# zpbtf2.f(3) [centos man page]

```zpbtf2.f(3)							      LAPACK							       zpbtf2.f(3)

NAME
zpbtf2.f -

SYNOPSIS
Functions/Subroutines
subroutine zpbtf2 (UPLO, N, KD, AB, LDAB, INFO)
ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Function/Subroutine Documentation
subroutine zpbtf2 (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, integerINFO)
ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

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.

Parameters:
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U':  Upper triangular
= 'L':  Lower triangular

N

N is INTEGER
The order of the matrix A.  N >= 0.

KD

KD is 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

AB is 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

LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

INFO

INFO is 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.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

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.

Definition at line 143 of file zpbtf2.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zpbtf2.f(3)```

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```zpbtf2.f(3)							      LAPACK							       zpbtf2.f(3)

NAME
zpbtf2.f -

SYNOPSIS
Functions/Subroutines
subroutine zpbtf2 (UPLO, N, KD, AB, LDAB, INFO)
ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Function/Subroutine Documentation
subroutine zpbtf2 (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, integerINFO)
ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

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.

Parameters:
UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U':  Upper triangular
= 'L':  Lower triangular

N

N is INTEGER
The order of the matrix A.  N >= 0.

KD

KD is 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

AB is 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

LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

INFO

INFO is 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.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

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.

Definition at line 143 of file zpbtf2.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zpbtf2.f(3)```
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