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## 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 AT X = B or AH 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.

 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

Next: Linear Least Squares (LLS) Up: Driver Routines Previous: Driver Routines   Contents   Index
Susan Blackford
1999-10-01