!-----------------------------------------------------------------
!
! Purpose
! =======
!
! LA_SYTRD / LA_HETRD reduces a real symmetric or complex Hermitian 
! matrix A to real symmetric tridiagonal form T by an orthogonal 
! or unitary similarity transformation:
! Q**H * A * Q = T.
!
! =======
!
!    SUBROUTINE LA_HETRD / LA_SYTRD|( A, TAU, UPLO, INFO )
!    .. Scalar Arguments ..
!       CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
!       INTEGER, INTENT(OUT), OPTIONAL :: INFO
!    .. Array Arguments ..
!       <type>(<wp>), INTENT(INOUT) :: A(:,:)
!       <type>(<wp>), INTENT(OUT) :: TAU(:)
!    where
!       <type> ::= REAL | COMPLEX
!       <wp>   ::= KIND(1.0) | KIND(1.0D0)
!
! Defaults
! ========
!
! 1. If UPLO is not present then UPLO = 'U' is assumed.
!
! Arguments
! =========
!
! A       (input/output) either REAL or COMPLEX square array, 
!         shape (:,:), size(A,1) == size(A,2) >= 0.
!         On entry, the symmetric (Hermitian) matrix A.  
!            If UPLO = 'U', the upper triangular part of A contains
!               the upper triangular part of the matrix A.
!            If UPLO = 'L', the lower triangular part of A contains
!               the lower triangular part of the matrix A.
!         On exit:
!            If UPLO = 'U', the diagonal and first superdiagonal
!               of A are overwritten by the corresponding elements of the
!               tridiagonal matrix T, and the elements above the first
!               superdiagonal, with the array TAU, represent the unitary
!               matrix Q as a product of elementary reflectors.
!            If UPLO = 'L', the diagonal and first subdiagonal of A are 
!               overwritten by the corresponding elements of the tridiagonal
!               matrix T, 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.
!
! TAU     (output) either REAL or COMPLEX array,
!         shape (:), size(TAU) == size(A,1)-1.
!         The scalar factors of the elementary reflectors.
!         See Further Details.
!
! UPLO    Optional, (input) CHARACTER*1
!         If UPLO is present then:
!            = 'U':  Upper triangle of A is stored
!            = 'L':  Lower triangle of A is stored
!         otherwise UPLO = 'U' is assumed.
!
! INFO    Optional, (output) INTEGER
!         If INFO is present:
!            = 0: successful exit
!            < 0: if INFO = -i, the i-th argument had an illegal value
!         If INFO is not present and an error occurs, then the program
!            is terminated with an error message.
!
! Further Details
! ===============
!
! If UPLO = 'U', the matrix Q is represented as a product of elementary
! reflectors
!
!    Q = H(n-1) . . . H(2) H(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(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
! A(1:i-1,i+1), and tau in TAU(i).
!
! If UPLO = 'L', the matrix Q is represented as a product of elementary
! reflectors
!
!    Q = H(1) H(2) . . . H(n-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 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
! and tau in TAU(i).
!
! The contents of A on exit are illustrated by the following examples
! with n = 5:
!
! if UPLO = 'U':                       if UPLO = 'L':
!
!   (  d   e   v2  v3  v4 )              (  d                  )
!   (      d   e   v3  v4 )              (  e   d              )
!   (          d   e   v4 )              (  v1  e   d          )
!   (              d   e  )              (  v1  v2  e   d      )
!   (                  d  )              (  v1  v2  v3  e   d  )
!
! where d and e denote diagonal and off-diagonal elements of T, and vi
! denotes an element of the vector defining H(i).
!
! --------------------------------------

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