# cpbstf.f - Man Page

SRC/cpbstf.f

## Synopsis

### Functions/Subroutines

subroutine cpbstf (uplo, n, kd, ab, ldab, info)
CPBSTF

## Function/Subroutine Documentation

### subroutine cpbstf (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, integer info)

CPBSTF

Purpose:

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

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

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 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

NAG Ltd.

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 152 of file cpbstf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cpbstf(3) is an alias of cpbstf.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK