Contents

# p?syngst

Reduces a complex Hermitian-definite generalized eigenproblem to standard form.

## Syntax

Include Files
• mkl_scalapack.h
Description
p?syngst
reduces a complex Hermitian-definite generalized eigenproblem to standard form.
p?syngst
performs the same function as
p?hegst
, but is based on rank 2K updates, which are faster and more scalable than triangular solves (the basis of
p?syngst
).
p?syngst
calls
p?hegst
when
uplo
='U', hence
p?hengst
provides improved performance only when
uplo
='L',
ibtype
=1.
p?syngst
also calls
p?hegst
when insufficient workspace is provided, hence
p?syngst
provides improved performance only when
lwork
>= 2 * NP0 * NB + NQ0 * NB + NB * NB
In the following sub(
A
) denotes
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1 ) and sub(
B
) denotes
B
(
ib
:
ib
+
n
-1,
jb
:
jb
+
n
-1 ).
If
ibtype
= 1, the problem is sub(
A
)*x = lambda*sub(
B
)*x, and sub(
A
) is overwritten by inv(
U
H
)*sub(
A
)*inv(
U
) or inv(
L
)*sub(
A
)*inv(
L
H
)
If
ibtype
= 2 or 3, the problem is sub(
A
)*sub(
B
)*x = lambda*x or sub(
B
)*sub(
A
)*x = lambda*x, and sub(
A
) is overwritten by
U
*sub(
A
)*
U
H
or
L
H
*sub(
A
)*
L
.
sub(
B
) must have been previously factorized as
U
H
*
U
or
L
*
L
H
by
p?potrf
.
Input Parameters
ibtype
(global)
= 1: compute inv(
U
H
)*sub(
A
)*inv(
U
) or inv(
L
)*sub(
A
)*inv(
L
H
);
= 2 or 3: compute
U
*sub(
A
)*
U
H
or
L
H
*sub(
A
)*
L
.
uplo
(global)
= 'U': Upper triangle of sub(
A
) is stored and sub(
B
) is factored as
U
H
*
U
;
= 'L': Lower triangle of sub(
A
) is stored and sub(
B
) is factored as
L
*
L
H
.
n
(global)
The order of the matrices sub(
A
) and sub(
B
).
n
>= 0.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
n
-1)
.
On entry, this array contains the local pieces of the
n
-by-
n
Hermitian distributed matrix sub(
A
). If
uplo
n
-by-
n
upper triangular part of sub(
A
) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. If
uplo
n
-by-
n
lower triangular part of sub(
A
) contains the lower triangular part of the matrix, and its strictly upper triangular part is not referenced.
ia
(global)
A
's global row index, which points to the beginning of the submatrix which is to be operated on.
ja
(global)
A
's global column index, which points to the beginning of the submatrix which is to be operated on.
desca
(global and local)
Array of size
dlen_
.
The array descriptor for the distributed matrix
A
.
b
(local)
Pointer into the local memory to an array of size
lld_b
*
LOCc
(
jb
+
n
-1)
.
On entry, this array contains the local pieces of the triangular factor from the Cholesky factorization of sub(
B
), as returned by
p?potrf
.
ib
(global)
B
's global row index, which points to the beginning of the submatrix which is to be operated on.
jb
(global)
B
's global column index, which points to the beginning of the submatrix which is to be operated on.
descb
(global and local)
Array of size
dlen_
.
The array descriptor for the distributed matrix
B
.
work
(local)
Array, size (
lwork
)
lwork
(local or global)
The size of the array
work
.
lwork
is local input and must be at least
lwork
>= MAX( NB * ( NP0 +1 ), 3 * NB )
When
ibtype
= 1 and
uplo
= 'L',
p?syngst
provides improved performance when
lwork
>= 2 * NP0 * NB + NQ0 * NB + NB * NB,
where NB =
mb_a
=
nb_a
,
NP0 =
numroc
(
n
, NB, 0, 0, NPROW ),
NQ0 =
numroc
(
n
, NB, 0, 0, NPROW ),
numroc
is a ScaLAPACK tool functions
MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine
blacs_gridinfo
.
If
lwork
= -1, then
lwork
is global input and a workspace query is assumed; the routine only calculates the optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by
pxerbla
.
Output Parameters
a
On exit, if
info
= 0, the transformed matrix, stored in the same format as sub(
A
).
scale
(global)
Amount by which the eigenvalues should be scaled to compensate for the scaling performed in this routine. At present,
scale
is always returned as 1.0, it is returned here to allow for future enhancement.
work
(local)
Array, size (
lwork
)
On exit,
work

returns the minimal and optimal
lwork
.
info
(global)
= 0: successful exit
< 0: If the
i
-th argument is an array and the
j
-th 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
.

#### Product and Performance Information

1

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