Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?sytrd

Reduces a real symmetric matrix to tridiagonal form.

Syntax

lapack_int
LAPACKE_ssytrd
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
float
*
d
,
float
*
e
,
float
*
tau
);
lapack_int
LAPACKE_dsytrd
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
double
*
d
,
double
*
e
,
double
*
tau
);
Include Files
  • mkl.h
Description
The routine reduces a real symmetric matrix
A
 to symmetric tridiagonal form
T
 by an orthogonal similarity transformation:
A
 =
Q*T*Q
T
. The orthogonal 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'
,
a
 stores the upper triangular part of
A
.
If
uplo
 =
'L'
,
a
 stores the lower triangular part of
A
.
n
The order of the matrix
A
 (
n
≥
 0
).
a
a
(size max(1,
lda
*
n
))
 is an array containing either upper or lower triangular part of the matrix
A
, as specified by
uplo
. If
uplo
 =
'U'
, the leading
n
-by-
n
 upper triangular part of
a
 contains the upper triangular part of the matrix
A
, and the strictly lower triangular part of
A
 is not referenced. If
uplo
 =
'L'
, the leading
n
-by-
n
 lower triangular part of
a
 contains the lower triangular part of the matrix
A
, and the strictly upper triangular part of
A
 is not referenced.
lda
The leading dimension of
a
; at least max(1,
n
).
Output Parameters
a
On exit,
if
uplo
 =
'U'
, the diagonal and first superdiagonal of
A
 are overwritten by the corresponding elements of the tridiagonal matrix
T
, and the elements above the first superdiagonal, with the array
tau
, represent the orthogonal matrix
Q
 as a product of elementary reflectors;
if
uplo
 =
'L'
, the diagonal and first subdiagonal of
A
 are overwritten by the corresponding elements of the tridiagonal matrix
T
, and the elements below the first subdiagonal, with the array
tau
, represent the orthogonal matrix
Q
 as a product of elementary reflectors.
d
,
e
,
tau
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
 stores (
n
-1) scalars that define elementary reflectors in decomposition of the orthogonal matrix
Q
 in a product of
n
-1
 elementary reflectors.
tau
(
n
) is used as workspace.
The size of
tau
 must be at least max(1,
n
).
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 (4/3)
n
3
.
After calling this routine, you can call the following:
to form the computed matrix
Q
 explicitly
to multiply a real matrix by
Q
.
The complex counterpart of this routine is ?hetrd.

Product and Performance Information

1

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