Uses of Interface
org.hipparchus.linear.RealMatrix

Packages that use RealMatrix

Package	Description
org.hipparchus.distribution.multivariate	Implementations of multivariate distributions.
org.hipparchus.linear	Linear algebra support.
org.hipparchus.random	Random number and random data generators.
org.hipparchus.util	Convenience routines and common data structures used throughout the Hipparchus library.

Uses of RealMatrix in org.hipparchus.distribution.multivariate

Methods in org.hipparchus.distribution.multivariate that return RealMatrix

Modifier and Type	Method	Description
RealMatrix	MultivariateNormalDistribution.getCovariances()	Gets the covariance matrix.

Uses of RealMatrix in org.hipparchus.linear

Subinterfaces of RealMatrix in org.hipparchus.linear

Modifier and Type	Interface	Description
interface	SparseRealMatrix	Marker interface for RealMatrix implementations that require sparse backing storage

Classes in org.hipparchus.linear that implement RealMatrix

Modifier and Type	Class	Description
class	AbstractRealMatrix	Basic implementation of RealMatrix methods regardless of the underlying storage.
class	Array2DRowRealMatrix	Implementation of RealMatrix using a double[][] array to store entries.
class	BlockRealMatrix	Cache-friendly implementation of RealMatrix using a flat arrays to store square blocks of the matrix.
class	DiagonalMatrix	Implementation of a diagonal matrix.
class	OpenMapRealMatrix	Sparse matrix implementation based on an open addressed map.

