LinearOperator<T>.LeastSquaresSolve Method

Definition

Namespace: Extreme.Mathematics.LinearAlgebra
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23

Solves the system of simultaneous linear equations represented by this instance in the least squares sense.

Overload List

LeastSquaresSolve(Matrix<T>)	Solves the system of linear equations for the specified right-hand side matrix in the least squares sense.
LeastSquaresSolve(Vector<T>)	Solves the system of linear equations for the specified right-hand side vector.
LeastSquaresSolve(DenseMatrix<T>, Boolean)	Solves the system of linear equations for the specified right-hand side dense matrix in the least squares sense and optionally overwrites the right-hand side with the solution.
LeastSquaresSolve(DenseVector<T>, Boolean)	Solves the system of linear equations for the specified right-hand side dense vector in the least squares sense and optionally overwrites the right-hand side with the solution.

LeastSquaresSolve(Matrix<T>)

Solves the system of linear equations for the specified right-hand side matrix in the least squares sense.

public Matrix<T> LeastSquaresSolve(
	Matrix<T> rightHandSide
)

Visual Basic

Public Function LeastSquaresSolve ( 
	rightHandSide As Matrix(Of T)
) As Matrix(Of T)

C++/CLI

public:
Matrix<T>^ LeastSquaresSolve(
	Matrix<T>^ rightHandSide
)

member LeastSquaresSolve : 
        rightHandSide : Matrix<'T> -> Matrix<'T>

Parameters

rightHandSide Matrix<T>: A Matrix<T>.

Return Value

Matrix<T>
A DenseMatrix<T> containing the solution of the system of simultaneous linear equations.

Exceptions

ArgumentNullException	rightHandSide is null.
DimensionMismatchException	The length of rightHandSide does not equal the number of rows of the matrix underlying this system of equations. -or- The matrix is not square.
MatrixSingularException	The Matrix<T> underlying this system of equations is singular and does not have an inverse.
DimensionMismatchException

LeastSquaresSolve(Vector<T>)

Solves the system of linear equations for the specified right-hand side vector.

public Vector<T> LeastSquaresSolve(
	Vector<T> rightHandSide
)

Visual Basic

Public Function LeastSquaresSolve ( 
	rightHandSide As Vector(Of T)
) As Vector(Of T)

C++/CLI

public:
Vector<T>^ LeastSquaresSolve(
	Vector<T>^ rightHandSide
)

member LeastSquaresSolve : 
        rightHandSide : Vector<'T> -> Vector<'T>

Parameters

rightHandSide Vector<T>: A Vector<T>.

Return Value

Vector<T>
A DenseVector<T> containing the solution of the system of simultaneous linear equations.

Exceptions

ArgumentNullException	rightHandSide is null.
DimensionMismatchException	The length of rightHandSide does not equal the number of rows in the matrix underlying this system of equations.
MatrixSingularException	The Matrix<T> underlying this system of equations is singular and does not have an inverse.
DimensionMismatchException	The Matrix<T> underlying this system of equations is not square.

LeastSquaresSolve(DenseMatrix<T>, Boolean)

Solves the system of linear equations for the specified right-hand side dense matrix in the least squares sense and optionally overwrites the right-hand side with the solution.

public Matrix<T> LeastSquaresSolve(
	DenseMatrix<T> rightHandSide,
	bool overwrite
)

Visual Basic

Public Function LeastSquaresSolve ( 
	rightHandSide As DenseMatrix(Of T),
	overwrite As Boolean
) As Matrix(Of T)

C++/CLI

public:
Matrix<T>^ LeastSquaresSolve(
	DenseMatrix<T>^ rightHandSide, 
	bool overwrite
)

member LeastSquaresSolve : 
        rightHandSide : DenseMatrix<'T> * 
        overwrite : bool -> Matrix<'T>

Parameters

rightHandSide DenseMatrix<T>: A DenseMatrix<T>.
overwrite Boolean: If false, a new DenseMatrix<T> instance containing the solution to the system of equations is returned. (This is the default.) If true, the matrix rightHandSide is overwritten by the solution.

Return Value

Matrix<T>
A DenseMatrix<T> containing the solution of the system of simultaneous linear equations.

Remarks

Note that the first parameter must be a DenseMatrix<T>. This is because this is the only matrix type whose elements are guaranteed to be all writable.

Exceptions

ArgumentNullException	rightHandSide is null.
DimensionMismatchException	The number of rows of rightHandSide does not equal the number of rows of the matrix underlying this system of equations.
MatrixSingularException	The Matrix<T> underlying this system of equations is singular and does not have an inverse.
DimensionMismatchException	The Matrix<T> underlying this system of equations is not square.

LeastSquaresSolve(DenseVector<T>, Boolean)

Solves the system of linear equations for the specified right-hand side dense vector in the least squares sense and optionally overwrites the right-hand side with the solution.

public Vector<T> LeastSquaresSolve(
	DenseVector<T> rightHandSide,
	bool overwrite
)

Visual Basic

Public Function LeastSquaresSolve ( 
	rightHandSide As DenseVector(Of T),
	overwrite As Boolean
) As Vector(Of T)

C++/CLI

public:
Vector<T>^ LeastSquaresSolve(
	DenseVector<T>^ rightHandSide, 
	bool overwrite
)

member LeastSquaresSolve : 
        rightHandSide : DenseVector<'T> * 
        overwrite : bool -> Vector<'T>

Parameters

rightHandSide DenseVector<T>: A Vector<T>.
overwrite Boolean: If false, a new Vector<T> instance containing the solution to the system of equations is returned. If false, the vector rightHandSide is overwritten by the solution.

Return Value

Vector<T>
A DenseVector<T> containing the solution of the system of simultaneous linear equations.

Exceptions

ArgumentNullException	rightHandSide is null.
DimensionMismatchException	The length of rightHandSide does not equal the number of rows of the matrix underlying this system of equations.
MatrixSingularException	The Matrix<T> underlying this system of equations is singular and does not have an inverse.
DimensionMismatchException	The Matrix<T> underlying this system of equations is not square.

LinearOperator<T>.LeastSquaresSolve Method

Definition

Overload List

LeastSquaresSolve(Matrix<T>)

Parameters

Return Value

Exceptions

LeastSquaresSolve(Vector<T>)

Parameters

Return Value

Exceptions

LeastSquaresSolve(DenseMatrix<T>, Boolean)

Parameters

Return Value

Remarks

Exceptions

LeastSquaresSolve(DenseVector<T>, Boolean)

Parameters

Return Value

Exceptions

See Also

Reference