GenericDecompositionOperations<T> Class

Specifies the methods that must be implemented by a class to support complex LAPACK routines for general matrices.

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.3
C# 
public class GenericDecompositionOperations<T> : DecompositionOperations<T>
Inheritance
Object  →  DecompositionOperations<T, Complex<T>>  →  DecompositionOperations<T>  →  GenericDecompositionOperations<T>

Type Parameters

T

Remarks

The Linear Algebra PACKage (LAPACK) is the de facto standard for more complex linear algebra problems. It complements the Basic Linear Algebra Subroutines (BLAS), which defines standards for low level vector and matrix operations.

Properties

HasSharedDegreeOfParallelism Indicates whether the degree of parallelism is a property that is shared across instances.
(Inherited from DecompositionOperations<TReal, TComplex>)
ImplementedType Gets the base type of the implementation.
(Inherited from DecompositionOperations<TReal, TComplex>)
MaxDegreeOfParallelism Gets or sets the maximum degree of parallelism enabled by the instance.
(Inherited from DecompositionOperations<TReal, TComplex>)
Name Gets the name of the implementation.
(Overrides DecompositionOperations<TReal, TComplex>.Name)
Platform Gets the processor architecture supported by the implementation.
(Overrides DecompositionOperations<TReal, TComplex>.Platform)

Methods

BandCholeskyDecompose(MatrixTriangle, Int32, Int32, Array2D<TComplex>, Int32)

Computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandCholeskyDecompose(MatrixTriangle, Int32, Int32, Span2D<TComplex>, Int32)

Computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandCholeskyDecompose(MatrixTriangle, Int32, Int32, Span<T>, Int32, Int32)

Computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.


(Overrides DecompositionOperations<TReal, TComplex>.BandCholeskyDecompose(MatrixTriangle, Int32, Int32, Span<TComplex>, Int32, Int32))
BandCholeskyDecompose(MatrixTriangle, Int32, Int32, Span<Complex<T>>, Int32, Int32)

Computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.


(Overrides DecompositionOperations<TReal, TComplex>.BandCholeskyDecompose(MatrixTriangle, Int32, Int32, Span<TComplex>, Int32, Int32))
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Array2D<TComplex>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span2D<TReal>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan<Complex<T>>, Int32, T, T, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = UH*U or A = L*LH computed by ZPBTRF.


(Overrides DecompositionOperations<TReal, TComplex>.BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, TReal, TReal, Int32))
BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span<T>, Int32, T, T, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.


(Overrides DecompositionOperations<TReal, TComplex>.BandCholeskyEstimateCondition(MatrixTriangle, Int32, Int32, Span<TReal>, Int32, TReal, TReal, Int32))
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Int32)

Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = UH *U or A = L*LH computed by ZPBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32)

Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = UH *U or A = L*LH computed by ZPBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span2D<TReal>, Span2D<TReal>, Int32)

Solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32, Int32)

Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = UH *U or A = L*LH computed by ZPBTRF.


(Overrides DecompositionOperations<TReal, TComplex>.BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32))
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span<T>, Int32, Span<T>, Int32, Int32)

Solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF.


(Overrides DecompositionOperations<TReal, TComplex>.BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span<TReal>, Int32, Span<TReal>, Int32, Int32))
BandLUDecompose(Int32, Int32, Int32, Int32, Array2D<TComplex>, Array1D<Int32>, Int32)

Computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandLUDecompose(Int32, Int32, Int32, Int32, Span2D<TComplex>, Span<Int32>, Int32)

Computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandLUDecompose(Int32, Int32, Int32, Int32, Span<T>, Int32, Span<Int32>, Int32)

Computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.


(Overrides DecompositionOperations<TReal, TComplex>.BandLUDecompose(Int32, Int32, Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
BandLUDecompose(Int32, Int32, Int32, Int32, Span<Complex<T>>, Int32, Span<Int32>, Int32)

Computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.


(Overrides DecompositionOperations<TReal, TComplex>.BandLUDecompose(Int32, Int32, Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, Array2D<TComplex>, Array1D<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, ReadOnlySpan2D<TComplex>, Span<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, ReadOnlySpan<T>, Int32, Span<Int32>, T, T, Int32)

Estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGBTRF.


(Overrides DecompositionOperations<TReal, TComplex>.BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<Int32>, TReal, TReal, Int32))
BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, ReadOnlySpan<Complex<T>>, Int32, Span<Int32>, T, T, Int32)

Estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGBTRF.


(Overrides DecompositionOperations<TReal, TComplex>.BandLUEstimateCondition(MatrixNorm, Int32, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<Int32>, TReal, TReal, Int32))
BandLUSolve(TransposeOperation, Int32, Int32, Int32, Int32, Array2D<TComplex>, Array1D<Int32>, Array2D<TComplex>, Int32)

Solves a system of linear equations A * X = B, AT * X = B, or AH * X = B with a general band matrix A using the LU factorization computed by ZGBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandLUSolve(TransposeOperation, Int32, Int32, Int32, Int32, Span2D<TComplex>, Span<Int32>, Span2D<TComplex>, Int32)

Solves a system of linear equations A * X = B, AT * X = B, or AH * X = B with a general band matrix A using the LU factorization computed by ZGBTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandLUSolve(TransposeOperation, Int32, Int32, Int32, Int32, Span<T>, Int32, Span<Int32>, Span<T>, Int32, Int32)

Solves a system of linear equations A * X = B, AT * X = B, or AH * X = B with a general band matrix A using the LU factorization computed by ZGBTRF.


(Overrides DecompositionOperations<TReal, TComplex>.BandLUSolve(TransposeOperation, Int32, Int32, Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Span<TComplex>, Int32, Int32))
BandLUSolve(TransposeOperation, Int32, Int32, Int32, Int32, Span<Complex<T>>, Int32, Span<Int32>, Span<Complex<T>>, Int32, Int32)

Solves a system of linear equations A * X = B, AT * X = B, or AH * X = B with a general band matrix A using the LU factorization computed by ZGBTRF.


