GaussianEliminationSolver (FsODE)

FsODE

Documentation for 0.0.2

GaussianEliminationSolver Type

Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore.Redist.dll
Base Type: obj
All Interfaces: ILinearEquationSolver<float>

Provides implementation of Gaussian elimination with partial pivoting

Constructors

Constructor	Description
`GaussianEliminationSolver()` Full Usage: `GaussianEliminationSolver()`

Instance members

Instance member	Description
`this.Solve` Full Usage: `this.Solve` Parameters: A : `IROMatrix<float>` - Elements of matrix 'A'. This array is modified during solution! b : `IReadOnlyList<float>` - Right part 'b'. This array is also modified during solution! x : `IVector<float>` - Vector to store the result, i.e. the solution to the problem a x = b. Modifiers: abstract	Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting. A : `IROMatrix<float>` Elements of matrix 'A'. This array is modified during solution! b : `IReadOnlyList<float>` Right part 'b'. This array is also modified during solution! x : `IVector<float>` Vector to store the result, i.e. the solution to the problem a x = b.
`this.Solve` Full Usage: `this.Solve` Parameters: A : `IROMatrix<float>` - Elements of matrix 'A'. b : `IReadOnlyList<float>` - Right part 'b' vectorCreation : `Func<int, 'VectorT>` - Function to create the resulting vector. Argument is the length of the vector. Returns: `'VectorT` Modifiers: abstract Type parameters: 'VectorT	Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting. A : `IROMatrix<float>` Elements of matrix 'A'. b : `IReadOnlyList<float>` Right part 'b' vectorCreation : `Func<int, 'VectorT>` Function to create the resulting vector. Argument is the length of the vector. Returns: `'VectorT`
`this.SolveDestructive` Full Usage: `this.SolveDestructive` Parameters: A : `IMatrix<float>` - Elements of matrix 'A'. This array is modified! b : `float[]` - Right part 'b'. This array is also modified! x : `float[]` - Vector to store the result, i.e. the solution to the problem a x = b.	Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting. Attention! Both matrix A and vector b are destroyed (changed). A : `IMatrix<float>` Elements of matrix 'A'. This array is modified! b : `float[]` Right part 'b'. This array is also modified! x : `float[]` Vector to store the result, i.e. the solution to the problem a x = b.
`this.SolveDestructive` Full Usage: `this.SolveDestructive` Parameters: A : `MatrixWrapperStructForLeftSpineJaggedArray<float>` - Elements of matrix 'A'. This array is modified! b : `float[]` - Right part 'b'. This array is also modified! x : `float[]` - Vector to store the result, i.e. the solution to the problem a x = b.	Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting. Attention! Both matrix A and vector b are destroyed (changed). A : `MatrixWrapperStructForLeftSpineJaggedArray<float>` Elements of matrix 'A'. This array is modified! b : `float[]` Right part 'b'. This array is also modified! x : `float[]` Vector to store the result, i.e. the solution to the problem a x = b.
`this.SolveDestructive` Full Usage: `this.SolveDestructive` Parameters: A : `IMatrix<float>` - Elements of matrix 'A'. The matrix is modified in this call! b : `IVector<float>` - Right part 'b'. The vector is modified in this call! x : `IVector<float>` - Vector to store the result, i.e. the solution to the problem A*x = b. Modifiers: abstract	Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting. Attention! Both matrix a and vector b are destroyed (changed). A : `IMatrix<float>` Elements of matrix 'A'. The matrix is modified in this call! b : `IVector<float>` Right part 'b'. The vector is modified in this call! x : `IVector<float>` Vector to store the result, i.e. the solution to the problem A*x = b.
`this.SolveDestructive` Full Usage: `this.SolveDestructive` Parameters: A : `IMatrix<float>` - Elements of matrix 'A'. This matrix is modified during solution! b : `IVector<float>` - Right part 'b'. This vector is also modified during solution! vectorCreation : `Func<int, 'VectorT>` - Function to create the resulting vector. Argument is the length of the vector. Returns: `'VectorT` Modifiers: abstract Type parameters: 'VectorT	Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting. A : `IMatrix<float>` Elements of matrix 'A'. This matrix is modified during solution! b : `IVector<float>` Right part 'b'. This vector is also modified during solution! vectorCreation : `Func<int, 'VectorT>` Function to create the resulting vector. Argument is the length of the vector. Returns: `'VectorT`
`this.SolveDestructive` Full Usage: `this.SolveDestructive` Parameters: A : `SparseDoubleMatrix` - Sparse matrix, 'A'. This matrix is modified during solution! b : `float[]` - Right part, 'b', is modified during solution. Returns: `float[]` Vector x with the result.	Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting A : `SparseDoubleMatrix` Sparse matrix, 'A'. This matrix is modified during solution! b : `float[]` Right part, 'b', is modified during solution. Returns: `float[]` Vector x with the result.
`this.SolveDestructive` Full Usage: `this.SolveDestructive` Parameters: A : `SparseDoubleMatrix` - Sparse matrix, 'A'. This matrix is modified during solution! b : `float[]` - Right part, 'b', is modified during solution. x : `float[]` - Vector to store the solution.	Solves system of linear equations Ax = b using Gaussian elimination with partial pivoting A : `SparseDoubleMatrix` Sparse matrix, 'A'. This matrix is modified during solution! b : `float[]` Right part, 'b', is modified during solution. x : `float[]` Vector to store the solution.
`this.SolveDestructiveBanded` Full Usage: `this.SolveDestructiveBanded` Parameters: A : `MatrixWrapperStructForLeftSpineJaggedArray<float>` - Elements of matrix 'A'. The matrix is modified! lowerBandwidth : `int` - Lower band width of the matrix. It is not checked whether the matrix contains non-zero elements outside of the band! upperBandwidth : `int` - Upper band width of the matrix. It is not checked whether the matrix contains non-zero elements outside of the band! b : `float[]` - Right part 'b'. This array is also modified! x : `float[]` - Vector to store the result, i.e. the solution to the problem a x = b.	Solves a system of linear equations Ax = b with a band matrix A, using Gaussian elimination with partial pivoting. Attention! Both matrix A and vector b are destroyed (changed). A : `MatrixWrapperStructForLeftSpineJaggedArray<float>` Elements of matrix 'A'. The matrix is modified! lowerBandwidth : `int` Lower band width of the matrix. It is not checked whether the matrix contains non-zero elements outside of the band! upperBandwidth : `int` Upper band width of the matrix. It is not checked whether the matrix contains non-zero elements outside of the band! b : `float[]` Right part 'b'. This array is also modified! x : `float[]` Vector to store the result, i.e. the solution to the problem a x = b.

