Contents

# ?larot

Applies a Givens rotation to two adjacent rows or columns.

## Syntax

Include Files
• mkl.h
Description
The routine
?larot
applies a Givens rotation to two adjacent rows or columns, where one element of the first or last column or row is stored in some format other than GE so that elements of the matrix may be used or modified for which no array element is provided.
One example is a symmetric matrix in SB format (bandwidth = 4), for which
uplo
=
'L'
. Two adjacent rows will have the format:
```row j :      C > C > C > C > C > . . . .
row j + 1 :  C > C > C > C > C > . . . .```
'*'
indicates elements for which storage is provided.
'.'
indicates elements for which no storage is provided, but are not necessarily zero; their values are determined by symmetry.
' '
indicates elements which are required to be zero, and have no storage provided.
Those columns which have two
'*'
entries can be handled by
srot
(for
slarot
and
clarot
), or by
drot
( for
dlarot
and
zlarot
).
Those columns which have no
'*'
entries can be ignored, since as long as the Givens rotations are carefully applied to preserve symmetry, their values are determined.
Those columns which have one
'*'
have to be handled separately, by using separate variables
p
and
q
:
```row j :      C > C > C > C > C > p. . . .
row j + 1 :  q  C > C > C > C > C > . . . . ```
If element
p
is set correctly,
?larot
rotates the column and sets
p
to its new value. The next call to
?larot
rotates columns
j
and
j
+1, and restore symmetry. The element
q
is zero at the beginning, and non-zero after the rotation. Later, rotations would presumably be chosen to zero
q
out.
Typical Calling Sequences: rotating the
i
-th and
(
i
+1)-
st rows.
Input Parameters
lrows
If
lrows
=
1
,
?larot
rotates two rows.
If
lrows
=
0
,
?larot
rotates two columns.
lleft
If
lleft
=
1
,
xleft
is used instead of the corresponding element of
a
for the first element in the second row (if
lrows
=
0
) or column (if
lrows
=
1
).
If
lleft
=
0
, the corresponding element of
a
is used.
lright
If
lleft
=
1
,
xright
is used instead of the corresponding element of
a
for the first element in the second row (if
lrows
=
0
) or column (if
lrows
=
1
).
If
lright
=
0
, the corresponding element of
a
is used.
nl
The length of the rows (if
lrows
=
1
) or columns (if
lrows
=
1
) to be rotated.
If
xleft
or
xright
are used, the columns or rows they are in should be included in
nl
, e.g., if
lleft
=
lright
=
1
, then
nl
must be at least 2.
The number of rows or columns to be rotated exclusive of those involving
xleft
and/or
xright
may not be negative, i.e.,
nl
minus how many of
lleft
and
lright
are
1
must be at least zero; if not,
xerbla
is called.
c, s
Specify the Givens rotation to be applied.
If
lrows
=
1
, then the matrix is applied from the left.
If
lrows
=
0
, then the transpose thereof is applied from the right.
a
The array containing the rows or columns to be rotated. The first element of
a
should be the upper left element to be rotated.
lda
a
.
If
a
contains a matrix stored in GE or SY format, then this is just the leading dimension of
A
.
If
a
contains a matrix stored in band (GB or SB) format, then this should be one less than the leading dimension used in the calling routine. Thus, if
a
in
?larot
is of size
lda
*
n
, then
a
[(
j
- 1)*
lda
]
would be the
j
-th element in the first of the two rows to be rotated, and
a
[(
j
- 1)*
lda
+ 1]
would be the
j
-th in the second, regardless of how the array may be stored in the calling routine.
a
cannot be dimensioned, because for band format the row number may exceed
lda
, which is not legal FORTRAN.
If
lrows
=
1
, then
lda
must be at least 1, otherwise it must be at least
nl
minus the number of
1
values in
xleft
and
xright
.
xleft
If
lrows
=
1
,
xleft
is used and modified instead of
a

(if
lrows
=
1
) or
a
[
lda
+ 1]
(if
lrows
=
0
).
xright
If
lright
=
1
,
xright
is used and modified instead of
a
[(
nl
- 1)*
lda
]
(if
lrows
=
1
) or
a
[
nl
- 1]
(if
lrows
=
0
).
Output Parameters
a
On exit, modified array
A
.

#### Product and Performance Information

1

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Notice revision #20110804