Extended Eigensolver Naming Conventions

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/31/2024

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Extended Eigensolver Naming Conventions

There are two different types of interfaces available in the Extended Eigensolver routines:

The reverse communication interfaces (RCI):
```
?feast_<matrix type>_rci
```
These interfaces are matrix free format (the interfaces are independent of the matrix data formats). You must provide matrix-vector multiply and direct/iterative linear system solvers for your own explicit or implicit data format.
The predefined interfaces:
```
?feast_<matrix type><type of eigenvalue problem>
```
are predefined drivers for ?feast reverse communication interface that act on commonly used matrix data storage (dense, banded and compressed sparse row representation), using internal matrix-vector routines and selected inner linear system solvers.

For these interfaces:

? indicates the data type of matrix A (and matrix B if any) defined as follows:

s

float

d

double

c

MKL_Complex8

z

MKL_Complex16

<matrix type> defined as follows:

Value of `<matrix type>`		Matrix format	Inner linear system solver used by Extended Eigensolver
`sy`	(symmetric real)	Dense	LAPACK dense solvers
`he`	(Hermitian complex)	Dense	LAPACK dense solvers
`sb`	(symmetric banded real)	Banded-LAPACK	Internal banded solver
`hb`	(Hermitian banded complex)	Banded-LAPACK	Internal banded solver
`scsr`	(symmetric real)	Compressed sparse row	PARDISO solver
`hcsr`	(Hermitian complex)	Compressed sparse row	PARDISO solver
`s`	(symmetric real)	Reverse communications interfaces	User defined
`h`	(Hermitian complex)	Reverse communications interfaces	User defined

<type of eigenvalue problem> is:

gv

generalized eigenvalue problem

ev

standard eigenvalue problem

For example, sfeast_scsrev is a single-precision routine with a symmetric real matrix stored in sparse compressed-row format for a standard eigenvalue problem, and zfeast_hrci is a complex double-precision routine with a Hermitian matrix using the reverse communication interface.

Note that:

? can be s or d if a matrix is real symmetric: <matrix type> is sy, sb, or scsr.
? can be c or z if a matrix is complex Hermitian: <matrix type> is he, hb, or hcsr.
? can be c or z if the Extended Eigensolver RCI interface is used for solving a complex Hermitian problem.
? can be s or d if the Extended Eigensolver RCI interface is used for solving a real symmetric problem.

Parent topic: Extended Eigensolver Interfaces for Eigenvalues within Interval

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Extended Eigensolver Naming Conventions