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sgbtf2.f(3)				      LAPACK				      sgbtf2.f(3)

       sgbtf2.f -

       subroutine sgbtf2 (M, N, KL, KU, AB, LDAB, IPIV, INFO)
	   SGBTF2 computes the LU factorization of a general band matrix using the unblocked
	   version of the algorithm.

Function/Subroutine Documentation
   subroutine sgbtf2 (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB,
       integerLDAB, integer, dimension( * )IPIV, integerINFO)
       SGBTF2 computes the LU factorization of a general band matrix using the unblocked version
       of the algorithm.


	    SGBTF2 computes an LU factorization of a real m-by-n band matrix A
	    using partial pivoting with row interchanges.

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


		     M is INTEGER
		     The number of rows of the matrix A.  M >= 0.


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


		     KL is INTEGER
		     The number of subdiagonals within the band of A.  KL >= 0.


		     KU is INTEGER
		     The number of superdiagonals within the band of A.  KU >= 0.


		     AB is REAL array, dimension (LDAB,N)
		     On entry, the matrix A in band storage, in rows KL+1 to
		     2*KL+KU+1; rows 1 to KL of the array need not be set.
		     The j-th column of A is stored in the j-th column of the
		     array AB as follows:
		     AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)

		     On exit, details of the factorization: U is stored as an
		     upper triangular band matrix with KL+KU superdiagonals in
		     rows 1 to KL+KU+1, and the multipliers used during the
		     factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
		     See below for further details.


		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.


		     IPIV is INTEGER array, dimension (min(M,N))
		     The pivot indices; for 1 <= i <= min(M,N), row i of the
		     matrix was interchanged with row IPIV(i).


		     INFO is INTEGER
		     = 0: successful exit
		     < 0: if INFO = -i, the i-th argument had an illegal value
		     > 0: if INFO = +i, U(i,i) is exactly zero. The factorization
			  has been completed, but the factor U is exactly
			  singular, and division by zero will occur if it is used
			  to solve a system of equations.

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   September 2012

       Further Details:

	     The band storage scheme is illustrated by the following example, when
	     M = N = 6, KL = 2, KU = 1:

	     On entry:			     On exit:

		 *    *    *	+    +	  +	  *    *    *	u14  u25  u36
		 *    *    +	+    +	  +	  *    *   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
		a21  a32  a43  a54  a65   *	 m21  m32  m43	m54  m65   *
		a31  a42  a53  a64   *	  *	 m31  m42  m53	m64   *    *

	     Array elements marked * are not used by the routine; elements marked
	     + need not be set on entry, but are required by the routine to store
	     elements of U, because of fill-in resulting from the row

       Definition at line 146 of file sgbtf2.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      sgbtf2.f(3)
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