MAN page from OpenSuSE 12.X lapack-man-3.3.1-15.1.noarch.rpm

CGBTF2

Section: LAPACK routine (version 3.2) (1)
Updated: April 2011
Index

NAME

LAPACK-3 - computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges

SYNOPSIS

SUBROUTINE CGBTF2(: M, N, KL, KU, AB, LDAB, IPIV, INFO )
: INTEGERINFO, KL, KU, LDAB, M, N
: INTEGERIPIV( * )
: COMPLEXAB( LDAB, * )

PURPOSE

CGBTF2 computes an LU factorization of a complex m-by-n band matrixA using partial pivoting with row interchanges.
This is the unblocked version of the algorithm, calling Level 2 BLAS.

ARGUMENTS

M (input) INTEGER: The number of rows of the matrix A. M >= 0.
N (input) INTEGER: The number of columns of the matrix A. N >= 0.
KL (input) INTEGER: The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER: The number of superdiagonals within the band of A. KU >= 0.
AB (input/output) COMPLEX 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 (input) INTEGER: The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
IPIV (output) 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 (output) 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.

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

interchanges.

This document was created byman2html,using the manual pages.