redhat man page for cgehrd

CGEHRD(l)								 )								 CGEHRD(l)

NAME
       CGEHRD - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation

SYNOPSIS
       SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )

	   INTEGER	  IHI, ILO, INFO, LDA, LWORK, N

	   COMPLEX	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       CGEHRD reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation: Q' * A * Q = H .

ARGUMENTS
       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       ILO     (input) INTEGER
	       IHI	(input)  INTEGER It is assumed that A is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are
	       normally set by a previous call to CGEBAL; otherwise they should be set to 1 and N respectively. See Further Details.

       A       (input/output) COMPLEX array, dimension (LDA,N)
	       On entry, the N-by-N general matrix to be reduced.  On exit, the upper triangle and the first subdiagonal of A are overwritten with
	       the  upper Hessenberg matrix H, and the elements below the first subdiagonal, with the array TAU, represent the unitary matrix Q as
	       a product of elementary reflectors. See Further Details.  LDA	 (input) INTEGER The leading dimension of the  array  A.   LDA	>=
	       max(1,N).

       TAU     (output) COMPLEX array, dimension (N-1)
	       The scalar factors of the elementary reflectors (see Further Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to zero.

       WORK    (workspace/output) COMPLEX array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The length of the array WORK.  LWORK >= max(1,N).  For optimum performance LWORK >= N*NB, where NB is the optimal blocksize.

	       If  LWORK  =  -1,  then	a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this
	       value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

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

FURTHER DETAILS
       The matrix Q is represented as a product of (ihi-ilo) elementary reflectors

	  Q = H(ilo) H(ilo+1) . . . H(ihi-1).

       Each H(i) has the form

	  H(i) = I - tau * v * v'

       where tau is a complex scalar, and v is a complex vector with v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored  on  exit	in
       A(i+2:ihi,i), and tau in TAU(i).

       The contents of A are illustrated by the following example, with n = 7, ilo = 2 and ihi = 6:

       on entry,			on exit,

       ( a   a	 a   a	 a   a	 a )	(  a   a   h   h   h   h   a ) (     a	 a   a	 a   a	 a )	(      a   h   h   h   h   a ) (     a	 a
       a   a   a   a )	  (	 h   h	 h   h	 h   h ) (     a   a   a   a   a   a )	  (	 v2  h	 h   h	 h   h ) (     a   a   a    a	 a
       a  )	(	v2  v3	h   h	h   h ) (     a   a   a   a   a   a )	 (	v2  v3	v4  h	h   h ) (			  a )	 (
       a )

       where a denotes an element of the original matrix A, h denotes a modified element of the upper Hessenberg matrix H, and vi denotes an  ele-
       ment of the vector defining H(i).

LAPACK version 3.0						   15 June 2000 							 CGEHRD(l)