## Developer Reference

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

# p?hentrd

Reduces a complex Hermitian matrix
to Hermitian tridiagonal form.

## Syntax

Description
p?hentrd
is a prototype version of
p?hetrd
which uses tailored codes (either the serial,
?hetrd
, or the parallel code,
p?hettrd
) when adequate workspace is provided.
p?hentrd
reduces a complex Hermitian matrix sub(
A
) to Hermitian tridiagonal form
T
by an unitary similarity transformation:
Q
' * sub(
A
) *
Q
=
T
, where sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1).
p?hentrd
is faster than
p?hetrd
on almost all matrices, particularly small ones (i.e.
n
< 500 * sqrt(P) ), provided that enough workspace is available to use the tailored codes.
The tailored codes provide performance that is essentially independent of the input data layout.
The tailored codes place no restrictions on
ia
,
ja
, MB or NB. At present,
ia
,
ja
, MB and NB are restricted to those values allowed by
p?hetrd
Input Parameters
uplo
(global)
CHARACTER.
Specifies whether the upper or lower triangular part of the Hermitian matrix sub(
A
) is stored:
= 'U': Upper triangular
= 'L': Lower triangular
n
(global)
INTEGER.
The number of rows and columns to be operated on, i.e. the order of the distributed submatrix sub(
A
).
n
>= 0.
a
(local)
COMPLEX
for
pchentrd
DOUBLE COMPLEX
for
pzhentrd
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 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)
INTEGER.
The row index in the global array
a
indicating the first row of sub(
A
).
ja
(global)
INTEGER.
The column index in the global array
a
indicating the first column of sub(
A
).
desca
(global and local)
INTEGER.
Array of size
dlen_
.
The array descriptor for the distributed matrix
A
.
work
(local)
COMPLEX
for
pchentrd
DOUBLE COMPLEX
for
pzhentrd
Array, size (
lwork
)
lwork
(local or global)
INTEGER.
The size of the array
work
.
lwork
is local input and must be at least
lwork
>= MAX( NB * ( NP +1 ), 3 * NB ).
For optimal performance, greater workspace is needed:
lwork
>= 2*(
ANB
+1 )*( 4*
NPS
+2 ) + (
NPS
+ 4 ) *
NPS
ANB
=
pjlaenv
(
ICTXT
, 3, '
p?hettrd
', 'L', 0, 0, 0, 0 )
ICTXT
=
desca
(
ctxt_
)
SQNPC
= INT(
sqrt
( REAL(
NPROW
*
NPCOL
) ) )
NPS
= MAX(
numroc
(
n
, 1, 0, 0,
SQNPC
), 2*
ANB
)
numroc
is a ScaLAPACK tool function.