Developer Reference

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

?hptrd

Reduces a complex Hermitian matrix to tridiagonal form using packed storage.

Syntax

call chptrd
(
uplo
,
n
,
ap
,
d
,
e
,
tau
,
info
)
call zhptrd
(
uplo
,
n
,
ap
,
d
,
e
,
tau
,
info
)
call hptrd
(
ap
,
tau
[
,
uplo
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine reduces a packed complex Hermitian matrix
A
to symmetric tridiagonal form
T
by a unitary similarity transformation:
A
=
Q*T*Q
H
. The unitary matrix
Q
is not formed explicitly but is represented as a product of
n
-1 elementary reflectors. Routines are provided for working with
Q
in this representation (see
Application Notes
below).
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
If
uplo
=
'U'
,
ap
stores the packed upper triangle of
A
.
If
uplo
=
'L'
,
ap
stores the packed lower triangle of
A
.
n
INTEGER
.
The order of the matrix
A
(
n
0
).
ap
COMPLEX
for
chptrd
DOUBLE COMPLEX
for
zhptrd
.
Array, size at least max(1,
n
(
n
+1)/2). Contains either upper or lower triangle of
A
(as specified by
uplo
) in the packed form described in "Matrix Storage Schemes.
Output Parameters
ap
Overwritten by the tridiagonal matrix
T
and details of the unitary matrix
Q
, as specified by
uplo
.
d
,
e
REAL
for
chptrd
DOUBLE PRECISION
for
zhptrd
.
Arrays:
d
(*)
contains the diagonal elements of the matrix
T
.
The size of
d
must be at least max(1,
n
).
e
(*)
contains the off-diagonal elements of
T
.
The size of
e
must be at least max(1,
n
-1).
tau
COMPLEX
for
chptrd
DOUBLE COMPLEX
for
zhptrd
.
Array, size at least max(1,
n
-1). Stores (
n
-1) scalars that define elementary reflectors in decomposition of the unitary matrix
Q
in a product of reflectors.
info
INTEGER
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, the
i-
th parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine
hptrd
interface are the following:
ap
Holds the array
A
of size (
n*(n+1)/2
).
tau
Holds the vector with the number of elements
n
- 1.
uplo
Must be
'U'
or
'L'
. The default value is
'U'
.
Note that diagonal (
d
) and off-diagonal (
e
) elements of the matrix