Contents

# ?lasd8

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
?lasd8
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.
?lasd8
is called from
?lasd6
.
Input Parameters
icompq
Specifies whether singular vectors are to be computed in factored form in the calling routine:
= 0: Compute singular values only.
= 1: Compute singular vectors in factored form as well.
k
The number of terms in the rational function to be solved by
?lasd4
.
k
1
.
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
dbede8
.
vl
Array,
DIMENSION
(
k
). On entry,
vl
contains information passed through
dbede8
.
lddifr
The leading dimension of the output array
difr
, must be at least
k
.
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.
work
Workspace array,
DIMENSION
at least (3
k
).
Output Parameters
d
Array,
DIMENSION
(
k
).
On output,
D
contains the updated singular values.
z
Updated on exit.
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
(
lddifr
, 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.
dsigma
The elements of this array may be very slightly altered in value.
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.