(Overrides DecompositionOperations<TReal, TComplex>.BandLUSolve(TransposeOperation, Int32, Int32, Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Span<TComplex>, Int32, Int32))
BandTriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Int32, Array2D<TReal>, Array2D<TReal>, Int32)

Solves a triangular system of the form A * X = B or AT * X = B, where A is a triangular band matrix of order N, and B is an N-by NRHS matrix.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandTriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Int32, ReadOnlySpan2D<TReal>, Span2D<TReal>, Int32)

Solves a triangular system of the form A * X = B or AT * X = B, where A is a triangular band matrix of order N, and B is an N-by NRHS matrix.


(Inherited from DecompositionOperations<TReal, TComplex>)
BandTriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32, Int32)

Solves a triangular system of the form A * X = B or AT * X = B, where A is a triangular band matrix of order N, and B is an N-by NRHS matrix.


(Overrides DecompositionOperations<TReal, TComplex>.BandTriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Int32, ReadOnlySpan<TReal>, Int32, Span<TReal>, Int32, Int32))
CholeskyDecompose(MatrixTriangle, Int32, Array2D<TComplex>, Int32) Factors a symmetric positive definite matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
CholeskyDecompose(MatrixTriangle, Int32, Span2D<TComplex>, Int32) Factors a symmetric positive definite matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
CholeskyDecompose(MatrixTriangle, Int32, Span<T>, Int32, Int32) Factors a symmetric positive definite matrix.
(Overrides DecompositionOperations<TReal, TComplex>.CholeskyDecompose(MatrixTriangle, Int32, Span<TComplex>, Int32, Int32))
CholeskyDecompose(MatrixTriangle, Int32, Span<Complex<T>>, Int32, Int32) Factors a symmetric positive definite matrix.
(Overrides DecompositionOperations<TReal, TComplex>.CholeskyDecompose(MatrixTriangle, Int32, Span<TComplex>, Int32, Int32))
CholeskyEstimateCondition(MatrixTriangle, Int32, Array2D<TComplex>, TReal, TReal, Int32) Estimates the reciprocal of the condition number of a factored hermitian matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
CholeskyEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan2D<TComplex>, TReal, TReal, Int32) Estimates the reciprocal of the condition number of a factored hermitian matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
CholeskyEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<T>, Int32, T, T, Int32) Estimates the reciprocal of the condition number of a factored hermitian matrix.
(Overrides DecompositionOperations<TReal, TComplex>.CholeskyEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<TComplex>, Int32, TReal, TReal, Int32))
CholeskyEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<Complex<T>>, Int32, T, T, Int32) Estimates the reciprocal of the condition number of a factored hermitian matrix.
(Overrides DecompositionOperations<TReal, TComplex>.CholeskyEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<TComplex>, Int32, TReal, TReal, Int32))
CholeskyInvert(MatrixTriangle, Int32, Array2D<TComplex>, Int32) Computes the inverse of a factored hermitian matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
CholeskyInvert(MatrixTriangle, Int32, Span2D<TComplex>, Int32) Computes the inverse of a factored hermitian matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
CholeskyInvert(MatrixTriangle, Int32, Span<T>, Int32, Int32) Computes the inverse of a factored hermitian matrix.
(Overrides DecompositionOperations<TReal, TComplex>.CholeskyInvert(MatrixTriangle, Int32, Span<TComplex>, Int32, Int32))
CholeskyInvert(MatrixTriangle, Int32, Span<Complex<T>>, Int32, Int32) Computes the inverse of a factored hermitian matrix.
(Overrides DecompositionOperations<TReal, TComplex>.CholeskyInvert(MatrixTriangle, Int32, Span<TComplex>, Int32, Int32))
CholeskySolve(MatrixTriangle, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Int32) Solves a hermitian system of equations.
(Inherited from DecompositionOperations<TReal, TComplex>)
CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32) Solves a hermitian system of equations.
(Inherited from DecompositionOperations<TReal, TComplex>)
CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32, Int32) Solves a hermitian system of equations.
(Overrides DecompositionOperations<TReal, TComplex>.CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32))
CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32, Int32) Solves a hermitian system of equations.
(Overrides DecompositionOperations<TReal, TComplex>.CholeskySolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32))
EigenvalueDecompose(Char, Char, Int32, Array2D<TComplex>, Array1D<TComplex>, Array2D<TComplex>, Array2D<TComplex>, Int32)

Computes for an N-by-N complex non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.


(Inherited from DecompositionOperations<TReal, TComplex>)
EigenvalueDecompose(Char, Char, Int32, Span2D<TComplex>, Span<TComplex>, Span2D<TComplex>, Span2D<TComplex>, Int32)

Computes for an N-by-N complex non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.


(Inherited from DecompositionOperations<TReal, TComplex>)
EigenvalueDecompose(Char, Char, Int32, Array2D<TReal>, Array1D<TReal>, Array1D<TReal>, Array2D<TReal>, Array2D<TReal>, Int32)

Computes for an N-by-N real non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.


(Inherited from DecompositionOperations<TReal, TComplex>)
EigenvalueDecompose(Char, Char, Int32, Span2D<TReal>, Span<TReal>, Span<TReal>, Span2D<TReal>, Span2D<TReal>, Int32)

Computes for an N-by-N real non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.


(Inherited from DecompositionOperations<TReal, TComplex>)
EigenvalueDecompose(Char, Char, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Int32)

Computes for an N-by-N complex non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.


(Overrides DecompositionOperations<TReal, TComplex>.EigenvalueDecompose(Char, Char, Int32, Span<TComplex>, Int32, Span<TComplex>, Span<TComplex>, Int32, Span<TComplex>, Int32, Int32))
EigenvalueDecompose(Char, Char, Int32, Span<T>, Int32, Span<T>, Span<T>, Span<T>, Int32, Span<T>, Int32, Int32)

Computes for an N-by-N real non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.


