﻿DoubleComplexCholeskyLeastSq Class

# DoubleComplexCholeskyLeastSq Class

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

Namespace:  CenterSpace.NMath.Core
Assembly:  NMath (in NMath.dll) Version: 7.3
Syntax
```[SerializableAttribute]
public class DoubleComplexCholeskyLeastSq : ICloneable```

The DoubleComplexCholeskyLeastSq type exposes the following members.

Constructors
NameDescription
DoubleComplexCholeskyLeastSq
Constructs a DoubleComplexCholeskyLeastSq instance with all sizes zero.
DoubleComplexCholeskyLeastSq(DoubleComplexMatrix)
Constructs a DoubleComplexCholeskyLeastSq instance from the given matrix.
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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.
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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.
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Remarks
The normal equations for the least squares problem Ax = b are:
`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.