absoluteSymmetryThreshold - the absolute symmetry threshold, above which off-diagonal elements are considered different

relativeSymmetryThreshold - the relative symmetry threshold, above which off-diagonal elements are considered different

absolutePositivityThreshold - the absolute positivity threshold, above which a value is considered to be strictly positive

relativePositivityThreshold - the relative positivity threshold, above which a value is considered to be numerically significant when compared to anothervalue

ArrayRowSymmetricPositiveMatrix

public ArrayRowSymmetricPositiveMatrix(ArrayRowSymmetricMatrix.SymmetryType symmetryType,
                                       RealMatrix matrix)

Builds a new ArrayRowSymmetricPositiveMatrix from the provided matrix, using the default symmetry and positivity thresholds.

Parameters:

symmetryType - the type of symmetry enforced at construction

matrix - the matrix (must NxN)

See Also:

ArrayRowSymmetricMatrix.getDefaultRelativeSymmetryThreshold(), getDefaultAbsolutePositivityThreshold()

ArrayRowSymmetricPositiveMatrix

public ArrayRowSymmetricPositiveMatrix(ArrayRowSymmetricMatrix.SymmetryType symmetryType,
                                       RealMatrix matrix,
                                       Double absoluteSymmetryThreshold,
                                       Double relativeSymmetryThreshold,
                                       Double absolutePositivityThreshold,
                                       Double relativePositivityThreshold)

Builds a new ArrayRowSymmetricPositiveMatrix from the provided matrix, using the specified symmetry and positivity thresholds.

The provided thresholds must either be null, or set to a positive value. Setting both the absolute and relative thresholds to null completely disables the associated symmetry or positivity check. Any null threshold is considered to be equal to zero if the associated check is not disabled.

Parameters:

symmetryType - the type of symmetry enforced at construction

matrix - the matrix (must NxN)

absoluteSymmetryThreshold - the absolute symmetry threshold, above which off-diagonal elements are considered different

relativeSymmetryThreshold - the relative symmetry threshold, above which off-diagonal elements are considered different

absolutePositivityThreshold - the absolute positivity threshold, above which a value is considered to be strictly positive

relativePositivityThreshold - the relative positivity threshold, above which a value is considered to be numerically significant when compared to another value

Throws:

NonPositiveDefiniteMatrixException - if the matrix is not positive semi-definite

ArrayRowSymmetricPositiveMatrix

protected ArrayRowSymmetricPositiveMatrix(double[] dataIn,
                                          boolean copyArray)

Builds a new ArrayRowSymmetricPositiveMatrix by specifying the lower triangular part of the matrix directly.

No check is made on the positivity or definiteness of the matrix. This constructor should only be used when the matrix defined by the provided data is positive semi-definite by construction.

Parameters:

dataIn - the array storing the lower triangular part of the matrix

copyArray - if true, the provided array will be copied, otherwise it will be passed by reference

Method Detail

setEntry

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

Sets the entry at the specified row and column to a new value.

Row and column indices start at 0.

This method automatically modify the symmetric element to ensure the symmetry of the matrix is preserved.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

setEntry in interface RealMatrix

Overrides:

setEntry in class ArrayRowSymmetricMatrix

Parameters:

row - the row index of entry to be set

column - the column index of entry to be set

value - the new value of the entry

Throws:

MathUnsupportedOperationException - systematically (this operation is forbidden)

addToEntry

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

Adds (in place) a given value to the specified entry of this matrix.

Row and column indices start at 0.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

addToEntry in interface RealMatrix

Overrides:

addToEntry in class ArrayRowSymmetricMatrix

Parameters:

row - the row index of the entry to be modified

column - the column index of the entry to be modified

increment - the value to add to the matrix entry

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

multiplyEntry

public void multiplyEntry(int row,
                          int column,
                          double factor)

Multiplies (in place) the specified entry of this matrix by a given value.

Row and column indices start at 0.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

multiplyEntry in interface RealMatrix

Overrides:

multiplyEntry in class ArrayRowSymmetricMatrix

Parameters:

row - the row index of the entry to be modified

column - the column index of the entry to be modified

factor - the multiplication factor for the matrix entry

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

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.

The returned matrix is an ArrayRowSymmetricMatrix if the selected indices are the same for the rows and the columns, and an Array2DRowRealMatrix or a BlockRealMatrix otherwise.