(Overrides DecompositionOperations<TReal, TComplex>.EigenvalueDecompose(Char, Char, Int32, Span<TReal>, Int32, Span<TReal>, Span<TReal>, Span<TReal>, Int32, Span<TReal>, Int32, Int32))
EqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
FinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
GeneralizedEigenvalueDecompose(Char, Char, Int32, Array2D<TComplex>, Array2D<TComplex>, Array1D<TComplex>, Array1D<TComplex>, Array2D<TComplex>, Array2D<TComplex>, Int32)

Computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.


(Inherited from DecompositionOperations<TReal, TComplex>)
GeneralizedEigenvalueDecompose(Char, Char, Int32, Span2D<TComplex>, Span2D<TComplex>, Span<TComplex>, Span<TComplex>, Span2D<TComplex>, Span2D<TComplex>, Int32)

Computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.


(Inherited from DecompositionOperations<TReal, TComplex>)
GeneralizedEigenvalueDecompose(Char, Char, Int32, Array2D<TReal>, Array2D<TReal>, Array1D<TReal>, Array1D<TReal>, Array1D<TReal>, Array2D<TReal>, Array2D<TReal>, Int32)

Computes for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.


(Inherited from DecompositionOperations<TReal, TComplex>)
GeneralizedEigenvalueDecompose(Char, Char, Int32, Span2D<TReal>, Span2D<TReal>, Span<TReal>, Span<TReal>, Span<TReal>, Span2D<TReal>, Span2D<TReal>, Int32)

Computes for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.


(Inherited from DecompositionOperations<TReal, TComplex>)
GeneralizedEigenvalueDecompose(Char, Char, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Span<Complex<T>>, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Int32)

Computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.


(Overrides DecompositionOperations<TReal, TComplex>.GeneralizedEigenvalueDecompose(Char, Char, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32, Span<TComplex>, Span<TComplex>, Span<TComplex>, Int32, Span<TComplex>, Int32, Int32))
GeneralizedEigenvalueDecompose(Char, Char, Int32, Span<T>, Int32, Span<T>, Int32, Span<T>, Span<T>, Span<T>, Span<T>, Int32, Span<T>, Int32, Int32)

Computes for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.


(Overrides DecompositionOperations<TReal, TComplex>.GeneralizedEigenvalueDecompose(Char, Char, Int32, Span<TReal>, Int32, Span<TReal>, Int32, Span<TReal>, Span<TReal>, Span<TReal>, Span<TReal>, Int32, Span<TReal>, Int32, Int32))
GeneralizedSchurDecompose(Char, Char, Char, Func<Complex<T>, Complex<T>, Boolean>, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Int32, Span<Complex<T>>, Span<Complex<T>>, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Int32)

C# 
Computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the generalized complex Schur
form (S, T), and optionally left and/or right Schur vectors (VSL
and VSR).


(Overrides DecompositionOperations<TReal, TComplex>.GeneralizedSchurDecompose(Char, Char, Char, Func<TComplex, TComplex, Boolean>, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32, Int32, Span<TComplex>, Span<TComplex>, Span<TComplex>, Int32, Span<TComplex>, Int32, Int32))
GeneralizedSchurDecompose(Char, Char, Char, Func<T, T, T, Boolean>, Int32, Span<T>, Int32, Span<T>, Int32, Int32, Span<T>, Span<T>, Span<T>, Span<T>, Int32, Span<T>, Int32, Int32)

C# 
Computes for a pair of N-by-N real nonsymmetric matrices (A,B),
the generalized eigenvalues, the generalized real Schur form (S,T),
optionally, the left and/or right matrices of Schur vectors (VSL and
VSR).


(Overrides DecompositionOperations<TReal, TComplex>.GeneralizedSchurDecompose(Char, Char, Char, Func<TReal, TReal, TReal, Boolean>, Int32, Span<TReal>, Int32, Span<TReal>, Int32, Int32, Span<TReal>, Span<TReal>, Span<TReal>, Span<TReal>, Int32, Span<TReal>, Int32, Int32))
GeneralizedSingularValueDecompose(Char, Char, Char, Int32, Int32, Int32, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Array1D<TReal>, Array1D<TReal>, Array2D<TComplex>, Array2D<TComplex>, Array2D<TComplex>, Array1D<Int32>, Int32)

Computes the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B: U**H*A*Q = D1*( 0 R ), V**H*B*Q = D2*( 0 R ) where U, V and Q are unitary matrices.


(Inherited from DecompositionOperations<TReal, TComplex>)
GeneralizedSingularValueDecompose(Char, Char, Char, Int32, Int32, Int32, Int32, Int32, Span2D<TComplex>, Span2D<TComplex>, Span<TReal>, Span<TReal>, Span2D<TComplex>, Span2D<TComplex>, Span2D<TComplex>, Span<Int32>, Int32)

Computes the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B: U**H*A*Q = D1*( 0 R ), V**H*B*Q = D2*( 0 R ) where U, V and Q are unitary matrices.


(Inherited from DecompositionOperations<TReal, TComplex>)
GeneralizedSingularValueDecompose(Char, Char, Char, Int32, Int32, Int32, Int32, Int32, Span<T>, Int32, Span<T>, Int32, Span<T>, Span<T>, Span<T>, Int32, Span<T>, Int32, Span<T>, Int32, Span<Int32>, Int32)

Computes the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B: U**H*A*Q = D1*( 0 R ), V**H*B*Q = D2*( 0 R ) where U, V and Q are unitary matrices.


