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CentOS 7.0 - man page for cpbstf.f (centos section 3)

cpbstf.f(3)				      LAPACK				      cpbstf.f(3)

       cpbstf.f -

       subroutine cpbstf (UPLO, N, KD, AB, LDAB, INFO)

Function/Subroutine Documentation
   subroutine cpbstf (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB,
       integerLDAB, integerINFO)


	    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.


		     UPLO is CHARACTER*1
		     = 'U':  Upper triangle of A is stored;
		     = 'L':  Lower triangle of A is stored.


		     N is INTEGER
		     The order of the matrix A.  N >= 0.


		     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 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 is INTEGER
		     The leading dimension of the array AB.  LDAB >= KD+1.


		     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.

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   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**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 154 of file cpbstf.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      cpbstf.f(3)

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