The returned matrix is an ArrayRowSymmetricPositiveMatrix if the selected indices are the same for the rows and the columns, and an Array2DRowRealMatrix or a BlockRealMatrix otherwise.

Specified by:

getSubMatrix in interface RealMatrix

Overrides:

getSubMatrix in class ArrayRowSymmetricMatrix

Parameters:

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the 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.

The returned matrix is an ArrayRowSymmetricMatrix if the selected indices are the same for the rows and the columns (same indices, same order), and an Array2DRowRealMatrix or a BlockRealMatrix otherwise.

The returned matrix is an ArrayRowSymmetricPositiveMatrix if the selected indices are the same for the rows and the columns (same indices, same order), and an Array2DRowRealMatrix or a BlockRealMatrix otherwise.

Specified by:

getSubMatrix in interface RealMatrix

Overrides:

getSubMatrix in class ArrayRowSymmetricMatrix

Parameters:

selectedRows - the selected row indices

selectedColumns - the selected column indices

Returns:

the submatrix containing the data in the specified rows and columns

getSubMatrix

public ArrayRowSymmetricPositiveMatrix 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]
 

Specified by:

getSubMatrix in interface SymmetricMatrix

Specified by:

getSubMatrix in interface SymmetricPositiveMatrix

Overrides:

getSubMatrix in class ArrayRowSymmetricMatrix

Parameters:

startIndex - the initial row/column index

endIndex - the final row/column index (inclusive)

Returns:

the extracted submatrix

getSubMatrix

public ArrayRowSymmetricPositiveMatrix getSubMatrix(int[] index)

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]
 

Specified by:

getSubMatrix in interface SymmetricMatrix

Specified by:

getSubMatrix in interface SymmetricPositiveMatrix

Overrides:

getSubMatrix in class ArrayRowSymmetricMatrix

Parameters:

index - the selected indices

Returns:

the extracted submatrix

setSubMatrix

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

Replaces part of the matrix with a given submatrix, starting at the specified row and column.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

setSubMatrix in interface RealMatrix

Overrides:

setSubMatrix in class ArrayRowSymmetricMatrix

Parameters:

subMatrix - the array containing the replacement data of the targeted submatrix

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

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

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

setRow

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

Replaces the entries of a given row with the entries of the specified data array.

Row indices start at 0.
The size of the provided data array must match the column dimension of this matrix.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

setRow in interface RealMatrix

Overrides:

setRow in class AbstractRealMatrix

Parameters:

row - the index of the row to be replaced

array - the row data array to be copied

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

setRowVector

public void setRowVector(int row,
                         RealVector vector)

Replaces the entries of a given row with the entries of the specified vector.

Row indices start at 0.
The size of the provided vector must match the column dimension of this matrix.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

setRowVector in interface RealMatrix

Overrides:

setRowVector in class AbstractRealMatrix

Parameters:

row - the index of the row to be replaced

vector - the row vector to be copied

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

setRowMatrix

public void setRowMatrix(int row,
                         RealMatrix matrix)

Replaces the entries of a given row with the entries of the specified row matrix.

Row indices start at 0.
The provided matrix must have one row and the same number of columns as this matrix.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

setRowMatrix in interface RealMatrix

Overrides:

setRowMatrix in class AbstractRealMatrix

Parameters:

row - the index of the row to be replaced

matrix - the row matrix to be copied

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

setColumn

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

Replaces the entries of a given column with the entries of the specified data array.

Column indices start at 0.
The size of the provided data array must match the row dimension of this matrix.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

setColumn in interface RealMatrix

Overrides:

setColumn in class AbstractRealMatrix

Parameters:

column - the index of the column to be replaced

array - the column data array to be copied

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

setColumnVector

public void setColumnVector(int column,
                            RealVector vector)

Replaces the entries of a given column with the entries of the specified vector.

Column indices start at 0.
The size of the provided vector must match the row dimension of this matrix.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

setColumnVector in interface RealMatrix

Overrides:

setColumnVector in class AbstractRealMatrix

Parameters:

column - the index of the column to be replaced

vector - the column vector to be copied

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

setColumnMatrix

public void setColumnMatrix(int column,
                            RealMatrix matrix)

Replaces the entries of a given column with the entries of the specified column matrix.

