!>
!> CLABRD reduces the first NB rows and columns of a complex general
!> m by n matrix A to upper or lower real bidiagonal form by a unitary
!> transformation Q**H * A * P, and returns the matrices X and Y which
!> are needed to apply the transformation to the unreduced part of A.
!>
!> If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
!> bidiagonal form.
!>
!> This is an auxiliary routine called by CGEBRD
!> 

M

!>          M is INTEGER
!>          The number of rows in the matrix A.
!> 

N

!>          N is INTEGER
!>          The number of columns in the matrix A.
!> 

NB

!>          NB is INTEGER
!>          The number of leading rows and columns of A to be reduced.
!> 

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the m by n general matrix to be reduced.
!>          On exit, the first NB rows and columns of the matrix are
!>          overwritten; the rest of the array is unchanged.
!>          If m >= n, elements on and below the diagonal in the first NB
!>            columns, with the array TAUQ, represent the unitary
!>            matrix Q as a product of elementary reflectors; and
!>            elements above the diagonal in the first NB rows, with the
!>            array TAUP, represent the unitary matrix P as a product
!>            of elementary reflectors.
!>          If m < n, elements below the diagonal in the first NB
!>            columns, with the array TAUQ, represent the unitary
!>            matrix Q as a product of elementary reflectors, and
!>            elements on and above the diagonal in the first NB rows,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors.
!>          See Further Details.
!> 

LDA

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

D

!>          D is REAL array, dimension (NB)
!>          The diagonal elements of the first NB rows and columns of
!>          the reduced matrix.  D(i) = A(i,i).
!> 

E

!>          E is REAL array, dimension (NB)
!>          The off-diagonal elements of the first NB rows and columns of
!>          the reduced matrix.
!> 

TAUQ

!>          TAUQ is COMPLEX array, dimension (NB)
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix Q. See Further Details.
!> 

TAUP

!>          TAUP is COMPLEX array, dimension (NB)
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix P. See Further Details.
!> 

X

!>          X is COMPLEX array, dimension (LDX,NB)
!>          The m-by-nb matrix X required to update the unreduced part
!>          of A.
!> 

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X. LDX >= max(1,M).
!> 

Y

!>          Y is COMPLEX array, dimension (LDY,NB)
!>          The n-by-nb matrix Y required to update the unreduced part
!>          of A.
!> 

LDY

!>          LDY is INTEGER
!>          The leading dimension of the array Y. LDY >= max(1,N).
!> 

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!>
!>  The matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>     Q = H(1) H(2) . . . H(nb)  and  P = G(1) G(2) . . . G(nb)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors.
!>
!>  If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in
!>  A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in
!>  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in
!>  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in
!>  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  The elements of the vectors v and u together form the m-by-nb matrix
!>  V and the nb-by-n matrix U**H which are needed, with X and Y, to apply
!>  the transformation to the unreduced part of the matrix, using a block
!>  update of the form:  A := A - V*Y**H - X*U**H.
!>
!>  The contents of A on exit are illustrated by the following examples
!>  with nb = 2:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 )
!>    (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 )
!>    (  v1  v2  a   a   a  )           (  v1  1   a   a   a   a  )
!>    (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
!>    (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
!>    (  v1  v2  a   a   a  )
!>
!>  where a denotes an element of the original matrix which is unchanged,
!>  vi denotes an element of the vector defining H(i), and ui an element
!>  of the vector defining G(i).
!>