SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          UPLO
INTEGER            INFO, KD, LDAB, N
*     ..
*     .. Array Arguments ..
COMPLEX*16         AB( LDAB, * )
*     ..
*
*  Purpose
*  =======
*
*  ZPBTF2 computes the Cholesky factorization of a complex Hermitian
*  positive definite band matrix A.
*
*  The factorization has the form
*     A = U' * U ,  if UPLO = 'U', or
*     A = L  * L',  if UPLO = 'L',
*  where U is an upper triangular matrix, U' is the conjugate transpose
*  of U, and L is lower triangular.
*
*  This is the unblocked version of the algorithm, calling Level 2 BLAS.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the upper or lower triangular part of the
*          Hermitian matrix A is stored:
*          = 'U':  Upper triangular
*          = 'L':  Lower triangular
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  KD      (input) INTEGER
*          The number of super-diagonals of the matrix A if UPLO = 'U',
*          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
*
*  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
*          On entry, the upper or lower triangle of the Hermitian 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).
*
*          On exit, if INFO = 0, the triangular factor U or L from the
*          Cholesky factorization A = U'*U or A = L*L' of the band
*          matrix A, in the same storage format as A.
*
*  LDAB    (input) INTEGER
*          The leading dimension of the array AB.  LDAB >= KD+1.
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -k, the k-th argument had an illegal value
*          > 0: if INFO = k, the leading minor of order k is not
*               positive definite, and the factorization could not be
*               completed.
*
*  Further Details
*  ===============
*
*  The band storage scheme is illustrated by the following example, when
*  N = 6, KD = 2, and UPLO = 'U':
*
*  On entry:                       On exit:
*
*      *    *   a13  a24  a35  a46      *    *   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
*
*  Similarly, if UPLO = 'L' the format of A is as follows:
*
*  On entry:                       On exit:
*
*     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
*     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
*     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
*
*  Array elements marked * are not used by the routine.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ONE, ZERO
PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
LOGICAL            UPPER
INTEGER            J, KLD, KN
DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
LOGICAL            LSAME
EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL           XERBLA, ZDSCAL, ZHER, ZLACGV
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          DBLE, MAX, MIN, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KD.LT.0 ) THEN
INFO = -3
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZPBTF2', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
KLD = MAX( 1, LDAB-1 )
*
IF( UPPER ) THEN
*
*        Compute the Cholesky factorization A = U'*U.
*
DO 10 J = 1, N
*
*           Compute U(J,J) and test for non-positive-definiteness.
*
AJJ = DBLE( AB( KD+1, J ) )
IF( AJJ.LE.ZERO ) THEN
AB( KD+1, J ) = AJJ
GO TO 30
END IF
AJJ = SQRT( AJJ )
AB( KD+1, J ) = AJJ
*
*           Compute elements J+1:J+KN of row J and update the
*           trailing submatrix within the band.
*
KN = MIN( KD, N-J )
IF( KN.GT.0 ) THEN
CALL ZDSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD )
CALL ZLACGV( KN, AB( KD, J+1 ), KLD )
CALL ZHER( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD,
\$                    AB( KD+1, J+1 ), KLD )
CALL ZLACGV( KN, AB( KD, J+1 ), KLD )
END IF
10    CONTINUE
ELSE
*
*        Compute the Cholesky factorization A = L*L'.
*
DO 20 J = 1, N
*
*           Compute L(J,J) and test for non-positive-definiteness.
*
AJJ = DBLE( AB( 1, J ) )
IF( AJJ.LE.ZERO ) THEN
AB( 1, J ) = AJJ
GO TO 30
END IF
AJJ = SQRT( AJJ )
AB( 1, J ) = AJJ
*
*           Compute elements J+1:J+KN of column J and update the
*           trailing submatrix within the band.
*
KN = MIN( KD, N-J )
IF( KN.GT.0 ) THEN
CALL ZDSCAL( KN, ONE / AJJ, AB( 2, J ), 1 )
CALL ZHER( 'Lower', KN, -ONE, AB( 2, J ), 1,
\$                    AB( 1, J+1 ), KLD )
END IF
20    CONTINUE
END IF
RETURN
*
30 CONTINUE
INFO = J
RETURN
*
*     End of ZPBTF2
*
END