```      SUBROUTINE ZLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X,
\$                   SCALE, CNORM, INFO )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          DIAG, NORMIN, TRANS, UPLO
INTEGER            INFO, KD, LDAB, N
DOUBLE PRECISION   SCALE
*     ..
*     .. Array Arguments ..
DOUBLE PRECISION   CNORM( * )
COMPLEX*16         AB( LDAB, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  ZLATBS solves one of the triangular systems
*
*     A * x = s*b,  A**T * x = s*b,  or  A**H * x = s*b,
*
*  with scaling to prevent overflow, where A is an upper or lower
*  triangular band matrix.  Here A' denotes the transpose of A, x and b
*  are n-element vectors, and s is a scaling factor, usually less than
*  or equal to 1, chosen so that the components of x will be less than
*  the overflow threshold.  If the unscaled problem will not cause
*  overflow, the Level 2 BLAS routine ZTBSV is called.  If the matrix A
*  is singular (A(j,j) = 0 for some j), then s is set to 0 and a
*  non-trivial solution to A*x = 0 is returned.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the matrix A is upper or lower triangular.
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  TRANS   (input) CHARACTER*1
*          Specifies the operation applied to A.
*          = 'N':  Solve A * x = s*b     (No transpose)
*          = 'T':  Solve A**T * x = s*b  (Transpose)
*          = 'C':  Solve A**H * x = s*b  (Conjugate transpose)
*
*  DIAG    (input) CHARACTER*1
*          Specifies whether or not the matrix A is unit triangular.
*          = 'N':  Non-unit triangular
*          = 'U':  Unit triangular
*
*  NORMIN  (input) CHARACTER*1
*          Specifies whether CNORM has been set or not.
*          = 'Y':  CNORM contains the column norms on entry
*          = 'N':  CNORM is not set on entry.  On exit, the norms will
*                  be computed and stored in CNORM.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of subdiagonals or superdiagonals in the
*          triangular matrix A.  KD >= 0.
*
*  AB      (input) COMPLEX*16 array, dimension (LDAB,N)
*          The upper or lower triangular band matrix A, stored in the
*          first KD+1 rows of the array. The j-th column of A is stored
*          in the j-th column of the array AB as follows:
*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
*  X       (input/output) COMPLEX*16 array, dimension (N)
*          On entry, the right hand side b of the triangular system.
*          On exit, X is overwritten by the solution vector x.
*
*  SCALE   (output) DOUBLE PRECISION
*          The scaling factor s for the triangular system
*             A * x = s*b,  A**T * x = s*b,  or  A**H * x = s*b.
*          If SCALE = 0, the matrix A is singular or badly scaled, and
*          the vector x is an exact or approximate solution to A*x = 0.
*
*  CNORM   (input or output) DOUBLE PRECISION array, dimension (N)
*
*          If NORMIN = 'Y', CNORM is an input argument and CNORM(j)
*          contains the norm of the off-diagonal part of the j-th column
*          of A.  If TRANS = 'N', CNORM(j) must be greater than or equal
*          to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j)
*          must be greater than or equal to the 1-norm.
*
*          If NORMIN = 'N', CNORM is an output argument and CNORM(j)
*          returns the 1-norm of the offdiagonal part of the j-th column
*          of A.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -k, the k-th argument had an illegal value
*
*  Further Details
*  ======= =======
*
*  A rough bound on x is computed; if that is less than overflow, ZTBSV
*  is called, otherwise, specific code is used which checks for possible
*  overflow or divide-by-zero at every operation.
*
*  A columnwise scheme is used for solving A*x = b.  The basic algorithm
*  if A is lower triangular is
*
*       x[1:n] := b[1:n]
*       for j = 1, ..., n
*            x(j) := x(j) / A(j,j)
*            x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j]
*       end
*
*  Define bounds on the components of x after j iterations of the loop:
*     M(j) = bound on x[1:j]
*     G(j) = bound on x[j+1:n]
*  Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}.
