GenericDecompositionOperations<T>.QROrthogonalMultiply Method

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) .

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics.Generic (in Extreme.Numerics.Generic.dll) Version: 8.1.4
C# 
public override void QROrthogonalMultiply(
	MatrixOperationSide side,
	TransposeOperation trans,
	int m,
	int n,
	int k,
	Array2D<T> a,
	Array1D<T> tau,
	Array2D<T> c,
	out int info
)

Parameters

side  MatrixOperationSide
            = 'L': apply Q or QT from the Left;
            = 'R': apply Q or QT from the Right.
trans  TransposeOperation
            = 'N':  No transpose, apply Q;
            = 'T':  Transpose, apply QT.
m  Int32
            The number of rows of the matrix C. M >= 0.
n  Int32
            The number of columns of the matrix C. N >= 0.
k  Int32
            The number of elementary reflectors whose product defines
            the matrix Q.
            If SIDE = 'L', M >= K >= 0;
            if SIDE = 'R', N >= K >= 0.
a  Array2D<T>
            Dimension (LDA,K)
            The i-th column must contain the vector which defines the
            elementary reflector H(i), for i = 1,2,...,k, as returned by
            DGEQRF in the first k columns of its array argument A.
            A is modified by the routine but restored on exit.
            
            The leading dimension of the array A.
            If SIDE = 'L', LDA >= max(1,M);
            if SIDE = 'R', LDA >= max(1,N).
tau  Array1D<T>
            Dimension (K)
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by DGEQRF.
c  Array2D<T>
            Dimension (LDC,N)
            On entry, the M-by-N matrix C.
            On exit, C is overwritten by Q*C or QT*C or C*QT or C*Q.
            
            The leading dimension of the array C. LDC >= max(1,M).
info  Int32
info is INTEGER
            = 0:  successful exit
            < 0:  if info = -i, the i-th argument had an illegal value

Remarks

            . . H(k)
            as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
            if SIDE = 'R'.

This method corresponds to the LAPACK routine DORMQR.

See Also