## Developer Reference

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

# ?larfy

Applies an elementary reflector, or Householder matrix, H, to an
n
by
n
symmetric or Hermitian matrix C, from both the left and the right.
Description
?larfy
applies an elementary reflector, or Householder matrix, H, to an
n
by
n
symmetric or Hermitian matrix C, from both the left and the right. H is represented in the form H = I -
tau
*
v
*
v
T
(for real flavors) or H = I -
tau
*
v
*
v
H
(for complex flavors), where tau is a scalar and
v
is a vector. If
tau
is zero, H is taken to be the unit matrix.
Input Parameters
uplo
CHARACTER*1
Specifies whether the upper or lower triangular part of the symmetric or Hermitian matrix C is stored.
• =
'U'
: Upper triangular part of C is stored.
• =
'L'
: Lower triangular part of C is stored.
n
INTEGER
The number of rows and columns of the matrix C.
n
≥ 0.
v
REAL
for
slarfy
DOUBLE PRECISION
for
dlarfy
COMPLEX
for
clarfy
COMPLEX*16
for
zlarfy
Array, dimension (1 + (
n
-
1)*abs(
incv
)). The vector
v
as described above.
incv
INTEGER
The increment between successive elements of v.
incv
must not be zero.
tau
REAL
for
slarfy
DOUBLE PRECISION
for
dlarfy
COMPLEX
for
clarfy
COMPLEX*16
for
zlarfy
The value
tau
as described above.
C
REAL
for
slarfy
DOUBLE PRECISION
for
dlarfy
COMPLEX
for
clarfy
COMPLEX*16
for
zlarfy
Array, dimension (
ldc
,
n
). On entry, the matrix C.
ldc
INTEGER
The leading dimension of the array
C
.
ldc
≥ max( 1,
n
).
Output Parameters
C
REAL
for
slarfy
DOUBLE PRECISION
for
dlarfy
COMPLEX
for
clarfy
COMPLEX*16
for
zlarfy
On exit,
C
is overwritten by H *
C
* H
T
(for real flavors) or H *
C
* H
H
(for complex flavors).
work
REAL
for
slarfy
DOUBLE PRECISION
for
dlarfy
COMPLEX
for
clarfy
COMPLEX*16
for
zlarfy
Array, dimension (
n
).