Portability | non-portable |
---|---|
Stability | experimental |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | None |
Lenses and traversals for complex numbers
- _realPart :: Simple Lens (Complex a) a
- _imagPart :: Simple Lens (Complex a) a
- _polar :: RealFloat a => Simple Iso (Complex a) (a, a)
- _magnitude :: RealFloat a => Simple Lens (Complex a) a
- _phase :: RealFloat a => Simple Lens (Complex a) a
- _conjugate :: RealFloat a => Simple Iso (Complex a) (Complex a)
- complex :: Traversal (Complex a) (Complex b) a b
Documentation
_polar :: RealFloat a => Simple Iso (Complex a) (a, a)Source
This isn't quite a legal lens. Notably the
view
l (set
l b a) = b
law is violated when you set a polar
value with 0 magnitude
and non-zero
phase
as the phase
information is lost, or with a negative magnitude
which flips the phase
and retains a positive magnitude
. So don't do
that!
Otherwise, this is a perfectly cromulent Lens
.
_magnitude :: RealFloat a => Simple Lens (Complex a) aSource
Access the magnitude
of a Complex
number
>>>
(10.0 :+ 20.0) & _magnitude *~ 2
20.0 :+ 40.0
This isn't quite a legal lens. Notably the
view
l (set
l b a) = b
law is violated when you set a negative magnitude
. This flips the phase
and retains a positive magnitude
. So don't do that!
Otherwise, this is a perfectly cromulent Lens
.
Setting the magnitude
of a zero Complex
number assumes the phase
is 0.
_phase :: RealFloat a => Simple Lens (Complex a) aSource
Access the phase
of a Complex
number
>>>
(mkPolar 10 (2-pi) & _phase +~ pi & view _phase) ≈ 2
True
This isn't quite a legal lens. Notably the
view
l (set
l b a) = b
law is violated when you set a phase
outside the range (-
.
The phase is always in that range when queried. So don't do that!
pi
, pi
]
Otherwise, this is a perfectly cromulent Lens
.