cpbstf man page on Scientific

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CPBSTF(1)		 LAPACK routine (version 3.2)		     CPBSTF(1)

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

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

CHARACTER	  UPLO

INTEGER	  INFO, KD, LDAB, N

COMPLEX	  AB( LDAB, * )

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  tri‐
angular 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 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 routine (version 3.2)	 November 2008			     CPBSTF(1)
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