DecompositionOperations<TReal, TComplex>.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': Q^T * C C * Q^T 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': Q^T * C C * Q^T 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<TReal>, Int32, ReadOnlySpan<TReal>, Span<TReal>, 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(1) H(2) .

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': Q^T * C C * Q^T where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q = H(1) H(2) .

public void QROrthogonalMultiply(
	MatrixOperationSide side,
	TransposeOperation trans,
	int m,
	int n,
	int k,
	Array2D<TReal> a,
	Array1D<TReal> tau,
	Array2D<TReal> c,
	out int info
)

Visual Basic

Public Sub QROrthogonalMultiply ( 
	side As MatrixOperationSide,
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	a As Array2D(Of TReal),
	tau As Array1D(Of TReal),
	c As Array2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void QROrthogonalMultiply(
	MatrixOperationSide side, 
	TransposeOperation trans, 
	int m, 
	int n, 
	int k, 
	Array2D<TReal> a, 
	Array1D<TReal> tau, 
	Array2D<TReal> c, 
	[OutAttribute] int% info
)

member QROrthogonalMultiply : 
        side : MatrixOperationSide * 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        a : Array2D<'TReal> * 
        tau : Array1D<'TReal> * 
        c : Array2D<'TReal> * 
        info : int byref -> unit

Parameters

side MatrixOperationSide

            = 'L': apply Q or Q^T from the Left;
            = 'R': apply Q or Q^T from the Right.

trans TransposeOperation

            = 'N':  No transpose, apply Q;
            = 'T':  Transpose, apply Q^T.

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<TReal>

            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.

            The leading dimension of the array A.
            If SIDE = 'L', LDA >= max(1,M);
            if SIDE = 'R', LDA >= max(1,N).

tau Array1D<TReal>

            TAU is TReal array, dimension (K)
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by DGEQRF.

c Array2D<TReal>

            C is TReal 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.

            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.

QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TReal>, ReadOnlySpan<TReal>, Span2D<TReal>, Int32)

public void QROrthogonalMultiply(
	MatrixOperationSide side,
	TransposeOperation trans,
	int m,
	int n,
	int k,
	Span2D<TReal> a,
	ReadOnlySpan<TReal> tau,
	Span2D<TReal> c,
	out int info
)

Visual Basic

Public Sub QROrthogonalMultiply ( 
	side As MatrixOperationSide,
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	a As Span2D(Of TReal),
	tau As ReadOnlySpan(Of TReal),
	c As Span2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void QROrthogonalMultiply(
	MatrixOperationSide side, 
	TransposeOperation trans, 
	int m, 
	int n, 
	int k, 
	Span2D<TReal> a, 
	ReadOnlySpan<TReal> tau, 
	Span2D<TReal> c, 
	[OutAttribute] int% info
)

member QROrthogonalMultiply : 
        side : MatrixOperationSide * 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        a : Span2D<'TReal> * 
        tau : ReadOnlySpan<'TReal> * 
        c : Span2D<'TReal> * 
        info : int byref -> unit

Parameters

side MatrixOperationSide

            = 'L': apply Q or Q^T from the Left;
            = 'R': apply Q or Q^T from the Right.

trans TransposeOperation

            = 'N':  No transpose, apply Q;
            = 'T':  Transpose, apply Q^T.

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 Span2D<TReal>

            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.

            The leading dimension of the array A.
            If SIDE = 'L', LDA >= max(1,M);
            if SIDE = 'R', LDA >= max(1,N).

tau ReadOnlySpan<TReal>

            TAU is TReal array, dimension (K)
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by DGEQRF.

c Span2D<TReal>

            C is TReal 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.

            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.

QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TReal>, Int32, ReadOnlySpan<TReal>, Span<TReal>, Int32, Int32)

public abstract void QROrthogonalMultiply(
	MatrixOperationSide side,
	TransposeOperation trans,
	int m,
	int n,
	int k,
	Span<TReal> a,
	int lda,
	ReadOnlySpan<TReal> tau,
	Span<TReal> c,
	int ldc,
	out int info
)

Visual Basic

Public MustOverride Sub QROrthogonalMultiply ( 
	side As MatrixOperationSide,
	trans As TransposeOperation,
	m As Integer,
	n As Integer,
	k As Integer,
	a As Span(Of TReal),
	lda As Integer,
	tau As ReadOnlySpan(Of TReal),
	c As Span(Of TReal),
	ldc As Integer,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
virtual void QROrthogonalMultiply(
	MatrixOperationSide side, 
	TransposeOperation trans, 
	int m, 
	int n, 
	int k, 
	Span<TReal> a, 
	int lda, 
	ReadOnlySpan<TReal> tau, 
	Span<TReal> c, 
	int ldc, 
	[OutAttribute] int% info
) abstract

abstract QROrthogonalMultiply : 
        side : MatrixOperationSide * 
        trans : TransposeOperation * 
        m : int * 
        n : int * 
        k : int * 
        a : Span<'TReal> * 
        lda : int * 
        tau : ReadOnlySpan<'TReal> * 
        c : Span<'TReal> * 
        ldc : int * 
        info : int byref -> unit

Parameters

side MatrixOperationSide

            = 'L': apply Q or Q^T from the Left;
            = 'R': apply Q or Q^T from the Right.

trans TransposeOperation

            = 'N':  No transpose, apply Q;
            = 'T':  Transpose, apply Q^T.

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<TReal>

            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<TReal>

            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<TReal>

            C is TReal 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

            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.

DecompositionOperations<TReal, TComplex>.QROrthogonalMultiply Method

Definition

Overload List

QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Array2D<TReal>, Array1D<TReal>, Array2D<TReal>, Int32)

Parameters

Remarks

QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span2D<TReal>, ReadOnlySpan<TReal>, Span2D<TReal>, Int32)

Parameters

Remarks

QROrthogonalMultiply(MatrixOperationSide, TransposeOperation, Int32, Int32, Int32, Span<TReal>, Int32, ReadOnlySpan<TReal>, Span<TReal>, Int32, Int32)

Parameters

Remarks

See Also

Reference