## Developer Reference

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

# ?laed9

Used by
sstedc
/
dstedc
. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

## Syntax

Include Files
• mkl.fi
Description
The routine finds the roots of the secular equation, as defined by the values in
d
,
z
, and
rho
, between
kstart
and
kstop
. It makes the appropriate calls to
slaed4
/
dlaed4
and then stores the new matrix of eigenvectors for use in calculating the next level of
z
vectors.
Input Parameters
k
INTEGER
. The number of terms in the rational function to be solved by
slaed4
/
dlaed4
(
k
0
).
kstart
,
kstop
INTEGER
. The updated eigenvalues
lambda
(i),
kstart
≤ i ≤
kstop
are to be computed.
1 ≤
kstart
kstop
k
.
n
INTEGER
. The number of rows and columns in the
Q
matrix.
n
k
(deflation may result in
n
>
k
).
q
REAL
for
slaed9
DOUBLE PRECISION
for
dlaed9
.
Workspace array, dimension (
ldq, *
).
The second dimension of
q
must be at least
max(1,
n
)
.
ldq
INTEGER
. The leading dimension of the array
q
;
ldq
max(1,
n
)
.
rho
REAL
for
slaed9
DOUBLE PRECISION
for
dlaed9
The value of the parameter in the rank one update equation.
rho
0
required.
dlamda
,
w
REAL
for
slaed9
DOUBLE PRECISION
for
dlaed9
Arrays, dimension (
k
) each. The first
k
elements of the array
dlamda
(*) contain the old roots of the deflated updating problem. These are the poles of the secular equation.
The first
k
elements of the array
w
(*) contain the components of the deflation-adjusted updating vector.
lds
INTEGER
. The leading dimension of the output array
s
;
lds
max(1,
k
)
.
Output Parameters
d
REAL
for
slaed9
DOUBLE PRECISION
for
dlaed9
Array, dimension (
n
). Elements in
d(i)
are not referenced for
1 ≤
i
<
kstart
or
kstop
<
i
n
.
s
REAL
for
slaed9
DOUBLE PRECISION
for
dlaed9
.
Array, dimension (
lds, *
) .
The second dimension of
s
must be at least
max(1,
k
)
. Will contain the eigenvectors of the repaired matrix which will be stored for subsequent
z
vector calculation and multiplied by the previously accumulated eigenvectors to update the system.
dlamda
On exit, the value is modified to make sure all
dlamda
(
i
) -
dlamda
(
j
)
can be computed with high relative accuracy, barring overflow and underflow.
w
Destroyed on exit.
info
INTEGER
.
If
info
= 0
, the execution is successful.