﻿FloatCholeskyLeastSq Class

# FloatCholeskyLeastSq Class

Class FloatCholeskyLeastSq solves least square problems by using the Cholesky factorization to solve the normal equations.
Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreFloatCholeskyLeastSq

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4
Syntax
```[SerializableAttribute]
public class FloatCholeskyLeastSq : ICloneable```

The FloatCholeskyLeastSq type exposes the following members.

Constructors
NameDescription
FloatCholeskyLeastSq Constructs a FloatCholeskyLeastSq instance with all sizes zero.
FloatCholeskyLeastSq(FloatMatrix) Constructs a FloatCholeskyLeastSq instance from the given matrix.
Top
Properties
NameDescription
Cols Gets the number of columns in the matrix.
IsGood Gets a boolean value which is true if the Cholesky factorization succeeded and may be used to solve least square problems; otherwise false.
Rows Gets the number of rows in the matrix.
Top
Methods
NameDescription
Clone Creates a deep copy of this least squares instance.
Factor Factors a given matrix so that it may be used to solve least squares problems.
OnSerializing processing following deserialization
ResidualNormSqr Computes the 2-norm squared of the residual vector.
ResidualVector Computes and returns the residual vector.
Solve Computes the solution to the least squares problem Ax = b.
Top
Remarks
The normal equations for the least squares problem Ax = b are:
C#
`A'Ax = A'b`
where A' denotes the transpose of the matrix A. If A has full rank, then A'A is symmetric positive definite (and, in fact, the converse is true). Thus, the Cholesky factorization may be used to solve the normal equations. Note this implies that this method will fail if A is rank deficiennt.
See Also

#### Reference

CenterSpace.NMath.Core Namespace