Contents

# p?sygst

Reduces a real symmetric-definite generalized eigenvalue problem to the standard form.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?sygst
function
reduces real symmetric-definite generalized eigenproblems to the standard form.
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
=
λ*
sub(
B
)*
x
,
and sub(
A
) is overwritten by inv(
U
T
)*sub(
A
)*inv(
U
), or inv(
L
)*sub(
A
)*inv(
L
T
).
If
ibtype
= 2
or 3, the problem is
sub(
A
)*sub(
B
)*
x
=
λ*
x
, or sub(
B
)*sub(
A
)*
x
=
λ*
x
,
and sub(
A
) is overwritten by
U
*sub(
A
)*
U
T
, or
L
T
*sub(
A
)
*L
.
sub(
B
) must have been previously factorized as
U
T
*U
or
L*L
T
by
p?potrf
.
Input Parameters
ibtype
(global) Must be 1 or 2 or 3.
If
itype
= 1
, compute inv(
U
T
)*sub(
A
)*inv(
U
), or inv(
L
)*sub(
A
)*inv(
L
T
);
If
itype
= 2 or 3
, compute
U
*sub(
A
)*
U
T
, or
L
T
*sub(
A
)*
L
.
uplo
(global) Must be
'U'
or
'L'
.
If
uplo
=
'U'
, the upper triangle of sub(
A
) is stored and sub (
B
) is factored as
U
T
*U
.
If
uplo
=
'L'
, the lower triangle of sub(
A
) is stored and sub (
B
) is factored as
L*L
T
.
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, the array contains the local pieces of the
n
-by-
n
symmetric distributed matrix sub(
A
).
If
uplo
=
'U'
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
=
'L'
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
,
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
.
b
(local)
Pointer into the local memory to an array of size
lld_b
*
LOCc
(
jb
+
n
-1)
. On entry, the array contains the local pieces of the triangular factor from the Cholesky factorization of sub (
B
) as returned by
p?potrf
.
ib
,
jb
(global) The row and column indices in the global matrix
B
indicating the first row and the first column of the submatrix
B
, respectively.
descb
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix B.
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
function
. At present,
scale
is always returned as 1.0, it is returned here to allow for future enhancement.
info
(global)
If
info
= 0, the execution is successful. If
info
< 0
, if the
i
-th argument is an array and the
j-
th entry
, indexed
j
- 1,
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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804