## Developer Reference

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

# ?laed4

Used by
sstedc
/
dstedc
. Finds a single root of the secular equation.

## Syntax

Include Files
• mkl.fi
Description
This routine computes the
i
-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array
d
, and that
D
(i) <
D
(
j
) for
i
<
j
and that
rho
> 0
. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus
diag(
D
) +
rho
*
Z
* transpose(
Z
)
.
where we assume the Euclidean norm of
Z
is 1.
The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.
Input Parameters
n
INTEGER
. The length of all arrays.
i
INTEGER
. The index of the eigenvalue to be computed;
1 ≤ i ≤
n
.
d
,
z
REAL
for
slaed4
DOUBLE PRECISION
for
dlaed4
Arrays, dimension (
n
) each. The array
d
contains the original eigenvalues. It is assumed that they are in order,
d
(i) <
d
(
j
) for
i
<
j
.
The array
z
contains the components of the updating vector
Z
.
rho
REAL
for
slaed4
DOUBLE PRECISION
for
dlaed4
The scalar in the symmetric updating formula.
Output Parameters
delta
REAL
for
slaed4
DOUBLE PRECISION
for
dlaed4
Array, dimension (
n
).
If
n
1
,
delta
contains (
d
(
j
) -
lambda_i
) in its
j
-th component. If
n
= 1
, then
delta
(1) = 1
. The vector
delta
contains the information necessary to construct the eigenvectors.
dlam
REAL
for
slaed4
DOUBLE PRECISION
for
dlaed4
The computed
lambda_i
, the
i
-th updated eigenvalue.
info
INTEGER
.
If
info
= 0
, the execution is successful.
If
info
= 1
, the updating process failed.

#### 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