Methods in org.hipparchus.linear that return RealMatrix

Modifier and Type	Method	Description
RealMatrix	AbstractRealMatrix.add(RealMatrix m)	Returns the sum of this and m.
RealMatrix	RealMatrix.add(RealMatrix m)	Returns the sum of this and m.
default RealMatrix	RealMatrix.blendArithmeticallyWith(RealMatrix other, double blendingValue)	Blend arithmetically this instance with another one.
static RealMatrix	MatrixUtils.blockInverse(RealMatrix m, int splitIndex)	Computes the inverse of the given matrix by splitting it into 4 sub-matrices.
abstract RealMatrix	AbstractRealMatrix.copy()	Returns a (deep) copy of this.
RealMatrix	Array2DRowRealMatrix.copy()	Returns a (deep) copy of this.
RealMatrix	DiagonalMatrix.copy()	Returns a (deep) copy of this.
RealMatrix	RealMatrix.copy()	Returns a (deep) copy of this.
static RealMatrix	MatrixUtils.createColumnRealMatrix(double[] columnData)	Creates a column RealMatrix using the data from the input array.
abstract RealMatrix	AbstractRealMatrix.createMatrix(int rowDimension, int columnDimension)	Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
RealMatrix	Array2DRowRealMatrix.createMatrix(int rowDimension, int columnDimension)	Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
RealMatrix	DiagonalMatrix.createMatrix(int rowDimension, int columnDimension)	Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
RealMatrix	RealMatrix.createMatrix(int rowDimension, int columnDimension)	Create a new RealMatrix of the same type as the instance with the supplied row and column dimensions.
static RealMatrix	MatrixUtils.createRealDiagonalMatrix(double[] diagonal)	Returns a diagonal matrix with specified elements.
static RealMatrix	MatrixUtils.createRealIdentityMatrix(int dimension)	Returns dimension x dimension identity matrix.
static RealMatrix	MatrixUtils.createRealMatrix(double[][] data)	Returns a RealMatrix whose entries are the the values in the the input array.
static RealMatrix	MatrixUtils.createRealMatrix(int rows, int columns)	Returns a RealMatrix with specified dimensions.
static RealMatrix	MatrixUtils.createRowRealMatrix(double[] rowData)	Create a row RealMatrix using the data from the input array.
RealMatrix	AbstractRealMatrix.getColumnMatrix(int column)	Get the entries at the given column index as a column matrix.
RealMatrix	RealMatrix.getColumnMatrix(int column)	Get the entries at the given column index as a column matrix.
RealMatrix	SingularValueDecomposition.getCovariance(double minSingularValue)	Returns the n × n covariance matrix.
RealMatrix	EigenDecompositionNonSymmetric.getD()	Gets the block diagonal matrix D of the decomposition.
RealMatrix	HessenbergTransformer.getH()	Returns the Hessenberg matrix H of the transform.
RealMatrix	QRDecomposition.getH()	Returns the Householder reflector vectors.
RealMatrix	DecompositionSolver.getInverse()	Get the pseudo-inverse of the decomposed matrix.
RealMatrix	RiccatiEquationSolver.getK()	Get the linear controller k.
RealMatrix	RiccatiEquationSolverImpl.getK()	{inheritDoc}
RealMatrix	CholeskyDecomposition.getL()	Returns the matrix L of the decomposition.
RealMatrix	LUDecomposition.getL()	Returns the matrix L of the decomposition.
RealMatrix	SemiDefinitePositiveCholeskyDecomposition.getL()	Returns the matrix L of the decomposition.
RealMatrix	CholeskyDecomposition.getLT()	Returns the transpose of the matrix L of the decomposition.
RealMatrix	SemiDefinitePositiveCholeskyDecomposition.getLT()	Returns the transpose of the matrix L of the decomposition.
RealMatrix	HessenbergTransformer.getP()	Returns the matrix P of the transform.
RealMatrix	LUDecomposition.getP()	Returns the P rows permutation matrix.
RealMatrix	RiccatiEquationSolver.getP()	Get the solution.
RealMatrix	RiccatiEquationSolverImpl.getP()	{inheritDoc}
RealMatrix	RRQRDecomposition.getP()	Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.
RealMatrix	SchurTransformer.getP()	Returns the matrix P of the transform.
RealMatrix	HessenbergTransformer.getPT()	Returns the transpose of the matrix P of the transform.
RealMatrix	SchurTransformer.getPT()	Returns the transpose of the matrix P of the transform.
RealMatrix	QRDecomposition.getQ()	Returns the matrix Q of the decomposition.
RealMatrix	QRDecomposition.getQT()	Returns the transpose of the matrix Q of the decomposition.
RealMatrix	QRDecomposition.getR()	Returns the matrix R of the decomposition.
RealMatrix	RectangularCholeskyDecomposition.getRootMatrix()	Get the root of the covariance matrix.
RealMatrix	AbstractRealMatrix.getRowMatrix(int row)	Get the entries at the given row index as a row matrix.
RealMatrix	RealMatrix.getRowMatrix(int row)	Get the entries at the given row index as a row matrix.
RealMatrix	SingularValueDecomposition.getS()	Returns the diagonal matrix Σ of the decomposition.
RealMatrix	EigenDecompositionSymmetric.getSquareRoot()	Computes the square-root of the matrix.
RealMatrix	AbstractRealMatrix.getSubMatrix(int[] selectedRows, int[] selectedColumns)	Gets a submatrix.
RealMatrix	AbstractRealMatrix.getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)	Gets a submatrix.
