CHBTRD man page on IRIX

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CHBTRD(3F)							    CHBTRD(3F)

NAME
     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 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 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 offdiagonal elements of T; the rest of AB is overwritten by
	     values generated during the reduction.

									Page 1

CHBTRD(3F)							    CHBTRD(3F)

     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 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 array, dimension (N)

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

									Page 2

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