vsip_dqrsol_p - Solve Linear Systems Using QR Decomposition

Core

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6.5.5 vsip_dqrsol_p - Solve Linear Systems Using QR Decomposition

typedef enum _vsip_qrd_prob { 
  VSIP_COV = 0, /* Solve a covariance linear system problem */ 
  VSIP_LLS = 1  /* Solve a linear least squares problem */ 
} vsip_qrd_prob; 
 
int vsip_qrsol_f(const vsip_qr_f *qrd, vsip_qrd_prob prob, const vsip_mview_f *xb); 
int vsip_cqrsol_f(const vsip_cqr_f *qrd, vsip_qrd_prob prob, const vsip_cmview_f *xb);

Description

This function solves linear systems of equations using a previously computed QR decomposition for a matrix $A$ with $m ×n$ with rank $n$ . It can solve a covariance linear system problem

ATAX = B

for real or

AHAX = B

for complex. Or a linear least squares problem,

min ∥AX -B ∥2

Parameters

const vsip_dqr_p* qrd: Pointer to the QR decomposition object containing a previously computed decomposition.
vsip_qrd_prob prob: Type of problem to solve.
const vsip_dmview_p* xb: On input, contains the right-hand side matrix $B$ of size $n× k$ for a covariance problem and $m ×k$ for a least squares problem. 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 QR object must have been created with an option that saves the $Q$ matrix to use this function.

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