RealMatrix	Array2DRowRealMatrix.getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)	Gets a submatrix.
RealMatrix	RealMatrix.getSubMatrix(int[] selectedRows, int[] selectedColumns)	Gets a submatrix.
RealMatrix	RealMatrix.getSubMatrix(int startRow, int endRow, int startColumn, int endColumn)	Gets a submatrix.
RealMatrix	SchurTransformer.getT()	Returns the quasi-triangular Schur matrix T of the transform.
RealMatrix	LUDecomposition.getU()	Returns the matrix U of the decomposition.
RealMatrix	SingularValueDecomposition.getU()	Returns the matrix U of the decomposition.
RealMatrix	SingularValueDecomposition.getUT()	Returns the transpose of the matrix U of the decomposition.
RealMatrix	EigenDecompositionNonSymmetric.getV()	Gets the matrix V of the decomposition.
RealMatrix	EigenDecompositionSymmetric.getV()	Gets the matrix V of the decomposition.
RealMatrix	SingularValueDecomposition.getV()	Returns the matrix V of the decomposition.
RealMatrix	EigenDecompositionNonSymmetric.getVInv()	Gets the inverse of the matrix V of the decomposition.
RealMatrix	EigenDecompositionSymmetric.getVT()	Gets the transpose of the matrix V of the decomposition.
RealMatrix	SingularValueDecomposition.getVT()	Returns the transpose of the matrix V of the decomposition.
static RealMatrix	MatrixUtils.inverse(RealMatrix matrix)	Computes the inverse of the given matrix.
static RealMatrix	MatrixUtils.inverse(RealMatrix matrix, double threshold)	Computes the inverse of the given matrix.
RealMatrix	Array2DRowRealMatrix.kroneckerProduct(RealMatrix b)	Kronecker product of the current matrix and the parameter matrix.
default RealMatrix	RealMatrix.map(UnivariateFunction function)	Acts as if implemented as:
default RealMatrix	RealMatrix.mapToSelf(UnivariateFunction function)	Replace each entry by the result of applying the function to it.
static RealMatrix	MatrixUtils.matrixExponential(RealMatrix rm)	Computes the matrix exponential of the given matrix.
RealMatrix	AbstractRealMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
RealMatrix	DiagonalMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
RealMatrix	OpenMapRealMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
RealMatrix	RealMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
RealMatrix	Array2DRowRealMatrix.multiplyTransposed(Array2DRowRealMatrix m)	Returns the result of postmultiplying this by m^T.
RealMatrix	Array2DRowRealMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
RealMatrix	DiagonalMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
RealMatrix	OpenMapRealMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
default RealMatrix	RealMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
RealMatrix	ArrayRealVector.outerProduct(RealVector v)	Compute the outer product.
RealMatrix	RealVector.outerProduct(RealVector v)	Compute the outer product.
RealMatrix	RealMatrixFormat.parse(String source)	Parse a string to produce a RealMatrix object.
RealMatrix	RealMatrixFormat.parse(String source, ParsePosition pos)	Parse a string to produce a RealMatrix object.
RealMatrix	AbstractRealMatrix.power(int p)	Returns the result of multiplying this with itself p times.
RealMatrix	RealMatrix.power(int p)	Returns the result of multiplying this with itself p times.
RealMatrix	AbstractRealMatrix.preMultiply(RealMatrix m)	Returns the result of premultiplying this by m.
RealMatrix	RealMatrix.preMultiply(RealMatrix m)	Returns the result of premultiplying this by m.
RealMatrix	AbstractRealMatrix.scalarAdd(double d)	Returns the result of adding d to each entry of this.
RealMatrix	RealMatrix.scalarAdd(double d)	Returns the result of adding d to each entry of this.
RealMatrix	AbstractRealMatrix.scalarMultiply(double d)	Returns the result of multiplying each entry of this by d.
RealMatrix	BlockRealMatrix.scalarMultiply(double d)	Returns the result of multiplying each entry of this by d.
RealMatrix	RealMatrix.scalarMultiply(double d)	Returns the result of multiplying each entry of this by d.
RealMatrix	DecompositionSolver.solve(RealMatrix b)	Solve the linear equation A × X = B for matrices A.
RealMatrix	Array2DRowRealMatrix.stack()	Transforms a matrix in a vector (Vectorization).
RealMatrix	AbstractRealMatrix.subtract(RealMatrix m)	Returns this minus m.
RealMatrix	RealMatrix.subtract(RealMatrix m)	Returns this minus m.
RealMatrix	AbstractRealMatrix.transpose()	Returns the transpose of this matrix.
RealMatrix	RealMatrix.transpose()	Returns the transpose of this matrix.
RealMatrix	Array2DRowRealMatrix.transposeMultiply(Array2DRowRealMatrix m)	Returns the result of postmultiplying this^T by m.
RealMatrix	Array2DRowRealMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.
RealMatrix	DiagonalMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.
RealMatrix	OpenMapRealMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.
default RealMatrix	RealMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.
RealMatrix	Array2DRowRealMatrix.unstackSquare()	Transforms a one-column stacked matrix into a squared matrix (devectorization).

