..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PSGEBRD reduces a real general M-by-N distributed matrix
  sub( A ) = A(IA:IA+M-1,JA:JA+N-1) to upper or lower bidiagonal
  form B by an orthogonal transformation: Q' * sub( A ) * P = B.
  If M >= N, B is upper bidiagonal; if M < N, B is lower bidiagonal.
  Notes
  =====
  Each global data object is described by an associated description
  vector.  This vector stores the information required to establish
  the mapping between an object element and its corresponding process
  and memory location.
  Let A be a generic term for any 2D block cyclicly distributed array.
  Such a global array has an associated description vector DESCA.
  In the following comments, the character _ should be read as
  "of the global array".
  NOTATION        STORED IN      EXPLANATION
  --------------- -------------- --------------------------------------
  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
                                 DTYPE_A = 1.
  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
                                 the BLACS process grid A is distribu-
                                 ted over. The context itself is glo-
                                 bal, but the handle (the integer
                                 value) may vary.
  M_A    (global) DESCA( M_ )    The number of rows in the global
                                 array A.
  N_A    (global) DESCA( N_ )    The number of columns in the global
                                 array A.
  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
                                 the rows of the array.
  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
                                 the columns of the array.
  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
                                 row of the array A is distributed.
  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
                                 first column of the array A is
                                 distributed.
  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
  Let K be the number of rows or columns of a distributed matrix,
  and assume that its process grid has dimension p x q.
  LOCr( K ) denotes the number of elements of K that a process
  would receive if K were distributed over the p processes of its
  process column.
  Similarly, LOCc( K ) denotes the number of elements of K that a
  process would receive if K were distributed over the q processes of
  its process row.
  The values of LOCr() and LOCc() may be determined via a call to the
  ScaLAPACK tool function, NUMROC:
          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
  An upper bound for these quantities may be computed by:
          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
  Arguments
  =========
  M       (global input) INTEGER
          The number of rows to be operated on, i.e. the number of rows
          of the distributed submatrix sub( A ). M >= 0.
  N       (global input) INTEGER
          The number of columns to be operated on, i.e. the number of
          columns of the distributed submatrix sub( A ). N >= 0.
  A       (local input/local output) REAL pointer into the
          local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
          On entry, this array contains the local pieces of the
          general distributed matrix sub( A ). On exit, if M >= N,
          the diagonal and the first superdiagonal of sub( A ) are
          overwritten with the upper bidiagonal matrix B; the elements
          below the diagonal, with the array TAUQ, represent the
          orthogonal matrix Q as a product of elementary reflectors,
          and the elements above the first superdiagonal, with the
          array TAUP, represent the orthogonal 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 orthogonal matrix Q as a product of
          elementary reflectors, and the elements above the diagonal,
          with the array TAUP, represent the orthogonal matrix P as a
          product of elementary reflectors. See Further Details.
  IA      (global input) INTEGER
          The row index in the global array A indicating the first
          row of sub( A ).
  JA      (global input) INTEGER
          The column index in the global array A indicating the
          first column of sub( A ).
  DESCA   (global and local input) INTEGER array of dimension DLEN_.
          The array descriptor for the distributed matrix A.
  D       (local output) REAL array, dimension
          LOCc(JA+MIN(M,N)-1) if M >= N; LOCr(IA+MIN(M,N)-1) otherwise.
          The distributed diagonal elements of the bidiagonal matrix
          B: D(i) = A(i,i). D is tied to the distributed matrix A.
  E       (local output) REAL array, dimension
          LOCr(IA+MIN(M,N)-1) if M >= N; LOCc(JA+MIN(M,N)-2) otherwise.
          The distributed off-diagonal elements of the bidiagonal
          distributed 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.
          E is tied to the distributed matrix A.
  TAUQ    (local output) REAL array dimension
          LOCc(JA+MIN(M,N)-1). The scalar factors of the elementary
          reflectors which represent the orthogonal matrix Q. TAUQ
          is tied to the distributed matrix A. See Further Details.
  TAUP    (local output) REAL array, dimension
          LOCr(IA+MIN(M,N)-1). The scalar factors of the elementary
          reflectors which represent the orthogonal matrix P. TAUP
          is tied to the distributed matrix A. See Further Details.
  WORK    (local workspace/local output) REAL array,
                                                 dimension (LWORK)
          On exit, WORK( 1 ) returns the minimal and optimal LWORK.
  LWORK   (local or global input) INTEGER
          The dimension of the array WORK.
          LWORK is local input and must be at least
          LWORK >= NB*( MpA0 + NqA0 + 1 ) + NqA0
          where NB = MB_A = NB_A,
          IROFFA = MOD( IA-1, NB ), ICOFFA = MOD( JA-1, NB ),
          IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ),
          IACOL = INDXG2P( JA, NB, MYCOL, CSRC_A, NPCOL ),
          MpA0 = NUMROC( M+IROFFA, NB, MYROW, IAROW, NPROW ),
          NqA0 = NUMROC( N+ICOFFA, NB, MYCOL, IACOL, NPCOL ).
          INDXG2P and NUMROC are ScaLAPACK tool functions;
          MYROW, MYCOL, NPROW and NPCOL can be determined by calling
          the subroutine BLACS_GRIDINFO.
          If LWORK = -1, then LWORK is global input and a workspace
          query is assumed; the routine only calculates the minimum
          and optimal size for all work arrays. Each of these
          values is returned in the first entry of the corresponding
          work array, and no error message is issued by PXERBLA.
  INFO    (global output) INTEGER
          = 0:  successful exit
          < 0:  If the i-th argument is an array and the j-entry had
                an illegal value, then INFO = -(i*100+j), if the i-th
                argument is a scalar and had an illegal value, then
                INFO = -i.
  Further Details
  ===============
  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'  and G(i) = I - taup * u * u'
  where tauq and taup are real scalars, and v and u are real vectors;
  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
  A(ia+i:ia+m-1,ja+i-1);
  u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
  A(ia+i-1,ja+i+1:ja+n-1);
  tauq is stored in TAUQ(ja+i-1) and taup in TAUP(ia+i-1).
  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'  and G(i) = I - taup * u * u'
  where tauq and taup are real scalars, and v and u are real vectors;
  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
  A(ia+i+1:ia+m-1,ja+i-1);
  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in
  A(ia+i-1,ja+i:ja+n-1);
  tauq is stored in TAUQ(ja+i-1) and taup in TAUP(ia+i-1).
  The contents of sub( 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).
  Alignment requirements
  ======================
  The distributed submatrix sub( A ) must verify some alignment proper-
  ties, namely the following expressions should be true:
  ( MB_A.EQ.NB_A .AND. IROFFA.EQ.ICOFFA )
  =====================================================================
     .. Parameters ..