?hetrd
?hetrd
Reduces a complex Hermitian matrix to tridiagonal form.
Syntax
lapack_int LAPACKE_chetrd
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float*
a
,
lapack_int
lda
,
float*
d
,
float*
e
,
lapack_complex_float*
tau
);
lapack_int LAPACKE_zhetrd
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double*
a
,
lapack_int
lda
,
double*
d
,
double*
e
,
lapack_complex_double*
tau
);
Include Files
- mkl.h
Description
The routine reduces a complex Hermitian matrix . The unitary matrix
A
to symmetric tridiagonal form T
by a unitary similarity transformation: A
= Q*T*Q
H
Q
is not formed explicitly but is represented as a product of n
-1 elementary reflectors. Routines are provided to work with Q
in this representation. (They are described later in this
topic
.)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'astores the upper triangular part ofA.If,uplo='L'astores the lower triangular part ofA.
- n
- The order of the matrixA().n≥0
- a
- a(size max(1,is an array containing either upper or lower triangular part of the matrixlda*n))A, as specified byuplo. If, the leadinguplo='U'n-by-nupper triangular part ofacontains the upper triangular part of the matrixA, and the strictly lower triangular part ofAis not referenced. If, the leadinguplo='L'n-by-nlower triangular part ofacontains the lower triangular part of the matrixA, and the strictly upper triangular part ofAis not referenced.
- lda
- The leading dimension ofa; at least max(1,n).
Output Parameters
- a
- On exit,if, the diagonal and first superdiagonal ofuplo='U'Aare overwritten by the corresponding elements of the tridiagonal matrixT, and the elements above the first superdiagonal, with the arraytau, represent the orthogonal matrixQas a product of elementary reflectors;if, the diagonal and first subdiagonal ofuplo='L'Aare overwritten by the corresponding elements of the tridiagonal matrixT, and the elements below the first subdiagonal, with the arraytau, represent the orthogonal matrixQas a product of elementary reflectors.
- d,e
- Arrays:dcontains the diagonal elements of the matrixT.The dimension ofdmust be at least max(1,n).econtains the off-diagonal elements ofT.The dimension ofemust 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 matrixQin a product ofn-1 elementary reflectors.
Return Values
This function returns a value
info
.If , the execution is successful.
info
=0If , the
info
= -i
i
-th parameter had an illegal value.Application Notes
The computed matrix
T
is exactly similar to a matrix A
+ E
, where ||
is a modestly increasing function of E
||2
= c
(n
)*ε
*||A
||2
, c
(n
)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:
The real counterpart of this routine is ?sytrd.