*
*  Then for iteration j+1 we have
*     M(j+1) <= G(j) / | A(j+1,j+1) |
*     G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] |
*            <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | )
*
*  where CNORM(j+1) is greater than or equal to the infinity-norm of
*  column j+1 of A, not counting the diagonal.  Hence
*
*     G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | )
*                  1<=i<=j
*  and
*
*     |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| )
*                                   1<=i< j
*
*  Since |x(j)| <= M(j), we use the Level 2 BLAS routine ZTBSV if the
*  reciprocal of the largest M(j), j=1,..,n, is larger than
*  max(underflow, 1/overflow).
*
*  The bound on x(j) is also used to determine when a step in the
*  columnwise method can be performed without fear of overflow.  If
*  the computed bound is greater than a large constant, x is scaled to
*  prevent overflow, but if the bound overflows, x is set to 0, x(j) to
*  1, and scale to 0, and a non-trivial solution to A*x = 0 is found.
*
*  Similarly, a row-wise scheme is used to solve A**T *x = b  or
*  A**H *x = b.  The basic algorithm for A upper triangular is
*
*       for j = 1, ..., n
*            x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j)
*       end
*
*  We simultaneously compute two bounds
*       G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j
*       M(j) = bound on x(i), 1<=i<=j
*
*  The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we
*  add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1.
*  Then the bound on x(j) is
*
*       M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) |
*
*            <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| )
*                      1<=i<=j
*
*  and we can safely call ZTBSV if 1/M(n) and 1/G(n) are both greater
*  than max(underflow, 1/overflow).
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ZERO, HALF, ONE, TWO
PARAMETER          ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0,
\$                   TWO = 2.0D+0 )
*     ..
*     .. Local Scalars ..
LOGICAL            NOTRAN, NOUNIT, UPPER
INTEGER            I, IMAX, J, JFIRST, JINC, JLAST, JLEN, MAIND
DOUBLE PRECISION   BIGNUM, GROW, REC, SMLNUM, TJJ, TMAX, TSCAL,
\$                   XBND, XJ, XMAX
COMPLEX*16         CSUMJ, TJJS, USCAL, ZDUM
*     ..
*     .. External Functions ..
LOGICAL            LSAME
INTEGER            IDAMAX, IZAMAX
DOUBLE PRECISION   DLAMCH, DZASUM
EXTERNAL           LSAME, IDAMAX, IZAMAX, DLAMCH, DZASUM, ZDOTC,
*     ..
*     .. External Subroutines ..
EXTERNAL           DSCAL, XERBLA, ZAXPY, ZDSCAL, ZTBSV
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, MIN
*     ..
*     .. Statement Functions ..
DOUBLE PRECISION   CABS1, CABS2
*     ..
*     .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
CABS2( ZDUM ) = ABS( DBLE( ZDUM ) / 2.D0 ) +
\$                ABS( DIMAG( ZDUM ) / 2.D0 )
*     ..
*     .. Executable Statements ..
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
NOTRAN = LSAME( TRANS, 'N' )
NOUNIT = LSAME( DIAG, 'N' )
*
*     Test the input parameters.
*
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
\$         LSAME( TRANS, 'C' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -3
ELSE IF( .NOT.LSAME( NORMIN, 'Y' ) .AND. .NOT.
\$         LSAME( NORMIN, 'N' ) ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
ELSE IF( KD.LT.0 ) THEN
INFO = -6
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZLATBS', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
*     Determine machine dependent parameters to control overflow.
*
SMLNUM = DLAMCH( 'Safe minimum' )
BIGNUM = ONE / SMLNUM
SMLNUM = SMLNUM / DLAMCH( 'Precision' )
BIGNUM = ONE / SMLNUM
SCALE = ONE
*
IF( LSAME( NORMIN, 'N' ) ) THEN
*
*        Compute the 1-norm of each column, not including the diagonal.
*
IF( UPPER ) THEN
*
*           A is upper triangular.
*
DO 10 J = 1, N
JLEN = MIN( KD, J-1 )
CNORM( J ) = DZASUM( JLEN, AB( KD+1-JLEN, J ), 1 )
10       CONTINUE
ELSE
*
*           A is lower triangular.
*
DO 20 J = 1, N
JLEN = MIN( KD, N-J )
IF( JLEN.GT.0 ) THEN
CNORM( J ) = DZASUM( JLEN, AB( 2, J ), 1 )
ELSE
CNORM( J ) = ZERO
END IF
20       CONTINUE
END IF
END IF
*
*     Scale the column norms by TSCAL if the maximum element in CNORM is
*     greater than BIGNUM/2.
