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Re: Linear Interpolation problems
*To*: mathgroup at smc.vnet.net
*Subject*: [mg102377] Re: Linear Interpolation problems
*From*: Bill Rowe <readnews at sbcglobal.net>
*Date*: Fri, 7 Aug 2009 05:30:41 -0400 (EDT)
On 8/6/09 at 6:33 AM, leekosal at yahoo.com (kosal lee) wrote:
>First, suppose I have two real values
>year earnings
>x = 3 f(x) = 20
>x= 10 f(x) = 50
>I want to have the interpolated values of f(4), f(5), to f(9) which
>is between actual values of f(3) and f(10). How can I do that with
>Mathematica?
The Mathematica functions most specific to this problem are
Interpolation, Map and Range. They can be used to do what you
want as follows:
In[6]:= f =
Interpolation[{{3, 20}, {10, 50}}, InterpolationOrder -> 1];
f /@ Range[3, 10]
Out[7]= {20, 170/7, 200/7, 230/7, 260/7, 290/7, 320/7, 50}
The first line creates the linear interpolation function. The
second line maps that function to the desired range of values.
Note, I've used the shorthand notation /@ for Map.
>Second, suppose I have an excel spreadsheet having those above
>values for multiples firms as of the following
>firm f(3) f(10)
>A 20 50
>B 30 55
>C 60 25
This can be done as follows:
In[8]:= g =
Interpolation[{{3, First@#}, {10, Last@#}},
InterpolationOrder -> 1] & /@ {{20, 50}, {30, 55}, {60, 25}};
data = Table[g[[n]] /@ Range[3, 10], {n, 3}]
Out[9]= {{20, 170/7, 200/7, 230/7, 260/7, 290/7, 320/7, 50},
{30, 235/
7, 260/7, 285/7, 310/7, 335/7, 360/7, 55}, {60, 55, 50, 45,
40, 35,
30, 25}}
>I want to have the values of f(4) till f(9) as above and are stored
>in excel spreadsheet as of the following:
>firm f(3) f(4) f(5) ... (f9) f(10)
>A 20 50
>B 30 55
>C 60 25
Writing the information to Excel can be done by
Export["filename.xls", data//N, "XLS"]
Here, I've converted the exact results returned by Mathematica
to machine precision numbers since I don't think Export converts
exact results to something Excel understands as a number. This
may not be needed. But since I have little use for Excel, I've
not taken the time to determine the need for this conversion.
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