Provided by: liblapack-doc_3.3.1-1_all bug


       LAPACK-3  -  computes  the Cholesky factorization of a complex Hermitian positive definite
       band matrix A



           CHARACTER      UPLO

           INTEGER        INFO, KD, LDAB, N

           COMPLEX*16     AB( LDAB, * )


       ZPBTRF computes the Cholesky factorization of a complex Hermitian positive  definite  band
       matrix A.
        The factorization has the form
           A = U**H * U,  if UPLO = 'U', or
           A = L  * L**H,  if UPLO = 'L',
        where U is an upper triangular matrix and L is lower triangular.


        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

        N       (input) INTEGER
                The order of the matrix A.  N >= 0.

        KD      (input) INTEGER
                The number of superdiagonals of the matrix A if UPLO = 'U',
                or the number of subdiagonals 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**H*U or A = L*L**H 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 = -i, the i-th argument had an illegal value
                > 0:  if INFO = i, the leading minor of order i is not
                positive definite, and the factorization could not be


        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.
        Contributed by
        Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

 LAPACK routine (version 3.2)               April 2011                            ZPBTRF(3lapack)