Visible to Intel only — GUID: GUID-2046459C-7738-44B5-BF85-A723AEDDE5F3
Visible to Intel only — GUID: GUID-2046459C-7738-44B5-BF85-A723AEDDE5F3
LAPACK Linear Equation Computational Routines
Table "Computational Routines for Systems of Equations with Real Matrices" lists the LAPACK computational routines (FORTRAN 77 and Fortran 95 interfaces) for factorizing, equilibrating, and inverting real matrices, estimating their condition numbers, solving systems of equations with real matrices, refining the solution, and estimating its error. Table "Computational Routines for Systems of Equations with Complex Matrices" lists similar routines for complex matrices. Respective routine names in the Fortran 95 interface are without the first symbol (see Routine Naming Conventions).
Matrix type, storage scheme |
Factorize matrix |
Equilibrate matrix |
Solve system |
Condition number |
Estimate error |
Invert matrix |
---|---|---|---|---|---|---|
general |
||||||
general band |
|
|||||
general tridiagonal |
|
|
||||
diagonally dominant tridiagonal |
|
|
||||
symmetric positive-definite |
||||||
symmetric positive-definite, packed storage |
||||||
symmetric positive-definite, RFP storage |
|
|
|
|||
symmetric positive-definite, band |
|
|||||
symmetric positive-definite, tridiagonal |
|
|
||||
symmetric indefinite |
||||||
symmetric indefinite, packed storage |
|
|||||
triangular |
|
|
||||
triangular, packed storage |
|
|
||||
triangular, RFP storage |
|
|
|
|
|
|
triangular band |
|
|
|
In the table above, ? denotes s (single precision) or d (double precision) for the FORTRAN 77 interface.
Matrix type, storage scheme |
Factorize matrix |
Equilibrate matrix |
Solve system |
Condition number |
Estimate error |
Invert matrix |
---|---|---|---|---|---|---|
general |
||||||
general band |
|
|||||
general tridiagonal |
|
|
||||
Hermitian positive-definite |
||||||
Hermitian positive-definite, packed storage |
||||||
Hermitian positive-definite, RFP storage |
||||||
Hermitian positive-definite, band |
|
|||||
Hermitian positive-definite, tridiagonal |
|
|
||||
Hermitian indefinite |
||||||
symmetric indefinite |
||||||
Hermitian indefinite, packed storage |
|
|||||
symmetric indefinite, packed storage |
|
|||||
triangular |
|
|
||||
triangular, packed storage |
|
|
||||
triangular, RFP storage |
|
|
||||
triangular band |
|
|
|
In the table above, ? stands for c (single precision complex) or z (double precision complex) for FORTRAN 77 interface.