-
template<typename T>
void hetrd_he2hb(char *uplo, integer *n, integer *kd, T *a, integer *lda, T *ab, integer *ldab, T *tau, T *work, integer *lwork, integer *info)# HETRD_HE2HB reduces a complex Hermitian matrix A to complex Hermitian band-diagonal form AB.
Purpose:
HETRD_HE2HB reduces a complex Hermitian matrix A to complex Hermitian band-diagonal form AB by a unitary similarity transformation: Q**H * A * Q = AB.
- Parameters:
UPLO – [in]
UPLO is CHARACTER*1
= ‘U’: Upper triangle of A is stored;
= ‘L’: Lower triangle of A is stored.N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
KD – [in]
KD is INTEGER
The number of superdiagonals of the reduced matrix if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0. The reduced matrix is stored in the array AB.
A – [inout]
A is COMPLEX 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 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.
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 unitary matrix Q as a product of elementary reflectors; if UPLO = ‘L’, the diagonal and first subdiagonal of A are over- 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 – [in]
LDA is INTEGER
The leading dimension of the array A. LDA >= fla_max(1,N).
AB – [out]
AB is COMPLEX array, dimension (LDAB,N)
On exit, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
if UPLO = ‘U’, AB(kd+1+i-j,j) = A(i,j) for fla_max(1,j-kd)<=i<=j;
if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB – [in]
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
TAU – [out]
TAU is COMPLEX array, dimension (N-KD)
The scalar factors of the elementary reflectors (see Further Details).
WORK – [out]
WORK is COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, or if LWORK=-1, WORK(1) returns the size of LWORK.
LWORK – [in]
LWORK is INTEGER
The dimension of the array WORK which should be calculated by a workspace query. LWORK = MAX(1, LWORK_QUERY)
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.
LWORK_QUERY = N*KD + N*max(KD,FACTOPTNB) + 2*KD*KD
where FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice otherwise putting LWORK=-1 will provide the size of WORK.INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value