## Developer Reference

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

# p?sygst

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

## Syntax

Include Files
Description
The
p?sygst
routine
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)
INTEGER
.
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)
CHARACTER
.
Must be
'U'
or
'L'
.
If
uplo
=
'U'
, the upper triangle of sub(
A
) is stored and sub (
B
) is factored as
U