Decomposition Operations<TReal, TComplex>.RQOrthogonal Multiply Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
RQOrthogonal | 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) . |
RQOrthogonal | 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) . |
RQOrthogonal | 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) . |
RQOrthogonalMultiply(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 RQOrthogonalMultiply(
MatrixOperationSide side,
TransposeOperation trans,
int m,
int n,
int k,
Array2D<TReal> a,
Array1D<TReal> tau,
Array2D<TReal> c,
out int info
)
Parameters
- side MatrixOperationSide
-
C# SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
- trans TransposeOperation
-
C# TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
- 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<TReal>
-
C# 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 DGERQF in the last k rows of its array argument A.
- tau Array1D<TReal>
-
C# TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGERQF.
- c Array2D<TReal>
-
C# 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.
- info Int32
-
C# INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Remarks
. . H(k)
as returned by DGERQF. 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
RQOrthogonalMultiply(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) .
public void RQOrthogonalMultiply(
MatrixOperationSide side,
TransposeOperation trans,
int m,
int n,
int k,
Span2D<TReal> a,
ReadOnlySpan<TReal> tau,
Span2D<TReal> c,
out int info
)
Parameters
- side MatrixOperationSide
-
C# SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
- trans TransposeOperation
-
C# TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
- 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 Span2D<TReal>
-
C# 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 DGERQF in the last k rows of its array argument A.
- tau ReadOnlySpan<TReal>
-
C# TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGERQF.
- c Span2D<TReal>
-
C# 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.
- info Int32
-
C# INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Remarks
. . H(k)
as returned by DGERQF. 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
RQOrthogonalMultiply(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) .
public abstract void RQOrthogonalMultiply(
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
)
Parameters
- side MatrixOperationSide
-
C# SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
- trans TransposeOperation
-
C# TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
- 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<TReal>
-
C# 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 DGERQF in the last 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<TReal>
-
C# TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGERQF.
- c Span<TReal>
-
C# 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
-
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
. . H(k)
as returned by DGERQF. 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