Contents

# p?trevc

Computes right and/or left eigenvectors of a complex upper triangular matrix in parallel.

## Syntax

Include Files
• mkl_scalapack.h
Description
p?trevc
computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix
T
in parallel.
The right eigenvector x and the left eigenvector y of
T
corresponding to an eigenvalue w are defined by:
T
*x = w*x,
y'*
T
= w*y'
where y' denotes the conjugate transpose of the vector y.
If all eigenvectors are requested, the routine may either return the matrices
X
and/or
Y
of right or left eigenvectors of
T
, or the products
Q
*
X
and/or
Q
*
Y
, where
Q
is an input unitary matrix. If
T
was obtained from the Schur factorization of an original matrix
A
=
Q
*
T
*Q', then
Q
*
X
and
Q
*
Y
are the matrices of right or left eigenvectors of
A
.
Input Parameters
side
(global)
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
howmny
(global)
= 'A': compute all right and/or left eigenvectors;
= 'B': compute all right and/or left eigenvectors, and backtransform them using the input matrices supplied in
vr
and/or
vl
;
= 'S': compute selected right and/or left eigenvectors, specified by the logical array
select
.
select
(global)
Array, size (
n
)
If
howmny
= 'S',
select
specifies the eigenvectors to be computed.
If
howmny
= 'A' or 'B',
select
is not referenced. To select the eigenvector corresponding to the
j
-th eigenvalue,
select
[
j
- 1]
must be set to
non-zero
.
n
(global)
The order of the matrix
T
.
n
>= 0.
t
(local)
Array, size
lld_t
*
LOCc
(
n
)
.
The upper triangular matrix
T
.
T
is modified, but restored on exit.
desct
(global and local)
Array of size
dlen_
.
The array descriptor for the distributed matrix
T
.
vl
(local)
Array, size (
descvl
(
lld_
),
mm
)
On entry, if
side
= 'L' or 'B' and
howmny
= 'B',
vl
must contain an
n
-by-
n
matrix
Q
(usually the unitary matrix
Q
of Schur vectors returned by
?hseqr
).
descvl
(global and local)
Array of size
dlen_
.
The array descriptor for the distributed matrix
VL
.
vr
(local)
Array, size
descvr
(
lld_
)*
mm
.
On entry, if
side
= 'R' or 'B' and
howmny
= 'B',
vr
must contain an
n
-by-
n
matrix
Q
(usually the unitary matrix
Q
of Schur vectors returned by
?hseqr
).
descvr
(global and local)
Array of size
dlen_
.
The array descriptor for the distributed matrix
VR
.
mm
(global)
The number of columns in the arrays
vl
and/or
vr
.
mm
>=
m
.
work
(local)
Array, size ( 2*
desct
(
lld_
) )
Additional workspace may be required if
p?lattrs
is updated to use
work
.
rwork
Array, size (
desct
(
lld_
) )
Output Parameters
t
The upper triangular matrix
T
.
T
is modified, but restored on exit.
vl
On exit, if
side
= 'L' or 'B',
vl
contains:
if
howmny
= 'A', the matrix
Y
of left eigenvectors of
T
;
if
howmny
= 'B', the matrix
Q
*
Y
;
if
howmny
= 'S', the left eigenvectors of
T
specified by
select
, stored consecutively in the columns of
vl
, in the same order as their eigenvalues. If
side
= 'R',
vl
is not referenced.
vr
On exit, if
side
= 'R' or 'B',
vr
contains:
if
howmny
= 'A', the matrix
X
of right eigenvectors of
T
;
if
howmny
= 'B', the matrix
Q
*
X
;
if
howmny
= 'S', the right eigenvectors of
T
specified by
select
, stored consecutively in the columns of
vr
, in the same order as their eigenvalues. If
side
= 'L',
vr
is not referenced.
m
(global)
The number of columns in the arrays
vl
and/or
vr
actually used to store the eigenvectors. If
howmny
= 'A' or 'B',
m
is set to
n
. Each selected eigenvector occupies one column.
info
(global)
= 0: successful exit
< 0: if
info
= -i, the i-th argument had an illegal value
Application Notes
The algorithm used in this program is basically backward (forward) substitution. Scaling should be used to make the code robust against possible overflow. But scaling has not yet been implemented in
p?lattrs
which is called by this routine to solve the triangular systems.
p?lattrs
just calls
p?trsv
.
Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|.

#### Product and Performance Information

1

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