ManagedLapack.QROrthogonalMultiply Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3

Overload List

QROrthogonalMultiply(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': QT * C C * QT where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .

QROrthogonalMultiply(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': QT * C C * QT where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .

QROrthogonalMultiply(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': QT * C C * QT where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .

QROrthogonalMultiply(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': QT * C C * QT where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .

C#
public override void QROrthogonalMultiply(
	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
            = '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  Span<Double>
            A is TReal 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
            DGEQRF in the first k columns of its array argument A.
            A is modified by the routine but restored on exit.
            
lda  Int32
            The leading dimension of the array A.
            If SIDE = 'L', LDA >= max(1,M);
            if SIDE = 'R', LDA >= max(1,N).
            
tau  ReadOnlySpan<Double>
            TAU is TReal array, dimension (K)
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by DGEQRF.
            
c  Span<Double>
            C is TReal array, 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.
            
ldc  Int32
            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 DGEQRF. Q is of order M if SIDE = 'L' and of order N
            if SIDE = 'R'.
            

This method corresponds to the LAPACK routine ?ORMQR.

See Also