ManagedLapack.LQOrthogonalMultiply Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.3.0

Overload List

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) .

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) .

LQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<Double>, Int32, ReadOnlySpan<Double>, Span<Double>, 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) .

LQOrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<Double>, Int32, ReadOnlySpan<Double>, Span<Double>, 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) .

C#
public override void LQOrthogonalMultiply(
	MatrixOperationSide side,
	TransposeOperation trans,
	int m,
	int n,
	int k,
	Span<double> a,
	int lda,
	ReadOnlySpan<double> tau,
	Span<double> c,
	int ldc,
	out int info
)

Parameters

side  MatrixOperationSide
SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
trans  TransposeOperation
TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
m  Int32
M is INTEGER The number of rows of the matrix C. M >= 0.
n  Int32
N is INTEGER The number of columns of the matrix C. N >= 0.
k  Int32
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<Double>
A is DOUBLE PRECISION 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 DGELQF in the first k rows of its array argument A.
lda  Int32
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K).
tau  ReadOnlySpan<Double>
TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGELQF.
c  Span<Double>
C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
ldc  Int32
LDC is INTEGER 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(2) H(1) as returned by DGELQF. 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