(Overrides DecompositionOperations<TReal, TComplex>.GeneralizedSingularValueDecompose(Char, Char, Char, Int32, Int32, Int32, Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32, Span<TReal>, Span<TReal>, Span<TComplex>, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
GeneralizedSingularValueDecompose(Char, Char, Char, Int32, Int32, Int32, Int32, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Span<T>, Span<T>, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Span<Int32>, Int32)

Computes the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B: U**H*A*Q = D1*( 0 R ), V**H*B*Q = D2*( 0 R ) where U, V and Q are unitary matrices.


(Overrides DecompositionOperations<TReal, TComplex>.GeneralizedSingularValueDecompose(Char, Char, Char, Int32, Int32, Int32, Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32, Span<TReal>, Span<TReal>, Span<TComplex>, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
GetHashCodeServes as the default hash function.
(Inherited from Object)
GetTypeGets the Type of the current instance.
(Inherited from Object)
HermitianDecompose(MatrixTriangle, Int32, Array2D<TComplex>, Array1D<Int32>, Int32)

Computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianDecompose(MatrixTriangle, Int32, Span2D<TComplex>, Span<Int32>, Int32)

Computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianDecompose(MatrixTriangle, Int32, Span<Complex<T>>, Int32, Span<Int32>, Int32)

Computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.


(Overrides DecompositionOperations<TReal, TComplex>.HermitianDecompose(MatrixTriangle, Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
HermitianEigenvalueDecompose(Char, MatrixTriangle, Int32, Array2D<TComplex>, Array1D<TReal>, Int32)

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianEigenvalueDecompose(Char, MatrixTriangle, Int32, Span2D<TComplex>, Span<TReal>, Int32)

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianEigenvalueDecompose(Char, MatrixTriangle, Int32, Span<Complex<T>>, Int32, Span<T>, Int32)

Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.


(Overrides DecompositionOperations<TReal, TComplex>.HermitianEigenvalueDecompose(Char, MatrixTriangle, Int32, Span<TComplex>, Int32, Span<TReal>, Int32))
HermitianEstimateCondition(MatrixTriangle, Int32, Array2D<TComplex>, Array1D<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan2D<TComplex>, Span<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<Complex<T>>, Int32, ReadOnlySpan<Int32>, T, T, Int32)

Estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Overrides DecompositionOperations<TReal, TComplex>.HermitianEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<TComplex>, Int32, ReadOnlySpan<Int32>, TReal, TReal, Int32))
HermitianGeneralizedEigenvalueDecompose(Int32, Char, MatrixTriangle, Int32, Array2D<TComplex>, Array2D<TComplex>, Array1D<TReal>, Int32)

Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianGeneralizedEigenvalueDecompose(Int32, Char, MatrixTriangle, Int32, Span2D<TComplex>, Span2D<TComplex>, Span<TReal>, Int32)

Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianGeneralizedEigenvalueDecompose(Int32, Char, MatrixTriangle, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Span<T>, Int32)

Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.


(Overrides DecompositionOperations<TReal, TComplex>.HermitianGeneralizedEigenvalueDecompose(Int32, Char, MatrixTriangle, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32, Span<TReal>, Int32))
HermitianInvert(MatrixTriangle, Int32, Array2D<TComplex>, Array1D<Int32>, Int32)

Computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianInvert(MatrixTriangle, Int32, Span2D<TComplex>, Span<Int32>, Int32)

Computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianInvert(MatrixTriangle, Int32, Span<Complex<T>>, Int32, ReadOnlySpan<Int32>, Int32)

Computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Overrides DecompositionOperations<TReal, TComplex>.HermitianInvert(MatrixTriangle, Int32, Span<TComplex>, Int32, ReadOnlySpan<Int32>, Int32))
HermitianSolve(MatrixTriangle, Int32, Int32, Array2D<TComplex>, Array1D<Int32>, Array2D<TComplex>, Int32)

Solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianSolve(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TComplex>, Span<Int32>, Span2D<TComplex>, Int32)

Solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
HermitianSolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<Complex<T>>, Int32, ReadOnlySpan<Int32>, Span<Complex<T>>, Int32, Int32)

Solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*UH or A = L*D*LH computed by ZHETRF.


(Overrides DecompositionOperations<TReal, TComplex>.HermitianSolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<TComplex>, Int32, ReadOnlySpan<Int32>, Span<TComplex>, Int32, Int32))
LQDecompose(Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Int32)

Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.


(Inherited from DecompositionOperations<TReal, TComplex>)
LQDecompose(Int32, Int32, Span2D<TComplex>, Span<TComplex>, Int32)

Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.


(Inherited from DecompositionOperations<TReal, TComplex>)
LQDecompose(Int32, Int32, Span<T>, Int32, Span<T>, Int32)

Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.


(Overrides DecompositionOperations<TReal, TComplex>.LQDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32))
LQDecompose(Int32, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.


(Overrides DecompositionOperations<TReal, TComplex>.LQDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32))
LQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TReal>, Array1D<TReal>, Array2D<TReal>, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) .


(Inherited from DecompositionOperations<TReal, TComplex>)
LQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TReal>, ReadOnlySpan<TReal>, Span2D<TReal>, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) .


(Inherited from DecompositionOperations<TReal, TComplex>)
LQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<T>, Int32, ReadOnlySpan<T>, Span<T>, Int32, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) .


(Overrides DecompositionOperations<TReal, TComplex>.LQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TReal>, Int32, ReadOnlySpan<TReal>, Span<TReal>, Int32, Int32))
LQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Array2D<TComplex>, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)**H .


(Inherited from DecompositionOperations<TReal, TComplex>)
LQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TComplex>, ReadOnlySpan<TComplex>, Span2D<TComplex>, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)**H .


(Inherited from DecompositionOperations<TReal, TComplex>)
LQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Span<Complex<T>>, Int32, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k)**H .


(Overrides DecompositionOperations<TReal, TComplex>.LQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TComplex>, Int32, ReadOnlySpan<TComplex>, Span<TComplex>, Int32, Int32))
LUDecompose(Int32, Int32, Array2D<TComplex>, Array1D<Int32>, Int32)

ZGETRF computes an LU decomposition of a general M-by-N matrix A using partial pivoting with row interchanges.