*
IMAX = IDAMAX( N, CNORM, 1 )
TMAX = CNORM( IMAX )
IF( TMAX.LE.BIGNUM*HALF ) THEN
TSCAL = ONE
ELSE
TSCAL = HALF / ( SMLNUM*TMAX )
CALL DSCAL( N, TSCAL, CNORM, 1 )
END IF
*
*     Compute a bound on the computed solution vector to see if the
*     Level 2 BLAS routine ZTBSV can be used.
*
XMAX = ZERO
DO 30 J = 1, N
XMAX = MAX( XMAX, CABS2( X( J ) ) )
30 CONTINUE
XBND = XMAX
IF( NOTRAN ) THEN
*
*        Compute the growth in A * x = b.
*
IF( UPPER ) THEN
JFIRST = N
JLAST = 1
JINC = -1
MAIND = KD + 1
ELSE
JFIRST = 1
JLAST = N
JINC = 1
MAIND = 1
END IF
*
IF( TSCAL.NE.ONE ) THEN
GROW = ZERO
GO TO 60
END IF
*
IF( NOUNIT ) THEN
*
*           A is non-unit triangular.
*
*           Compute GROW = 1/G(j) and XBND = 1/M(j).
*           Initially, G(0) = max{x(i), i=1,...,n}.
*
GROW = HALF / MAX( XBND, SMLNUM )
XBND = GROW
DO 40 J = JFIRST, JLAST, JINC
*
*              Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
\$            GO TO 60
*
TJJS = AB( MAIND, J )
TJJ = CABS1( TJJS )
*
IF( TJJ.GE.SMLNUM ) THEN
*
*                 M(j) = G(j-1) / abs(A(j,j))
*
XBND = MIN( XBND, MIN( ONE, TJJ )*GROW )
ELSE
*
*                 M(j) could overflow, set XBND to 0.
*
XBND = ZERO
END IF
*
IF( TJJ+CNORM( J ).GE.SMLNUM ) THEN
*
*                 G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) )
*
GROW = GROW*( TJJ / ( TJJ+CNORM( J ) ) )
ELSE
*
*                 G(j) could overflow, set GROW to 0.
*
GROW = ZERO
END IF
40       CONTINUE
GROW = XBND
ELSE
*
*           A is unit triangular.
*
*           Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
*
GROW = MIN( ONE, HALF / MAX( XBND, SMLNUM ) )
DO 50 J = JFIRST, JLAST, JINC
*
*              Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
\$            GO TO 60
*
*              G(j) = G(j-1)*( 1 + CNORM(j) )
*
GROW = GROW*( ONE / ( ONE+CNORM( J ) ) )
50       CONTINUE
END IF
60    CONTINUE
*
ELSE
*
*        Compute the growth in A**T * x = b  or  A**H * x = b.
*
IF( UPPER ) THEN
JFIRST = 1
JLAST = N
JINC = 1
MAIND = KD + 1
ELSE
JFIRST = N
JLAST = 1
JINC = -1
MAIND = 1
END IF
*
IF( TSCAL.NE.ONE ) THEN
GROW = ZERO
GO TO 90
END IF
*
IF( NOUNIT ) THEN
*
*           A is non-unit triangular.
*
*           Compute GROW = 1/G(j) and XBND = 1/M(j).
*           Initially, M(0) = max{x(i), i=1,...,n}.
*
GROW = HALF / MAX( XBND, SMLNUM )
XBND = GROW
DO 70 J = JFIRST, JLAST, JINC
*
*              Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
\$            GO TO 90
*
*              G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) )
*
XJ = ONE + CNORM( J )
GROW = MIN( GROW, XBND / XJ )
*
TJJS = AB( MAIND, J )
TJJ = CABS1( TJJS )
*
IF( TJJ.GE.SMLNUM ) THEN
*
*                 M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j))
*
IF( XJ.GT.TJJ )
\$               XBND = XBND*( TJJ / XJ )
ELSE
*
*                 M(j) could overflow, set XBND to 0.
