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} 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