zhetd2 - reduce a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm)
SUBROUTINE ZHETD2(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER*1 UPLO INTEGER INFO, LDA, N DOUBLE PRECISION D(*), E(*) DOUBLE COMPLEX A(LDA,*), TAU(*) SUBROUTINE ZHETD2_64(UPLO, N, A, LDA, D, E, TAU, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, LDA, N DOUBLE PRECISION D(*), E(*) DOUBLE COMPLEX A(LDA,*), TAU(*) F95 INTERFACE SUBROUTINE HETD2(UPLO, N, A, LDA, D, E, TAU, INFO) INTEGER :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: TAU REAL(8), DIMENSION(:) :: D, E COMPLEX(8), DIMENSION(:,:) :: A SUBROUTINE HETD2_64(UPLO, N, A, LDA, D, E, TAU, INFO) INTEGER(8) :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: TAU REAL(8), DIMENSION(:) :: D, E COMPLEX(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void zhetd2 (char uplo, int n, doublecomplex *a, int lda, double *d, double *e, doublecomplex *tau, int *info); void zhetd2_64 (char uplo, long n, doublecomplex *a, long lda, double *d, double *e, doublecomplex *tau, long *info);
Oracle Solaris Studio Performance Library zhetd2(3P)
NAME
zhetd2 - reduce a Hermitian matrix to real symmetric tridiagonal form
by an unitary similarity transformation (unblocked algorithm)
SYNOPSIS
SUBROUTINE ZHETD2(UPLO, N, A, LDA, D, E, TAU, INFO)
CHARACTER*1 UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION D(*), E(*)
DOUBLE COMPLEX A(LDA,*), TAU(*)
SUBROUTINE ZHETD2_64(UPLO, N, A, LDA, D, E, TAU, INFO)
CHARACTER*1 UPLO
INTEGER*8 INFO, LDA, N
DOUBLE PRECISION D(*), E(*)
DOUBLE COMPLEX A(LDA,*), TAU(*)
F95 INTERFACE
SUBROUTINE HETD2(UPLO, N, A, LDA, D, E, TAU, INFO)
INTEGER :: N, LDA, INFO
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: TAU
REAL(8), DIMENSION(:) :: D, E
COMPLEX(8), DIMENSION(:,:) :: A
SUBROUTINE HETD2_64(UPLO, N, A, LDA, D, E, TAU, INFO)
INTEGER(8) :: N, LDA, INFO
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: TAU
REAL(8), DIMENSION(:) :: D, E
COMPLEX(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void zhetd2 (char uplo, int n, doublecomplex *a, int lda, double *d,
double *e, doublecomplex *tau, int *info);
void zhetd2_64 (char uplo, long n, doublecomplex *a, long lda, double
*d, double *e, doublecomplex *tau, long *info);
PURPOSE
zhetd2 reduces a complex Hermitian matrix A to real symmetric tridiago-
nal form T by a unitary similarity transformation: Q**H*A*Q=T.
ARGUMENTS
UPLO (input)
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular,
= 'L': Lower triangular.
N (input)
N is INTEGER
The order of the matrix A. N >= 0.
A (input/output)
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper triangu-
lar 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.
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 super-
diagonal, with the array TAU, represent the unitary matrix Q
as a product of elementary reflectors; if UPLO='L', the diag-
onal and first subdiagonal of A are overwritten written by
the corresponding elements of the tridiagonal matrix T, and
the elements below the first subdiagonal, with the array TAU,
represent the unitary matrix Q as a product of elementary
reflectors. See Further Details.
LDA (input)
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
D (output)
D is DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i)=A(i,i).
E (output)
E is DOUBLE PRECISION array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i)=A(i,i+1) if UPLO = 'U', E(i)=A(i+1,i) if UPLO = 'L'.
TAU (output)
TAU is COMPLEX*16 array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
INFO (output)
INFO is INTEGER
= 0: successful exit,
< 0: if INFO = -i, the i-th argument had an illegal value.
FURTHER DETAILS
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v**H
where tau is a complex scalar, and v is a complex vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v**H
where tau is a complex scalar, and v is a complex vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
7 Nov 2015 zhetd2(3P)