## Developer Reference

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

# ?gbtf2

Computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

## Syntax

Include Files
• mkl.fi
Description
The routine forms the
LU
factorization of a general real/complex
m
-by-
n
band matrix
A
with
kl
sub-diagonals and
ku
super-diagonals. The routine uses partial pivoting with row interchanges and implements the unblocked version of the algorithm, calling Level 2 BLAS. See also
?gbtrf
.
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
sgbtf2
DOUBLE PRECISION
for
dgbtf2
COMPLEX
for
cgbtf2
DOUBLE COMPLEX
for
zgbtf2
.
Array,
DIMENSION
(
ldab
,*).
The array
ab
contains the matrix
A
in band storage (see Matrix Arguments).
The second dimension of
ab
must be at least
max(1,
n
)
.
ldab
INTEGER
. The leading dimension of the array
ab
.
(
ldab
2
kl
+
ku
+1)
Output Parameters
ab
Overwritten by details of the factorization. The diagonal and
kl
+
ku
super-diagonals of
U
are stored in the first 1 +
kl
+
ku
rows of
ab
. The multipliers used during the factorization are stored in the next
kl
rows.
ipiv
INTEGER
.
Array,
DIMENSION
at least max(1,min(
m
,
n
)).
The pivot indices: row
i
was interchanged with row
ipiv
(
i
).
info
INTEGER
. If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
If
info
=
i
,
u
i
i
is 0. The factorization has been completed, but
U
is exactly singular. Division by 0 will occur if you use the factor
U
for solving a system of linear equations.