Developer Reference

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

?lanhb

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

Syntax

val
=
clanhb
(
norm
,
uplo
,
n
,
k
,
ab
,
ldab
,
work
)
val
=
zlanhb
(
norm
,
uplo
,
n
,
k
,
ab
,
ldab
,
work
)
Include Files
  • mkl.fi
Description
The routine 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
Hermitian band matrix
A
, with
k
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).
uplo
CHARACTER*1
.
Specifies whether the upper or lower triangular part of the band matrix
A
is supplied.
If
uplo
=
'U'
: upper triangular part is supplied;
If
uplo
=
'L'
: lower triangular part is supplied.
n
INTEGER
. The order of the matrix
A
.
n
0
. When
n
= 0
,
?lanhb
is set to zero.
k
INTEGER
. The number of super-diagonals or sub-diagonals of the band matrix
A
.
k
0
.
ab
COMPLEX
for
clanhb
.
DOUBLE COMPLEX
for
zlanhb
.
Array,
DIMENSION
(
ldaB
,
n
). The upper or lower triangle of the Hermitian band matrix
A
, stored in the first
k
+1 rows of
ab
. The
j
-th column of
A
is stored in the
j
-th column of the array
ab
as follows:
if
uplo
=
'U'
,
ab
(
k
+1+
i
-
j
,
j
) =
a
(
i
,
j
)
for
max(1,
j
-
k
) ≤
i
j
;
if
uplo
=
'L'
,
ab
(1+
i
-
j
,
j
) =
a
(
i
,
j
)
for
j
i
≤ min(
n
,
j
+
k
)
.
Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
ldab
INTEGER
. The leading dimension of the array
ab
.
ldab
k
+1.