SRC/zgbsv.f(3)             Library Functions Manual             SRC/zgbsv.f(3)

NAME
       SRC/zgbsv.f

SYNOPSIS
   Functions/Subroutines
       subroutine zgbsv (n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
            ZGBSV computes the solution to system of linear equations A * X =
           B for GB matrices (simple driver)

Function/Subroutine Documentation
   subroutine zgbsv (integer n, integer kl, integer ku, integer nrhs,
       complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension(
       * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)
        ZGBSV computes the solution to system of linear equations A * X = B
       for GB matrices (simple driver)

       Purpose:


            ZGBSV computes the solution to a complex 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.

       Parameters
           N

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

           KL

                     KL is INTEGER
                     The number of subdiagonals within the band of A.  KL >= 0.

           KU

                     KU is INTEGER
                     The number of superdiagonals within the band of A.  KU >= 0.

           NRHS

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

           AB

                     AB is COMPLEX*16 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

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

           IPIV

                     IPIV is 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

                     B is COMPLEX*16 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

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

           INFO

                     INFO is 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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

       Definition at line 161 of file zgbsv.f.

Author
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LAPACK                          Version 3.12.0                  SRC/zgbsv.f(3)