*
XBND = ZERO
END IF
70       CONTINUE
GROW = MIN( GROW, XBND )
ELSE
*
*           A is unit triangular.
*
*           Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}.
*
GROW = MIN( ONE, HALF / MAX( XBND, SMLNUM ) )
DO 80 J = JFIRST, JLAST, JINC
*
*              Exit the loop if the growth factor is too small.
*
IF( GROW.LE.SMLNUM )
\$            GO TO 90
*
*              G(j) = ( 1 + CNORM(j) )*G(j-1)
*
XJ = ONE + CNORM( J )
GROW = GROW / XJ
80       CONTINUE
END IF
90    CONTINUE
END IF
*
IF( ( GROW*TSCAL ).GT.SMLNUM ) THEN
*
*        Use the Level 2 BLAS solve if the reciprocal of the bound on
*        elements of X is not too small.
*
CALL ZTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, X, 1 )
ELSE
*
*        Use a Level 1 BLAS solve, scaling intermediate results.
*
IF( XMAX.GT.BIGNUM*HALF ) THEN
*
*           Scale X so that its components are less than or equal to
*           BIGNUM in absolute value.
*
SCALE = ( BIGNUM*HALF ) / XMAX
CALL ZDSCAL( N, SCALE, X, 1 )
XMAX = BIGNUM
ELSE
XMAX = XMAX*TWO
END IF
*
IF( NOTRAN ) THEN
*
*           Solve A * x = b
*
DO 120 J = JFIRST, JLAST, JINC
*
*              Compute x(j) = b(j) / A(j,j), scaling x if necessary.
*
XJ = CABS1( X( J ) )
IF( NOUNIT ) THEN
TJJS = AB( MAIND, J )*TSCAL
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
\$               GO TO 110
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
*                    abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                          Scale x by 1/b(j).
*
REC = ONE / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J ) = ZLADIV( X( J ), TJJS )
XJ = CABS1( X( J ) )
ELSE IF( TJJ.GT.ZERO ) THEN
*
*                    0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                       Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM
*                       to avoid overflow when dividing by A(j,j).
*
REC = ( TJJ*BIGNUM ) / XJ
IF( CNORM( J ).GT.ONE ) THEN
*
*                          Scale by 1/CNORM(j) to avoid overflow when
*                          multiplying x(j) times column j.
*
REC = REC / CNORM( J )
END IF
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
X( J ) = ZLADIV( X( J ), TJJS )
XJ = CABS1( X( J ) )
ELSE
*
*                    A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and
*                    scale = 0, and compute a solution to A*x = 0.
*
DO 100 I = 1, N
X( I ) = ZERO
100             CONTINUE
X( J ) = ONE
XJ = ONE
SCALE = ZERO
XMAX = ZERO
END IF
110          CONTINUE
*
*              Scale x if necessary to avoid overflow when adding a
*              multiple of column j of A.
*
IF( XJ.GT.ONE ) THEN
REC = ONE / XJ
IF( CNORM( J ).GT.( BIGNUM-XMAX )*REC ) THEN
*
*                    Scale x by 1/(2*abs(x(j))).
*
REC = REC*HALF
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
END IF
ELSE IF( XJ*CNORM( J ).GT.( BIGNUM-XMAX ) ) THEN
*
*                 Scale x by 1/2.
*
CALL ZDSCAL( N, HALF, X, 1 )
SCALE = SCALE*HALF
END IF
*
IF( UPPER ) THEN
IF( J.GT.1 ) THEN
*
*                    Compute the update
*                       x(max(1,j-kd):j-1) := x(max(1,j-kd):j-1) -
*                                             x(j)* A(max(1,j-kd):j-1,j)
*
JLEN = MIN( KD, J-1 )
CALL ZAXPY( JLEN, -X( J )*TSCAL,
\$                           AB( KD+1-JLEN, J ), 1, X( J-JLEN ), 1 )
I = IZAMAX( J-1, X, 1 )
XMAX = CABS1( X( I ) )
END IF
ELSE IF( J.LT.N ) THEN
*
*                 Compute the update
*                    x(j+1:min(j+kd,n)) := x(j+1:min(j+kd,n)) -
*                                          x(j) * A(j+1:min(j+kd,n),j)
*
JLEN = MIN( KD, N-J )
IF( JLEN.GT.0 )
\$               CALL ZAXPY( JLEN, -X( J )*TSCAL, AB( 2, J ), 1,
\$                           X( J+1 ), 1 )
I = J + IZAMAX( N-J, X( J+1 ), 1 )
XMAX = CABS1( X( I ) )
END IF
120       CONTINUE
*
ELSE IF( LSAME( TRANS, 'T' ) ) THEN
*
*           Solve A**T * x = b
*
DO 170 J = JFIRST, JLAST, JINC
*
*              Compute x(j) = b(j) - sum A(k,j)*x(k).
