1ZHBTRD(1)                LAPACK routine (version 3.1)                ZHBTRD(1)
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NAME

6       ZHBTRD  - a complex Hermitian band matrix A to real symmetric tridiago‐
7       nal form T by a unitary similarity transformation
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SYNOPSIS

10       SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D,  E,  Q,  LDQ,  WORK,
11                          INFO )
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13           CHARACTER      UPLO, VECT
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15           INTEGER        INFO, KD, LDAB, LDQ, N
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17           DOUBLE         PRECISION D( * ), E( * )
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19           COMPLEX*16     AB( LDAB, * ), Q( LDQ, * ), WORK( * )
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PURPOSE

22       ZHBTRD  reduces  a  complex  Hermitian  band matrix A to real symmetric
23       tridiagonal form T by a unitary similarity transformation: Q**H * A * Q
24       = T.
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ARGUMENTS

28       VECT    (input) CHARACTER*1
29               = 'N':  do not form Q;
30               = 'V':  form Q;
31               = 'U':  update a matrix X, by forming X*Q.
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33       UPLO    (input) CHARACTER*1
34               = 'U':  Upper triangle of A is stored;
35               = 'L':  Lower triangle of A is stored.
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37       N       (input) INTEGER
38               The order of the matrix A.  N >= 0.
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40       KD      (input) INTEGER
41               The  number of superdiagonals of the matrix A if UPLO = 'U', or
42               the number of subdiagonals if UPLO = 'L'.  KD >= 0.
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44       AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
45               On entry, the upper or lower triangle  of  the  Hermitian  band
46               matrix A, stored in the first KD+1 rows of the array.  The j-th
47               column of A is stored in the j-th column of  the  array  AB  as
48               follows:  if  UPLO  = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
49               kd)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
50               j<=i<=min(n,j+kd).   On  exit,  the diagonal elements of AB are
51               overwritten by the diagonal elements of the tridiagonal  matrix
52               T;  if KD > 0, the elements on the first superdiagonal (if UPLO
53               = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten
54               by  the off-diagonal elements of T; the rest of AB is overwrit‐
55               ten by values generated during the reduction.
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57       LDAB    (input) INTEGER
58               The leading dimension of the array AB.  LDAB >= KD+1.
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60       D       (output) DOUBLE PRECISION array, dimension (N)
61               The diagonal elements of the tridiagonal matrix T.
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63       E       (output) DOUBLE PRECISION array, dimension (N-1)
64               The off-diagonal elements of the tridiagonal matrix T:  E(i)  =
65               T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
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67       Q       (input/output) COMPLEX*16 array, dimension (LDQ,N)
68               On  entry,  if VECT = 'U', then Q must contain an N-by-N matrix
69               X; if VECT = 'N' or 'V', then Q need not be set.
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71               On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q;
72               if  VECT  = 'U', Q contains the product X*Q; if VECT = 'N', the
73               array Q is not referenced.
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75       LDQ     (input) INTEGER
76               The leading dimension of the array Q.  LDQ >= 1, and LDQ  >=  N
77               if VECT = 'V' or 'U'.
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79       WORK    (workspace) COMPLEX*16 array, dimension (N)
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81       INFO    (output) INTEGER
82               = 0:  successful exit
83               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

86       Modified by Linda Kaufman, Bell Labs.
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91 LAPACK routine (version 3.1)    November 2006                       ZHBTRD(1)