table of contents
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sgbtf2.f(3) | Library Functions Manual | /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sgbtf2.f(3) |
NAME¶
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sgbtf2.f
SYNOPSIS¶
Functions/Subroutines¶
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 (integer m, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)¶
SGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.
Purpose:
!> !> 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. !>
Parameters
M
!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>
N
!> N is INTEGER !> The number of columns of the matrix A. N >= 0. !>
KL
!> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !>
KU
!> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !>
AB
!> 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
!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= 2*KL+KU+1. !>
IPIV
!> 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
!> 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. !>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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. !>
Definition at line 144 of file sgbtf2.f.
Author¶
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