*                                    k<>j
*
XJ = CABS1( X( J ) )
USCAL = TSCAL
REC = ONE / MAX( XMAX, ONE )
IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN
*
*                 If x(j) could overflow, scale x by 1/(2*XMAX).
*
REC = REC*HALF
IF( NOUNIT ) THEN
TJJS = AB( MAIND, J )*TSCAL
ELSE
TJJS = TSCAL
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.ONE ) THEN
*
*                       Divide by A(j,j) when scaling x if A(j,j) > 1.
*
REC = MIN( ONE, REC*TJJ )
USCAL = ZLADIV( USCAL, TJJS )
END IF
IF( REC.LT.ONE ) THEN
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
*
CSUMJ = ZERO
IF( USCAL.EQ.DCMPLX( ONE ) ) THEN
*
*                 If the scaling needed for A in the dot product is 1,
*                 call ZDOTU to perform the dot product.
*
IF( UPPER ) THEN
JLEN = MIN( KD, J-1 )
CSUMJ = ZDOTU( JLEN, AB( KD+1-JLEN, J ), 1,
\$                       X( J-JLEN ), 1 )
ELSE
JLEN = MIN( KD, N-J )
IF( JLEN.GT.1 )
\$                  CSUMJ = ZDOTU( JLEN, AB( 2, J ), 1, X( J+1 ),
\$                          1 )
END IF
ELSE
*
*                 Otherwise, use in-line code for the dot product.
*
IF( UPPER ) THEN
JLEN = MIN( KD, J-1 )
DO 130 I = 1, JLEN
CSUMJ = CSUMJ + ( AB( KD+I-JLEN, J )*USCAL )*
\$                          X( J-JLEN-1+I )
130                CONTINUE
ELSE
JLEN = MIN( KD, N-J )
DO 140 I = 1, JLEN
CSUMJ = CSUMJ + ( AB( I+1, J )*USCAL )*X( J+I )
140                CONTINUE
END IF
END IF
*
IF( USCAL.EQ.DCMPLX( TSCAL ) ) THEN
*
*                 Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j)
*                 was not used to scale the dotproduct.
*
X( J ) = X( J ) - CSUMJ
XJ = CABS1( X( J ) )
IF( NOUNIT ) THEN
*
*                    Compute x(j) = x(j) / A(j,j), scaling if necessary.
*
TJJS = AB( MAIND, J )*TSCAL
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
\$                  GO TO 160
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
*                       abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                             Scale X by 1/abs(x(j)).
*
REC = ONE / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J ) = ZLADIV( X( J ), TJJS )
ELSE IF( TJJ.GT.ZERO ) THEN
*
*                       0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                          Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM.
*
REC = ( TJJ*BIGNUM ) / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
X( J ) = ZLADIV( X( J ), TJJS )
ELSE
*
*                       A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and
*                       scale = 0 and compute a solution to A**T *x = 0.
*
DO 150 I = 1, N
X( I ) = ZERO
150                CONTINUE
X( J ) = ONE
SCALE = ZERO
XMAX = ZERO
END IF
160             CONTINUE
ELSE
*
*                 Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot
*                 product has already been divided by 1/A(j,j).
*
X( J ) = ZLADIV( X( J ), TJJS ) - CSUMJ
END IF
XMAX = MAX( XMAX, CABS1( X( J ) ) )
170       CONTINUE
*
ELSE
*
*           Solve A**H * x = b
*
DO 220 J = JFIRST, JLAST, JINC
*
*              Compute x(j) = b(j) - sum A(k,j)*x(k).
