Re: TableForm and NumberForm (2)

*To*: mathgroup at smc.vnet.net*Subject*: [mg34766] Re: TableForm and NumberForm (2)*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Wed, 5 Jun 2002 03:38:27 -0400 (EDT)*References*: <adhs5i$4gt$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Prompted by Bobby Treat I have tried to make my previous posting a bit more reproducible and readable (and I have corrected a couple or typing errors). In particular I have included te line $Line=0 that sets the input/output numbering so that the next input/output number will be 1. Also, I post this as a notebook expression. To read it copy the text between (*Start*) and (*End*) and paste into a Mathematica notebook; click the "Yes" button in the panel that pops up. (* Start*) Notebook[{ Cell["\<\ Some examples supporting Bobby's explanation that the outer wrapper \ is used in displaying the output but is not included in the output. Showing the In and Out labels helps.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \($Line = 0\)], "Input"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(e1 = {1.23456789}\)], "Input"], Cell[BoxData[ \({1.23456789`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(e2 = NumberForm[e1, {12, 2}]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"{", InterpretationBox["\<\"1.23\"\>", 1.2345678899999999, AutoDelete->True], "}"}], (NumberForm[ #, {12, 2}]&)]], "Output"] }, Open ]], Cell["\<\ (1) The above means what it says: it is Out[2] displayed using \ NumberForm: Notice that the NumbeForm is not included in Out[2].\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Out[2]\)], "Input"], Cell[OutputFormData["\<\ {1.23456789}\ \>", "\<\ {1.23457}\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Out[2] // NumberForm[#, {12, 2}] &\)], "Input"], Cell[OutputFormData["\<\ {1.23456789}\ \>", "\<\ {1.23}\ \>"], "Output"] }, Open ]], Cell["\<\ (2) But NumberForm is is included in e2:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(e2\)], "Input"], Cell[OutputFormData["\<\ {1.23456789}\ \>", "\<\ {1.23}\ \>"], "Output"] }, Open ]], Cell["\<\ (3) Wrappers other those round the whole expression are not \ removed:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(e3 = \(NumberForm[#, {12, 2}] &\) /@ e1\)], "Input"], Cell[OutputFormData["\<\ {NumberForm[1.23456789, {12, 2}]}\ \>", "\<\ {1.23}\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(% // InputForm\)], "Input"], Cell["{NumberForm[1.23456789, {12, 2}]}", "Output"] }, Open ]], Cell["\<\ (4) Multiple wrappers round the full expression are discarded in the \ output. If the wrappers are of different types then both wrappers are \ effective (in spite of only NumberForm appearing in the cell label below). If they \ are of the same type then only the inner one is used (see (5) below)\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(e4 = Table[Random[], {2}, {2}, {2}]\)], "Input"], Cell[OutputFormData["\<\ {{{0.3370688535874288, 0.05788748716942282}, {0.04796294831324889, 0.5300925627462034}}, {{0.9921185798241328, 0.7817148000400453}, {0.4000373844310341, 0.533468899804961}}}\ \>", "\<\ {{{0.337069, 0.0578875}, {0.0479629, 0.530093}}, {{0.992119, 0.781715}, {0.400037, 0.533469}}}\ \>"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(NumberForm[TableForm[e4], {12, 3}]\)], "Input"], Cell[OutputFormData["\<\ {{{0.3370688535874288, 0.05788748716942282}, {0.04796294831324889, 0.5300925627462034}}, {{0.9921185798241328, 0.7817148000400453}, {0.4000373844310341, 0.533468899804961}}}\ \>", "\<\ 0.337 0.048 0.058 0.53 0.992 0.4 0.782 0.533\ \>"], "Output", LineSpacing->{1, 0}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(InputForm[%]\)], "Input"], Cell["\<\ {{{0.3370688535874288, 0.05788748716942282}, {0.04796294831324889, 0.5300925627462034}}, {{0.9921185798241328, 0.7817148000400453}, {0.4000373844310341, 0.533468899804961}}}\ \>", "Output"] }, Open ]], Cell["(5)", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(NumberForm[NumberForm[e4, {12, 3}], {12, 8}]\)], "Input"], Cell[OutputFormData["\<\ {{{0.3370688535874288, 0.05788748716942282}, {0.04796294831324889, 0.5300925627462034}}, {{0.9921185798241328, 0.7817148000400453}, {0.4000373844310341, 0.533468899804961}}}\ \>", "\<\ {{{0.337, 0.058}, {0.048, 0.53}}, {{0.992, 0.782}, {0.4, 0.533}}}\ \>"], "Output"] }, Open ]], Cell["\<\ I expect that multiple wrappers round proper parts will behave \ similarly, except that they will not be discarded. \ \>", "Text"] }, FrontEndVersion->"4.2 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 723}}, WindowSize->{496, 565}, WindowMargins->{{127, Automatic}, {Automatic, 10}} ] (*End *) -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "DrBob" <majort at cox-internet.com> wrote in message news:adhs5i$4gt$1 at smc.vnet.net... > Here's another manifestation of the problem (notice a semicolon in the > fifth line but not the second): > > NumberForm[tb2, {12, 11}]; > % > % // FullForm > NumberForm[tb2, {12, 11}]; > %; > % // FullForm > > It is display of NumberForm objects (not the use of TableForm) that > sometimes removes the NumberForm head. It only removes an outermost > NumberForm head, not NumberForm heads embedded within another Head. > > Isn't that the pattern we're seeing? > > In a construct like TableForm[NumberForm...]