Contents

# p?syevd

Computes all eigenvalues and eigenvectors of a real symmetric matrix by using a divide and conquer algorithm.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?syevd
function
computes all eigenvalues and eigenvectors of a real symmetric matrix
A
by using a divide and conquer algorithm.
Input Parameters
np
= the number of rows local to a given process.
nq
= the number of columns local to a given process.
jobz
(global) Must be
'N'
or
'V'
.
Specifies if it is necessary to compute the eigenvectors:
If
jobz
=
'N'
, then only eigenvalues are computed.
If
jobz
=
'V'
, then eigenvalues and eigenvectors are computed.
uplo
(global) Must be
'U'
or
'L'
.
Specifies whether the upper or lower triangular part of the Hermitian matrix
A
is stored:
If
uplo
=
'U'
,
a
stores the upper triangular part of
A
.
If
uplo
=
'L'
,
a
stores the lower triangular part of
A
.
n
(global) The number of rows and columns of the matrix
A
(
n
0)
.
a
(local).
Block cyclic array of global size
n
*
n
and local size
lld_a
*
LOC
c
(
ja
+
n
-1)
. On entry, the symmetric matrix
A
.
If
uplo
=
'U'
, only the upper triangular part of
A
is used to define the elements of the symmetric matrix.
If
uplo
=
'L'
, only the lower triangular part of
A
is used to define the elements of the symmetric matrix.
ia
,
ja
(global) The row and column indices in the global matrix
A
indicating the first row and the first column of the submatrix
A
, respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
. If
desca
[
ctxt_
- 1]
is incorrect,
p?syevd
cannot guarantee correct error reporting.
iz
,
jz
(global) The row and column indices in the global matrix
Z
indicating the first row and the first column of the submatrix
Z
, respectively.
descz
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
Z
.
descz
[
ctxt_
- 1]
must equal
desca
[
ctxt_
- 1]
.
work
(local).
Array of size
lwork
.
lwork
(local) The size of the array
work
.
If eigenvalues are requested:
lwork
max( 1+6*
n
+ 2*
np
*
nq
,
trilwmin
) + 2*
n
with
trilwmin
= 3*
n
+ max(
nb
*(
np
+ 1), 3*
nb
)
np
=
numroc
(
n
,
nb
,
myrow
,
iarow
,
NPROW
)
nq
=
numroc
(
n
,
nb
,
mycol
,
iacol
,
NPCOL
)
If
lwork
= -1
, then
lwork
is global input and a workspace query is assumed; the
function
only calculates the size required for optimal performance for all work arrays. The required workspace is returned as the first element of the corresponding work arrays, and no error message is issued by
pxerbla
.
iwork
(local) Workspace array of size
liwork
.
liwork
(local) , size of
iwork
.
liwork
= 7*
n
+ 8*
npcol
+ 2
.
Output Parameters
a
On exit, the lower triangle (if
uplo
=
'L'
), or the upper triangle (if
uplo
=
'U'
) of
A
, including the diagonal, is overwritten.
w
(global).
Array of size
n
. If
info
= 0
,
w
contains the eigenvalues in the ascending order.
z
(local).
Array, global size (
n
,
n
), local size
lld_z
*
LOCc
(
jz
+
n
-1)
.
The
z
parameter contains the orthonormal eigenvectors of the matrix
A
.
work

On exit, returns adequate workspace to allow optimal performance.
iwork

(local).
On exit, if
liwork
> 0,
iwork

returns the optimal
liwork
.
info
(global)
If
info
= 0
, the execution is successful.
If
info
< 0
:
If the
i
-th argument is an array and the
j
-entry had an illegal value, then
info
= -(
i
*100+
j
)
. If the
i
-th argument is a scalar and had an illegal value, then
info
= -
i
.
If
info
>
0
:
The algorithm failed to compute the
info
/(
n
+1)
-th eigenvalue while working on the submatrix lying in global rows and columns
mod(
info
,
n
+1).
mod(
x
,
y
)
is the integer remainder of
x
/
y
.

#### Product and Performance Information

1

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