Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  reduces  a  complex general m by n matrix A to upper or lower real bidiagonal
       form B by a unitary transformation

SYNOPSIS

       SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO )

           INTEGER        INFO, LDA, M, N

           REAL           D( * ), E( * )

           COMPLEX        A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * )

PURPOSE

       CGEBD2 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.

ARGUMENTS

        M       (input) INTEGER
                The number of rows in the matrix A.  M >= 0.

        N       (input) INTEGER
                The number of columns in the matrix A.  N >= 0.

        A       (input/output) COMPLEX 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     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,M).

        D       (output) REAL array, dimension (min(M,N))
                The diagonal elements of the bidiagonal matrix B:
                D(i) = A(i,i).

        E       (output) REAL 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    (output) COMPLEX array dimension (min(M,N))
                The scalar factors of the elementary reflectors which
                represent the unitary matrix Q. See Further Details.
                TAUP    (output) COMPLEX array, dimension (min(M,N))
                The scalar factors of the elementary reflectors which
                represent the unitary matrix P. See Further Details.
                WORK    (workspace) COMPLEX array, dimension (max(M,N))

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

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**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).

 LAPACK routine (version 3.3.1)             April 2011                            CGEBD2(3lapack)