SGBBRD (3lapack)

reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation

SYNOPSIS

  SUBROUTINE SGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT,
                     LDPT, C, LDC, WORK, INFO )

      CHARACTER      VECT

      INTEGER        INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC

      REAL           AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), PT( LDPT, *
                     ), Q( LDQ, * ), WORK( * )

PURPOSE

  SGBBRD reduces a real general m-by-n band matrix A to upper bidiagonal form
  B by an orthogonal transformation: Q' * A * P = B.

  The routine computes B, and optionally forms Q or P', or computes Q'*C for
  a given matrix C.

ARGUMENTS

  VECT    (input) CHARACTER*1
          Specifies whether or not the matrices Q and P' are to be formed.  =
          'N': do not form Q or P';
          = 'Q': form Q only;
          = 'P': form P' only;
          = 'B': form both.

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

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

  NCC     (input) INTEGER
          The number of columns of the matrix C.  NCC >= 0.

  KL      (input) INTEGER
          The number of subdiagonals of the matrix A. KL >= 0.

  KU      (input) INTEGER
          The number of superdiagonals of the matrix A. KU >= 0.

  AB      (input/output) REAL array, dimension (LDAB,N)
          On entry, the m-by-n band matrix A, stored in rows 1 to KL+KU+1.
          The j-th column of A is stored in the j-th column of the array AB
          as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-
          ku)<=i<=min(m,j+kl).  On exit, A is overwritten by values generated
          during the reduction.

  LDAB    (input) INTEGER
          The leading dimension of the array A. LDAB >= KL+KU+1.

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

  E       (output) REAL array, dimension (min(M,N)-1)
          The superdiagonal elements of the bidiagonal matrix B.

  Q       (output) REAL array, dimension (LDQ,M)
          If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.  If VECT =
          'N' or 'P', the array Q is not referenced.

  LDQ     (input) INTEGER
          The leading dimension of the array Q.  LDQ >= max(1,M) if VECT =
          'Q' or 'B'; LDQ >= 1 otherwise.

  PT      (output) REAL array, dimension (LDPT,N)
          If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.  If VECT =
          'N' or 'Q', the array PT is not referenced.

  LDPT    (input) INTEGER
          The leading dimension of the array PT.  LDPT >= max(1,N) if VECT =
          'P' or 'B'; LDPT >= 1 otherwise.

  C       (input/output) REAL array, dimension (LDC,NCC)
          On entry, an m-by-ncc matrix C.  On exit, C is overwritten by Q'*C.
          C is not referenced if NCC = 0.

  LDC     (input) INTEGER
          The leading dimension of the array C.  LDC >= max(1,M) if NCC > 0;
          LDC >= 1 if NCC = 0.

  WORK    (workspace) REAL array, dimension (2*max(M,N))

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