dgbtrf.f man page
dgbtrf.f subroutine dgbtrf (M, N, KL, KU, AB, LDAB, IPIV, INFO) DGBTRF Purpose: M N KL KU AB LDAB IPIV INFO Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. December 2016 Further Details: Definition at line 146 of file dgbtrf.f. Generated automatically by Doxygen for LAPACK from the source code. The man page dgbtrf(3) is an alias of dgbtrf.f(3).
subroutine dgbtrf (integer M, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, integer, dimension( * ) IPIV, integer INFO)
DGBTRF computes an LU factorization of a real m-by-n band matrix A
using partial pivoting with row interchanges.
This is the blocked version of the algorithm, calling Level 3 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 DOUBLE PRECISION 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.
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.
subroutine dgbtrf (M, N, KL, KU, AB, LDAB, IPIV, INFO)
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
Definition at line 146 of file dgbtrf.f.
Generated automatically by Doxygen for LAPACK from the source code.
The man page dgbtrf(3) is an alias of dgbtrf.f(3).