Static members

Static member	Description
`GaussianEliminationSolver.SolvePentaDiagonal(A, a, x)` Full Usage: `GaussianEliminationSolver.SolvePentaDiagonal(A, a, x)` Parameters: A : `IMatrix<float>` - Pentadiagonal matrix. a : `float[]` - Right part of the solution (remains unmodified). x : `float[]` - Vector to store the result, i.e. the solution to the problem A x = a.	Solves a system where the matrix a is pentadiagonal, i.e. has two lower and two upper bands. The method is non-destructive, i.e. both matrix m and vector a are not changed. References: [1] Engeln-Müllges, Numerik-Algorithmen, 10th ed., page 177 A : `IMatrix<float>` Pentadiagonal matrix. a : `float[]` Right part of the solution (remains unmodified). x : `float[]` Vector to store the result, i.e. the solution to the problem A x = a.
`GaussianEliminationSolver.SolvePentaDiagonal(A, a, x, tempStorage)` Full Usage: `GaussianEliminationSolver.SolvePentaDiagonal(A, a, x, tempStorage)` Parameters: A : `IMatrix<float>` - Pentadiagonal matrix. a : `float[]` - Right part of the solution (remains unmodified). x : `float[]` - Vector to store the result, i.e. the solution to the problem A x = a. tempStorage : `byref<obj>` - Object that accomodates temporary storage. Can be reused in repeated calls.	Solves a system where the matrix a is five diagonal, i.e. has two lower and two upper bands. The method is non-destructive, i.e. both matrix m and vector a are not changed. References: [1] Engeln-Müllges, Numerik-Algorithmen, 10th ed., page 177 A : `IMatrix<float>` Pentadiagonal matrix. a : `float[]` Right part of the solution (remains unmodified). x : `float[]` Vector to store the result, i.e. the solution to the problem A x = a. tempStorage : `byref<obj>` Object that accomodates temporary storage. Can be reused in repeated calls.
`GaussianEliminationSolver.SolveTriDiagonal(A, a, x)` Full Usage: `GaussianEliminationSolver.SolveTriDiagonal(A, a, x)` Parameters: A : `IMatrix<float>` - Tridiagonal matrix. a : `float[]` - Right part of the solution (remains unmodified). x : `float[]` - Vector to store the result, i.e. the solution to the problem A x = a.	Solves a system where the matrix a is tri diagonal, i.e. has one lower and one upper band. The method is non-destructive, i.e. both matrix m and vector a are not changed. References: [1] Engeln-Müllges, Numerik-Algorithmen, 10th ed., page 165 A : `IMatrix<float>` Tridiagonal matrix. a : `float[]` Right part of the solution (remains unmodified). x : `float[]` Vector to store the result, i.e. the solution to the problem A x = a.
`GaussianEliminationSolver.SolveTriDiagonal(A, a, x, tempStorage)` Full Usage: `GaussianEliminationSolver.SolveTriDiagonal(A, a, x, tempStorage)` Parameters: A : `IMatrix<float>` - Tridiagonal matrix. a : `float[]` - Right part of the solution (remains unmodified). x : `float[]` - Vector to store the result, i.e. the solution to the problem A x = a. tempStorage : `byref<obj>` - Object that accomodates temporary storage. Can be reused in repeated calls.	Solves a system where the matrix a is tri diagonal, i.e. has one lower and one upper band. The method is non-destructive, i.e. both matrix m and vector a are not changed. References: [1] Engeln-Müllges, Numerik-Algorithmen, 10th ed., page 165 A : `IMatrix<float>` Tridiagonal matrix. a : `float[]` Right part of the solution (remains unmodified). x : `float[]` Vector to store the result, i.e. the solution to the problem A x = a. tempStorage : `byref<obj>` Object that accomodates temporary storage. Can be reused in repeated calls.