Complex numbers

[Jon Harrop]

I can't seem to find an implementation of complex numbers in the C# standard
library. Is there one?

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journal
http://www.ffconsultancy.com/product...ournal/?usenet

[Marc Gravell]

Not buit in AFAIK, but a quick google yields:

http://www.codeproject.com/dotnet/complex_math.asp

Marc

[Nicholas Paldino [.NET/C# MVP]]

Jon,

No, there is not. You will have to implement it yourself, or use a
third-party implementation.
--
- Nicholas Paldino [.NET/C# MVP]
- mv*@spam.guard.caspershouse.com

"Jon Harrop" <jo*@ffconsultancy.comwrote in message
news:46**********************@ptn-nntp-reader02.plus.net...

>
I can't seem to find an implementation of complex numbers in the C#
standard
library. Is there one?

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journal
http://www.ffconsultancy.com/product...ournal/?usenet

[zacks]

On May 3, 3:34 pm, Marc Gravell <[e-mail]:

Not buit in AFAIK, but a quick google yields:

http://www.codeproject.com/dotnet/complex_math.asp

Marc

Or another one:

http://www.extremeoptimization.com/m...s/default.aspx

[zacks]

On May 3, 3:36 pm, "Nicholas Paldino [.NET/C# MVP]"
<[e-mail]:

Jon,

No, there is not. You will have to implement it yourself, or use a
third-party implementation.

And I don't think it would be all that hard to implement. All you need
is a class with two properties, real part and imaginary part, and then
a series of methods to do things like add, suntract, etc.

>
--
- Nicholas Paldino [.NET/C# MVP]
- [e-mail]

"Jon Harrop" <[e-mail] in message

news:46**********************@ptn-nntp-reader02.plus.net...

I can't seem to find an implementation of complex numbers in the C#
standard
library. Is there one?

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journal
http://www.ffconsultancy.com/product...urnal/?usenet- Hide quoted text -

- Show quoted text -

[Marc Gravell]

All you need is a class with two properties, real part and imaginary part
IMO, this would be one of the (few) occasions when a struct
(immutable) would be in order. The painful part here is having to
choose a type for the 2 components (or duplicate the code) - since
unfortunately generics do not allow you to efficiently use operators
such as *, +, - (and hence you can't do Complex<Tfor T in {int,
decimal, etc...})

Marc

[Bruce Wood]

I would use a struct here, not a class.

Nonetheless, you are right: it wouldn't be hard to implement.

On May 3, 1:53 pm, [e-mail] wrote:

On May 3, 3:36 pm, "Nicholas Paldino [.NET/C# MVP]"

<[e-mail]:

Jon,

No, there is not. You will have to implement it yourself, or use a
third-party implementation.

And I don't think it would be all that hard to implement. All you need
is a class with two properties, real part and imaginary part, and then
a series of methods to do things like add, suntract, etc.

--
- Nicholas Paldino [.NET/C# MVP]
- [e-mail]

"Jon Harrop" <[e-mail] in message

news:46**********************@ptn-nntp-reader02.plus.net...

I can't seem to find an implementation of complex numbers in the C#
standard
library. Is there one?

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journal
>http://www.ffconsultancy.com/product...ournal/?usenet

[Jon Harrop]

za***@construction-imaging.com wrote:

On May 3, 3:36 pm, "Nicholas Paldino [.NET/C# MVP]"
<[e-mail]:

>Jon,

No, there is not. You will have to implement it yourself, or use a
third-party implementation.

And I don't think it would be all that hard to implement. All you need
is a class with two properties, real part and imaginary part, and then
a series of methods to do things like add, suntract, etc.

Ugh. That really sucks. I appreciate that it is faily easy to implement
yourself but I'd really expect to see complex numbers in a modern
language...

