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Mathematica

Vector as an argument in function definition

Al Guy

Posted 10 years ago

Can I somehow specify that `G` is a vector in function definition so that it won't complain? c0[G_, \[Theta]0_, \[CapitalPhi]0_, Q_] := Normal@SeriesCoefficient[Sqrt[ G[[1]]^2 + G[[2]]^2 - 2 Q Sin[\[Theta]] (G[[1]] Cos[\[Phi]] + G[[2]] Sin[\[Phi]])], {\[Theta], \[Theta]0, 0}, {\[Phi], \[Phi]0, 0}]

Can I somehow specify that G is a vector in function definition so that it won't complain?

c0[G_, \[Theta]0_, \[CapitalPhi]0_, Q_] := 
 Normal@SeriesCoefficient[Sqrt[
   G[[1]]^2  + G[[2]]^2 - 
    2 Q Sin[\[Theta]] (G[[1]] Cos[\[Phi]] + 
       G[[2]] Sin[\[Phi]])], {\[Theta], \[Theta]0, 
    0}, {\[Phi], \[Phi]0, 0}]

POSTED BY: Al Guy

8 Replies

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 10 years ago

What function of G do you have in mind? The following works with immediate assignment, but it won't speed up calculations, I am afraid: f[u_?VectorQ, v_?VectorQ] = u.v Using vector notation you may write your function a little more elegantly c02[g_?VectorQ, \[Theta]0_, \[CapitalPhi]0_, Q_] := Normal@SeriesCoefficient[ Sqrt[g.g - 2 Q Sin[\[Theta]] g.{Cos[\[Phi]], Sin[\[Phi]]}], {\[Theta], \[Theta]0, 0}, {\[Phi], \[Phi]0, 0}] but it only makes sense for a 2-dimensional g, and it only works with delayed assignment. Also, I think SeriesCoefficient does not need Normal.

POSTED BY: Gianluca Gorni

Al Guy

Posted 10 years ago

I was just thinking that if G is multidimensional, say 100, there should be a way to pass it as an argument to a function.

POSTED BY: Al Guy

David Keith

Posted 10 years ago

There are ways to use Hold to defer evaluation, but I have not encountered many cases where that is preferable to just defering the entire expression with SetDelayed. In[1]:= tuplesPlus[x_, n_, y_] = Tuples[x, n] + y During evaluation of In[1]:= Tuples::normal: Nonatomic expression expected at position 1 in Tuples[x,n]. >> Out[1]= y + Tuples[x, n] In[2]:= tuplesHeld[x_, n_, y_] = Hold[Tuples[x, n]] + y Out[2]= y + Hold[Tuples[x, n]] In[3]:= tuplesHeld[{a, b, c}, 2, d] // ReleaseHold Out[3]= {{a + d, a + d}, {a + d, b + d}, {a + d, c + d}, {b + d, a + d}, {b + d, b + d}, {b + d, c + d}, {c + d, a + d}, {c + d, b + d}, {c + d, c + d}}

There are ways to use Hold to defer evaluation, but I have not encountered many cases where that is preferable to just defering the entire expression with SetDelayed.

In[1]:= tuplesPlus[x_, n_, y_] = Tuples[x, n] + y

During evaluation of In[1]:= Tuples::normal: Nonatomic expression expected at position 1 in Tuples[x,n]. >>

Out[1]= y + Tuples[x, n]

In[2]:= tuplesHeld[x_, n_, y_] = Hold[Tuples[x, n]] + y

Out[2]= y + Hold[Tuples[x, n]]

In[3]:= tuplesHeld[{a, b, c}, 2, d] // ReleaseHold

Out[3]= {{a + d, a + d}, {a + d, b + d}, {a + d, c + d}, {b + d, 
  a + d}, {b + d, b + d}, {b + d, c + d}, {c + d, a + d}, {c + d, 
  b + d}, {c + d, c + d}}

POSTED BY: David Keith

David Keith

Posted 10 years ago

In[17]:= c02[{g1_, g2_}, \[Theta]0_, \[CapitalPhi]0_, Q_] = Normal@SeriesCoefficient[ Sqrt[g1^2 + g2^2 - 2 Q Sin[\[Theta]] (g1 Cos[\[Phi]] + g2 Sin[\[Phi]])], {\[Theta], \[Theta]0, 0}, {\[Phi], \[Phi]0, 0}] Out[17]= Sqrt[g1^2 + g2^2 - 2 g1 Q Cos[\[Phi]0] Sin[\[Theta]0] - 2 g2 Q Sin[\[Theta]0] Sin[\[Phi]0]] In[18]:= c02[{a, b}, c, d, e] Out[18]= Sqrt[a^2 + b^2 - 2 a e Cos[\[Phi]0] Sin[c] - 2 b e Sin[c] Sin[\[Phi]0]]

In[17]:= c02[{g1_, g2_}, \[Theta]0_, \[CapitalPhi]0_, Q_] = 
 Normal@SeriesCoefficient[
   Sqrt[g1^2 + g2^2 - 
     2 Q Sin[\[Theta]] (g1 Cos[\[Phi]] + 
        g2 Sin[\[Phi]])], {\[Theta], \[Theta]0, 0}, {\[Phi], \[Phi]0, 
    0}]

Out[17]= Sqrt[g1^2 + g2^2 - 2 g1 Q Cos[\[Phi]0] Sin[\[Theta]0] - 
 2 g2 Q Sin[\[Theta]0] Sin[\[Phi]0]]

In[18]:= c02[{a, b}, c, d, e]

Out[18]= Sqrt[a^2 + b^2 - 2 a e Cos[\[Phi]0] Sin[c] - 
 2 b e Sin[c] Sin[\[Phi]0]]

POSTED BY: David Keith

Al Guy

Posted 10 years ago

You are right, it works with SetDelayed, can we make it work with Set, so that the function will be evaluated right away instead of waiting? Part::partd: Part specification G[[1]] is longer than depth of object. >>

POSTED BY: Al Guy

David Keith

Posted 10 years ago

Could you post an example of a complaint? In[12]:= c0[G_, \[Theta]0_, \[CapitalPhi]0_, Q_] := Normal@SeriesCoefficient[ Sqrt[G[[1]]^2 + G[[2]]^2 - 2 Q Sin[\[Theta]] (G[[1]] Cos[\[Phi]] + G[[2]] Sin[\[Phi]])], {\[Theta], \[Theta]0, 0}, {\[Phi], \[Phi]0, 0}] In[13]:= c0[{a, b}, c, d, e] Out[13]= Sqrt[a^2 + b^2 - 2 a e Cos[\[Phi]0] Sin[c] - 2 b e Sin[c] Sin[\[Phi]0]]

Could you post an example of a complaint?

In[12]:= c0[G_, \[Theta]0_, \[CapitalPhi]0_, Q_] := 
 Normal@SeriesCoefficient[
   Sqrt[G[[1]]^2 + G[[2]]^2 - 
     2 Q Sin[\[Theta]] (G[[1]] Cos[\[Phi]] + 
        G[[2]] Sin[\[Phi]])], {\[Theta], \[Theta]0, 
    0}, {\[Phi], \[Phi]0, 0}]

In[13]:= c0[{a, b}, c, d, e]

Out[13]= Sqrt[a^2 + b^2 - 2 a e Cos[\[Phi]0] Sin[c] - 
 2 b e Sin[c] Sin[\[Phi]0]]

POSTED BY: David Keith