Methods in org.hipparchus.linear with parameters of type RealMatrix

Modifier and Type	Method	Description
RealMatrix	AbstractRealMatrix.add(RealMatrix m)	Returns the sum of this and m.
BlockRealMatrix	BlockRealMatrix.add(RealMatrix m)	Returns the sum of this and m.
RealMatrix	RealMatrix.add(RealMatrix m)	Returns the sum of this and m.
default RealMatrix	RealMatrix.blendArithmeticallyWith(RealMatrix other, double blendingValue)	Blend arithmetically this instance with another one.
static RealMatrix	MatrixUtils.blockInverse(RealMatrix m, int splitIndex)	Computes the inverse of the given matrix by splitting it into 4 sub-matrices.
protected void	ComplexEigenDecomposition.checkDefinition(RealMatrix matrix)	Check definition of the decomposition in runtime.
static void	MatrixUtils.checkSymmetric(RealMatrix matrix, double eps)	Checks whether a matrix is symmetric.
DecompositionSolver	CholeskyDecomposer.decompose(RealMatrix a)	Get a solver for finding the A × X = B solution in least square sense.
DecompositionSolver	LUDecomposer.decompose(RealMatrix a)	Get a solver for finding the A × X = B solution in least square sense.
DecompositionSolver	MatrixDecomposer.decompose(RealMatrix a)	Get a solver for finding the A × X = B solution in least square sense.
DecompositionSolver	QRDecomposer.decompose(RealMatrix a)	Get a solver for finding the A × X = B solution in least square sense.
DecompositionSolver	SingularValueDecomposer.decompose(RealMatrix a)	Get a solver for finding the A × X = B solution in least square sense.
protected void	ComplexEigenDecomposition.findEigenValues(RealMatrix matrix)	Compute eigen values using the Schur transform.
String	RealMatrixFormat.format(RealMatrix m)	This method calls RealMatrixFormat.format(RealMatrix,StringBuffer,FieldPosition).
StringBuffer	RealMatrixFormat.format(RealMatrix matrix, StringBuffer toAppendTo, FieldPosition pos)	Formats a RealMatrix object to produce a string.
static RealMatrix	MatrixUtils.inverse(RealMatrix matrix)	Computes the inverse of the given matrix.
static RealMatrix	MatrixUtils.inverse(RealMatrix matrix, double threshold)	Computes the inverse of the given matrix.
static boolean	MatrixUtils.isSymmetric(RealMatrix matrix, double eps)	Checks whether a matrix is symmetric.
RealMatrix	Array2DRowRealMatrix.kroneckerProduct(RealMatrix b)	Kronecker product of the current matrix and the parameter matrix.
static RealMatrix	MatrixUtils.matrixExponential(RealMatrix rm)	Computes the matrix exponential of the given matrix.
RealMatrix	AbstractRealMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
BlockRealMatrix	BlockRealMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
RealMatrix	DiagonalMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
RealMatrix	OpenMapRealMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
RealMatrix	RealMatrix.multiply(RealMatrix m)	Returns the result of postmultiplying this by m.
RealMatrix	Array2DRowRealMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
BlockRealMatrix	BlockRealMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
RealMatrix	DiagonalMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
RealMatrix	OpenMapRealMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
default RealMatrix	RealMatrix.multiplyTransposed(RealMatrix m)	Returns the result of postmultiplying this by m^T.
RealMatrix	AbstractRealMatrix.preMultiply(RealMatrix m)	Returns the result of premultiplying this by m.
RealMatrix	RealMatrix.preMultiply(RealMatrix m)	Returns the result of premultiplying this by m.
void	AbstractRealMatrix.setColumnMatrix(int column, RealMatrix matrix)	Sets the specified column of this matrix to the entries of the specified column matrix.
void	BlockRealMatrix.setColumnMatrix(int column, RealMatrix matrix)	Sets the specified column of this matrix to the entries of the specified column matrix.
void	RealMatrix.setColumnMatrix(int column, RealMatrix matrix)	Sets the specified column of this matrix to the entries of the specified column matrix.
void	AbstractRealMatrix.setRowMatrix(int row, RealMatrix matrix)	Sets the specified row of this matrix to the entries of the specified row matrix.
void	BlockRealMatrix.setRowMatrix(int row, RealMatrix matrix)	Sets the specified row of this matrix to the entries of the specified row matrix.
void	RealMatrix.setRowMatrix(int row, RealMatrix matrix)	Sets the specified row of this matrix to the entries of the specified row matrix.
RealMatrix	DecompositionSolver.solve(RealMatrix b)	Solve the linear equation A × X = B for matrices A.
static void	MatrixUtils.solveLowerTriangularSystem(RealMatrix rm, RealVector b)	Solve a system of composed of a Lower Triangular Matrix RealMatrix.
static void	MatrixUtils.solveUpperTriangularSystem(RealMatrix rm, RealVector b)	Solver a system composed of an Upper Triangular Matrix RealMatrix.
RealMatrix	AbstractRealMatrix.subtract(RealMatrix m)	Returns this minus m.
BlockRealMatrix	BlockRealMatrix.subtract(RealMatrix m)	Returns this minus m.
OpenMapRealMatrix	OpenMapRealMatrix.subtract(RealMatrix m)	Returns this minus m.
RealMatrix	RealMatrix.subtract(RealMatrix m)	Returns this minus m.
RealMatrix	Array2DRowRealMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.
BlockRealMatrix	BlockRealMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.
RealMatrix	DiagonalMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.
RealMatrix	OpenMapRealMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.
default RealMatrix	RealMatrix.transposeMultiply(RealMatrix m)	Returns the result of postmultiplying this^T by m.

