Developer Reference

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

?lar1v

Computes the (scaled)
r
-th column of the inverse of the submatrix in rows
b1
through
bn
of tridiagonal matrix.

Syntax

call slar1v
(
n
,
b1
,
bn
,
lambda
,
d
,
l
,
ld
,
lld
,
pivmin
,
gaptol
,
z
,
wantnc
,
negcnt
,
ztz
,
mingma
,
r
,
isuppz
,
nrminv
,
resid
,
rqcorr
,
work
)
call dlar1v
(
n
,
b1
,
bn
,
lambda
,
d
,
l
,
ld
,
lld
,
pivmin
,
gaptol
,
z
,
wantnc
,
negcnt
,
ztz
,
mingma
,
r
,
isuppz
,
nrminv
,
resid
,
rqcorr
,
work
)
call clar1v
(
n
,
b1
,
bn
,
lambda
,
d
,
l
,
ld
,
lld
,
pivmin
,
gaptol
,
z
,
wantnc
,
negcnt
,
ztz
,
mingma
,
r
,
isuppz
,
nrminv
,
resid
,
rqcorr
,
work
)
call zlar1v
(
n
,
b1
,
bn
,
lambda
,
d
,
l
,
ld
,
lld
,
pivmin
,
gaptol
,
z
,
wantnc
,
negcnt
,
ztz
,
mingma
,
r
,
isuppz
,
nrminv
,
resid
,
rqcorr
,
work
)
Include Files
  • mkl.fi
Description
The routine
?lar1v
computes the (scaled)
r
-th column of the inverse of the submatrix in rows
b1
through
bn
of the tridiagonal matrix
L*D*L
T
-
λ
*
I
. When
λ
is close to an eigenvalue, the computed vector is an accurate eigenvector. Usually,
r
corresponds to the index where the eigenvector is largest in magnitude.
The following steps accomplish this computation :
  • Stationary
    qd
    transform,
    L*D*L
    T
    -
    λ
    *
    I
    =
    L(+)
    *
    D(+)
    *
    L(+)
    T
  • Progressive
    qd
    transform,
    L*D*L
    T
    -
    λ
    *
    I
    =
    U(-)
    *
    D(-)
    *
    U(-)
    T
    ,
  • Computation of the diagonal elements of the inverse of
    L*D*L
    T
    -
    λ
    *
    I
    by combining the above transforms, and choosing
    r
    as the index where the diagonal of the inverse is (one of the) largest in magnitude.
  • Computation of the (scaled)
    r
    -th column of the inverse using the twisted factorization obtained by combining the top part of the stationary and the bottom part of the progressive transform.
Input Parameters
n
INTEGER
. The order of the matrix
L*D*L