1ZHBGST(1)                LAPACK routine (version 3.2)                ZHBGST(1)
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NAME

6       ZHBGST - reduces a complex Hermitian-definite banded generalized eigen‐
7       problem A*x = lambda*B*x to standard form C*y = lambda*y,
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SYNOPSIS

10       SUBROUTINE ZHBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,  X,  LDX,
11                          WORK, RWORK, INFO )
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13           CHARACTER      UPLO, VECT
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15           INTEGER        INFO, KA, KB, LDAB, LDBB, LDX, N
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17           DOUBLE         PRECISION RWORK( * )
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19           COMPLEX*16     AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )
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PURPOSE

22       ZHBGST  reduces  a complex Hermitian-definite banded generalized eigen‐
23       problem  A*x = lambda*B*x  to standard form  C*y = lambda*y, such  that
24       C has the same bandwidth as A.
25       B  must  have  been  previously factorized as S**H*S by ZPBSTF, using a
26       split Cholesky factorization. A is overwritten by C = X**H*A*X, where X
27       =  S**(-1)*Q and Q is a unitary matrix chosen to preserve the bandwidth
28       of A.
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ARGUMENTS

31       VECT    (input) CHARACTER*1
32               = 'N':  do not form the transformation matrix X;
33               = 'V':  form X.
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35       UPLO    (input) CHARACTER*1
36               = 'U':  Upper triangle of A is stored;
37               = 'L':  Lower triangle of A is stored.
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39       N       (input) INTEGER
40               The order of the matrices A and B.  N >= 0.
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42       KA      (input) INTEGER
43               The number of superdiagonals of the matrix A if UPLO = 'U',  or
44               the number of subdiagonals if UPLO = 'L'.  KA >= 0.
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46       KB      (input) INTEGER
47               The  number of superdiagonals of the matrix B if UPLO = 'U', or
48               the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.
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50       AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
51               On entry, the upper or lower triangle  of  the  Hermitian  band
52               matrix A, stored in the first ka+1 rows of the array.  The j-th
53               column of A is stored in the j-th column of  the  array  AB  as
54               follows:  if  UPLO  = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-
55               ka)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
56               j<=i<=min(n,j+ka).   On  exit, the transformed matrix X**H*A*X,
57               stored in the same format as A.
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59       LDAB    (input) INTEGER
60               The leading dimension of the array AB.  LDAB >= KA+1.
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62       BB      (input) COMPLEX*16 array, dimension (LDBB,N)
63               The banded factor S from the split Cholesky factorization of B,
64               as  returned  by  ZPBSTF,  stored in the first kb+1 rows of the
65               array.
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67       LDBB    (input) INTEGER
68               The leading dimension of the array BB.  LDBB >= KB+1.
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70       X       (output) COMPLEX*16 array, dimension (LDX,N)
71               If VECT = 'V', the n-by-n matrix X.  If VECT = 'N', the array X
72               is not referenced.
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74       LDX     (input) INTEGER
75               The  leading dimension of the array X.  LDX >= max(1,N) if VECT
76               = 'V'; LDX >= 1 otherwise.
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78       WORK    (workspace) COMPLEX*16 array, dimension (N)
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80       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
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82       INFO    (output) INTEGER
83               = 0:  successful exit
84               < 0:  if INFO = -i, the i-th argument had an illegal value.
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88 LAPACK routine (version 3.2)    November 2008                       ZHBGST(1)
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