Linear Equations

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

• a simple driver (name ending -SV), which solves the system AX = B by factorizing A and overwriting B with the solution X;

• an expert driver (name ending -SVX), which can also perform the following functions (some of them optionally):
  • 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 in order to perform these extra functions.

Both types of driver routines can handle multiple right hand sides (the columns of B).

Different driver routines are provided to take advantage of special properties or storage schemes of the matrix A, as shown in Table 2.2.

These driver routines cover all the functionality of the computational routines for linear systems, except matrix inversion. It is seldom necessary to compute the inverse of a matrix explicitly, and it is certainly not recommended as a means of solving linear systems.

Table 2.2: Driver routines for linear equations

Type of matrix	Operation	Single precision		Double precision
and storage scheme		real	complex	real	complex
general	simple driver	SGESV	CGESV	DGESV	ZGESV
	expert driver	SGESVX	CGESVX	DGESVX	ZGESVX
general band	simple driver	SGBSV	CGBSV	DGBSV	ZGBSV
	expert driver	SGBSVX	CGBSVX	DGBSVX	ZGBSVX
general tridiagonal	simple driver	SGTSV	CGTSV	DGTSV	ZGTSV
	expert driver	SGTSVX	CGTSVX	DGTSVX	ZGTSVX
symmetric/Hermitian	simple driver	SPOSV	CPOSV	DPOSV	ZPOSV
positive definite	expert driver	SPOSVX	CPOSVX	DPOSVX	ZPOSVX
symmetric/Hermitian	simple driver	SPPSV	CPPSV	DPPSV	ZPPSV
positive definite (packed storage)	expert driver	SPPSVX	CPPSVX	DPPSVX	ZPPSVX
symmetric/Hermitian	simple driver	SPBSV	CPBSV	DPBSV	ZPBSV
positive definite band	expert driver	SPBSVX	CPBSVX	DPBSVX	ZPBSVX
symmetric/Hermitian	simple driver	SPTSV	CPTSV	DPTSV	ZPTSV
positive definite tridiagonal	expert driver	SPTSVX	CPTSVX	DPTSVX	ZPTSVX
symmetric/Hermitian	simple driver	SSYSV	CHESV	DSYSV	ZHESV
indefinite	expert driver	SSYSVX	CHESVX	DSYSVX	ZHESVX
complex symmetric	simple driver		CSYSV		ZSYSV
	expert driver		CSYSVX		ZSYSVX
symmetric/Hermitian	simple driver	SSPSV	CHPSV	DSPSV	ZHPSV
indefinite (packed storage)	expert driver	SSPSVX	CHPSVX	DSPSVX	ZHPSVX
complex symmetric	simple driver		CSPSV		ZSPSV
(packed storage)	expert driver		CSPSVX		ZSPSVX