...] we want to remove > NumberForm heads that enclose lists but not when they enclose numbers. > And, we want to propagate those NumberForm heads downward TO the numbers > rather than simply removing them, so we have this option: > > numRule := NumberForm[a_List, b_] :> (NumberForm[#, b] & /@ a) > TableForm[NumberForm[tb2, {12, 11}] //. numRule] > > This is no easier than mapping NumberForm onto individual array elements > (that IS what we're doing), but it postpones that to the last moment, in > case that's useful. However, it would be tedious to format different > columns differently with a variation of this. For that, I gave a better > solution earlier: > > formRule := {a_Real, b_Real, c_Real, d_Real} :> { > NumberForm[a, {15, 14}], > NumberForm[b, {3, 2}], > ScientificForm[c, {3, 2}], > AccountingForm[d, 8]} > TableForm[tb2 /. formRule, TableHeadings -> {None, {"a", "b", "c", > "d"}}] > > Use of numRule is simpler if all numbers in the table need the same > formatting. In more complicated settings, both techniques could be used > at once. > > The key (am I right?) is that TableForm doesn't remove NumberForm heads > at all, and displaying an object only removes the outermost NumberForm > head. > > Bobby Treat > > -----Original Message----- > From: David Park [mailto:djmp at earthlink.net] To: mathgroup at smc.vnet.net > Subject: [mg34766] TableForm and NumberForm > > I've renamed this thread because it is a separate subject, probably > interesting to a number of people. > > What is the interaction between NumberForm and TableForm? It seems like > I've > butted my head against this problem a number of times. > > In the following, NumberForm produces an array with the desired number > format. If you look at FullForm, the whole array is wrapped in > NumberForm. > But when the TableForm statement is evaluated, the NumberForm is thrown > away. It is as if TableForm was Applied. Or else NumberForm is stripped > away. We revert to the default 6 place display. > > tbl = Table[Random[], {3}, {4}]; > NumberForm[tbl, {12, 11}] > TableForm[%] > > In the following NumberForm is mapped onto the individual array > elements. > The array displays with the desired number format. Now, when we use > TableForm, the number format is preserved and we obtain the desired > display. > So, why is NumberForm stripped away in the first case and not in this > case. > > tb2 = Table[Random[], {3}, {4}]; > Map[NumberForm[#, {12, 11}] &, %, {-1}] > TableForm[%] > > If we map NumberForm onto each row in the array, then TableForm acts as > if > it had a list of three elements, each element with the Head NumberForm. > This > displays as a column of three lists. > > tb3 = Table[Random[], {3}, {4}]; > Map[NumberForm[#, {12, 11}] &, %, {1}] > TableForm[%] > > So why didn't the first case act as a TableForm of a single element? If > we > rewrite the first case this way, it does. We obtain a single element in > our > table, namely the entire array wrapped in NumberForm. > > tb4 = Table[Random[], {3}, {4}]; > TableForm[NumberForm[tb4, {12, 11}]] > > In any case, it appears that when using TableForm and NumberForm, the > surest > procedure is to map NumberForm onto the individual array elements. > > David Park > djmp at earthlink.net > http://home.earthlink.net/~djmp/ > > > > > From: DrBob [mailto:majort at cox-internet.com] To: mathgroup at smc.vnet.net > > > > Bob, > > > > Thanks! My first attempt was evidently too simplistic. But look at > the > > difference between these two output forms: > > > > tbl = Table[Random[], {3}, {4}] > > NumberForm[TableForm[tbl], {12, 11}] > > TableForm[NumberForm[tbl, {12, 11}]] > > > > Is that what you'd expect? (I'm seeing brackets, etc. displayed in > the > > second version.) > > > > Bobby > > > > From: BobHanlon at aol.com [mailto:BobHanlon at aol.com] To: mathgroup at smc.vnet.net > > > > > > In a message dated 6/3/02 3:12:04 AM, majort at cox-internet.com writes: > > > > >ODDLY ENOUGH, when I tried to use NumberForm within TableForm, the > > >result didn't display as a table, so I don't know how to show > different > > >columns of the table at different display precisions. > > > > > >QUESTION: Does anybody know how to do that? > > > > TableForm[ > > Map[ > > NumberForm[#, {4, 3}, > > NumberPadding->{"", "0"}]&, > > > > Table[Random[], {3}, {4}], {2}], > > > > TableHeadings->{Automatic, Automatic}] > > > > TableForm[ > > Table[ > > NumberForm[ > > Random[], {5, n}, > > NumberPadding->{"", "0"}], > > > > {3}, {n, 4}], > > TableHeadings->{Automatic, Automatic}] > > > > > > Bob Hanlon > > Chantilly, VA USA > > > > > > > >

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