Contents

# ?lasd9

Finds the square roots of the roots of the secular equation, and stores, for each element in
D
, the distance to its two nearest poles. Used by
?bdsdc
.

## Syntax

Include Files
• mkl.h
Description
The routine
?lasd9
finds the square roots of the roots of the secular equation, as defined by the values in
dsigma
and
z
. It makes the appropriate calls to
?lasd4
, and stores, for each element in
d
, the distance to its two nearest poles (elements in
dsigma
). It also updates the arrays
vf
and
vl
, the first and last components of all the right singular vectors of the original bidiagonal matrix.
?lasd9
is called from
?lasd7
.
Input Parameters
icompq
Specifies whether singular vectors are to be computed in factored form in the calling routine:
If
icompq
= 0
, compute singular values only;
If
icompq
= 1
, compute singular vector matrices in factored form also.
k
The number of terms in the rational function to be solved by
slasd4
.
k
1
.
dsigma
Array,
DIMENSION
(
k
).
The first
k
elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation.
z
Array,
DIMENSION
(
k
). The first
k
elements of this array contain the components of the deflation-adjusted updating row vector.
vf
Array,
DIMENSION
(
k
). On entry,
vf
contains information passed through
sbede8
.
vl
Array,
DIMENSION
(
k
). On entry,
vl
contains information passed through
sbede8
.
work
Workspace array,
DIMENSION
at least (3
k
).
Output Parameters
d
Array,
DIMENSION
(
k
).
d
(
i
) contains the updated singular values.
vf
On exit,
vf
contains the first
k
components of the first components of all right singular vectors of the bidiagonal matrix.
vl
On exit,
vl
contains the first
k
components of the last components of all right singular vectors of the bidiagonal matrix.
difl
Array,
DIMENSION
(
k
).
On exit,
difl
(
i
) =
d
(
i
) -
dsigma
(
i
)
.
difr
Array,
DIMENSION
(
ldu
, 2) if
icompq
=1
and
DIMENSION
(
k
) if
icompq
= 0
.
On exit,
difr
(
i
, 1) =
d
(
i
) -
dsigma
(
i
+1)
,
difr
(
k
, 1) is not defined and will not be referenced.
If
icompq
= 1
,
difr
(1:
k
, 2)
is an array containing the normalizing factors for the right singular vector matrix.
info
= 0: successful exit.
< 0: if
info
= -
i
, the
i
-th argument had an illegal value.
> 0: If
info
= 1
, an singular value did not converge

#### Product and Performance Information

1

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