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    1:       SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
    2:      $                   LDB, INFO )
    3: *
    4: *  -- LAPACK routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          DIAG, TRANS, UPLO
   11:       INTEGER            INFO, KD, LDAB, LDB, N, NRHS
   12: *     ..
   13: *     .. Array Arguments ..
   14:       COMPLEX*16         AB( LDAB, * ), B( LDB, * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  ZTBTRS solves a triangular system of the form
   21: *
   22: *     A * X = B,  A**T * X = B,  or  A**H * X = B,
   23: *
   24: *  where A is a triangular band matrix of order N, and B is an
   25: *  N-by-NRHS matrix.  A check is made to verify that A is nonsingular.
   26: *
   27: *  Arguments
   28: *  =========
   29: *
   30: *  UPLO    (input) CHARACTER*1
   31: *          = 'U':  A is upper triangular;
   32: *          = 'L':  A is lower triangular.
   33: *
   34: *  TRANS   (input) CHARACTER*1
   35: *          Specifies the form of the system of equations:
   36: *          = 'N':  A * X = B     (No transpose)
   37: *          = 'T':  A**T * X = B  (Transpose)
   38: *          = 'C':  A**H * X = B  (Conjugate transpose)
   39: *
   40: *  DIAG    (input) CHARACTER*1
   41: *          = 'N':  A is non-unit triangular;
   42: *          = 'U':  A is unit triangular.
   43: *
   44: *  N       (input) INTEGER
   45: *          The order of the matrix A.  N >= 0.
   46: *
   47: *  KD      (input) INTEGER
   48: *          The number of superdiagonals or subdiagonals of the
   49: *          triangular band matrix A.  KD >= 0.
   50: *
   51: *  NRHS    (input) INTEGER
   52: *          The number of right hand sides, i.e., the number of columns
   53: *          of the matrix B.  NRHS >= 0.
   54: *
   55: *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)
   56: *          The upper or lower triangular band matrix A, stored in the
   57: *          first kd+1 rows of AB.  The j-th column of A is stored
   58: *          in the j-th column of the array AB as follows:
   59: *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
   60: *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
   61: *          If DIAG = 'U', the diagonal elements of A are not referenced
   62: *          and are assumed to be 1.
   63: *
   64: *  LDAB    (input) INTEGER
   65: *          The leading dimension of the array AB.  LDAB >= KD+1.
   66: *
   67: *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
   68: *          On entry, the right hand side matrix B.
   69: *          On exit, if INFO = 0, the solution matrix X.
   70: *
   71: *  LDB     (input) INTEGER
   72: *          The leading dimension of the array B.  LDB >= max(1,N).
   73: *
   74: *  INFO    (output) INTEGER
   75: *          = 0:  successful exit
   76: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   77: *          > 0:  if INFO = i, the i-th diagonal element of A is zero,
   78: *                indicating that the matrix is singular and the
   79: *                solutions X have not been computed.
   80: *
   81: *  =====================================================================
   82: *
   83: *     .. Parameters ..
   84:       COMPLEX*16         ZERO
   85:       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
   86: *     ..
   87: *     .. Local Scalars ..
   88:       LOGICAL            NOUNIT, UPPER
   89:       INTEGER            J
   90: *     ..
   91: *     .. External Functions ..
   92:       LOGICAL            LSAME
   93:       EXTERNAL           LSAME
   94: *     ..
   95: *     .. External Subroutines ..
   96:       EXTERNAL           XERBLA, ZTBSV
   97: *     ..
   98: *     .. Intrinsic Functions ..
   99:       INTRINSIC          MAX
  100: *     ..
  101: *     .. Executable Statements ..
  102: *
  103: *     Test the input parameters.
  104: *
  105:       INFO = 0
  106:       NOUNIT = LSAME( DIAG, 'N' )
  107:       UPPER = LSAME( UPLO, 'U' )
  108:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  109:          INFO = -1
  110:       ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
  111:      $         LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
  112:          INFO = -2
  113:       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
  114:          INFO = -3
  115:       ELSE IF( N.LT.0 ) THEN
  116:          INFO = -4
  117:       ELSE IF( KD.LT.0 ) THEN
  118:          INFO = -5
  119:       ELSE IF( NRHS.LT.0 ) THEN
  120:          INFO = -6
  121:       ELSE IF( LDAB.LT.KD+1 ) THEN
  122:          INFO = -8
  123:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  124:          INFO = -10
  125:       END IF
  126:       IF( INFO.NE.0 ) THEN
  127:          CALL XERBLA( 'ZTBTRS', -INFO )
  128:          RETURN
  129:       END IF
  130: *
  131: *     Quick return if possible
  132: *
  133:       IF( N.EQ.0 )
  134:      $   RETURN
  135: *
  136: *     Check for singularity.
  137: *
  138:       IF( NOUNIT ) THEN
  139:          IF( UPPER ) THEN
  140:             DO 10 INFO = 1, N
  141:                IF( AB( KD+1, INFO ).EQ.ZERO )
  142:      $            RETURN
  143:    10       CONTINUE
  144:          ELSE
  145:             DO 20 INFO = 1, N
  146:                IF( AB( 1, INFO ).EQ.ZERO )
  147:      $            RETURN
  148:    20       CONTINUE
  149:          END IF
  150:       END IF
  151:       INFO = 0
  152: *
  153: *     Solve A * X = B,  A**T * X = B,  or  A**H * X = B.
  154: *
  155:       DO 30 J = 1, NRHS
  156:          CALL ZTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, B( 1, J ), 1 )
  157:    30 CONTINUE
  158: *
  159:       RETURN
  160: *
  161: *     End of ZTBTRS
  162: *
  163:       END