Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.