Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?stegr2a

Computes selected eigenvalues and initial representations needed for eigenvector computations.

Syntax

void sstegr2a
(
char*
jobz
,
char*
range
,
MKL_INT*
n
,
float*
d
,
float*
e
,
float*
vl
,
float*
vu
,
MKL_INT*
il
,
MKL_INT*
iu
,
MKL_INT*
m
,
float*
w
,
float*
z
,
MKL_INT*
ldz
,
MKL_INT*
nzc
,
float*
work
,
MKL_INT*
lwork
,
MKL_INT*
iwork
,
MKL_INT*
liwork
,
MKL_INT*
dol
,
MKL_INT*
dou
,
MKL_INT*
needil
,
MKL_INT*
neediu
,
MKL_INT*
inderr
,
MKL_INT*
nsplit
,
float*
pivmin
,
float*
scale
,
float*
wl
,
float*
wu
,
MKL_INT*
info
);
void dstegr2a
(
char*
jobz
,
char*
range
,
MKL_INT*
n
,
double*
d
,
double*
e
,
double*
vl
,
double*
vu
,
MKL_INT*
il
,
MKL_INT*
iu
,
MKL_INT*
m
,
double*
w
,
double*
z
,
MKL_INT*
ldz
,
MKL_INT*
nzc
,
double*
work
,
MKL_INT*
lwork
,
MKL_INT*
iwork
,
MKL_INT*
liwork
,
MKL_INT*
dol
,
MKL_INT*
dou
,
MKL_INT*
needil
,
MKL_INT*
neediu
,
MKL_INT*
inderr
,
MKL_INT*
nsplit
,
double*
pivmin
,
double*
scale
,
double*
wl
,
double*
wu
,
MKL_INT*
info
);
Include Files
  • mkl_scalapack.h
Description
?stegr2a
 computes selected eigenvalues and initial representations needed for eigenvector computations in
?stegr2b
. It is invoked in the ScaLAPACK MRRR driver
p?syevr
 and the corresponding Hermitian version when both eigenvalues and eigenvectors are computed in parallel on multiple processors. For this case,
?stegr2a
 implements the first part of the MRRR algorithm, parallel eigenvalue computation and finding the root RRR. At the end of
?stegr2a
, other processors might have a part of the spectrum that is needed to continue the computation locally. Once this eigenvalue information has been received by the processor, the computation can then proceed by calling the second part of the parallel MRRR algorithm,
?stegr2b
.
Please note:
  • The calling sequence has two additional integer parameters, (compared to LAPACK's
    stegr
    ), these are
    dol
     and
    dou
     and should satisfy
    m
    ≥
    dou
    ≥
    dol
    ≥
    1. These parameters are only relevant for the case
    jobz
     = 'V'.
    Globally invoked over all processors,
    ?stegr2a
     computes all the eigenvalues specified by
    range
    .
    ?stegr2a
     locally only computes the eigenvalues corresponding to eigenvalues
    dol
     through
    dou
     in
    w
    , indexed
    dol
    -1 through
    dou
    -1
    . (That is, instead of computing the eigenvectors belonging to
    w
    ([0] through
    w
    [
    m
    -1]
    , only the eigenvectors belonging to eigenvalues
    w
    [
    dol
    -1] through
    w
    [
    dou
    -1]
     are computed. In this case, only the eigenvalues
    dol
     through
    dou
     are guaranteed to be fully accurate.
  • m
     is not the number of eigenvalues specified by
    range
    , but it is
    m
     =
    dou
     -
    dol
     + 1. Instead,
    m
     refers to the number of eigenvalues computed on this processor.
  • While no eigenvectors are computed in
    ?stegr2a
     itself (this is done later in
    ?stegr2b
    ), the interface
    If
    jobz
     = 'V' then, depending on
    range
     and
    dol
    ,
    dou
    ,
    ?stegr2a
     might need more workspace in
    z
     then the original
    ?stegr
    . In particular, the arrays
    w
     and
    z
     might not contain all the wanted eigenpairs locally, instead this information is distributed over other processors.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
Notice revision #20201201
Input Parameters
jobz
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
range
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (
vl
,
vu
] will be found.
= 'I':
eigenvalues of the entire matrix with the indices in a given range
 will be found.
n
The order of the matrix.
n
≥
 0.
d
Array of size
n
The
n
 diagonal elements of the tridiagonal matrix
T
. Overwritten on exit.
e
Array of size
n
On entry, the (
n
-1) subdiagonal elements of the tridiagonal matrix
T
 in elements
0 to
n
-2
 of
e
.
e
[
n
-1]
