dgbbrd(3S)

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

SYNOPSIS
     SUBROUTINE DGBBRD( 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

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     DGBBRD 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N))
             The diagonal elements of the bidiagonal matrix B.

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

     Q       (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2*max(M,N))

     INFO    (output) INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.
SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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