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    1:       SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
    2: *
    3: *  -- LAPACK driver routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
   10: *     ..
   11: *     .. Array Arguments ..
   12:       INTEGER            IPIV( * )
   13:       COMPLEX*16         AB( LDAB, * ), B( LDB, * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  ZGBSV computes the solution to a complex system of linear equations
   20: *  A * X = B, where A is a band matrix of order N with KL subdiagonals
   21: *  and KU superdiagonals, and X and B are N-by-NRHS matrices.
   22: *
   23: *  The LU decomposition with partial pivoting and row interchanges is
   24: *  used to factor A as A = L * U, where L is a product of permutation
   25: *  and unit lower triangular matrices with KL subdiagonals, and U is
   26: *  upper triangular with KL+KU superdiagonals.  The factored form of A
   27: *  is then used to solve the system of equations A * X = B.
   28: *
   29: *  Arguments
   30: *  =========
   31: *
   32: *  N       (input) INTEGER
   33: *          The number of linear equations, i.e., the order of the
   34: *          matrix A.  N >= 0.
   35: *
   36: *  KL      (input) INTEGER
   37: *          The number of subdiagonals within the band of A.  KL >= 0.
   38: *
   39: *  KU      (input) INTEGER
   40: *          The number of superdiagonals within the band of A.  KU >= 0.
   41: *
   42: *  NRHS    (input) INTEGER
   43: *          The number of right hand sides, i.e., the number of columns
   44: *          of the matrix B.  NRHS >= 0.
   45: *
   46: *  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
   47: *          On entry, the matrix A in band storage, in rows KL+1 to
   48: *          2*KL+KU+1; rows 1 to KL of the array need not be set.
   49: *          The j-th column of A is stored in the j-th column of the
   50: *          array AB as follows:
   51: *          AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
   52: *          On exit, details of the factorization: U is stored as an
   53: *          upper triangular band matrix with KL+KU superdiagonals in
   54: *          rows 1 to KL+KU+1, and the multipliers used during the
   55: *          factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
   56: *          See below for further details.
   57: *
   58: *  LDAB    (input) INTEGER
   59: *          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
   60: *
   61: *  IPIV    (output) INTEGER array, dimension (N)
   62: *          The pivot indices that define the permutation matrix P;
   63: *          row i of the matrix was interchanged with row IPIV(i).
   64: *
   65: *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
   66: *          On entry, the N-by-NRHS right hand side matrix B.
   67: *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
   68: *
   69: *  LDB     (input) INTEGER
   70: *          The leading dimension of the array B.  LDB >= max(1,N).
   71: *
   72: *  INFO    (output) INTEGER
   73: *          = 0:  successful exit
   74: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   75: *          > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization
   76: *                has been completed, but the factor U is exactly
   77: *                singular, and the solution has not been computed.
   78: *
   79: *  Further Details
   80: *  ===============
   81: *
   82: *  The band storage scheme is illustrated by the following example, when
   83: *  M = N = 6, KL = 2, KU = 1:
   84: *
   85: *  On entry:                       On exit:
   86: *
   87: *      *    *    *    +    +    +       *    *    *   u14  u25  u36
   88: *      *    *    +    +    +    +       *    *   u13  u24  u35  u46
   89: *      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
   90: *     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
   91: *     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
   92: *     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
   93: *
   94: *  Array elements marked * are not used by the routine; elements marked
   95: *  + need not be set on entry, but are required by the routine to store
   96: *  elements of U because of fill-in resulting from the row interchanges.
   97: *
   98: *  =====================================================================
   99: *
  100: *     .. External Subroutines ..
  101:       EXTERNAL           XERBLA, ZGBTRF, ZGBTRS
  102: *     ..
  103: *     .. Intrinsic Functions ..
  104:       INTRINSIC          MAX
  105: *     ..
  106: *     .. Executable Statements ..
  107: *
  108: *     Test the input parameters.
  109: *
  110:       INFO = 0
  111:       IF( N.LT.0 ) THEN
  112:          INFO = -1
  113:       ELSE IF( KL.LT.0 ) THEN
  114:          INFO = -2
  115:       ELSE IF( KU.LT.0 ) THEN
  116:          INFO = -3
  117:       ELSE IF( NRHS.LT.0 ) THEN
  118:          INFO = -4
  119:       ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
  120:          INFO = -6
  121:       ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
  122:          INFO = -9
  123:       END IF
  124:       IF( INFO.NE.0 ) THEN
  125:          CALL XERBLA( 'ZGBSV ', -INFO )
  126:          RETURN
  127:       END IF
  128: *
  129: *     Compute the LU factorization of the band matrix A.
  130: *
  131:       CALL ZGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
  132:       IF( INFO.EQ.0 ) THEN
  133: *
  134: *        Solve the system A*X = B, overwriting B with X.
  135: *
  136:          CALL ZGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
  137:      $                B, LDB, INFO )
  138:       END IF
  139:       RETURN
  140: *
  141: *     End of ZGBSV
  142: *
  143:       END