Provided by: liblapack-doc_3.3.1-1_all

#### NAME

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

```

#### SYNOPSIS

```       SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )

CHARACTER      UPLO

INTEGER        INFO, KD, LDAB, N

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**H * U ,  if UPLO = 'U', or
A = L  * L**H,  if UPLO = 'L',
where U is an upper triangular matrix, U**H 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**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 = -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.

```

#### FURTHERDETAILS

```        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.

LAPACK routine (version 3.3.1)             April 2011                            ZPBTF2(3lapack)
```