The decomposition has the form

A = P * L * U.

where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.


(Inherited from DecompositionOperations<TReal, TComplex>)
LUDecompose(Int32, Int32, Span2D<TComplex>, Span<Int32>, Int32)

ZGETRF computes an LU decomposition of a general M-by-N matrix A using partial pivoting with row interchanges.

The decomposition has the form

A = P * L * U.

where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.


(Inherited from DecompositionOperations<TReal, TComplex>)
LUDecompose(Int32, Int32, Span<T>, Int32, Span<Int32>, Int32)

ZGETRF computes an LU decomposition of a general M-by-N matrix A using partial pivoting with row interchanges.

The decomposition has the form

A = P * L * U.

where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.


(Overrides DecompositionOperations<TReal, TComplex>.LUDecompose(Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
LUDecompose(Int32, Int32, Span<Complex<T>>, Int32, Span<Int32>, Int32)

ZGETRF computes an LU decomposition of a general M-by-N matrix A using partial pivoting with row interchanges.

The decomposition has the form

A = P * L * U.

where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the right-looking Level 3 BLAS version of the algorithm.


(Overrides DecompositionOperations<TReal, TComplex>.LUDecompose(Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
LUEstimateCondition(MatrixNorm, Int32, Array2D<TComplex>, TReal, TReal, Int32) ZGECON estimates the reciprocal of the condition number of a general real matrix A, inthis. either the 1-norm or the infinity-norm, using the LU decomposition computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Arguments ========= NORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). ANORM (input) DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) DOUBLE PRECISION array, dimension (4*N) IWORK (workspace) INTEGER array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
(Inherited from DecompositionOperations<TReal, TComplex>)
LUEstimateCondition(MatrixNorm, Int32, Span2D<TComplex>, TReal, TReal, Int32) ZGECON estimates the reciprocal of the condition number of a general real matrix A, inthis. either the 1-norm or the infinity-norm, using the LU decomposition computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Arguments ========= NORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). ANORM (input) DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) DOUBLE PRECISION array, dimension (4*N) IWORK (workspace) INTEGER array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
(Inherited from DecompositionOperations<TReal, TComplex>)
LUEstimateCondition(MatrixNorm, Int32, Span<T>, Int32, T, T, Int32) ZGECON estimates the reciprocal of the condition number of a general real matrix A, inthis. either the 1-norm or the infinity-norm, using the LU decomposition computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Arguments ========= NORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). ANORM (input) DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) DOUBLE PRECISION array, dimension (4*N) IWORK (workspace) INTEGER array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
(Overrides DecompositionOperations<TReal, TComplex>.LUEstimateCondition(MatrixNorm, Int32, Span<TComplex>, Int32, TReal, TReal, Int32))
LUEstimateCondition(MatrixNorm, Int32, Span<Complex<T>>, Int32, T, T, Int32) ZGECON estimates the reciprocal of the condition number of a general real matrix A, inthis. either the 1-norm or the infinity-norm, using the LU decomposition computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Arguments ========= NORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). ANORM (input) DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND (output) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK (workspace) DOUBLE PRECISION array, dimension (4*N) IWORK (workspace) INTEGER array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
(Overrides DecompositionOperations<TReal, TComplex>.LUEstimateCondition(MatrixNorm, Int32, Span<TComplex>, Int32, TReal, TReal, Int32))
LUInvert(Int32, Array2D<TComplex>, Array1D<Int32>, Int32) ZGETRI computes the inverse of a matrix using the LU decomposition computed by ZGETRF. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A). Arguments ========= N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the factors L and U from the decomposition A = P*L*U as computed by ZGETRF. On exit, if INFO = 0, the inverse of the original matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO =0, then WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= Max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero; the matrix is singular and its inverse could not be computed.
(Inherited from DecompositionOperations<TReal, TComplex>)
LUInvert(Int32, Span2D<TComplex>, Span<Int32>, Int32) ZGETRI computes the inverse of a matrix using the LU decomposition computed by ZGETRF. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A). Arguments ========= N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the factors L and U from the decomposition A = P*L*U as computed by ZGETRF. On exit, if INFO = 0, the inverse of the original matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO =0, then WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= Max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero; the matrix is singular and its inverse could not be computed.
(Inherited from DecompositionOperations<TReal, TComplex>)
LUInvert(Int32, Span<T>, Int32, Span<Int32>, Int32) ZGETRI computes the inverse of a matrix using the LU decomposition computed by ZGETRF. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A). Arguments ========= N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the factors L and U from the decomposition A = P*L*U as computed by ZGETRF. On exit, if INFO = 0, the inverse of the original matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO =0, then WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= Max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero; the matrix is singular and its inverse could not be computed.
(Overrides DecompositionOperations<TReal, TComplex>.LUInvert(Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
LUInvert(Int32, Span<Complex<T>>, Int32, Span<Int32>, Int32) ZGETRI computes the inverse of a matrix using the LU decomposition computed by ZGETRF. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A). Arguments ========= N (input) INTEGER The elementOrder of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the factors L and U from the decomposition A = P*L*U as computed by ZGETRF. On exit, if INFO = 0, the inverse of the original matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO =0, then WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= Max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, U(i,i) is exactly zero; the matrix is singular and its inverse could not be computed.
(Overrides DecompositionOperations<TReal, TComplex>.LUInvert(Int32, Span<TComplex>, Int32, Span<Int32>, Int32))
LUSolve(TransposeOperation, Int32, Int32, Array2D<TComplex>, Array1D<Int32>, Array2D<TComplex>, Int32) ZGETRS solves a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU decomposition computed by ZGETRF. Arguments ========= TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = TransposeOperation.Transpose: A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose) N (input) INTEGER The elementOrder of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= Max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value =====================================================================
(Inherited from DecompositionOperations<TReal, TComplex>)
LUSolve(TransposeOperation, Int32, Int32, Span2D<TComplex>, Span<Int32>, Span2D<TComplex>, Int32) ZGETRS solves a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU decomposition computed by ZGETRF. Arguments ========= TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = TransposeOperation.Transpose: A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose) N (input) INTEGER The elementOrder of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= Max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value =====================================================================
(Inherited from DecompositionOperations<TReal, TComplex>)
LUSolve(TransposeOperation, Int32, Int32, Span<T>, Int32, Span<Int32>, Span<T>, Int32, Int32) ZGETRS solves a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU decomposition computed by ZGETRF. Arguments ========= TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = TransposeOperation.Transpose: A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose) N (input) INTEGER The elementOrder of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= Max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value =====================================================================
(Overrides DecompositionOperations<TReal, TComplex>.LUSolve(TransposeOperation, Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Span<TComplex>, Int32, Int32))
LUSolve(TransposeOperation, Int32, Int32, Span<Complex<T>>, Int32, Span<Int32>, Span<Complex<T>>, Int32, Int32) ZGETRS solves a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU decomposition computed by ZGETRF. Arguments ========= TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = TransposeOperation.Transpose: A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose) N (input) INTEGER The elementOrder of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= Max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value =====================================================================
(Overrides DecompositionOperations<TReal, TComplex>.LUSolve(TransposeOperation, Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Span<TComplex>, Int32, Int32))
MemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
QLDecompose(Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Int32)

