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RedHat 9 (Linux i386) - man page for zhbtrd (redhat section l)

ZHBTRD(l)					)					ZHBTRD(l)

NAME
       ZHBTRD  - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by
       a unitary similarity transformation

SYNOPSIS
       SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO )

	   CHARACTER	  UPLO, VECT

	   INTEGER	  INFO, KD, LDAB, LDQ, N

	   DOUBLE	  PRECISION D( * ), E( * )

	   COMPLEX*16	  AB( LDAB, * ), Q( LDQ, * ), WORK( * )

PURPOSE
       ZHBTRD 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 sub-
	       diagonals if UPLO = 'L'.  KD >= 0.

       AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
	       On entry, 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 col-
	       umn 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 elements of AB are overwritten by the diagonal  elements  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 rest of AB is overwritten by values generated during
	       the reduction.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD+1.

       D       (output) DOUBLE PRECISION array, dimension (N)
	       The diagonal elements of the tridiagonal matrix T.

       E       (output) DOUBLE PRECISION 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*16 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 unitary matrix Q; if VECT =  'U',	Q
	       contains the product X*Q; if VECT = 'N', the array Q is not referenced.

       LDQ     (input) INTEGER
	       The  leading  dimension	of  the array Q.  LDQ >= 1, and LDQ >= N if VECT = 'V' or
	       'U'.

       WORK    (workspace) COMPLEX*16 array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
       Modified by Linda Kaufman, Bell Labs.

LAPACK version 3.0			   15 June 2000 				ZHBTRD(l)


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