Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?dbtf2

Computes an LU factorization of a general band matrix with no pivoting (local unblocked algorithm).

Syntax

call sdbtf2
(
m
,
n
,
kl
,
ku
,
ab
,
ldab
,
info
)
call ddbtf2
(
m
,
n
,
kl
,
ku
,
ab
,
ldab
,
info
)
call cdbtf2
(
m
,
n
,
kl
,
ku
,
ab
,
ldab
,
info
)
call zdbtf2
(
m
,
n
,
kl
,
ku
,
ab
,
ldab
,
info
)
Description
The
?dbtf2
routine
computes an
LU
factorization of a general real/complex
m
-by-
n
band matrix
A
without using partial pivoting with row interchanges.
This is the unblocked version of the algorithm, calling BLAS Routines and Functions .
Input Parameters
m
INTEGER
.
The number of rows of the matrix
A
(
m
0)
.
n
INTEGER
.
The number of columns in
A
(
n
0)
.
kl
INTEGER
.
The number of sub-diagonals within the band of
A
(
kl
0)
.
ku
INTEGER
.
The number of super-diagonals within the band of
A
(
ku
0)
.
ab
REAL
for
sdbtf2
DOUBLE PRECISION
for
ddbtf2
COMPLEX
for
cdbtf2
COMPLEX*16
for
zdbtf2
.
Array of size
ldab
by
n
.
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
).
ldab
INTEGER
.
The leading dimension of the array
ab
.
(
ldab
2
kl
+
ku
+1)
Output Parameters
ab
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<