ManagedLapackOfSingle.LQUnitaryMultiply Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET.SinglePrecision (in Numerics.NET.SinglePrecision.dll) Version: 9.0.0

Overload List

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 .

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 .

LQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<Complex<Single>>, Int32, ReadOnlySpan<Complex<Single>>, Span<Complex<Single>>, 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 .

LQUnitaryMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<Complex<Single>>, Int32, ReadOnlySpan<Complex<Single>>, Span<Complex<Single>>, 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 .

C#
public override void LQUnitaryMultiply(
	MatrixOperationSide side,
	TransposeOperation trans,
	int m,
	int n,
	int k,
	Span<Complex<float>> a,
	int lda,
	ReadOnlySpan<Complex<float>> tau,
	Span<Complex<float>> c,
	int ldc,
	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':  Conjugate 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  Span<Complex<Single>>
C#
A is COMPLEX*16 array, dimension
                     (LDA,M) if SIDE = 'L',
                     (LDA,N) if SIDE = 'R'
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
ZGELQF in the first k rows of its array argument A.
lda  Int32
C#
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,K).
tau  ReadOnlySpan<Complex<Single>>
C#
TAU is COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGELQF.
c  Span<Complex<Single>>
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.
ldc  Int32
C#
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
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 H(1)**H
as returned by ZGELQF. 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