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Re: logical indexing using more than one variable in a pure function

• To: mathgroup at smc.vnet.net
• Subject: [mg53360] Re: [mg53342] logical indexing using more than one variable in a pure function
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Sat, 8 Jan 2005 02:39:27 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

 
>-----Original Message-----
>From: Ben Barrowes [mailto:barrowes at alum.mit.edu]
To: mathgroup at smc.vnet.net
>Sent: Friday, January 07, 2005 4:01 AM
>Subject: [mg53360] [mg53342] logical indexing using more than one variable in a 
>pure function
>
>I am trying to pick out values from a matrix using a logical mask, i.e.
>using logical indexing.
>
>
>I wish the following:
>x = {2, 3, 4, 5, 6}
>y = {True, False, False, True, True}
>x[[y]]
>would produce:
>{2,5,6}
>but instead it produces:
>\!\(\*
>   RowBox[{\(Part::"pspec"\), \(\(:\)\(\ \)\), "\<\"Part specification 
>\ \\!\\({True, False, False, True, True}\\) is neither an integer nor a

>list of \ integers.
>\\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \
>ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \
>ButtonData:>\\\"General::pspec\\\"]\\)\"\>"}]\)
>{2, 3, 4, 5, 6}\[LeftDoubleBracket]{True, False, False, True,
>     True}\[RightDoubleBracket]
>
>
>Here are some working examples when the mask depends upon only one 
>variable:
>
>pick out values in x > 4
>Select[x, (#1 > 4 &)]
>{5, 6}
>
>BooleanSelect seems to do what I want if I have a logical mask already:
><< Statistics`DataManipulation`
>BooleanSelect[x, y]
>{2, 5, 6}
>And now in 5.1, "Pick" does the same thing as BooleanSelect.
>But how can I do this in one line? (no need to define y
>explicitly) Something like:
>Pick[x,x>3]
>
>
>
>This seems to work for cases:
>Cases[x, x_ /; x > 3]
>{4, 5, 6}
>and similarly for select:
>Select[x, # > 3 &]
>{4, 5, 6}
>
>
>But if I have a second List:
>x1 = {6, 5, 4, 3, 2}
>
>How would I index x based on a logical operation on both x and x1?
>I hoped something like this would work:
>Pick[x,x>x1]
>or
>Cases[x, {x_,x1_} /; x>x1]
>{}
>But only x is provided to the pattern match, not {x_,x1_}.
>
>Or maybe a better Select statement. But how do I make the pure function

>accept two arguments?
>
>For that matter, how can I perform an element by element logical 
>operation on a list? For example, I would like:
>x>3
>to return
>{False,False,True,True,True}
>instead of
>{2, 3, 4, 5, 6} > 3
>and
>x>x1
>to return
>{False,False,False,True,True}
>instead of
>{2, 3, 4, 5, 6} > {6, 5, 4, 3, 2}
>will something like:
>#1 > #2 &, x, x1
>work?
>
>I would appreciate any suggestions,
>Ben
>
>

Ben,

To answer your last question first:

In[13]:= Thread[{2,3,4,5,6} > 3]
Out[13]= {False,False,True,True,True}

In[10]:= Thread[x > x1]
Out[10]= {False, False, False, True, True}


In[12]:= BooleanSelect[x, Thread[x > x1]] 
Out[12]= {5, 6}


Try this with Pick (I just temporarily ran out ouf pickers).

--
Hartmut Wolf


P.S. for higher dimensions proceed along the lines

In[21]:= << DiscreteMath`Permutations`

In[22]:= xx = Partition[Range[16], 4]
Out[22]= {{1, 2, 3, 4},
          {5, 6, 7, 8},
          {9, 10, 11, 12},
          {13, 14, 15, 16}}

In[24]:= xx1 = Partition[RandomPermutation[16], 4] 
Out[24]= {{1, 5, 14, 2},
          {4, 6, 13, 9},
          {8, 15, 16, 11},
          {7, 10, 3, 12}}

In[32]:= yy = MapThread[Greater, {xx, xx1}, 2] 
Out[32]= {{False, False, False, True},
          {True, False, False, False},
          {True, False, False, True},
          {True, True, True, True}}

In[33]:= MapThread[BooleanSelect, {xx, yy}] 
Out[33]= {{4}, {5}, {9, 12}, {13, 14, 15, 16}}


Or if you prefer (as I do):

In[36]:= MapThread[If[#2, #1, Unevaluated[Sequence[]]] &, {xx, yy}, 2] 
Out[36]= {{4}, {5}, {9, 12}, {13, 14, 15, 16}}