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RE: Magnitude of Vector
*To*: mathgroup at smc.vnet.net
*Subject*: [mg19415] RE: [mg19339] Magnitude of Vector
*From*: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
*Date*: Mon, 23 Aug 1999 13:57:23 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
Ed McBride wrote:
----------------------
Was doing some stuff that required 3-D vectors. Found Dot and Cross,
but couldn't find a primitive operator for Magnitude. Is there one? If
not, there definitely should be.
---------------------
No it isn't built-in, and you have a good point. Until it is a built-in
function the following should do it quite efficiently, and even post
messages for invalid arguments. It also works for vectors of any dimension
(not only 3D).
I included the part about /;(Length[v]=!=0)
so that Magnitude[{}] would be undefined as I think it should.
---------------------
In[1]:=
Magnitude::vect="Mag is only defined for vectors. The expression `1` is not
a vector.";
Magnitude[v_?VectorQ]/;(Length[v]=!=0):=Sqrt[Plus@@(v^2)];
Magnitude[expr_]/;Message[Magnitude::vect,expr]:="Never get here";
Magnitude[_,more__]/;Message[Magnitude::argx,Magnitude,Length[{more}]+1]:="N
ever get here";
In[5]:=
Magnitude[{w,x,y,z}]
Out[5]=
Sqrt[w^2 + x^2 + y^2 + z^2]
In[6]:=
Magnitude[a+b]
Magnitude::vect: Mag is only defined for vectors. The expression a+b is not
a vector.
Out[6]=
Magnitude[a + b]
In[7]:=
Magnitude[{x,y,z},{a,b,c}]
Magnitude::argx: Magnitude called with 2 arguments; 1 argument is expected.
Out[7]=
Magnitude[{x, y, z}, {a, b, c}]
Notice when Magnitude gets invalid input a message is posted and the
expression is returned unevaluated. For the case when more than one
argument is given I used one of the
General::tag messages found in the (messages.m) file. For the case where
the argument isn't a vector I defined my own message (Message::vect).
You could make this a little more complicated and ensure a CompiledFunction
is used when possible. I tried that, but it the speed advantage was only
about 25% for very long vectors.
---------------------
Regards,
Ted Ersek
For Mathematica Tips, Tricks see
http://www.dot.net.au/~elisha/ersek/Tricks.html
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