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Re: Piecewise function generator
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg1189] Re: Piecewise function generator
*From*: Count Dracula <lk3a at kelvin.seas.virginia.edu>
*Date*: Mon, 22 May 1995 01:52:46 -0400
*Organization*: University of Virginia
In Message-ID: <3p8shv$6b8 at news0.cybernetics.net> Daryl Reece writes:
> I want to generate a piecewise continuous linear function by giving a
> function, call it F, a list of {x,y} values defining the corners of the
> function, e.g., pts={{20,0.08},{50,0.8},{250,0.8},{5000,0.004}}
If no symbolic expression for the function is needed
Interpolation[pts, InterpolationOrder -> 1]
is the briefest way. If symbolic expressions are needed,
Roman Maeder's program MakeFunctions.m in the Packages
directory shows a way to generate the rules needed.
For instance, the program below can be used.
__________________________________________________________________________________
LinearFunction::usage = "LinearFunction[f, {{x0, a}, {x1, b}}] defines rules for f
such that f[x] = a for x = x0, f[x] = b for x = x1 and
f is linear between x0 and x1. LinearFunction[f, pointslist] defines
rules for a piecewise linear function passing through the (x, y)
coordinates in the list pointslist."
MakeRuleConditional::usage = "MakeRuleConditional[f, x, rhs, cond]
globally defines the rule f[x_] := rhs /; cond."
Off[ RuleDelayed::rhs ]
SetAttributes[MakeRuleConditional, HoldAll]
MakeRuleConditional[f_Symbol, var_Symbol, rhs_, condition_] :=
(f[var_] := rhs /; condition)
LinearFunction[f_Symbol, {{x0_, a_}, {x1_, b_}}] :=
With[{slope = (b-a)/(x1-x0)},
MakeRuleConditional[f, x, a + (x-x0) slope, x0 <= x <= x1];
]
LinearFunction[f_Symbol, pointslist_List] :=
(Map[ LinearFunction[f, #1] &, Partition[ Union[pointslist], 2, 1]]; Null)
__________________________________________________________________________________
Example:
In[2]:= pts = {{20,0.08},{50,0.8},{250,0.8},{5000,0.004}};
In[3]:= LinearFunction[f, pts]
In[4]:= ?f
Global`f
f[x_] := 0.08 + (x - 20)*0.024 /; 20 <= x <= 50
f[x_] := 0.8 + (x - 50)*0. /; 50 <= x <= 250
f[x_] := 0.8 + (x - 250)*-0.0001675789473684211 /; 250 <= x <= 5000
In[4]:= pts2 = { {2,0.08}, {5,0.8}, {2.5,0.75}, {4,4}, {3, 9} };
In[5]:= LinearFunction[g, pts2]
In[6]:= ?g
Global`g
g[x_] := 0.08 + (x - 2)*1.34 /; 2 <= x <= 2.5
g[x_] := 0.75 + (x - 2.5)*16.5 /; 2.5 <= x <= 3
g[x_] := 9 + (x - 3)*-5 /; 3 <= x <= 4
g[x_] := 4 + (x - 4)*-3.2 /; 4 <= x <= 5
--
___________________________________________________________________________________
Levent Kitis lk3a at cars.mech.virginia.edu lk3a at kelvin.seas.virginia.edu
University of Virginia Department of Mechanical, Aerospace, and Nuclear Engineering
___________________________________________________________________________________
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