zpbtf2.f(3) [centos man page]

zpbtf2.f(3)							      LAPACK							       zpbtf2.f(3)

NAME

       zpbtf2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zpbtf2 (UPLO, N, KD, AB, LDAB, INFO)
	   ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Function/Subroutine Documentation
   subroutine zpbtf2 (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, integerINFO)
       ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

       Purpose:

	    ZPBTF2 computes the Cholesky factorization of a complex Hermitian
	    positive definite band matrix A.

	    The factorization has the form
	       A = U**H * U ,  if UPLO = 'U', or
	       A = L  * L**H,  if UPLO = 'L',
	    where U is an upper triangular matrix, U**H is the conjugate transpose
	    of U, and L is lower triangular.

	    This is the unblocked version of the algorithm, calling Level 2 BLAS.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     Specifies whether the upper or lower triangular part of the
		     Hermitian matrix A is stored:
		     = 'U':  Upper triangular
		     = 'L':  Lower triangular

	   N

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

	   KD

		     KD is INTEGER
		     The number of super-diagonals of the matrix A if UPLO = 'U',
		     or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

	   AB

		     AB is COMPLEX*16 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 triangular factor U or L from the
		     Cholesky factorization A = U**H *U or A = L*L**H of the band
		     matrix A, in the same storage format as A.

	   LDAB

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

	   INFO

		     INFO is INTEGER
		     = 0: successful exit
		     < 0: if INFO = -k, the k-th argument had an illegal value
		     > 0: if INFO = k, the leading minor of order k is not
			  positive definite, and the factorization could not be
			  completed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Further Details:

	     The band storage scheme is illustrated by the following example, when
	     N = 6, KD = 2, and UPLO = 'U':

	     On entry:			     On exit:

		 *    *   a13  a24  a35  a46	  *    *   u13	u24  u35  u46
		 *   a12  a23  a34  a45  a56	  *   u12  u23	u34  u45  u56
		a11  a22  a33  a44  a55  a66	 u11  u22  u33	u44  u55  u66

	     Similarly, if UPLO = 'L' the format of A is as follows:

	     On entry:			     On exit:

		a11  a22  a33  a44  a55  a66	 l11  l22  l33	l44  l55  l66
		a21  a32  a43  a54  a65   *	 l21  l32  l43	l54  l65   *
		a31  a42  a53  a64   *	  *	 l31  l42  l53	l64   *    *

	     Array elements marked * are not used by the routine.

       Definition at line 143 of file zpbtf2.f.

Author
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Version 3.4.2							  Tue Sep 25 2012						       zpbtf2.f(3)