ZGEBD2 reduces a complex general m by n matrix A to upper or lower
 real bidiagonal form B by a unitary transformation: Q**H * A * P = B.
 If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.

M

          M is INTEGER
          The number of rows in the matrix A.  M >= 0.

N

          N is INTEGER
          The number of columns in the matrix A.  N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the m by n general matrix to be reduced.
          On exit,
          if m >= n, the diagonal and the first superdiagonal are
            overwritten with the upper bidiagonal matrix B; the
            elements below the diagonal, with the array TAUQ, represent
            the unitary matrix Q as a product of elementary
            reflectors, and the elements above the first superdiagonal,
            with the array TAUP, represent the unitary matrix P as
            a product of elementary reflectors;
          if m < n, the diagonal and the first subdiagonal are
            overwritten with the lower bidiagonal matrix B; the
            elements below the first subdiagonal, with the array TAUQ,
            represent the unitary matrix Q as a product of
            elementary reflectors, and the elements above the diagonal,
            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 DOUBLE PRECISION array, dimension (min(M,N))
          The diagonal elements of the bidiagonal matrix B:
          D(i) = A(i,i).

E

          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
          The off-diagonal elements of the bidiagonal matrix B:
          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.

TAUQ

          TAUQ is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors which
          represent the unitary matrix Q. See Further Details.

TAUP

          TAUP is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors which
          represent the unitary matrix P. See Further Details.

WORK

          WORK is COMPLEX*16 array, dimension (max(M,N))

INFO

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

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  The matrices Q and P are represented as products of elementary
  reflectors:
  If m >= n,
     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
  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; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
  If m < n,
     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
  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, v and u are complex vectors;
  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
  u(1:i-1) = 0, u(i) = 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).
  The contents of A on exit are illustrated by the following examples:
  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
    (  v1  v2  v3  v4  v5 )
  where d and e denote diagonal and off-diagonal elements of B, vi
  denotes an element of the vector defining H(i), and ui an element of
  the vector defining G(i).