If you want to be accurate, the implementation isn't actually that
straightforward either. Check out these definitions from the OCaml standard
library, for example:

let div x y =
if abs_float y.re >= abs_float y.im then
let r = y.im /. y.re in
let d = y.re +. r *. y.im in
{ re = (x.re +. r *. x.im) /. d;
im = (x.im -. r *. x.re) /. d }
else
let r = y.re /. y.im in
let d = y.im +. r *. y.re in
{ re = (r *. x.re +. x.im) /. d;
im = (r *. x.im -. x.re) /. d }

let norm x =
(* Watch out for overflow in computing re^2 + im^2 *)
let r = abs_float x.re and i = abs_float x.im in
if r = 0.0 then i
else if i = 0.0 then r
else if r >= i then
let q = i /. r in r *. sqrt(1.0 +. q *. q)
else
let q = r /. i in i *. sqrt(1.0 +. q *. q)

let sqrt x =
if x.re = 0.0 && x.im = 0.0 then { re = 0.0; im = 0.0 }
else begin
let r = abs_float x.re and i = abs_float x.im in
let w =
if r >= i then begin
let q = i /. r in
sqrt(r) *. sqrt(0.5 *. (1.0 +. sqrt(1.0 +. q *. q)))
end else begin
let q = r /. i in
sqrt(i) *. sqrt(0.5 *. (q +. sqrt(1.0 +. q *. q)))
end in
if x.re >= 0.0
then { re = w; im = 0.5 *. x.im /. w }
else { re = 0.5 *. i /. w; im = if x.im >= 0.0 then w else -. w }
end

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journal
http://www.ffconsultancy.com/product...ournal/?usenet

[Jon Harrop]

Bruce Wood wrote:

I would use a struct here, not a class.

Yes. I've timed both on a simple all-n FFT implementation and using a struct
is >3x faster.

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journal
http://www.ffconsultancy.com/product...ournal/?usenet

[Jon Skeet [C# MVP]]

Jon Harrop <jo*@ffconsultancy.comwrote:

Bruce Wood wrote:

I would use a struct here, not a class.

Yes. I've timed both on a simple all-n FFT implementation and using a struct
is >3x faster.

Unless performance is absolutely critical (which it may be of course) I
wouldn't use it as a reason to choose a class over a struct or vice
versa. The reason for making it a struct is that it's a natural value
type in the same way that int and double are.

--
Jon Skeet - <sk***@pobox.com>
http://www.pobox.com/~skeet Blog: http://www.msmvps.com/jon.skeet
If replying to the group, please do not mail me too

[Chris Nahr]

On Fri, 04 May 2007 02:39:45 +0100, Jon Harrop <jo*@ffconsultancy.com>
wrote:

>Ugh. That really sucks. I appreciate that it is faily easy to implement
yourself but I'd really expect to see complex numbers in a modern
language...

That would be an unrealistic expectation. Microsoft isn't involved in
numerical computing, outside of MS Research. Also, neither C# nor
Visual Basic have any ancestry or relationship (C, C++, Java, Basic
dialects) with built-in complex numbers -- unless you count Fortran.
It's just not a requirement for the business users MS is targeting.
--
http://www.kynosarges.de

[Bruce Wood]

On May 3, 6:39 pm, Jon Harrop <[e-mail]:

[e-mail] wrote:

On May 3, 3:36 pm, "Nicholas Paldino [.NET/C# MVP]"
<[e-mail]:

Jon,

No, there is not. You will have to implement it yourself, or use a
third-party implementation.

And I don't think it would be all that hard to implement. All you need
is a class with two properties, real part and imaginary part, and then
a series of methods to do things like add, suntract, etc.

Ugh. That really sucks. I appreciate that it is faily easy to implement
yourself but I'd really expect to see complex numbers in a modern
language...

If you want to be accurate, the implementation isn't actually that
straightforward either. Check out these definitions from the OCaml standard
library, for example:

let div x y =
if abs_float y.re >= abs_float y.im then
let r = y.im /. y.re in
let d = y.re +. r *. y.im in
{ re = (x.re +. r *. x.im) /. d;
im = (x.im -. r *. x.re) /. d }
else
let r = y.re /. y.im in
let d = y.im +. r *. y.re in
{ re = (r *. x.re +. x.im) /. d;
im = (r *. x.im -. x.re) /. d }

let norm x =
(* Watch out for overflow in computing re^2 + im^2 *)
let r = abs_float x.re and i = abs_float x.im in
if r = 0.0 then i
else if i = 0.0 then r
else if r >= i then
let q = i /. r in r *. sqrt(1.0 +. q *. q)
else
let q = r /. i in i *. sqrt(1.0 +. q *. q)

