## Developer Reference

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

# ?langb

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

## Syntax

Include Files
• mkl.fi
Description
The function returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an
n
-by-
n
band matrix
A
, with
kl
sub-diagonals and
ku
super-diagonals.
Input Parameters
norm
CHARACTER*1
. Specifies the value to be returned by the routine:
=
'M'
or
'm':
val
=
max
(
abs
(
A
i
j
))
, largest absolute value of the matrix
A
.
=
'1'
or
'O'
or
'o':
val
=
norm1
(
A
)
, 1-norm of the matrix
A
(maximum column sum),
=
'I'
or
'i':
val
=
normI
(
A
)
, infinity norm of the matrix
A
(maximum row sum),
=
'F'
,
'f'
,
'E'
or
'e':
val
=
normF
(
A
)
, Frobenius norm of the matrix
A
(square root of sum of squares).
n
INTEGER
. The order of the matrix
A
.
n
0
. When
n
= 0
,
?langb
is set to zero.
kl
INTEGER
. The number of sub-diagonals of the matrix
A
.
kl
0
.
ku
INTEGER
. The number of super-diagonals of the matrix
A
.
ku
0
.
ab
REAL
for
slangb
DOUBLE PRECISION
for
dlangb
COMPLEX
for
clangb
DOUBLE COMPLEX
for
zlangb
Array,
DIMENSION
(
ldab
,
n
).
The band matrix
A
, stored in rows 1 to
kl
+
ku
+1. The
j
-th column of
A
is stored in the
j
-th column of the array
ab
as follows:
ab
(
ku
+1+
i
-
j
,
j
) =
a
(
i
,
j
)
for
max(1,
j
-
k
u
) ≤
i
≤ min(
n
,
j
+
k
l
)
.
ldab
INTEGER
. The leading dimension of the array
ab
.
ldab
kl
+
ku
+1
.
work
REAL
for
slangb
/
clangb
DOUBLE PRECISION
for
dlangb
/
zlangb
Workspace array,
DIMENSION
(
max(1,
lwork
)
), where
lwork
n
when
norm
=
'I'
; otherwise,
work
is not referenced.