Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

p?laiect

Exploits IEEE arithmetic to accelerate the computations of eigenvalues.

Syntax

void
pslaiect
(
float
*sigma
,
MKL_INT
*n
,
float
*d
,
MKL_INT
*count
);
void
pdlaiectb
(
float
*sigma
,
MKL_INT
*n
,
float
*d
,
MKL_INT
*count
);
void
pdlaiectl
(
float
*sigma
,
MKL_INT
*n
,
float
*d
,
MKL_INT
*count
);
Include Files
  • mkl_scalapack.h
Description
The
p?laiect
function
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
function
pslaiect
 is assumed to be bit 32. Double-precision
functions
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.
This is a ScaLAPACK internal
function
and arguments are not checked for unreasonable values.
Input Parameters
sigma
The shift.
p?laiect
 finds the number of eigenvalues less than equal to
sigma
.
n
The order of the tridiagonal matrix
T
.
n
≥
 1
.
d
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
[0],
d
[2],...,
d
[2
n
-2]
, while the squares of the off-diagonal entries are
d
[1],
d
[3], ...,
d
[2
n
-3]
. 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
The count of the number of eigenvalues of
T
 less than or equal to
sigma
.

Product and Performance Information

1

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