Column indices start at 0.
The provided matrix must have one column and the same number of rows as this matrix.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

setColumnMatrix in interface RealMatrix

Overrides:

setColumnMatrix in class AbstractRealMatrix

Parameters:

column - the index of the column to be replaced

matrix - the column matrix to be copied

Throws:

MathUnsupportedOperationException - systematically, since this operation is not supported

scalarAdd

public ArrayRowSymmetricMatrix scalarAdd(double d)

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

Specified by:

scalarAdd in interface RealMatrix

Specified by:

scalarAdd in interface SymmetricMatrix

Overrides:

scalarAdd in class ArrayRowSymmetricMatrix

Parameters:

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

Returns:

the matrix resulting from the addition this+d

positiveScalarAdd

public ArrayRowSymmetricPositiveMatrix positiveScalarAdd(double d)

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

Specified by:

positiveScalarAdd in interface SymmetricPositiveMatrix

Parameters:

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

Returns:

the symmetric positive semi-definite matrix resulting from the addition this+ d

scalarMultiply

public ArrayRowSymmetricMatrix scalarMultiply(double d)

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

Specified by:

scalarMultiply in interface RealMatrix

Specified by:

scalarMultiply in interface SymmetricMatrix

Overrides:

scalarMultiply in class ArrayRowSymmetricMatrix

Parameters:

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

Returns:

the matrix resulting from the product this×d

positiveScalarMultiply

public ArrayRowSymmetricPositiveMatrix positiveScalarMultiply(double d)

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

Specified by:

positiveScalarMultiply in interface SymmetricPositiveMatrix

Parameters:

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

Returns:

the symmetric positive semi-definite matrix resulting from the product d ×this

add

public ArrayRowSymmetricMatrix add(SymmetricMatrix m)

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

The returned matrix is, in order of priority:

• An ArrayRowSymmetricPositiveMatrix if it is a SymmetricPositiveMatrix;
• An ArrayRowSymmetricMatrix if it is any other type of SymmetricMatrix.

Specified by:

add in interface SymmetricMatrix

Overrides:

add in class ArrayRowSymmetricMatrix

Parameters:

m - the matrix to be added

Returns:

the matrix resulting from the addition this+m

add

public ArrayRowSymmetricPositiveMatrix add(SymmetricPositiveMatrix m)

Returns the result of adding the symmetric positive semi-definite matrix m to this matrix.

Specified by:

add in interface SymmetricPositiveMatrix

Parameters:

m - the symmetric positive semi-definite matrix to be added

Returns:

the symmetric positive semi-definite matrix resulting from the addition this+ m

quadraticMultiplication

public ArrayRowSymmetricPositiveMatrix quadraticMultiplication(RealMatrix m)

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

Specified by:

quadraticMultiplication in interface SymmetricMatrix

Specified by:

quadraticMultiplication in interface SymmetricPositiveMatrix

Overrides:

quadraticMultiplication in class ArrayRowSymmetricMatrix

Parameters:

m - the matrix M

Returns:

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

quadraticMultiplication

public ArrayRowSymmetricPositiveMatrix 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.

Specified by:

quadraticMultiplication in interface SymmetricMatrix

Specified by:

quadraticMultiplication in interface SymmetricPositiveMatrix

Overrides:

quadraticMultiplication in class ArrayRowSymmetricMatrix

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

power

public ArrayRowSymmetricPositiveMatrix 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

Specified by:

power in interface SymmetricMatrix

Specified by:

power in interface SymmetricPositiveMatrix

Overrides:

power in class ArrayRowSymmetricMatrix

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

createMatrix

public ArrayRowSymmetricPositiveMatrix 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).

Specified by:

createMatrix in interface RealMatrix

Specified by:

createMatrix in interface SymmetricMatrix

Specified by:

createMatrix in interface SymmetricPositiveMatrix

Overrides:

createMatrix in class ArrayRowSymmetricMatrix

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

createIdentityMatrix

public static ArrayRowSymmetricPositiveMatrix createIdentityMatrix(int dim)

Creates an identity matrix of the specified dimension.

Parameters:

dim - the dimension of the identity matrix

Returns:

the identity matrix built

copy

public ArrayRowSymmetricPositiveMatrix copy()

Returns a deep copy of this matrix.