let sqrt x =
if x.re = 0.0 && x.im = 0.0 then { re = 0.0; im = 0.0 }
else begin
let r = abs_float x.re and i = abs_float x.im in
let w =
if r >= i then begin
let q = i /. r in
sqrt(r) *. sqrt(0.5 *. (1.0 +. sqrt(1.0 +. q *. q)))
end else begin
let q = r /. i in
sqrt(i) *. sqrt(0.5 *. (q +. sqrt(1.0 +. q *. q)))
end in
if x.re >= 0.0
then { re = w; im = 0.5 *. x.im /. w }
else { re = 0.5 *. i /. w; im = if x.im >= 0.0 then w else -. w }
end

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journalhttp://www.ffconsultancy.com/products/fsharp_journal/?usenet

OK... maybe a caveat is in order. :-)

It would be relatively easy to implement a basic complex number type
yourself.

To get all of the boundary cases right, though, including avoiding
overflows when very close to the limits of what various types can
hold, and handling other odd situations... well, that would require
some serious study of numerical computing. (I don't count myself as an
expert... let's just say that I've taken enough courses to know what
it is that I don't know....)

So, if you're not going to push the limits, then it's probably pretty
easy to cobble something together. If, on the other hand, you need to
do some heavy-duty calculations that could involve values within an
order of magnitude of what the base type can handle, well then you're
probably better off looking for a commercial package, or something
developed by someone with a deep knowledge of numerical analysis.

[Jay]

If I were to implement complex numbers myself, or via a third party, would it work with normal
operators (eg * / + -)?

"Jon Harrop" <jo*@ffconsultancy.comwrote in message
news:46**********************@ptn-nntp-reader02.plus.net...

I can't seem to find an implementation of complex numbers in the C# standard
library. Is there one?

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journal
http://www.ffconsultancy.com/product...ournal/?usenet

[Jay]

Doesn't C++ have complex numbers as standard? If so, C++ is sounding more attractive for a programme
I have to write soon.

"Chris Nahr" <di******@kynosarges.dewrote in message
news:jh********************************@4ax.com...
On Fri, 04 May 2007 02:39:45 +0100, Jon Harrop <jo*@ffconsultancy.com>
wrote:

>Ugh. That really sucks. I appreciate that it is faily easy to implement
yourself but I'd really expect to see complex numbers in a modern
language...

That would be an unrealistic expectation. Microsoft isn't involved in
numerical computing, outside of MS Research. Also, neither C# nor
Visual Basic have any ancestry or relationship (C, C++, Java, Basic
dialects) with built-in complex numbers -- unless you count Fortran.
It's just not a requirement for the business users MS is targeting.
--
http://www.kynosarges.de

[Chris Nahr]

On Fri, 4 May 2007 12:33:40 +0100, "Jay" <nospamwrote:

>Doesn't C++ have complex numbers as standard? If so, C++ is sounding more attractive for a programme
I have to write soon.

Hey, you're right -- the STL defines a template class for complex
numbers. I wasn't aware of that.
--
http://www.kynosarges.de

[Christof Nordiek]

"Jay" <nospamschrieb im Newsbeitrag
news:e7**************@TK2MSFTNGP05.phx.gbl...

If I were to implement complex numbers myself, or via a third party, would
it work with normal
operators (eg * / + -)?

If the type is implemented to do so, yes. C# supports operator overloading.

[Jon Harrop]

Chris Nahr wrote:

Hey, you're right -- the STL defines a template class for complex
numbers. I wasn't aware of that.

C also provides complex numbers, in C99.

--
Dr Jon D Harrop, Flying Frog Consultancy
The F#.NET Journal
http://www.ffconsultancy.com/product...ournal/?usenet

[Chris Nahr]

On Fri, 04 May 2007 15:35:46 +0100, Jon Harrop <jo*@ffconsultancy.com>
wrote:

>C also provides complex numbers, in C99.

Of course, Microsoft doesn't support that standard either. ;)
--
http://www.kynosarges.de