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MathGroup Archive 2005

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Re: How build a function repeating the same pattern?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58467] Re: How build a function repeating the same pattern?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sun, 3 Jul 2005 03:57:24 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, England
  • References: <da5j11$20n$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

guillerm at aida.usal.es wrote:
> (*I have built this function*)
> 
> ss[ model1_, list1_, model2_, list2_, t_] := Module[{t1, y1, s1, t2,
> y2, s2,a, b},{t1, y1, s1} = Transpose[list1];
> {t2, y2, s2} = Transpose[list2];
> a = model1 /. t -> t1; b = model2 /. t -> t2;
> Plus @@ (a y1/s1) + Plus @@ (b y2/s2)];
> 
> (*It works as I wish. Example*)
> 
> q1[t_] = a1 Exp[-b1 t]; q2[t_] = a2 Exp[-b2 t];
> ss[ q1[t], {{t11, m11, s11}, {t12, m12, s12} }, q2[t], {{t21, m21,
>       s21}, {t22, m22, s22}, {t23, m23, s23}}, t]
> 
> Now  I want to extend this function such as the pattern  "model, list"
> can be repeated any number of times.Example
> 
> 
> q3[t_] = a3 Exp[-b3 t];
> 
> ss[ q1[t], {{t11, m11, s11}, {t12, m12, s12} },
> q2[t], {{t21, m21, s21}, {t22,m22, s22}, {t23, m23, s23}}, q3[t],
> {{t31, m31, s31}}, t]
> 
> Any help?
> 
> Guillermo
> 
Hi Guillermo,

You could use something along the lines:

In[1]:=
jm40[model_, param_] := Module[{pt, py, ps},
    {pt, py, ps} = Transpose[param];
     Plus @@ ((model /. t -> pt)*(py/ps))]

In[2]:=
jm44[listparam_] := Plus @@
    (jm40[#1[[1]], #1[[2]]] & ) /@ listparam

In[3]:=
q1[t_] = a1*Exp[(-b1)*t];
q2[t_] = a2*Exp[(-b2)*t];
q3[t_] = a3*Exp[(-b3)*t];

In[6]:=
jm44[{{q1[t], {{t11, m11, s11}, {t12, m12, s12}}},
    {q2[t], {{t21, m21, s21}, {t22, m22, s22},
      {t23, m23, s23}}}, {q3[t], {{t31, m31, s31}}}}]

Out[6]=
(a1*m11)/(E^(b1*t11)*s11) +
   (a1*m12)/(E^(b1*t12)*s12) +
   (a2*m21)/(E^(b2*t21)*s21) +
   (a2*m22)/(E^(b2*t22)*s22) +
   (a2*m23)/(E^(b2*t23)*s23) + (a3*m31)/(E^(b3*t31)*s31)

You have noticed that I removed the parameter "t_" since it is used by 
but not passed to the function and the parameters must be transmitted as 
a list of list of model + param, that is {{model1, param1},{model2, 
param2}...}.

Hope this helps,
/J.M.


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