Specified by:

copy in interface RealMatrix

Specified by:

copy in interface SymmetricMatrix

Specified by:

copy in interface SymmetricPositiveMatrix

Overrides:

copy in class ArrayRowSymmetricMatrix

Returns:

a deep copy of this matrix

transpose

public ArrayRowSymmetricPositiveMatrix 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 ArrayRowSymmetricMatrix

Returns:

the transpose of this matrix

transpose

public ArrayRowSymmetricPositiveMatrix 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

Specified by:

transpose in interface SymmetricMatrix

Specified by:

transpose in interface SymmetricPositiveMatrix

Overrides:

transpose in class ArrayRowSymmetricMatrix

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

getInverse

public ArrayRowSymmetricPositiveMatrix 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

Specified by:

getInverse in interface SymmetricMatrix

Specified by:

getInverse in interface SymmetricPositiveMatrix

Overrides:

getInverse in class ArrayRowSymmetricMatrix

Returns:

the inverse matrix

See Also:

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

getInverse

public ArrayRowSymmetricPositiveMatrix 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

Specified by:

getInverse in interface SymmetricMatrix

Specified by:

getInverse in interface SymmetricPositiveMatrix

Overrides:

getInverse in class ArrayRowSymmetricMatrix

Parameters:

decompositionBuilder - the decomposition builder to use

Returns:

the inverse matrix

isPositiveSemiDefinite

public boolean isPositiveSemiDefinite(double absoluteTolerance)

Determines if this matrix is positive semi-definite or not.

A symmetric matrix is considered to be positive semi-definite if its pivots are either strictly positive, or if the whole row is equal to zero after reduction (pivot included). In order to take into account possible numerical errors, the specified tolerance is added to the diagonal elements of the initial matrix.

Parameters:

absoluteTolerance - the absolute tolerance to take into account

Returns:

true if this matrix is positive semi-definite, false otherwise

isPositiveSemiDefinite

public static boolean isPositiveSemiDefinite(SymmetricMatrix symmetricMatrix,
                                             double absoluteTolerance)

Determines if a symmetric matrix is positive semi-definite or not.

A symmetric matrix is considered to be positive semi-definite if its pivots are either strictly positive, or if the whole row is equal to zero after reduction (pivot included). In order to take into account possible numerical errors, the specified tolerance is added to the diagonal elements of the initial matrix.

Parameters:

symmetricMatrix - the symmetric matrix to be checked

absoluteTolerance - the absolute tolerance to take into account

Returns:

true if the provided matrix is positive semi-definite, false otherwise

equals

public boolean equals(Object object)

Returns true if the provided object is a RealMatrix instance with the same dimensions as this matrix, whose entries are strictly equal to the entries of this matrix (no absolute or relative tolerance is taken into account when comparing the entries).

Overrides:

equals in class ArrayRowSymmetricMatrix

Parameters:

object - the object to be tested for equality

Returns:

true if the provided object is equal to this matrix

hashCode

public int hashCode()

Computes a hash code for the matrix.

Overrides:

hashCode in class ArrayRowSymmetricMatrix

Returns:

hash code for matrix

walkInRowOrder

public double walkInRowOrder(RealMatrixChangingVisitor visitor)

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

Row order starts at upper left element, iterating through all elements of a row from left to right before going to the leftmost element of the next row.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

walkInRowOrder in interface RealMatrix

Overrides:

walkInRowOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

Throws:

MathUnsupportedOperationException - systematically (this operation is forbidden)

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(RealMatrixChangingVisitor visitor,
                             int startRow,
                             int endRow,
                             int startColumn,
                             int endColumn)

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

Row order starts at upper left element, iterating through all elements of a row from left to right before going to the leftmost element of the next row.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

walkInRowOrder in interface RealMatrix

Overrides:

walkInRowOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the final column index

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

Throws:

MathUnsupportedOperationException - systematically (this operation is forbidden)

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)

walkInColumnOrder

public double walkInColumnOrder(RealMatrixChangingVisitor visitor)

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

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

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

walkInColumnOrder in interface RealMatrix

Overrides:

walkInColumnOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

Throws:

MathUnsupportedOperationException - systematically (this operation is forbidden)

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(RealMatrixChangingVisitor visitor,
                                int startRow,
                                int endRow,
                                int startColumn,
                                int endColumn)

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

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

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

walkInColumnOrder in interface RealMatrix

Overrides:

walkInColumnOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the final column index

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

Throws:

MathUnsupportedOperationException - systematically (this operation is forbidden)

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)

walkInOptimizedOrder

public double walkInOptimizedOrder(RealMatrixChangingVisitor visitor)

Visits (and possibly change) all matrix entries using the fastest possible order.

