logical indexing using more than one variable in a pure function

• To: mathgroup at smc.vnet.net
• Subject: [mg53342] logical indexing using more than one variable in a pure function
• From: Ben Barrowes <barrowes at alum.mit.edu>
• Date: Thu, 6 Jan 2005 22:00:43 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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}
\!\(\*
RowBox[{\(Part::"pspec"\), \(\(:\)\(\ \)\), "\<\"Part specification \
\\!\\({True, False, False, True, True}\\) is neither an integer nor a
list of \
integers. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \
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}
{2, 3, 4, 5, 6} > 3
and
x>x1
to return
{False,False,False,True,True}
{2, 3, 4, 5, 6} > {6, 5, 4, 3, 2}
will something like:
#1 > #2 &, x, x1
work?

I would appreciate any suggestions,
Ben

```

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