vsip_dqrdprodq_p - Multiply by Q Matrix from QR Decomposition

Core

6.5.7 vsip_dqrdprodq_p - Multiply by Q Matrix from QR Decomposition

typedef enum _vsip_mat_op { 
  VSIP_MAT_NTRANS = 0, // op(A) = A 
  VSIP_MAT_TRANS  = 1, // op(A) = A^T 
  VSIP_MAT_HERM   = 2, // op(A) = A^H (complex only) 
  VSIP_MAT_CONJ   = 3  // op(X) = A^* (complex only) 
} vsip_mat_op; 
 
typedef enum _vsip_mat_side { 
  VSIP_MAT_LSIDE = 0, 
  VSIP_MAT_RSIDE = 1 
} vsip_mat_side; 
 
int vsip_qrdprodq_f(const vsip_qr_f *qrd, vsip_mat_op opQ, vsip_mat_side apQ, const vsip_mview_f *c); 
int vsip_cqrdprodq_f(const vsip_cqr_f *qrd, vsip_mat_op opQ, vsip_mat_side apQ, const vsip_cmview_f *c);

Description

This function performs matrix multiplication with the orthogonal matrix $Q$ from a QR decomposition. It computes either $QC$ , $T Q C$ , $H Q C$ , $CQ$ , $T CQ$ or $H CQ$ , depending on the specified parameters.

The operation performed is determined by the opQ and apQ parameters:

opQ specifies whether to use $Q$ , $T Q$ or $H Q$
apQ specifies whether $Q$ is on the left or right of the multiplication

Parameters

const vsip_dqr_p* qrd: Pointer to the QR decomposition object containing a previously computed decomposition.
vsip_mat_op opQ: Operation to perform with Q:
- VSIP_MAT_NTRANS: Use $Q$ as is
- VSIP_MAT_TRANS: Use the transpose of $Q$ , $QT$
- VSIP_MAT_HERM: Use the conjugate transpose of $Q$ , $H Q$
vsip_mat_side apQ: Side of multiplication:
- VSIP_MAT_LEFT: $Q$ is on the left ( $QC$ , $QTC$ or $QHC$ )
- VSIP_MAT_RIGHT: $Q$ is on the right ( $CQ$ , $CQT$ or $CQH$ )
const vsip_dmview_p* c: On input, contains matrix $C$ . On output, contains the result of the multiplication.

Return Value

Returns 0 on success.
Returns a non-zero value on error.

Notes

The QR decomposition must have been previously computed using vsip_dqrd_p .
The QR object must have been created with an option that saves the $Q$ matrix (VSIP_QRD_SAVEQ or VSIP_QRD_SAVEQ1).

The input matrix $C$ must have appropriate dimensions for the operation.

For VSIP_QRD_SAVEQ1:


	Input		Output
	MAT_LSIDE	MAT_RSIDE	MAT_LSIDE	MAT_RSIDE

MAT_NTRANS	$n×s$	$r×m$	$m ×s$	$r ×n$
MAT_TRANS	$m× s$	$r×n$	$n ×s$	$r ×m$
MAT_HERM	$m× s$	$r×n$	$n ×s$	$r ×m$

For VSIP_QRD_SAVEQ:


	Input and Output
	MAT_LSIDE	MAT_RSIDE

MAT_NTRANS	$m× s$	$r×m$
MAT_TRANS	$m× s$	$r×m$
MAT_HERM	$m× s$	$r×m$

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