F06VXF applies to a complex rectangular matrix a sequence of plane rotations having real cosines and complex sines.
F06VXF performs the transformation
where
is an
by
complex matrix and
is a real orthogonal matrix, defined as a sequence of real plane rotations,
, applied in planes
to
.
The
by
plane rotation part of
is assumed to have the form
with
and
real.
None.
- 1: SIDE – CHARACTER(1)Input
On entry: specifies whether
is operated on from the left or the right.
- is pre-multiplied from the left.
- is post-multiplied from the right.
Constraint:
or .
- 2: PIVOT – CHARACTER(1)Input
On entry: specifies the plane rotated by
.
- (variable pivot)
- rotates the plane.
- (top pivot)
- rotates the plane.
- (bottom pivot)
- rotates the plane.
Constraint:
, or .
- 3: DIRECT – CHARACTER(1)Input
On entry: specifies the sequence direction.
- (forward sequence)
- .
- (backward sequence)
- .
Constraint:
or .
- 4: M – INTEGERInput
On entry: , the number of rows of the matrix .
Constraint:
.
- 5: N – INTEGERInput
On entry: , the number of columns of the matrix .
Constraint:
.
- 6: K1 – INTEGERInput
- 7: K2 – INTEGERInput
On entry: the values
and
.
If or , or and , or and , an immediate return is effected.
- 8: C() – REAL (KIND=nag_wp) arrayInput
-
Note: the dimension of the array
C
must be at least
.
On entry: must hold , the cosine of the rotation , for .
- 9: S() – REAL (KIND=nag_wp) arrayInput
-
Note: the dimension of the array
S
must be at least
.
On entry: must hold , the sine of the rotation , for .
- 10: A(LDA,) – COMPLEX (KIND=nag_wp) arrayInput/Output
-
Note: the second dimension of the array
A
must be at least
.
On entry: the by matrix .
On exit: the transformed matrix .
- 11: LDA – INTEGERInput
On entry: the first dimension of the array
A as declared in the (sub)program from which F06VXF is called.
Constraint:
.
None.
Not applicable.
None.
None.