Computes a QL factorization of a complex M-by-N matrix A: A = Q * L.


(Inherited from DecompositionOperations<TReal, TComplex>)
QLDecompose(Int32, Int32, Span2D<TComplex>, Span<TComplex>, Int32)

Computes a QL factorization of a complex M-by-N matrix A: A = Q * L.


(Inherited from DecompositionOperations<TReal, TComplex>)
QLDecompose(Int32, Int32, Span<T>, Int32, Span<T>, Int32)

Computes a QL factorization of a complex M-by-N matrix A: A = Q * L.


(Overrides DecompositionOperations<TReal, TComplex>.QLDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32))
QLDecompose(Int32, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Computes a QL factorization of a complex M-by-N matrix A: A = Q * L.


(Overrides DecompositionOperations<TReal, TComplex>.QLDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32))
QLOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TReal>, Array1D<TReal>, Array2D<TReal>, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) .


(Inherited from DecompositionOperations<TReal, TComplex>)
QLOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TReal>, ReadOnlySpan<TReal>, Span2D<TReal>, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) .


(Inherited from DecompositionOperations<TReal, TComplex>)
QLOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<T>, Int32, ReadOnlySpan<T>, Span<T>, Int32, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(k) .


(Overrides DecompositionOperations<TReal, TComplex>.QLOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TReal>, Int32, ReadOnlySpan<TReal>, Span<TReal>, Int32, Int32))
QLUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Array2D<TComplex>, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) .


(Inherited from DecompositionOperations<TReal, TComplex>)
QLUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TComplex>, ReadOnlySpan<TComplex>, Span2D<TComplex>, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) .


(Inherited from DecompositionOperations<TReal, TComplex>)
QLUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Span<Complex<T>>, Int32, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) .


(Overrides DecompositionOperations<TReal, TComplex>.QLUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TComplex>, Int32, ReadOnlySpan<TComplex>, Span<TComplex>, Int32, Int32))
QRDecompose(Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Int32) ZGEQRF computes a QR decomposition of a real M-by-N matrix A: A = Q * R. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Zetails). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Zetails). WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Zetails =============== The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit inthis. A(i+1:m,i), and tau inthis. TAU(i).
(Inherited from DecompositionOperations<TReal, TComplex>)
QRDecompose(Int32, Int32, Span2D<TComplex>, Span<TComplex>, Int32) ZGEQRF computes a QR decomposition of a real M-by-N matrix A: A = Q * R. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Zetails). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Zetails). WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Zetails =============== The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit inthis. A(i+1:m,i), and tau inthis. TAU(i).
(Inherited from DecompositionOperations<TReal, TComplex>)
QRDecompose(Int32, Int32, Array2D<TReal>, Array1D<Int32>, Array1D<TReal>, Int32)

Computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.


(Inherited from DecompositionOperations<TReal, TComplex>)
QRDecompose(Int32, Int32, Span2D<TReal>, Span<Int32>, Span<TReal>, Int32)

Computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.


(Inherited from DecompositionOperations<TReal, TComplex>)
QRDecompose(Int32, Int32, Span<T>, Int32, Span<T>, Int32) ZGEQRF computes a QR decomposition of a real M-by-N matrix A: A = Q * R. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Zetails). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Zetails). WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Zetails =============== The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit inthis. A(i+1:m,i), and tau inthis. TAU(i).
(Overrides DecompositionOperations<TReal, TComplex>.QRDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32))
QRDecompose(Int32, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32) ZGEQRF computes a QR decomposition of a real M-by-N matrix A: A = Q * R. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Zetails). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Zetails). WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Zetails =============== The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v' where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit inthis. A(i+1:m,i), and tau inthis. TAU(i).
(Overrides DecompositionOperations<TReal, TComplex>.QRDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32))
QRDecompose(Int32, Int32, Span<T>, Int32, Span<Int32>, Span<T>, Int32)

Computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.