*                                    k<>j
*
XJ = CABS1( X( J ) )
USCAL = TSCAL
REC = ONE / MAX( XMAX, ONE )
IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN
*
*                 If x(j) could overflow, scale x by 1/(2*XMAX).
*
REC = REC*HALF
IF( NOUNIT ) THEN
TJJS = DCONJG( AB( MAIND, J ) )*TSCAL
ELSE
TJJS = TSCAL
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.ONE ) THEN
*
*                       Divide by A(j,j) when scaling x if A(j,j) > 1.
*
REC = MIN( ONE, REC*TJJ )
USCAL = ZLADIV( USCAL, TJJS )
END IF
IF( REC.LT.ONE ) THEN
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
*
CSUMJ = ZERO
IF( USCAL.EQ.DCMPLX( ONE ) ) THEN
*
*                 If the scaling needed for A in the dot product is 1,
*                 call ZDOTC to perform the dot product.
*
IF( UPPER ) THEN
JLEN = MIN( KD, J-1 )
CSUMJ = ZDOTC( JLEN, AB( KD+1-JLEN, J ), 1,
\$                       X( J-JLEN ), 1 )
ELSE
JLEN = MIN( KD, N-J )
IF( JLEN.GT.1 )
\$                  CSUMJ = ZDOTC( JLEN, AB( 2, J ), 1, X( J+1 ),
\$                          1 )
END IF
ELSE
*
*                 Otherwise, use in-line code for the dot product.
*
IF( UPPER ) THEN
JLEN = MIN( KD, J-1 )
DO 180 I = 1, JLEN
CSUMJ = CSUMJ + ( DCONJG( AB( KD+I-JLEN, J ) )*
\$                          USCAL )*X( J-JLEN-1+I )
180                CONTINUE
ELSE
JLEN = MIN( KD, N-J )
DO 190 I = 1, JLEN
CSUMJ = CSUMJ + ( DCONJG( AB( I+1, J ) )*USCAL )
\$                          *X( J+I )
190                CONTINUE
END IF
END IF
*
IF( USCAL.EQ.DCMPLX( TSCAL ) ) THEN
*
*                 Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j)
*                 was not used to scale the dotproduct.
*
X( J ) = X( J ) - CSUMJ
XJ = CABS1( X( J ) )
IF( NOUNIT ) THEN
*
*                    Compute x(j) = x(j) / A(j,j), scaling if necessary.
*
TJJS = DCONJG( AB( MAIND, J ) )*TSCAL
ELSE
TJJS = TSCAL
IF( TSCAL.EQ.ONE )
\$                  GO TO 210
END IF
TJJ = CABS1( TJJS )
IF( TJJ.GT.SMLNUM ) THEN
*
*                       abs(A(j,j)) > SMLNUM:
*
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                             Scale X by 1/abs(x(j)).
*
REC = ONE / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J ) = ZLADIV( X( J ), TJJS )
ELSE IF( TJJ.GT.ZERO ) THEN
*
*                       0 < abs(A(j,j)) <= SMLNUM:
*
IF( XJ.GT.TJJ*BIGNUM ) THEN
*
*                          Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM.
*
REC = ( TJJ*BIGNUM ) / XJ
CALL ZDSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
X( J ) = ZLADIV( X( J ), TJJS )
ELSE
*
*                       A(j,j) = 0:  Set x(1:n) = 0, x(j) = 1, and
*                       scale = 0 and compute a solution to A**H *x = 0.
*
DO 200 I = 1, N
X( I ) = ZERO
200                CONTINUE
X( J ) = ONE
SCALE = ZERO
XMAX = ZERO
END IF
210             CONTINUE
ELSE
*
*                 Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot
*                 product has already been divided by 1/A(j,j).
*
X( J ) = ZLADIV( X( J ), TJJS ) - CSUMJ
END IF
XMAX = MAX( XMAX, CABS1( X( J ) ) )
220       CONTINUE
END IF
SCALE = SCALE / TSCAL
END IF
*
*     Scale the column norms by 1/TSCAL for return.
*
IF( TSCAL.NE.ONE ) THEN
CALL DSCAL( N, ONE / TSCAL, CNORM, 1 )
END IF
*
RETURN
*
*     End of ZLATBS
*
END

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