 need not be set on input, but is used internally as workspace. Overwritten on exit.
vl
,
vu
If
range
='V', the lower and upper bounds of the interval to be searched for eigenvalues.
vl
 <
vu
.
Not referenced if
range
 = 'A' or 'I'.
il
,
iu
If
range
='I', the indices (in ascending order) of the
smallest eigenvalue, to be returned in
w
[
il
-1], and largest eigenvalue, to be returned in
w
[
iu
-1]
. 1
≤
il
≤
iu
≤
n
, if
n
 > 0.
Not referenced if
range
 = 'A' or 'V'.
ldz
The leading dimension of the array
z
.
ldz
≥
 1, and if
jobz
 = 'V', then
ldz
≥
 max(1,
n
).
nzc
The number of eigenvectors to be held in the array
z
.
If
range
 = 'A', then
nzc
≥
 max(1,
n
).
If
range
 = 'V', then
nzc
≥
 the number of eigenvalues in (
vl
,
vu
].
If
range
 = 'I', then
nzc
≥
iu
-
il
+1.
If
nzc
 = -1, then a workspace query is assumed; the
function
calculates the number of columns of the
matrix stored in
array
z
 that are needed to hold the eigenvectors. This value is returned as the first entry of the
z
 array, and no error message related to
nzc
 is issued.
lwork
The size of the array
work
.
lwork
≥
 max(1,18*
n
) if
jobz
 = 'V', and
lwork
≥
 max(1,12*
n
) if
jobz
 = 'N'.
If
lwork
 = -1, then a workspace query is assumed; the
function
only calculates the optimal size of the
work
 array, returns this value as the first entry of the
work
 array, and no error message related to
lwork
 is issued.
liwork
The size of the array
iwork
.
liwork
≥
 max(1,10*
n
) if the eigenvectors are desired, and
liwork
≥
 max(1,8*
n
) if only the eigenvalues are to be computed.
If
liwork
 = -1, then a workspace query is assumed; the
function
only calculates the optimal size of the
iwork
 array, returns this value as the first entry of the
iwork
 array, and no error message related to
liwork
 is issued.
dol
,
dou
From all the eigenvalues
w
[0] through
w
[
m
-1]
, only eigenvalues
w
[
dol
-1] through
w
[
dou
-1]
 are computed.
OUTPUT Parameters
m
Globally summed over all processors,
m
 equals the total number of eigenvalues found. 0
≤
m
≤
n
.
If
range
 = 'A',
m
 =
n
, and if
range
 = 'I',
m
 =
iu
-
il
+1.
The local output equals
m
 =
dou
 -
dol
 + 1.
w
Array of size
n
The first
m
 elements contain approximations to the selected eigenvalues in ascending order. Note that immediately after exiting this
function
, only the eigenvalues
indexed
dol
-1 through
dou
-1
 are reliable on this processor because the eigenvalue computation is done in parallel. The other entries are very crude preliminary approximations. Other processors hold reliable information on these other parts of the
w
 array.
This information is communicated in the ScaLAPACK driver.
z
Array of size
ldz
 * max(1,
m
)
.
?stegr2a
 does not compute eigenvectors, this is done in
?stegr2b
. The argument
z
 as well as all related other arguments only appear to keep the interface consistent and to signal to the user that this
function
is meant to be used when eigenvectors are computed.
work
On exit, if
info
 = 0,
work
[0]
 returns the optimal (and minimal)
lwork
.
iwork
On exit, if
info
 = 0,
iwork
[0]
 returns the optimal
liwork
.
needil
,
neediu
The indices of the leftmost and rightmost eigenvalues needed to accurately compute the relevant part of the representation tree. This information can be used to find out which processors have the relevant eigenvalue information needed so that it can be communicated.
inderr
inderr
 points to the place in the work space where the eigenvalue uncertainties (errors) are stored.
nsplit
The number of blocks into which
T
 splits. 1
≤
nsplit
≤
n
.
pivmin
The minimum pivot in the sturm sequence for
T
.
scale
The scaling factor for the tridiagonal
T
.
wl
,
wu
The interval (
wl
,
wu
] contains all the wanted eigenvalues.
It is either given by the user or computed in
?larre2a
.
info
On exit,
info
 = 0: successful exit
other: if
info
 = -
i
, the
i
-th argument had an illegal value
if
info
 = 10
x
, internal error in
?larre2a
,
Here, the digit
x
 = abs(
iinfo
 ) < 10, where
iinfo
 is the nonzero error code returned by
?larre2a
.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.