Re: Two Questions
- To: mathgroup at smc.vnet.net
- Subject: [mg102919] Re: [mg102883] Two Questions
- From: "David Park" <djmpark at comcast.net>
- Date: Wed, 2 Sep 2009 04:03:10 -0400 (EDT)
- References: <5282041.1251792077869.JavaMail.root@n11>
Chris,
I usually can't resist Table questions because I'm so much in need of
practice with them.
I think that the best approach is to use Grid instead of TableForm. Grid
gives you much more control but also requires more learning. Let's say we
want to make our table out of sub-parts. In this case this is the table
proper, the x and y headings and a little something in the upper left hand
corner.
I think there are two approaches to this.
1) Consider the entire Grid as one table and write a function to fill in the
elements.
2) Write separate Grids for each of the sub-parts and then assemble them.
Here is the first approach:
f[x_, y_] := (2 x^2)/y^2
g[x_, y_] =
Piecewise[{{"x\y", x == y == 0}, {y, x == 0}, {x, y == 0}}, f[x, y]]
Then calculate all of the elements, Notice I used 0 for the heading row and
column and positive integers for the table proper.
elements =
Table[g[x, y], {x, {0, Sequence @@ Range[5, 20]}},
{y, {0, Sequence @@ Range[3, 10]}}];
Then put everything together in a Labeled Grid with Frame, Dividers and
Background for the various sub-parts. The options for Grid are so
complicated and they do most of the work so it is nice to calculate the
elements outside of the Grid statement just to simplify things. The most
fiddly thing is the Background, which has a lot of parentheses in it. We use
-1 to designate the last position in a range.
Labeled[
Grid[elements,
Frame -> True,
Dividers -> {{2 -> Black}, {2 -> Black}},
Background ->
{None, None,
{
{1, 1} -> Pink,
{{1, 1}, {2, -1}} -> GrayLevel[.9],
{{2, -1}, {1, 1}} -> GrayLevel[.9]}
}
],
Style["A Custom Table", FontFamily -> "Helvetica"]]
For the second method we calculate sub-grids for each of the pieces of the
table. If we want everything to fit together properly we have to specify the
ItemSizes for the entries. If we don't make the ItemSizes large enough the
Grid statement will give us mismatches. We have to specify the Background
coloring in the outer Grid.
With[
{xmin = 5, xmax = 20, ymin = 3, ymax = 10,
width1 = 1.7, width2 = 1.5, height1 = 1.5, height2 = 2.1},
grid[1, 1] = Grid[{{"x\y"}}, ItemSize -> {width1, height1}];
grid[1, 2] =
Grid[{Table[y, {y, ymin, ymax}]}, ItemSize -> {width2, height1}];
grid[2, 1] =
Grid[Transpose[{Table[x, {x, xmin, xmax}]}],
ItemSize -> {width1, height2}];
grid[2, 2] =
Grid[Table[f[x, y], {x, xmin, xmax}, {y, ymin, ymax}],
ItemSize -> {width2, height2}];
Labeled[
Grid[
{{grid[1, 1], grid[1, 2]},
{grid[2, 1], grid[2, 2]}},
Frame -> True,
Dividers -> {{2 -> Black}, {2 -> Black}},
Background ->
{None, None,
{{1, 1} -> Pink,
{1, 2} -> GrayLevel[.9],
{2, 1} -> GrayLevel[.9]
}
}](* Grid *),
Style["A Custom Table", FontFamily -> "Helvetica"]](* Labeled *)
]
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
From: cmoller [mailto:cmoller at dpbioventures.com]
Hi,
If I create a Table from this function f[x_, y_] := (2 x^2)/y^2 using
Table[f[x,y],{x,5,20},(y,3,10}] can I add a statement that will adjust
the table headings to conform with the selected ranges for x and y? I
have tried TableForm with TableHeadings -> etc, but I must specify the
exact headings. Can I use a formula with TableHeadings? To be direct,
in the case above I want the labels to read 5,6..20 and 3,4..10.
My second question is can I call Mathematica routines with Python?
All the best.. and thanks,
Chris