Linear Equations

Two types of driver routines are provided for solving systems of linear equations:

• the simple driver (name ending -SV) solves the system $AX = B$ by factorizing $A$ and overwriting $B$ with the solution $X$;
  
• the expert driver (name ending -SVX) can also perform the following functions:
  
  • solve $A^T X = B$ or $A^H X = B$ (unless $A$ is symmetric or Hermitian);
  • estimate the condition number of $A$, check for near-singularity, and check for pivot growth;
  • refine the solution and compute forward and backward error bounds;
  • equilibrate the system if $A$ is poorly scaled.
  
  The expert driver requires roughly twice as much storage as the simple driver.

Both types of driver routines handle single or multiple right hand sides by allowing $B$ to be a vector or matrix, respectively.
Different driver routines are provided to take advantage of special properties or storage schemes of the matrix $A$, as shown in Table 2.2.

Table 2.2: Driver routines for linear equations

Type of matrix	Simple	Expert
and storage scheme	driver	driver
General dense	LA_GESV	LA_GESVX
Real / complex
General band	LA_GBSV	LA_GBSVX
Real / complex
General tridiagonal	LA_GTSV	LA_GTSVX
Real / complex
Positive definite full storage	LA_POSV	LA_POSVX
Real symmetric / complex Hermitian
Positive definite packed storage	LA_PPSV	LA_PPSVX
Real symmetric / complex Hermitian
Positive definite band storage	LA_PBSV	LA_PBSVX
Real symmetric / complex Hermitian
Positive definite tridiagonal	LA_PTSV	LA_PTSVX
Real symmetric / complex Hermitian
Indefinite full storage	LA_SYSV /	LA_SYSVX /
Real symmetric / complex	LA_HESV	LA_HESVX
symmetric / complex Hermitian
Indefinite packed storage	LA_SPSV /	LA_SPSVX /
Real symmetric / complex	LA_HPSV	LA_HPSVX
symmetric / complex Hermitian