CHBTRD - reduce a complex Hermitian band matrix A to real
symmetric tridiagonal form T by a unitary similarity
transformation
SYNOPSIS
SUBROUTINE CHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q,
LDQ, WORK, INFO )
CHARACTER UPLO, VECT
INTEGER INFO, KD, LDAB, LDQ, N
REAL D( * ), E( * )
COMPLEX AB( LDAB, * ), Q( LDQ, * ), WORK( * )
PURPOSE
CHBTRD reduces a complex Hermitian band matrix A to real
symmetric tridiagonal form T by a unitary similarity
transformation: Q**H * A * Q = T.
ARGUMENTS
VECT (input) CHARACTER*1
= 'N': do not form Q;
= 'V': form Q;
= 'U': update a matrix X, by forming X*Q.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KD >= 0.
AB (input/output) COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the Her
mitian 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 max(1,j-
kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j)
for j<=i<=min(n,j+kd). On exit, the diagonal ele
ments of AB are overwritten by the diagonal ele
ments of the tridiagonal matrix T; if KD > 0, the
elements on the first superdiagonal (if UPLO =
'U') or the first subdiagonal (if UPLO = 'L') are
overwritten by the off-diagonal elements of T; the
ing the reduction.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >=
KD+1.
D (output) REAL array, dimension (N)
The diagonal elements of the tridiagonal matrix T.
E (output) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal
matrix T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) =
T(i+1,i) if UPLO = 'L'.
Q (input/output) COMPLEX array, dimension (LDQ,N)
On entry, if VECT = 'U', then Q must contain an N-
by-N matrix X; if VECT = 'N' or 'V', then Q need
not be set.
On exit: if VECT = 'V', Q contains the N-by-N uni
tary matrix Q; if VECT = 'U', Q contains the prod
uct X*Q; if VECT = 'N', the array Q is not refer
enced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= 1,
and LDQ >= N if VECT = 'V' or 'U'.
WORK (workspace) COMPLEX array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
FURTHER DETAILS
Modified by Linda Kaufman, Bell Labs.
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