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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(l)								 )								 SPBSTF(l)

NAME

       SPBSTF - compute a split Cholesky factorization of a real symmetric positive definite band matrix A

SYNOPSIS

       SUBROUTINE SPBSTF( UPLO, N, KD, AB, LDAB, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   REAL 	  AB( LDAB, * )

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.

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) 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	  (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.

LAPACK version 3.0						   15 June 2000 							 SPBSTF(l)
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