Developer Reference

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

?laic1

Applies one step of incremental condition estimation.

Syntax

call slaic1
(
job
,
j
,
x
,
sest
,
w
,
gamma
,
sestpr
,
s
,
c
)
call dlaic1
(
job
,
j
,
x
,
sest
,
w
,
gamma
,
sestpr
,
s
,
c
)
call claic1
(
job
,
j
,
x
,
sest
,
w
,
gamma
,
sestpr
,
s
,
c
)
call zlaic1
(
job
,
j
,
x
,
sest
,
w
,
gamma
,
sestpr
,
s
,
c
)
Include Files
  • mkl.fi
Description
The routine
?laic1
applies one step of incremental condition estimation in its simplest version.
Let
x
,
||
x
||
2
= 1
(where
||
a
||
2
denotes the 2-norm of
a
), be an approximate singular vector of an
j
-by-
j
lower triangular matrix
L
, such that
||
L
*
x
||
2
=
sest
Then
?laic1
computes
sestpr
,
s
,
c
such that the vector
Equation
is an approximate singular vector of
Equation (for complex flavors), or
Equation (for real flavors), in the sense that
||
Lhat
*
xhat
||
2
=
sestpr
.
Depending on
job
, an estimate for the largest or smallest singular value is computed.
For real flavors,
[
s
c
]
T
and
sestpr
2
is an eigenpair of the system
Equation
where
alpha
=
x
T
*
w
.
For complex flavors,
[
s
c
]
H
and
sestpr
2
is an eigenpair of the system
Equation
where
alpha
=
x
H
*
w
.
Input Parameters
job
INTEGER
.
If
job
=1
, an estimate for the largest singular value is computed;
If
job
=2
, an estimate for the smallest singular value is computed;
j
INTEGER
. Length of
x
and
w
.
x
,
w
REAL
for
slaic1
DOUBLE PRECISION
for
dlaic1
COMPLEX
for
claic1
DOUBLE COMPLEX
for
zlaic1
.