在Mathematica中写入文件时格式化数字 [英] Formatting numbers when writing to files in Mathematica
问题描述
这是此问题的延续，该问题与数字格式有关，并且与我之前的
This is a continuation of this question regarding number formatting, and related to my earlier question about obtaining very specific Mathematica output to text files.
我经常必须在Mathematica中使用高精度来生成数据，但出于可视化目的只需要相对较低的精度.我还想存储数据，以便以后完整使用所有符号名称和数组结构.为此，我一直在使用Save[]，但是有两个相关的问题.
I frequently have to use high precision in Mathematica for data generation but only need relatively low precision for visualization purposes. I also want to store the data for later use with all Symbol names and Array structures intact. For this I have been using Save[], but there are two related problems.
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高精度用多余的数字污染"了我的结果，这些数字很难摆脱:
The high precision "pollutes" my results with superfluous digits which are very hard to get rid of:
In[1] := b = SetPrecision[7, 50]; a = Pi/b
Out[1] := 0.44879895051282760549466334046850041202816705705358654585356351318683091518373`50.
In[2] := InputForm @ N[a, 6]
Out[2] := 0.44879895051282760549466334046850041203`6.
我真的只需要0.448799.
where I really only need 0.448799.
这两种方法都会给文件大小带来很大的开销，并且尽管硬盘存储很便宜，但是以后将文件加载回Mathematica时，文件大小会产生巨大的差异.
Both of these introduce significant overhead to the file size, and while hard disk storage is cheap, file size makes a huge difference when later loading the files back into Mathematica.
因此，例如从aa开始，该文件在不规则数组中包含50位任意精度数字，我是否有一种内置的方式来获取将读取类似内容的文本文件
So, starting with, e.g., aa that contains 50 digit arbitrary precision numbers in an irregular array, is there a built in way for me to get a text file that would read something like this
aa = {{2.0437`4, 4.7276`4, ...}, ...}
编辑:澄清一下，我在显示数字，跟踪数字的精度或更改数字的精度方面没有问题.我遇到的麻烦是控制如何将数字写入文件.
EDIT: To clarify, I am not having problems with the display of numbers or with tracking the precision of numbers or with changing the precision of numbers. What I am having trouble with is controlling how a number is written to a file.
使用N，NumberForm，OutputForm，InputForm，*Form等，均不能在Save下正常工作.而且Save是我可以找到的唯一导出选项，可以导出符号和数组结构. Export和Put*可以用来更好地控制格式，但是它们不包含符号(在Export的情况下，数组结构也会丢失).
Using N, NumberForm, OutputForm, InputForm, *Form, etc, all do not work properly with Save. And Save is the only exporting option I can find that exports the symbol and array structure. Export and Put* can be used to control the formatting better but they don't include the symbol (and in the case of Export the array structure is lost as well).
推荐答案
您是否真的需要2.0437`4之类的东西，还是该机器加倍2.0437就足够了?如果是后者，那么您可以做类似的事情
Do you really require things like 2.0437`4, or would the machine double 2.0437 suffice? If the latter then you could do something like
N[SetPrecision[values,6]]
强制转换为机器双打(大多数情况下将显示六位十进制数字).
to coerce to machine doubles that will (mostly) show six decimal digits.
可能的优点是回读它.您的阵列现在将是机器的双打，因此可打包.我不确定获取"或导入"是否会自动打包，但是Developer`ToPackedArray会做到这一点.
An possible advantage is in reading back it. Your array will now be machine doubles, hence packable. I'm not sure if Get or Import automatically pack, but Developer`ToPackedArray will do that.
---编辑2011-02-11 ---
现在我已经看到了可能出问题的地方...
Now that I've seen what can go wrong...
这里是一个示例，使用您以后的输入以及我希望可以代表的其他一些信息.
Here is an example, using your later input and a few others that I hope will be representative.
aa = {7.469702041097916467293771347613073888816285869`15.\
954589770191005*^-51, 5555.22222222222222222223,
.00000000002222222222222222222222222227777777777777, N[E, 22]^33}
首先转换为字符串.为了保存到文件，这实际上可能就是您真正想要的.我使用NumberForm，但是具有自定义格式设置功能(在文档页面中大体上被抄袭了.)
First convert to a string. This may actually be all you really want, for purposes of saving to a file. I use NumberForm, but with a custom formatting function (cribbed by and large from documentation pages).
In[39]:=
InputForm[ToString[
NumberForm[N[aa], 6,
NumberFormat :> (If[#3 != "", Row[{#1, "*^", #3}], #1] &)]]]
Out[39]//InputForm=
"{7.4697*^-51, 5555.22, 2.22222*^-11, 2.14644*^14}"
请注意，表达式转换对此可以很好地工作.
Notice that the expression conversion works fine on this.
In[40]:=
InputForm[ToExpression[
ToString[NumberForm[N[aa], 6,
NumberFormat :> (If[#3 != "", Row[{#1, "*^", #3}], #1] &)]]]]
Out[40]//InputForm=
{7.4697*^-51, 5555.22, 2.22222*^-11, 2.14644*^14}
---结束编辑---
丹尼尔·里奇布劳 Wolfram研究
Daniel Lichtblau Wolfram Research
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