The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

walkInOptimizedOrder in interface RealMatrix

Overrides:

walkInOptimizedOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

Throws:

MathUnsupportedOperationException - systematically (this operation is forbidden)

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

walkInOptimizedOrder

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

Visits (and possibly change) some matrix entries using the fastest possible order.

The fastest walking order depends on the exact matrix class. It may be different from traditional row or column orders.

Important:
This method systematically throws a MathUnsupportedOperationException since this operation is not safe when dealing with symmetric positive definite matrices (the properties of the matrix are not guaranteed to be preserved).

Specified by:

walkInOptimizedOrder in interface RealMatrix

Overrides:

walkInOptimizedOrder in class AbstractRealMatrix

Parameters:

visitor - the visitor used to process all matrix entries

startRow - the initial row index

endRow - the final row index (inclusive)

startColumn - the initial column index

endColumn - the final column index (inclusive)

Returns:

the value returned by RealMatrixChangingVisitor.end() at the end of the walk

Throws:

MathUnsupportedOperationException - systematically (this operation is forbidden)

See Also:

RealMatrix.walkInRowOrder(RealMatrixChangingVisitor), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor), RealMatrix.walkInRowOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInRowOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor), RealMatrix.walkInColumnOrder(RealMatrixChangingVisitor, int, int, int, int), RealMatrix.walkInColumnOrder(RealMatrixPreservingVisitor, int, int, int, int), RealMatrix.walkInOptimizedOrder(RealMatrixChangingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor), RealMatrix.walkInOptimizedOrder(RealMatrixPreservingVisitor, int, int, int, int)

getDefaultAbsolutePositivityThreshold

public static Double getDefaultAbsolutePositivityThreshold()

Gets the default absolute positivity threshold, above which a value is considered to be strictly positive.

Returns:

the default absolute positivity threshold (≥0 or null)

setDefaultAbsolutePositivityThreshold

public static void setDefaultAbsolutePositivityThreshold(Double threshold)

Sets the default absolute positivity threshold, above which a value is considered to be positive.

Parameters:

threshold - the new default absolute positivity threshold (≥0 or null)

Throws:

IllegalArgumentException - if the provided threshold is NaN or is strictly negative

getDefaultRelativePositivityThreshold

public static Double getDefaultRelativePositivityThreshold()

Gets the default relative positivity threshold, above which a value is considered to be numerically significant when compared to another value.

Returns:

the default relative positivity threshold (≥0 or null)

setDefaultRelativePositivityThreshold

public static void setDefaultRelativePositivityThreshold(Double threshold)

Sets the default relative positivity threshold, above which a value is considered to be numerically significant when compared to another value.

Parameters:

threshold - the new default relative positivity threshold (≥0 or null)

Throws:

IllegalArgumentException - if the provided threshold is NaN or is strictly negative

checkPositiveSemiDefinite

protected static void checkPositiveSemiDefinite(SymmetricMatrix symmetricMatrix,
                                                double tolerance)

Ensures a symmetric matrix is positive semi-definite and throws an exception if that's not the case.

A symmetric matrix is considered to be positive semi-definite if its pivots are either strictly positive, or if the whole row is equal to zero after reduction (pivot included). In order to take into account possible numerical errors, the specified tolerance is added to the diagonal elements of the initial matrix.

Parameters:

symmetricMatrix - the symmetric matrix to be checked

tolerance - the absolute tolerance to take into account

Throws:

NonPositiveDefiniteMatrixException - if the provided matrix is not positive semi-definite

getEffectiveTolerance

protected static double getEffectiveTolerance(Double absoluteTolerance,
                                              Double relativeTolerance,
                                              double maxValue)

Gets the effective tolerance from a given absolute and relative tolerance.

The effective tolerance is the largest value between the specified absolute tolerance and the relative tolerance multiplied by the provided element value. The provided tolerances default to zero when they are null.

Parameters:

absoluteTolerance - the absolute tolerance

relativeTolerance - the relative tolerance

maxValue - the value to which the relative tolerance is to be applied

Returns:

the effective tolerance