DecompositionOperations<TReal, TComplex>.QRUnitaryMultiply Method

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) .

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
C# 
public abstract void QRUnitaryMultiply(
	MatrixOperationSide side,
	TransposeOperation trans,
	int m,
	int n,
	int k,
	Array2D<TComplex> a,
	Array1D<TComplex> tau,
	Array2D<TComplex> c,
	out int info
)

Parameters

side  MatrixOperationSide
            = 'L': apply Q or QH from the Left;
            = 'R': apply Q or QH from the Right.
trans  TransposeOperation
            = 'N':  No transpose, apply Q;
            = 'C':  Conjugate transpose, apply QH.
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<TComplex>
            A is TComplex array, 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
            ZGEQRF in the first k columns of its array argument A.
            
            The leading dimension of the array A.
            If SIDE = 'L', LDA >= max(1,M);
            if SIDE = 'R', LDA >= max(1,N).
tau  Array1D<TComplex>
            TAU is TComplex array, dimension (K)
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by ZGEQRF.
c  Array2D<TComplex>
            C is TComplex array, dimension (LDC,N)
            On entry, the M-by-N matrix C.
            On exit, C is overwritten by Q*C or QH*C or C*QH or C*Q.
            
            The leading dimension of the array C. LDC >= max(1,M).
info  Int32
            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value

Remarks

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

See Also