Constructors in org.hipparchus.linear with parameters of type RealMatrix

Modifier	Constructor	Description
	CholeskyDecomposition(RealMatrix matrix)	Calculates the Cholesky decomposition of the given matrix.
	CholeskyDecomposition(RealMatrix matrix, double relativeSymmetryThreshold, double absolutePositivityThreshold)	Calculates the Cholesky decomposition of the given matrix.
	ComplexEigenDecomposition(RealMatrix matrix)	Constructor for decomposition.
	ComplexEigenDecomposition(RealMatrix matrix, double eigenVectorsEquality, double epsilon, double epsilonAVVDCheck)	Constructor for decomposition.
	EigenDecompositionNonSymmetric(RealMatrix matrix)	Calculates the eigen decomposition of the given real matrix.
	EigenDecompositionNonSymmetric(RealMatrix matrix, double epsilon)	Calculates the eigen decomposition of the given real matrix.
	EigenDecompositionSymmetric(RealMatrix matrix)	Calculates the eigen decomposition of the given symmetric real matrix.
	EigenDecompositionSymmetric(RealMatrix matrix, double epsilon, boolean decreasing)	Calculates the eigen decomposition of the given real matrix.
	HessenbergTransformer(RealMatrix matrix)	Build the transformation to Hessenberg form of a general matrix.
	LUDecomposition(RealMatrix matrix)	Calculates the LU-decomposition of the given matrix.
	LUDecomposition(RealMatrix matrix, double singularityThreshold)	Calculates the LU-decomposition of the given matrix.
	OrderedComplexEigenDecomposition(RealMatrix matrix)	Constructor for the decomposition.
	OrderedComplexEigenDecomposition(RealMatrix matrix, double eigenVectorsEquality, double epsilon, double epsilonAVVDCheck)	Constructor for decomposition.
	OrderedComplexEigenDecomposition(RealMatrix matrix, double eigenVectorsEquality, double epsilon, double epsilonAVVDCheck, Comparator<Complex> eigenValuesComparator)	Constructor for decomposition.
	QRDecomposition(RealMatrix matrix)	Calculates the QR-decomposition of the given matrix.
	QRDecomposition(RealMatrix matrix, double threshold)	Calculates the QR-decomposition of the given matrix.
	RectangularCholeskyDecomposition(RealMatrix matrix)	Decompose a symmetric positive semidefinite matrix.
	RectangularCholeskyDecomposition(RealMatrix matrix, double small)	Decompose a symmetric positive semidefinite matrix.
	RiccatiEquationSolverImpl(RealMatrix A, RealMatrix B, RealMatrix Q, RealMatrix R)	Constructor of the solver.
	RRQRDecomposition(RealMatrix matrix)	Calculates the QR-decomposition of the given matrix.
	RRQRDecomposition(RealMatrix matrix, double threshold)	Calculates the QR-decomposition of the given matrix.
	SchurTransformer(RealMatrix matrix)	Build the transformation to Schur form of a general real matrix.
	SchurTransformer(RealMatrix matrix, double epsilon)	Build the transformation to Schur form of a general real matrix.
	SemiDefinitePositiveCholeskyDecomposition(RealMatrix matrix)	Calculates the Cholesky decomposition of the given matrix.
	SemiDefinitePositiveCholeskyDecomposition(RealMatrix matrix, double positivityThreshold)	Calculates the Cholesky decomposition of the given matrix.
	SingularValueDecomposition(RealMatrix matrix)	Calculates the compact Singular Value Decomposition of the given matrix.

Uses of RealMatrix in org.hipparchus.random

Methods in org.hipparchus.random that return RealMatrix

Modifier and Type	Method	Description
RealMatrix	CorrelatedRandomVectorGenerator.getRootMatrix()	Get the root of the covariance matrix.

Constructors in org.hipparchus.random with parameters of type RealMatrix

Modifier	Constructor	Description
	CorrelatedRandomVectorGenerator(double[] mean, RealMatrix covariance, double small, NormalizedRandomGenerator generator)	Builds a correlated random vector generator from its mean vector and covariance matrix.
	CorrelatedRandomVectorGenerator(RealMatrix covariance, double small, NormalizedRandomGenerator generator)	Builds a null mean random correlated vector generator from its covariance matrix.

Uses of RealMatrix in org.hipparchus.util

Methods in org.hipparchus.util that return RealMatrix

Modifier and Type	Method	Description
default RealMatrix	UnscentedTransformProvider.getUnscentedCovariance(RealVector[] sigmaPoints, RealVector meanState)	Computes the unscented covariance matrix from a weighted mean state and a set of sigma points.

Methods in org.hipparchus.util that return types with arguments of type RealMatrix

Modifier and Type	Method	Description
default Pair<RealVector,RealMatrix>	UnscentedTransformProvider.inverseUnscentedTransform(RealVector[] sigmaPoints)	Perform the inverse unscented transform from an array of sigma points.

Methods in org.hipparchus.util with parameters of type RealMatrix

Modifier and Type	Method	Description
RealVector[]	AbstractUnscentedTransform.unscentedTransform(RealVector state, RealMatrix covariance)	Perform the unscented transform from a state and its covariance.
RealVector[]	UnscentedTransformProvider.unscentedTransform(RealVector state, RealMatrix covariance)	Perform the unscented transform from a state and its covariance.