cdbtrf(3) [debian man page]
CDBTRF - compute an LU factorization of a real m-by-n band matrix
A without using partial pivoting or row interchanges SUBROUTINE
CDBTRF( M, N, KL, KU, AB, LDAB, INFO )
INTEGER INFO, KL, KU, LDAB, M, N
COMPLEX AB( LDAB, * ) Cdbtrf computes an LU factorization of
a real m-by-n band matrix A without using partial pivoting or row
interchanges.
This is the blocked version of the algorithm, calling Level 3
BLAS.
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 num-
ber of superdiagonals within the band of A. KU >;= 0. AB
(input/output) REAL array, dimension (LDAB,N) On entry, the ma-
trix 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 de-
tails. LDAB (input) INTEGER The leading dimension of the ar-
ray AB. LDAB >;= 2*KL+KU+1. INFO (output) INTEGER = 0: suc-
cessful 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 divi-
sion by zero will occur if it is used to solve a system of equa-
tions. The band storage scheme is illustrated by the following
example, when M = N = 6, KL = 2, KU = 1:
On entry: On exit:
* 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.
Check Out this Related Man Page
SDBTF2 - compute an LU factorization of a real m-by-n band matrix
A without using partial pivoting with row interchanges SUBROUTINE
SDBTF2( M, N, KL, KU, AB, LDAB, INFO )
INTEGER INFO, KL, KU, LDAB, M, N
REAL AB( LDAB, * ) Sdbtrf computes an LU factorization of a
real m-by-n band matrix A without using partial pivoting with row
interchanges.
This is the unblocked version of the algorithm, calling Level 2
BLAS.
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 num-
ber of superdiagonals within the band of A. KU >;= 0. AB
(input/output) 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 de-
tails. LDAB (input) INTEGER The leading dimension of the ar-
ray AB. LDAB >;= 2*KL+KU+1. INFO (output) INTEGER = 0: suc-
cessful 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 divi-
sion by zero will occur if it is used to solve a system of equa-
tions. The band storage scheme is illustrated by the following
example, when M = N = 6, KL = 2, KU = 1:
On entry: On exit:
* 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 rou-
tine to store elements of U, because of fill-in resulting from
the row
interchanges.