Contents

# ?lasd4

Computes the square root of the
i
-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by
?bdsdc
.

## Syntax

Include Files
• mkl.h
Description
The routine computes the square root of the
i
-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array
d
, and that
0 ≤
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
)*diag(
d
) +
rho
*
Z
*
Z
T
,
where the Euclidean norm of
Z
is equal to 1.The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.
Input Parameters
n
The length of all arrays.
i
The index of the eigenvalue to be computed.
1 ≤
i
n
.
d
Array,
DIMENSION
(
n
).
The original eigenvalues. They must be in order,
0 ≤
d
(
i
) <
d
(
j
)
for
i
<
j
.
z
Array,
DIMENSION
(
n
).
The components of the updating vector.
rho
The scalar in the symmetric updating formula.
work
Workspace array,
DIMENSION
(
n
).
If
n
1
,
work
contains (
d
(
j
) +
sigma_i
) in its
j
-th component.
If
n
= 1
, then
work
( 1 ) = 1
.
Output Parameters
delta
Array,
DIMENSION
(
n
).
If
n
1
,
delta
contains (
d
(
j
) -
sigma_i
) in its
j
-th component.
If
n
= 1
, then
delta
(1) = 1
. The vector
delta
contains the information necessary to construct the (singular) eigenvectors.
sigma
The computed
sigma_i
, the
i
-th updated eigenvalue.
info
= 0: successful exit
> 0: 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