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

```zpbstf.f(3)							      LAPACK							       zpbstf.f(3)

NAME
zpbstf.f -

SYNOPSIS
Functions/Subroutines
subroutine zpbstf (UPLO, N, KD, AB, LDAB, INFO)
ZPBSTF

Function/Subroutine Documentation
subroutine zpbstf (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, integerINFO)
ZPBSTF

Purpose:

ZPBSTF computes a split Cholesky factorization of a complex
Hermitian positive definite band matrix A.

This routine is designed to be used in conjunction with ZHBGST.

The factorization has the form  A = S**H*S	where S is a band matrix
of the same bandwidth as A and the following structure:

S = ( U	 )
( M  L )

where U is upper triangular of order m = (n+kd)/2, and L is lower
triangular of order n-m.

Parameters:
UPLO

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

N

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

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals 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 factor S from the split Cholesky
factorization A = S**H*S. See Further Details.

LDAB

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

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the factorization could not be completed,
because the updated element a(i,i) was negative; the
matrix A is not positive definite.

Author:
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:
November 2011

Further Details:

The band storage scheme is illustrated by the following example, when
N = 7, KD = 2:

S = ( s11	s12  s13		     )
(	s22  s23  s24		     )
(	     s33  s34		     )
(		  s44		     )
(	     s53  s54  s55	     )
(		  s64  s65  s66      )
(		       s75  s76  s77 )

If UPLO = 'U', the array AB holds:

on entry:				on exit:

*    *   a13  a24  a35  a46  a57	 *    *   s13  s24  s53**H s64**H s75**H
*   a12  a23  a34  a45  a56  a67	 *   s12  s23  s34  s54**H s65**H s76**H
a11  a22  a33  a44  a55  a66  a77	s11  s22  s33  s44  s55    s66	  s77

If UPLO = 'L', the array AB holds:

on entry:				on exit:

a11  a22  a33  a44  a55  a66  a77	s11    s22    s33    s44  s55  s66  s77
a21  a32  a43  a54  a65  a76   *	s12**H s23**H s34**H s54  s65  s76   *
a31  a42  a53  a64  a64   *    *	s13**H s24**H s53    s64  s75	*    *

Array elements marked * are not used by the routine; s12**H denotes
conjg(s12); the diagonal elements of S are real.

Definition at line 154 of file zpbstf.f.

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

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

## Check Out this Related Man Page

```ZPBSTF(l)								 )								 ZPBSTF(l)

NAME
ZPBSTF - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A

SYNOPSIS
SUBROUTINE ZPBSTF( UPLO, N, KD, AB, LDAB, INFO )

CHARACTER	  UPLO

INTEGER	  INFO, KD, LDAB, N

COMPLEX*16	  AB( LDAB, * )

PURPOSE
ZPBSTF computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A.  This routine is designed to be used
in conjunction with ZHBGST.

The factorization has the form  A = S**H*S  where S is a band matrix of the same bandwidth as A and the following structure:

S = ( U    )
( M  L )

where U is upper triangular of order m = (n+kd)/2, and L is lower triangular of order n-m.

ARGUMENTS
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 factor S from the split Cholesky factorization A = S**H*S. See Further Details.  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 factorization could not be completed, because the updated element a(i,i) was negative; the matrix A is not
positive definite.

FURTHER DETAILS
The band storage scheme is illustrated by the following example, when N = 7, KD = 2:

S = ( s11  s12  s13		       )
(	  s22  s23  s24 	       )
(	       s33  s34 	       )
(		    s44 	       )
(	       s53  s54  s55	       )
(		    s64  s65  s66      )
(			 s75  s76  s77 )

If UPLO = 'U', the array AB holds:

on entry:			  on exit:

*    *	 a13  a24  a35	a46  a57   *	*   s13  s24  s53' s64' s75'
*   a12  a23  a34  a45	a56  a67   *   s12  s23  s34  s54' s65' s76' a11  a22  a33  a44  a55  a66  a77	s11  s22  s33  s44  s55  s66  s77

If UPLO = 'L', the array AB holds:

on entry:			  on exit:

a11  a22  a33  a44  a55	a66  a77  s11  s22  s33  s44  s55  s66	s77 a21  a32  a43  a54	a65  a76   *   s12' s23' s34' s54   s65   s76	 *
a31  a42  a53  a64  a64	 *    *   s13' s24' s53  s64  s75   *	 *

Array elements marked * are not used by the routine; s12' denotes conjg(s12); the diagonal elements of S are real.

LAPACK version 3.0						   15 June 2000 							 ZPBSTF(l)```
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