Gram |
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 HierarchySystemObject
Altaxo.Calc.LinearAlgebra.FactorizationQRT
Altaxo.Calc.LinearAlgebra.FactorizationGramSchmidtT
Altaxo.Calc.LinearAlgebra.FactorizationQRT
Altaxo.Calc.LinearAlgebra.FactorizationGramSchmidtT
Namespace: Altaxo.Calc.LinearAlgebra.Factorization
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3261.0 (4.8.3261.0)
SyntaxC#
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| Name | Description | |
|---|---|---|
 | GramSchmidtT | Initializes a new instance of the GramSchmidtT class |
Properties| Name | Description | |
|---|---|---|
 | Determinant |
Gets the absolute determinant value of the matrix for which the QR matrix was computed.
(Inherited from QRT) |
| IsFullRank |
Gets a value indicating whether the matrix is full rank or not.
(Inherited from QRT) |
| Q |
Gets or sets orthogonal Q matrix
(Inherited from QRT) |
| R |
Gets the upper triangular factor R.
(Inherited from QRT) |
Methods| Name | Description | |
|---|---|---|
 | Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
| Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Solve(MatrixT) |
Solves a system of linear equations, AX = B, with A QR factorized.
(Inherited from QRT) |
| Solve(VectorT) |
Solves a system of linear equations, Ax = b, with A QR factorized.
(Inherited from QRT) |
| Solve(MatrixT, MatrixT) |
Solves a system of linear equations, AX = B, with A QR factorized.
(Inherited from QRT) |
| Solve(VectorT, VectorT) |
Solves a system of linear equations, Ax = b, with A QR factorized.
(Inherited from QRT) |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
Fields
Remarks
The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
See Also