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

NAME

       LAPACK-3  -  computes the solution to a real system of linear equations A * X = B, where A
       is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-
       by-NRHS matrices

SYNOPSIS

       SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )

           INTEGER       INFO, KL, KU, LDAB, LDB, N, NRHS

           INTEGER       IPIV( * )

           DOUBLE        PRECISION AB( LDAB, * ), B( LDB, * )

PURPOSE

       DGBSV  computes  the solution to a real system of linear equations A * X = B, where A is a
       band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B  are  N-by-
       NRHS matrices.
        The LU decomposition with partial pivoting and row interchanges is
        used to factor A as A = L * U, where L is a product of permutation
        and unit lower triangular matrices with KL subdiagonals, and U is
        upper triangular with KL+KU superdiagonals.  The factored form of A
        is then used to solve the system of equations A * X = B.

ARGUMENTS

        N       (input) INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

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

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

        NRHS    (input) INTEGER
                The number of right hand sides, i.e., the number of columns
                of the matrix B.  NRHS >= 0.

        AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
                On entry, the matrix A in band storage, in rows KL+1 to
                2*KL+KU+1; rows 1 to KL of the array need not be set.
                The j-th column of A is stored in the j-th column of the
                array AB as follows:
                AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
                On exit, details of the factorization: U is stored as an
                upper triangular band matrix with KL+KU superdiagonals in
                rows 1 to KL+KU+1, and the multipliers used during the
                factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
                See below for further details.

        LDAB    (input) INTEGER
                The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

        IPIV    (output) INTEGER array, dimension (N)
                The pivot indices that define the permutation matrix P;
                row i of the matrix was interchanged with row IPIV(i).

        B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
                On entry, the N-by-NRHS right hand side matrix B.
                On exit, if INFO = 0, the N-by-NRHS solution matrix X.

        LDB     (input) INTEGER
                The leading dimension of the array B.  LDB >= max(1,N).

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
                > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization
                has been completed, but the factor U is exactly
                singular, and the solution has not been computed.

FURTHER DETAILS

        The band storage scheme is illustrated by the following example, when
        M = N = 6, KL = 2, KU = 1:
        On entry:                       On exit:
            *    *    *    +    +    +       *    *    *   u14  u25  u36
            *    *    +    +    +    +       *    *   u13  u24  u35  u46
            *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
           a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
           a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
           a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
        Array elements marked * are not used by the routine; elements marked
        + need not be set on entry, but are required by the routine to store
        elements of U because of fill-in resulting from the row interchanges.

 LAPACK driver routine (version 3.2)        April 2011                             DGBSV(3lapack)