.TH "SRC/dpbstf.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dpbstf.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdpbstf\fP (uplo, n, kd, ab, ldab, info)"
.br
.RI "\fBDPBSTF\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dpbstf (character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, integer info)"

.PP
\fBDPBSTF\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 0\&.
!> 
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= KD+1\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  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\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB151\fP of file \fBdpbstf\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.