(Overrides DecompositionOperations<TReal, TComplex>.QRDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Span<TReal>, Int32))
QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TReal>, Array1D<TReal>, Array2D<TReal>, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': QT * C C * QT where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Inherited from DecompositionOperations<TReal, TComplex>)
QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TReal>, ReadOnlySpan<TReal>, Span2D<TReal>, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': QT * C C * QT where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Inherited from DecompositionOperations<TReal, TComplex>)
QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<T>, Int32, ReadOnlySpan<T>, Span<T>, Int32, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': QT * C C * QT where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Overrides DecompositionOperations<TReal, TComplex>.QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TReal>, Int32, ReadOnlySpan<TReal>, Span<TReal>, Int32, Int32))
QRUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Array2D<TComplex>, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': QH * C C * QH where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Inherited from DecompositionOperations<TReal, TComplex>)
QRUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TComplex>, ReadOnlySpan<TComplex>, Span2D<TComplex>, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': QH * C C * QH where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Inherited from DecompositionOperations<TReal, TComplex>)
QRUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Span<Complex<T>>, Int32, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': QH * C C * QH where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Overrides DecompositionOperations<TReal, TComplex>.QRUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TComplex>, Int32, ReadOnlySpan<TComplex>, Span<TComplex>, Int32, Int32))
RQDecompose(Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Int32)

Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.


(Inherited from DecompositionOperations<TReal, TComplex>)
RQDecompose(Int32, Int32, Span2D<TComplex>, Span<TComplex>, Int32)

Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.


(Inherited from DecompositionOperations<TReal, TComplex>)
RQDecompose(Int32, Int32, Span<T>, Int32, Span<T>, Int32)

Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.


(Overrides DecompositionOperations<TReal, TComplex>.RQDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32))
RQDecompose(Int32, Int32, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32)

Computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.


(Overrides DecompositionOperations<TReal, TComplex>.RQDecompose(Int32, Int32, Span<TComplex>, Int32, Span<TComplex>, Int32))
RQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TReal>, Array1D<TReal>, Array2D<TReal>, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Inherited from DecompositionOperations<TReal, TComplex>)
RQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TReal>, ReadOnlySpan<TReal>, Span2D<TReal>, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Inherited from DecompositionOperations<TReal, TComplex>)
RQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<T>, Int32, ReadOnlySpan<T>, Span<T>, Int32, Int32)

Overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .


(Overrides DecompositionOperations<TReal, TComplex>.RQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TReal>, Int32, ReadOnlySpan<TReal>, Span<TReal>, Int32, Int32))
RQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TComplex>, Array1D<TComplex>, Array2D<TComplex>, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1)**H H(2)**H .


(Inherited from DecompositionOperations<TReal, TComplex>)
RQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TComplex>, ReadOnlySpan<TComplex>, Span2D<TComplex>, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1)**H H(2)**H .


(Inherited from DecompositionOperations<TReal, TComplex>)
RQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Span<Complex<T>>, Int32, Int32)

Overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1)**H H(2)**H .


(Overrides DecompositionOperations<TReal, TComplex>.RQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TComplex>, Int32, ReadOnlySpan<TComplex>, Span<TComplex>, Int32, Int32))
SchurDecompose(Char, Char, Func<Complex<T>, Boolean>, Int32, Span<Complex<T>>, Int32, Int32, Span<Complex<T>>, Span<Complex<T>>, Int32, Int32)

C# 
Computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, the Schur form T, and, optionally, the matrix of Schur
vectors Z.


(Overrides DecompositionOperations<TReal, TComplex>.SchurDecompose(Char, Char, Func<TComplex, Boolean>, Int32, Span<TComplex>, Int32, Int32, Span<TComplex>, Span<TComplex>, Int32, Int32))
SchurDecompose(Char, Char, Func<T, T, Boolean>, Int32, Span<T>, Int32, Int32, Span<T>, Span<T>, Span<T>, Int32, Int32)

C# 
Computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z.


(Overrides DecompositionOperations<TReal, TComplex>.SchurDecompose(Char, Char, Func<TReal, TReal, Boolean>, Int32, Span<TReal>, Int32, Int32, Span<TReal>, Span<TReal>, Span<TReal>, Int32, Int32))
SingularValueDecompose(Char, Int32, Int32, Array2D<TComplex>, Array1D<TReal>, Array2D<TComplex>, Array2D<TComplex>, Int32)

Computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method.


(Inherited from DecompositionOperations<TReal, TComplex>)
SingularValueDecompose(Char, Int32, Int32, Span2D<TComplex>, Span<TReal>, Span2D<TComplex>, Span2D<TComplex>, Int32)

Computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method.


(Inherited from DecompositionOperations<TReal, TComplex>)
SingularValueDecompose(Char, Int32, Int32, Span<T>, Int32, Span<T>, Span<T>, Int32, Span<T>, Int32, Int32)

Computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method.


(Overrides DecompositionOperations<TReal, TComplex>.SingularValueDecompose(Char, Int32, Int32, Span<TComplex>, Int32, Span<TReal>, Span<TComplex>, Int32, Span<TComplex>, Int32, Int32))
SingularValueDecompose(Char, Int32, Int32, Span<Complex<T>>, Int32, Span<T>, Span<Complex<T>>, Int32, Span<Complex<T>>, Int32, Int32)

Computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method.


(Overrides DecompositionOperations<TReal, TComplex>.SingularValueDecompose(Char, Int32, Int32, Span<TComplex>, Int32, Span<TReal>, Span<TComplex>, Int32, Span<TComplex>, Int32, Int32))
SymmetricDecompose(MatrixTriangle, Int32, Array2D<TReal>, Array1D<Int32>, Int32)

Computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricDecompose(MatrixTriangle, Int32, Span2D<TReal>, Span<Int32>, Int32)

Computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricDecompose(MatrixTriangle, Int32, Span<T>, Int32, Span<Int32>, Int32)

Computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.


(Overrides DecompositionOperations<TReal, TComplex>.SymmetricDecompose(MatrixTriangle, Int32, Span<TReal>, Int32, Span<Int32>, Int32))
SymmetricEigenvalueDecompose(Char, MatrixTriangle, Int32, Array2D<TReal>, Array1D<TReal>, Int32)

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricEigenvalueDecompose(Char, MatrixTriangle, Int32, Span2D<TReal>, Span<TReal>, Int32)

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricEigenvalueDecompose(Char, MatrixTriangle, Int32, Span<T>, Int32, Span<T>, Int32)

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.


