Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?larre2a

Given a tridiagonal matrix, sets small off-diagonal elements to zero and for each unreduced block, finds base representations and eigenvalues.

Syntax

call slarre2a
(
range
,
n
,
vl
,
vu
,
il
,
iu
,
d
,
e
,
e2
,
rtol1
,
rtol2
,
spltol
,
nsplit
,
isplit
,
m
,
dol
,
dou
,
needil
,
neediu
,
w
,
werr
,
wgap
,
iblock
,
indexw
,
gers
,
sdiam
,
pivmin
,
work
,
iwork
,
minrgp
,
info
)
call dlarre2a
(
range
,
n
,
vl
,
vu
,
il
,
iu
,
d
,
e
,
e2
,
rtol1
,
rtol2
,
spltol
,
nsplit
,
isplit
,
m
,
dol
,
dou
,
needil
,
neediu
,
w
,
werr
,
wgap
,
iblock
,
indexw
,
gers
,
sdiam
,
pivmin
,
work
,
iwork
,
minrgp
,
info
)
Description
To find the desired eigenvalues of a given real symmetric tridiagonal matrix
T
,
?larre2a
sets any "small" off-diagonal elements to zero, and for each unreduced block
T
i
, it finds
  • a suitable shift at one end of the block's spectrum,
  • the base representation,
    T
    i
    -
    σ
    i
    I
    =
    L
    i
    D
    i
    L
    i
    T
    , and
  • eigenvalues of each
    L
    i
    D
    i
    L
    i
    T
    .
The algorithm obtains a crude picture of all the wanted eigenvalues (as selected by
range
). However, to reduce work and improve scalability, only the eigenvalues
dol
to
dou
are refined. Furthermore, if the matrix splits into blocks, RRRs for blocks that do not contain eigenvalues from
dol
to
dou
are skipped. The DQDS algorithm (
subroutine
?lasq2
) is not used, unlike in the sequential case. Instead, eigenvalues are computed in parallel to some figures using bisection.
Optimization Notice
Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.
Notice revision #20110804
This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.
Input Parameters
range
CHARACTER
= 'A': ("All") all eigenvalues will be found.
= 'V': ("Value") all eigenvalues in the half-open interval (
vl
,
vu
] will be found.
= 'I': ("Index")
the
il
-th through
iu
-th eigenvalues (of the entire matrix)
will be found.
n
INTEGER
The order of the matrix.
n
> 0.
vl
,
vu