Developer Reference

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

?larre2

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

Syntax

call slarre2
(
range
,
n
,
vl
,
vu
,
il
,
iu
,
d
,
e
,
e2
,
rtol1
,
rtol2
,
spltol
,
nsplit
,
isplit
,
m
,
dol
,
dou
,
w
,
werr
,
wgap
,
iblock
,
indexw
,
gers
,
pivmin
,
work
,
iwork
,
info
)
call dlarre2
(
range
,
n
,
vl
,
vu
,
il
,
iu
,
d
,
e
,
e2
,
rtol1
,
rtol2
,
spltol
,
nsplit
,
isplit
,
m
,
dol
,
dou
,
w
,
werr
,
wgap
,
iblock
,
indexw
,
gers
,
pivmin
,
work
,
iwork
,
info
)
Description
To find the desired eigenvalues of a given real symmetric tridiagonal matrix
T
,
?larre2
sets, via
?larra
, "small" off-diagonal elements to zero. For each block
T
i
, it finds
  • a suitable shift at one end of the block's spectrum,
  • the root RRR, T
    i
    -
    σ
    i
    I
    =
    L
    i
    D
    i
    L
    i
    T
    , and
  • eigenvalues of each
    L
    i
    D
    i
    L
    i
    T
    .
The representations and eigenvalues found are then returned to
?stegr2
to compute the eigenvectors
T
.
?larre2
is more suitable for parallel computation than the original LAPACK code for computing the root RRR and its eigenvalues. When computing eigenvalues in parallel and the input tridiagonal matrix splits into blocks,
?larre2
can skip over blocks which contain none of the eigenvalues from
dol
to
dou
for which the processor is responsible. In extreme cases (such as large matrices consisting of many blocks of small size, e.g. 2x2), the gain can be substantial.
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