DecompositionOperations<TReal, TComplex>.QLUnitaryMultiply Method

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) .

Definition

Namespace: Extreme.Mathematics.LinearAlgebra.Implementation
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
C#
public abstract void QLUnitaryMultiply(
	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
C#
SIDE is CHARACTER*1
= 'L': apply Q or Q**H from the Left;
= 'R': apply Q or Q**H from the Right.
trans  TransposeOperation
C#
TRANS is CHARACTER*1
= 'N':  No transpose, apply Q;
= 'C':  Transpose, apply Q**H.
m  Int32
C#
M is INTEGER
The number of rows of the matrix C. M >= 0.
n  Int32
C#
N is INTEGER
The number of columns of the matrix C. N >= 0.
k  Int32
C#
K is INTEGER
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>
C#
A is COMPLEX*16 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
ZGEQLF in the last k columns of its array argument A.
tau  Array1D<TComplex>
C#
TAU is COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQLF.
c  Array2D<TComplex>
C#
C is COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
info  Int32
C#
INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Remarks

C#
. . H(2) H(1)
as returned by ZGEQLF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.

Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Date: November 2015

See Also