chetrd - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
SUBROUTINE CHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER * 1 UPLO COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER N, LDA, LWORK, INFO REAL D(*), E(*)
SUBROUTINE CHETRD_64( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER * 1 UPLO COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER*8 N, LDA, LWORK, INFO REAL D(*), E(*)
SUBROUTINE HETRD( UPLO, [N], A, [LDA], D, E, TAU, [WORK], [LWORK], * [INFO]) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: TAU, WORK COMPLEX, DIMENSION(:,:) :: A INTEGER :: N, LDA, LWORK, INFO REAL, DIMENSION(:) :: D, E
SUBROUTINE HETRD_64( UPLO, [N], A, [LDA], D, E, TAU, [WORK], [LWORK], * [INFO]) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: TAU, WORK COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, LWORK, INFO REAL, DIMENSION(:) :: D, E
#include <sunperf.h>
void chetrd(char uplo, int n, complex *a, int lda, float *d, float *e, complex *tau, int *info);
void chetrd_64(char uplo, long n, complex *a, long lda, float *d, float *e, complex *tau, long *info);
chetrd reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
D(i)
= A(i,i).
E(i)
= A(i,i+1)
if UPLO = 'U', E(i)
= A(i+1,i)
if UPLO = 'L'.
WORK(1)
returns the optimal LWORK.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
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'
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'
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).