Developer Reference

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

p?laiect

Exploits IEEE arithmetic to accelerate the computations of eigenvalues.
(C interface function).

Syntax

void pslaiect
(
float
*sigma
,
int
*n
,
float
*d
,
int
*count
)
;
void pdlaiectb
(
float
*sigma
,
int
*n
,
float
*d
,
int
*count
)
;
void pdlaiectl
(
float
*sigma
,
int
*n
,
float
*d
,
int
*count
)
;
Description
The
p?laiect
routine
computes the number of negative eigenvalues of (
A
-
σ
I
). This implementation of the Sturm Sequence loop exploits IEEE arithmetic and has no conditionals in the innermost loop. The signbit for real
routine
pslaiect
is assumed to be bit 32. Double-precision
routines
pdlaiectb
and
pdlaiectl
differ in the order of the double precision word storage and, consequently, in the signbit location. For
pdlaiectb
, the double precision word is stored in the big-endian word order and the signbit is assumed to be bit 32. For
pdlaiectl
, the double precision word is stored in the little-endian word order and the signbit is assumed to be bit 64.
Note that all arguments are call-by-reference so that this
routine
can be directly called from Fortran code.
This is a ScaLAPACK internal
subroutine
and arguments are not checked for unreasonable values.
Input Parameters
sigma
REAL
for
pslaiect
DOUBLE PRECISION
for
pdlaiectb/pdlaiectl
.
The shift.
p?laiect
finds the number of eigenvalues less than equal to
sigma
.
n
INTEGER
.
The order of the tridiagonal matrix
T
.
n
1
.
d
REAL
for
pslaiect
DOUBLE PRECISION
for
pdlaiectb/pdlaiectl
.
Array of size
2
n
-1
.
On entry, this array contains the diagonals and the squares of the off-diagonal elements of the tridiagonal matrix
T
. These elements are assumed to be interleaved in memory for better cache performance. The diagonal entries of
T
are in the entries
d
(1),
d
(3),...,
d
(2
n
-1)
, while the squares of the off-diagonal entries are
d
(2),
d
(4), ...,
d
(2
n
-2)
. To avoid overflow, the matrix must be scaled so that its largest entry is no greater than
overflow
(1/2)
*
underflow
(1/4)
in absolute value, and for greatest accuracy, it should not be much smaller than that.
Output Parameters
n
INTEGER
.
The count of the number of eigenvalues of
T
less than or equal to
sigma
.

Product and Performance Information

1

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