# dpbstf(3) [centos man page]

```dpbstf.f(3)							      LAPACK							       dpbstf.f(3)

NAME
dpbstf.f -

SYNOPSIS
Functions/Subroutines
subroutine dpbstf (UPLO, N, KD, AB, LDAB, INFO)
DPBSTF

Function/Subroutine Documentation
subroutine dpbstf (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, integerINFO)
DPBSTF

Purpose:

DPBSTF computes a split Cholesky factorization of a real
symmetric positive definite band matrix A.

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

The factorization has the form  A = S**T*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 DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric 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**T*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  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.

Definition at line 153 of file dpbstf.f.

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

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

## Check Out this Related Man Page

```spbstf.f(3)							      LAPACK							       spbstf.f(3)

NAME
spbstf.f -

SYNOPSIS
Functions/Subroutines
subroutine spbstf (UPLO, N, KD, AB, LDAB, INFO)
SPBSTF

Function/Subroutine Documentation
subroutine spbstf (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, integerINFO)
SPBSTF

Purpose:

SPBSTF computes a split Cholesky factorization of a real
symmetric positive definite band matrix A.

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

The factorization has the form  A = S**T*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 REAL array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric 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**T*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  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.

Definition at line 153 of file spbstf.f.

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

Version 3.4.1							  Sun May 26 2013						       spbstf.f(3)```
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