cgbtf2(3P) Sun Performance Library cgbtf2(3P)NAMEcgbtf2 - compute 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)
COMPLEX AB(LDAB,*)
INTEGER M, N, KL, KU, LDAB, INFO
INTEGER IPIV(*)
SUBROUTINE CGBTF2_64(M, N, KL, KU, AB, LDAB, IPIV, INFO)
COMPLEX AB(LDAB,*)
INTEGER*8 M, N, KL, KU, LDAB, INFO
INTEGER*8 IPIV(*)
F95 INTERFACE
SUBROUTINE GBTF2([M], [N], KL, KU, AB, [LDAB], IPIV, [INFO])
COMPLEX, DIMENSION(:,:) :: AB
INTEGER :: M, N, KL, KU, LDAB, INFO
INTEGER, DIMENSION(:) :: IPIV
SUBROUTINE GBTF2_64([M], [N], KL, KU, AB, [LDAB], IPIV, [INFO])
COMPLEX, DIMENSION(:,:) :: AB
INTEGER(8) :: M, N, KL, KU, LDAB, INFO
INTEGER(8), DIMENSION(:) :: IPIV
C INTERFACE
#include <sunperf.h>
void cgbtf2(int m, int n, int kl, int ku, complex *ab, int ldab, int
*ipiv, int *info);
void cgbtf2_64(long m, long n, long kl, long ku, complex *ab, long
ldab, long *ipiv, long *info);
PURPOSEcgbtf2 computes an LU factorization of a complex m-by-n band matrix A
using partial pivoting with row interchanges.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
ARGUMENTS
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrix A. N >= 0.
KL (input)
The number of subdiagonals within the band of A. KL >= 0.
KU (input)
The number of superdiagonals within the band of A. KU >= 0.
AB (input/output)
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 fac‐
torization are stored in rows KL+KU+2 to 2*KL+KU+1. See
below for further details.
LDAB (input)
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
IPIV (output)
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
INFO (output)
= 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 ele‐
ments of U, because of fill-in resulting from the row
interchanges.
6 Mar 2009 cgbtf2(3P)
