Re: Question on Rescale[]
- To: mathgroup at smc.vnet.net
- Subject: [mg103438] Re: Question on Rescale[]
- From: Anton Antonov <antononcube at gmail.com>
- Date: Mon, 21 Sep 2009 07:09:08 -0400 (EDT)
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Why Rescale should give Indeterminate or an error message? There are
lots of transformations that map infinite intervals to finite ones.
To answer Alexey's question, let us enter the more specific rescaling
command Rescale[x, {-Infinity, Infinity}]:
In[1]:= rx = Rescale[x, {-Infinity, Infinity}]
Out[1]= (-2 + x + Sqrt[4 + x^2])/(2*x)
This transformation maps (-Inf, Inf) to (0,1):
In[2]:= Limit[rx, x -> -Infinity]
Out[2]= 0
In[3]:= Limit[rx, x -> Infinity]
Out[3]= 1
We can also see that 2 is mapped to 1/Sqrt[2]:
In[6]:= rx /. x -> 2
Out[6]= 1/Sqrt[2]
This plot might be helpful:
Plot[Rescale[x, {-Infinity, Infinity}], {x, -200, 200}]
You can also experiment with:
In[7]:= Rescale[x, {-Infinity, Infinity}, {a, b}]
Out[7]= a + ((-a + b)*(-2 + x + Sqrt[4 + x^2]))/(2*x)
In[8]:= Rescale[x, {0, Infinity}, {a, b}]
Out[8]= b - (-a + b)/(1 + x)
In[9]:= Rescale[x, {-Infinity, Infinity}, {0, Infinity}]
Out[9]= -1 + 1/(1 - (-2 + x + Sqrt[4 + x^2])/(2*x))
Anton Antonov