(Overrides DecompositionOperations<TReal, TComplex>.SymmetricEigenvalueDecompose(Char, MatrixTriangle, Int32, Span<TReal>, Int32, Span<TReal>, Int32))
SymmetricEstimateCondition(MatrixTriangle, Int32, Array2D<TReal>, Array1D<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan2D<TReal>, ReadOnlySpan<Int32>, TReal, TReal, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<T>, Int32, ReadOnlySpan<Int32>, T, T, Int32)

Estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Overrides DecompositionOperations<TReal, TComplex>.SymmetricEstimateCondition(MatrixTriangle, Int32, ReadOnlySpan<TReal>, Int32, ReadOnlySpan<Int32>, TReal, TReal, Int32))
SymmetricGeneralizedEigenvalueDecompose(Int32, Char, MatrixTriangle, Int32, Array2D<TReal>, Array2D<TReal>, Array1D<TReal>, Int32)

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricGeneralizedEigenvalueDecompose(Int32, Char, MatrixTriangle, Int32, Span2D<TReal>, Span2D<TReal>, Span<TReal>, Int32)

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricGeneralizedEigenvalueDecompose(Int32, Char, MatrixTriangle, Int32, Span<T>, Int32, Span<T>, Int32, Span<T>, Int32)

Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.


(Overrides DecompositionOperations<TReal, TComplex>.SymmetricGeneralizedEigenvalueDecompose(Int32, Char, MatrixTriangle, Int32, Span<TReal>, Int32, Span<TReal>, Int32, Span<TReal>, Int32))
SymmetricInvert(MatrixTriangle, Int32, Array2D<TReal>, Array1D<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricInvert(MatrixTriangle, Int32, Span2D<TReal>, ReadOnlySpan<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricInvert(MatrixTriangle, Int32, Span<T>, Int32, ReadOnlySpan<Int32>, Int32)

Computes the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Overrides DecompositionOperations<TReal, TComplex>.SymmetricInvert(MatrixTriangle, Int32, Span<TReal>, Int32, ReadOnlySpan<Int32>, Int32))
SymmetricSolve(MatrixTriangle, Int32, Int32, Array2D<TReal>, Array1D<Int32>, Array2D<TReal>, Int32)

Solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricSolve(MatrixTriangle, Int32, Int32, ReadOnlySpan2D<TReal>, ReadOnlySpan<Int32>, Span2D<TReal>, Int32)

Solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Inherited from DecompositionOperations<TReal, TComplex>)
SymmetricSolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<T>, Int32, ReadOnlySpan<Int32>, Span<T>, Int32, Int32)

Solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*UT or A = L*D*LT computed by DSYTRF.


(Overrides DecompositionOperations<TReal, TComplex>.SymmetricSolve(MatrixTriangle, Int32, Int32, ReadOnlySpan<TReal>, Int32, ReadOnlySpan<Int32>, Span<TReal>, Int32, Int32))
ToStringReturns a string that represents the current object.
(Inherited from Object)
TriangularEstimateCondition(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, Array2D<TComplex>, TReal, Int32) Approximates the reciprocal of the condition number of a complex triangular matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
TriangularEstimateCondition(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, ReadOnlySpan2D<TComplex>, TReal, Int32) Approximates the reciprocal of the condition number of a complex triangular matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
TriangularEstimateCondition(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, ReadOnlySpan<T>, Int32, T, Int32) Approximates the reciprocal of the condition number of a complex triangular matrix.
(Overrides DecompositionOperations<TReal, TComplex>.TriangularEstimateCondition(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, ReadOnlySpan<TComplex>, Int32, TReal, Int32))
TriangularEstimateCondition(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, ReadOnlySpan<Complex<T>>, Int32, T, Int32) Approximates the reciprocal of the condition number of a complex triangular matrix.
(Overrides DecompositionOperations<TReal, TComplex>.TriangularEstimateCondition(MatrixNorm, MatrixTriangle, MatrixDiagonal, Int32, ReadOnlySpan<TComplex>, Int32, TReal, Int32))
TriangularInvert(MatrixTriangle, MatrixDiagonal, Int32, Array2D<TComplex>, Int32) Computes the inverse of a complex triangular matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
TriangularInvert(MatrixTriangle, MatrixDiagonal, Int32, Span2D<TComplex>, Int32) Computes the inverse of a complex triangular matrix.
(Inherited from DecompositionOperations<TReal, TComplex>)
TriangularInvert(MatrixTriangle, MatrixDiagonal, Int32, Span<T>, Int32, Int32) Computes the inverse of a complex triangular matrix.
(Overrides DecompositionOperations<TReal, TComplex>.TriangularInvert(MatrixTriangle, MatrixDiagonal, Int32, Span<TComplex>, Int32, Int32))
TriangularInvert(MatrixTriangle, MatrixDiagonal, Int32, Span<Complex<T>>, Int32, Int32) Computes the inverse of a complex triangular matrix.
(Overrides DecompositionOperations<TReal, TComplex>.TriangularInvert(MatrixTriangle, MatrixDiagonal, Int32, Span<TComplex>, Int32, Int32))
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Int32) Solves a complex triangular system of equations.
(Inherited from DecompositionOperations<TReal, TComplex>)
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32) Solves a complex triangular system of equations.
(Inherited from DecompositionOperations<TReal, TComplex>)
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<T>, Int32, Span<T>, Int32, Int32) Solves a complex triangular system of equations.
(Overrides DecompositionOperations<TReal, TComplex>.TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32))
TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<Complex<T>>, Int32, Span<Complex<T>>, Int32, Int32) Solves a complex triangular system of equations.
(Overrides DecompositionOperations<TReal, TComplex>.TriangularSolve(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32))

See Also