vsip_dqrdsolr_p - Solve Linear Systems with Modified R Matrix

Core

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6.5.6 vsip_dqrdsolr_p - Solve Linear Systems with Modified R Matrix

typedef enum _vsip_mat_side { 
  VSIP_MAT_LSIDE = 0, 
  VSIP_MAT_RSIDE = 1 
} vsip_mat_side; 
 
int vsip_qrdsolr_f(const vsip_qr_f *qrd, vsip_mat_op OpR, vsip_scalar_f alpha, const vsip_mview_f *xb); 
int vsip_cqrdsolr_f(const vsip_cqr_f *qrd, vsip_mat_op OpR, vsip_cscalar_f alpha, const vsip_cmview_f *xb);

Description

This function solves linear systems using a QR decomposition where the $R$ matrix has been modified by a specified operation. It provides more flexibility than vsip_dqrsol_p by allowing operations on the $R$ matrix before solving the system.

The function solves systems of the form:

op(R)X =αB

where $op(R)$ can be $R$ , $RT$ , or $RH$ (conjugate transpose, though for real matrices this is equivalent to $RT$ ).

Parameters

const vsip_dqr_p* qrd: Pointer to the QR decomposition object containing a previously computed decomposition.
vsip_mat_op OpR: Operation to perform on $R$ :
- VSIP_MAT_NTRANS: Use $R$ as is
- VSIP_MAT_TRANS: Use the transpose of $R$ , $RT$
- VSIP_MAT_HERM: Use the conjugate transpose of $R$ , $RH$
vsip_dscalar_p alpha: Scalar multiplier for the right-hand side.
const vsip_dmview_p* xb: On input, contains the right-hand side $B$ . On output, contains the solution $X$ .

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 input matrix $B$ must have appropriate dimensions for the operation:
- For VSIP_MAT_NTRANS: $B$ should be $n× k$ where $A$ is $m ×n$
- For VSIP_MAT_TRANS or VSIP_MAT_HERM: $B$ should be $m ×k$ where $A$ is $m ×n$
The input matrix $XB$ is overwritten with the solution.
The scalar $α$ allows scaling of the right-hand side without modifying the input matrix.
This function is more flexible than vsip_dqrsol_p but requires more understanding of the underlying linear algebra.
The QR object must have been created with an option that saves the $Q$ matrix to use this function.

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