Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?hptrd

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

Syntax

lapack_int LAPACKE_chptrd
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float*
ap
,
float*
d
,
float*
e
,
lapack_complex_float*
tau
);
lapack_int LAPACKE_zhptrd
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double*
ap
,
double*
d
,
double*
e
,
lapack_complex_double*
tau
);
Include Files
  • mkl.h
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
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
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
The order of the matrix
A
(
n
0
).
ap
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
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
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.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
Application Notes
The computed matrix
T
is exactly similar to a matrix
A
+
E
, where
||
E
||
2
=
c
(
n
)*
ε
*||
A
||
2
,
c
(
n
)
is a modestly increasing function of
n
, and
ε
is the machine precision.
The approximate number of floating-point operations is
(16/3)
n
3
.
After calling this routine, you can call the following:
to form the computed matrix
Q
explicitly
to multiply a complex matrix by
Q
.
The real counterpart of this routine is sptrd.

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