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GramSchmidtT Class

A class which encapsulates the functionality of the QR decomposition Modified Gram-Schmidt Orthogonalization.

Any real square matrix A may be decomposed as A = QR where Q is an orthogonal mxn matrix and R is an nxn upper triangular matrix.

Inheritance Hierarchy
SystemObject
  Altaxo.Calc.LinearAlgebra.FactorizationQRT
    Altaxo.Calc.LinearAlgebra.FactorizationGramSchmidtT

Namespace: Altaxo.Calc.LinearAlgebra.Factorization
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
public abstract class GramSchmidt<T> : QR<T>
where T : struct, new(), IEquatable<T>, IFormattable

Type Parameters

T
Supported data types are double, single, Altaxo.Calc.LinearAlgebra.Complex, and Altaxo.Calc.LinearAlgebra.Complex32.

The GramSchmidtT type exposes the following members.

Constructors
 NameDescription
Protected methodGramSchmidtTInitializes a new instance of the GramSchmidtT class
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Properties
 NameDescription
Public propertyDeterminant Gets the absolute determinant value of the matrix for which the QR matrix was computed.
(Inherited from QRT)
Public propertyIsFullRank Gets a value indicating whether the matrix is full rank or not.
(Inherited from QRT)
Public propertyQ Gets or sets orthogonal Q matrix
(Inherited from QRT)
Public propertyR Gets the upper triangular factor R.
(Inherited from QRT)
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Methods
 NameDescription
Public methodEqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodSolve(MatrixT) Solves a system of linear equations, AX = B, with A QR factorized.
(Inherited from QRT)
Public methodSolve(VectorT) Solves a system of linear equations, Ax = b, with A QR factorized.
(Inherited from QRT)
Public methodSolve(MatrixT, MatrixT) Solves a system of linear equations, AX = B, with A QR factorized.
(Inherited from QRT)
Public methodSolve(VectorT, VectorT) Solves a system of linear equations, Ax = b, with A QR factorized.
(Inherited from QRT)
Public methodToStringReturns a string that represents the current object.
(Inherited from Object)
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Fields
 NameDescription
Protected fieldFullR
(Inherited from QRT)
Protected fieldMethod
(Inherited from QRT)
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Remarks
The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
See Also