Developer Reference

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

?lanhs

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

Syntax

val
=
slanhs
(
norm
,
n
,
a
,
lda
,
work
)
val
=
dlanhs
(
norm
,
n
,
a
,
lda
,
work
)
val
=
clanhs
(
norm
,
n
,
a
,
lda
,
work
)
val
=
zlanhs
(
norm
,
n
,
a
,
lda
,
work
)
Include Files
  • mkl.fi
Description
The function
?lanhs
returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix
A
.
The value
val
returned by the function is:
val
= max(abs(
A
i
j
))
, if
norm
=
'M'
or
'm'
=
norm1
(
A
), if
norm
=
'1'
or
'O'
or
'o'
=
normI
(
A
), if
norm
=
'I'
or
'i'
=
normF
(
A
), if
norm
=
'F'
,
'f'
,
'E'
or
'e'
where
norm1
denotes the 1-norm of a matrix (maximum column sum),
normI
denotes the infinity norm of a matrix (maximum row sum) and
normF
denotes the Frobenius norm of a matrix (square root of sum of squares). Note that
max(abs(
A
i
j
))
is not a consistent matrix norm.
Input Parameters
norm
CHARACTER*1
. Specifies the value to be returned by the routine as described above.
n
INTEGER
. The order of the matrix
A
.
n
0
. When
n
= 0
,
?lanhs
is set to zero.
a
REAL
for
slanhs
DOUBLE PRECISION
for
dlanhs
COMPLEX
for
clanhs
DOUBLE COMPLEX
for
zlanhs
Array,
DIMENSION
(
lda
,
n
). The
n
-by-
n
upper Hessenberg matrix
A
; the part of
A
below the first sub-diagonal is not referenced.
lda
INTEGER
. The leading dimension of the array
a
.
lda
max(
n
,1)
.
work
REAL
for
slanhs
and
clanhs
.
DOUBLE PRECISION
for
dlange
and
zlange
.
Workspace array,
DIMENSION
(max(1,
lwork
))
, where
lwork
n
when
norm
=
'I'
; otherwise,
work
is not referenced.
Output Parameters
val
REAL
for
slanhs
/
clanhs
DOUBLE PRECISION
for
dlanhs
/
zlanhs
Value returned by the function.

Product and Performance Information