Contents

# ?dbtf2

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

## Syntax

Include Files
• mkl_scalapack.h
Description
The
?dbtf2
function
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
The number of rows of the matrix
A
(
m
0)
.
n
The number of columns in
A
(
n
0)
.
kl
The number of sub-diagonals within the band of
A
(
kl
0)
.
ku
The number of super-diagonals within the band of
A
(
ku
0)
.
ab
Array of size
ldab
*
n
.
The matrix
A
in band storage, in rows
kl
+1
to
2
kl
+
ku
+1
; rows 1 to
kl
of the
matrix
need not be set. The
j
-th column of
A
is stored in the array
ab
as follows:
ab
[
kl
+
ku
+
i
-
j
+(
j
-1)*
ldab
] =
A
(
i
,
j
) for
max
(1,
j
-
ku
) ≤
i
min
(
m
,
j
+
kl
).
ldab
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
+2
to
2*
kl
+
ku
+1
.
See the
Application Notes
below for further details
.
info
= 0
: successful exit
< 0
: if
info
= -
i
, the
i
-th argument had an illegal value,
>
0: if
info
= +
i
,
the matrix element
U
(
i
,
i
) is 0. The factorization has been completed, but the factor
U
is exactly singular. Division by 0 will occur if you use the factor
U
for solving a system of linear equations.
Application Notes
The band storage scheme is illustrated by the following example, when
m
=
n
= 6
,
kl
= 2
,
ku
= 1
: The
function
does not use array elements marked *; elements marked + need not be set on entry, but the
function
requires them to store elements of
U
, because of fill-in resulting from the row interchanges.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.