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zlatrd.f(3)				      LAPACK				      zlatrd.f(3)

NAME
       zlatrd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine zlatrd (UPLO, N, NB, A, LDA, E, TAU, W, LDW)
	   ZLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real
	   tridiagonal form by an unitary similarity transformation.

Function/Subroutine Documentation
   subroutine zlatrd (characterUPLO, integerN, integerNB, complex*16, dimension( lda, * )A,
       integerLDA, double precision, dimension( * )E, complex*16, dimension( * )TAU, complex*16,
       dimension( ldw, * )W, integerLDW)
       ZLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real
       tridiagonal form by an unitary similarity transformation.

       Purpose:

	    ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to
	    Hermitian tridiagonal form by a unitary similarity
	    transformation Q**H * A * Q, and returns the matrices V and W which are
	    needed to apply the transformation to the unreduced part of A.

	    If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a
	    matrix, of which the upper triangle is supplied;
	    if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a
	    matrix, of which the lower triangle is supplied.

	    This is an auxiliary routine called by ZHETRD.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     Specifies whether the upper or lower triangular part of the
		     Hermitian matrix A is stored:
		     = 'U': Upper triangular
		     = 'L': Lower triangular

	   N

		     N is INTEGER
		     The order of the matrix A.

	   NB

		     NB is INTEGER
		     The number of rows and columns to be reduced.

	   A

		     A is COMPLEX*16 array, dimension (LDA,N)
		     On entry, the Hermitian matrix A.	If UPLO = 'U', the leading
		     n-by-n upper triangular part of A contains the upper
		     triangular part of the matrix A, and the strictly lower
		     triangular part of A is not referenced.  If UPLO = 'L', the
		     leading n-by-n lower triangular part of A contains the lower
		     triangular part of the matrix A, and the strictly upper
		     triangular part of A is not referenced.
		     On exit:
		     if UPLO = 'U', the last NB columns have been reduced to
		       tridiagonal form, with the diagonal elements overwriting
		       the diagonal elements of A; the elements above the diagonal
		       with the array TAU, represent the unitary matrix Q as a
		       product of elementary reflectors;
		     if UPLO = 'L', the first NB columns have been reduced to
		       tridiagonal form, with the diagonal elements overwriting
		       the diagonal elements of A; the elements below the diagonal
		       with the array TAU, represent the  unitary matrix Q as a
		       product of elementary reflectors.
		     See Further Details.

	   LDA

		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= max(1,N).

	   E

		     E is DOUBLE PRECISION array, dimension (N-1)
		     If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
		     elements of the last NB columns of the reduced matrix;
		     if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
		     the first NB columns of the reduced matrix.

	   TAU

		     TAU is COMPLEX*16 array, dimension (N-1)
		     The scalar factors of the elementary reflectors, stored in
		     TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
		     See Further Details.

	   W

		     W is COMPLEX*16 array, dimension (LDW,NB)
		     The n-by-nb matrix W required to update the unreduced part
		     of A.

	   LDW

		     LDW is INTEGER
		     The leading dimension of the array W. LDW >= max(1,N).

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Further Details:

	     If UPLO = 'U', the matrix Q is represented as a product of elementary
	     reflectors

		Q = H(n) H(n-1) . . . H(n-nb+1).

	     Each H(i) has the form

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

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

	     If UPLO = 'L', the matrix Q is represented as a product of elementary
	     reflectors

		Q = H(1) H(2) . . . H(nb).

	     Each H(i) has the form

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

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

	     The elements of the vectors v together form the n-by-nb matrix V
	     which is needed, with W, to apply the transformation to the unreduced
	     part of the matrix, using a Hermitian rank-2k update of the form:
	     A := A - V*W**H - W*V**H.

	     The contents of A on exit are illustrated by the following examples
	     with n = 5 and nb = 2:

	     if UPLO = 'U':			  if UPLO = 'L':

	       (  a   a   a   v4  v5 )		    (  d		  )
	       (      a   a   v4  v5 )		    (  1   d		  )
	       (	  a   1   v5 )		    (  v1  1   a	  )
	       (	      d   1  )		    (  v1  v2  a   a	  )
	       (		  d  )		    (  v1  v2  a   a   a  )

	     where d denotes a diagonal element of the reduced matrix, a denotes
	     an element of the original matrix that is unchanged, and vi denotes
	     an element of the vector defining H(i).

       Definition at line 200 of file zlatrd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      zlatrd.f(3)
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