Developer Reference

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

?larrk

Computes one eigenvalue of a symmetric tridiagonal matrix
T
to suitable accuracy.

Syntax

call slarrk
(
n
,
iw
,
gl
,
gu
,
d
,
e2
,
pivmin
,
reltol
,
w
,
werr
,
info
)
call dlarrk
(
n
,
iw
,
gl
,
gu
,
d
,
e2
,
pivmin
,
reltol
,
w
,
werr
,
info
)
Include Files
  • mkl.fi
Description
The routine computes one eigenvalue of a symmetric tridiagonal matrix
T
to suitable accuracy. This is an auxiliary code to be called from
?stemr
.
To avoid overflow, the matrix must be scaled so that its largest element 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. For more details see [Kahan66].
Input Parameters
n
INTEGER
. The order of the matrix
T
. (
n
1
).
iw
INTEGER
.
The index of the eigenvalue to be returned.
gl
,
gu
REAL
for
slarrk
DOUBLE PRECISION
for
dlarrk
An upper and a lower bound on the eigenvalue.
d
REAL
for
slarrk
DOUBLE PRECISION
for
dlarrk
Array,
DIMENSION
(
n
).
Contains
n
diagonal elements of the matrix
T
.
e2
REAL
for
slarrk
DOUBLE PRECISION
for
dlarrk
Array,
DIMENSION
(
n
-1
).
Contains
(
n
-1)
squared off-diagonal elements of the
T
.
pivmin
REAL
for
slarrk
DOUBLE PRECISION
for
dlarrk
The minimum pivot in the Sturm sequence for the matrix
T
.
reltol
REAL
for
slarrk
DOUBLE PRECISION
for
dlarrk
The minimum relative width of an interval. When an interval is narrower than
reltol
times the larger (in magnitude) endpoint, then it is considered to be sufficiently small, that is converged. Note: this should always be at least
radix
*
machine epsilon
.
Output Parameters
w
REAL
for
slarrk
DOUBLE PRECISION
for
dlarrk
Contains the eigenvalue approximation.
werr
REAL
for
slarrk
DOUBLE PRECISION
for
dlarrk
Contains the error bound on the corresponding eigenvalue approximation in
w
.
info
INTEGER
.
= 0:
Eigenvalue converges
= -1:
Eigenvalue does not converge

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 I