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 matrix has been modified by a specified operation. It provides more flexibility than vsip_dqrsol_p by allowing operations on the matrix before solving the system.

The function solves systems of the form:

where can be , , or (conjugate transpose, though for real matrices this is equivalent to ).

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 :

  • VSIP_MAT_NTRANS: Use as is

  • VSIP_MAT_TRANS: Use the transpose of ,

  • VSIP_MAT_HERM: Use the conjugate transpose of ,

• vsip_dscalar_p alpha: Scalar multiplier for the right-hand side.

• const vsip_dmview_p* xb: On input, contains the right-hand side . On output, contains the solution .

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 must have appropriate dimensions for the operation:

  • For VSIP_MAT_NTRANS: should be where is

  • For VSIP_MAT_TRANS or VSIP_MAT_HERM: should be where is

• The input matrix is overwritten with the solution.

• The scalar 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 matrix to use this function.