5

我在尝试使符号替换更快时遇到了很多麻烦 - 也就是说，替换符号表达式中的变量并获得双精度。

我正在创建一个复杂的函数 f，并计算它的雅可比 df。这以合理的速度进行，我可以将其保存到文件中。但是当我尝试使用 matlabFunction 甚至 disp 或 fprintf 时，系统会挂起并且无法继续进行（即使 matlabFunction 设置为未优化）。这是一个主要问题，因为我需要能够进行相当快速的替换。

f 向量是 24 个元素，Jacobian 是 24 x 78（虽然这里只有 70 个变量，所以可以压缩到 70 列；不过我怀疑这是问题所在）。

我也知道 f 和 df 的某些元素在单独访问时很简单并且工作正常，但是 f 和 df 的某些更复杂的元素无法显示。我想它们很长，但是由于它们计算得很好，所以对我来说它们不能转换成 matlabFunction 或显示是没有意义的。

更奇怪的是，我可以用 in 替换我所有的符号变量，但是完全替换的 f 向量的最终显示（例如，通过 disp）或转换为 double（通过 double( )）似乎需要很长时间。

如果你想玩弄 .mat 文件，你可以在这里得到它（filedropper 链接，它是 288kb）。我该怎么做才能在合理的时间内写出这个文件？

4

1 回答 1

7

注意：从您的评论的角度来看，我专注于这个问题：

它是矩阵乘法和加法的结果。我一直尝试使用简化命令对其进行简化，但这非常慢。我曾经成功地将 f 写入一个未优化的文件（df 没有运气）——花了 2 个小时——但随后评估它花了 0.8 秒，这太慢了。我需要能够在大约 0.02 秒内执行评估。

我开始查看你的元素f，它很简单f(12)。然而，f(13)释放了地狱：

>> inp.f(13)

ans =

(2289*l4)/100 - (11371197146449238679*l3)/8112963841460668169578900514406400 - (2289*l2)/100 + (11371197146449238679*l5)/8112963841460668169578900514406400 - (2289*l8)/100 - (11371197146449238679*l9)/8112963841460668169578900514406400 + (2289*l10)/100 + (11371197146449238679*l11)/8112963841460668169578900514406400 - (2289*l14)/100 - (11371197146449238679*l15)/8112963841460668169578900514406400 + (2289*l16)/100 + (11371197146449238679*l17)/8112963841460668169578900514406400 - (2289*l20)/100 - (11371197146449238679*l21)/8112963841460668169578900514406400 + (2289*l22)/100 + (11371197146449238679*l23)/8112963841460668169578900514406400 - (2289*l26)/100 - (11371197146449238679*l27)/8112963841460668169578900514406400 + (2289*l28)/100 + (11371197146449238679*l29)/8112963841460668169578900514406400 - (2289*l32)/100 - (11371197146449238679*l33)/8112963841460668169578900514406400 + (2289*l34)/100 + (11371197146449238679*l35)/8112963841460668169578900514406400 - h1*(((cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))*(cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2)) + (sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2))*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) - cos(x5/2)^2*cos(x6/2)*sin(x6/2))*(((x17*(cos(x4/2)*cos(x5/2)*(cos(x6/2)*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) + sin(x6/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2))) - cos(x5/2)*sin(x4/2)*(cos(x6/2)*(cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2)) + sin(x6/2)*(cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2)))))/2 - (x18*(cos(x4/2)^2*cos(x5/2)^2 + cos(x5/2)^2*sin(x4/2)^2 + sin(x5/2)^2))/2 + (x16*(sin(x5/2)*(cos(x5/2)^2*cos(x6/2)^2 + cos(x5/2)^2*sin(x6/2)^2 + sin(x5/2)^2) + cos(x5/2)*sin(x4/2)*(cos(x5/2)*sin(x4/2)*sin(x5/2) + cos(x5/2)*cos(x6/2)*(cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2)) - cos(x5/2)*sin(x6/2)*(cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))) + cos(x4/2)*cos(x5/2)*(cos(x4/2)*cos(x5/2)*sin(x5/2) - cos(x5/2)*cos(x6/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + cos(x5/2)*sin(x6/2)*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)))))/2 - (x19*cos(x5/2)*sin(x4/2))/2)*((LEG_MASS*((cos(x7/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + cos(x5/2)*cos(x6/2)*sin(x7/2))*((cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))*(x2/2 - BASE_ORIGIN_Z*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) - (cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*sin(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4)) - (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*(x1/2 + BASE_ORIGIN_Z*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*cos(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4)) + cos(x5/2)*sin(x4/2)*(x3/2 - sin(x5/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4) + BASE_ORIGIN_Z*cos(x4/2)*cos(x5/2) - cos(x5/2)*sin(x4/2)*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2))) - (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*((sin(x5/2)*sin(x7/2) - cos(x4/2)*cos(x5/2)*cos(x7/2))*(x3/2 - sin(x5/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4) + BASE_ORIGIN_Z*cos(x4/2)*cos(x5/2) - cos(x5/2)*sin(x4/2)*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2)) - (cos(x7/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + cos(x5/2)*cos(x6/2)*sin(x7/2))*(x1/2 + BASE_ORIGIN_Z*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*cos(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4)) + (cos(x7/2)*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) - cos(x5/2)*sin(x6/2)*sin(x7/2))*(x2/2 - BASE_ORIGIN_Z*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) - (cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*sin(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4))))*(sin(x7/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) - cos(x5/2)*cos(x6/2)*cos(x7/2)) - LEG_MASS*((sin(x7/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) - cos(x5/2)*cos(x6/2)*cos(x7/2))*((cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))*(x2/2 - BASE_ORIGIN_Z*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) - (cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*sin(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4)) - (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*(x1/2 + BASE_ORIGIN_Z*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*cos(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4)) + cos(x5/2)*sin(x4/2)*(x3/2 - sin(x5/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4) + BASE_ORIGIN_Z*cos(x4/2)*cos(x5/2) - cos(x5/2)*sin(x4/2)*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2))) + (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*((cos(x7/2)*sin(x5/2) + cos(x4/2)*cos(x5/2)*sin(x7/2))*(x3/2 - sin(x5/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4) + BASE_ORIGIN_Z*cos(x4/2)*cos(x5/2) - cos(x5/2)*sin(x4/2)*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2)) + (sin(x7/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) - cos(x5/2)*cos(x6/2)*cos(x7/2))*(x1/2 + BASE_ORIGIN_Z*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*cos(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4)) - (sin(x7/2)*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) + cos(x5/2)*cos(x7/2)*sin(x6/2))*(x2/2 - BASE_ORIGIN_Z*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) - (cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*sin(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4))))*(cos(x7/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + cos(x5/2)*cos(x6/2)*sin(x7/2)) + LEG_MASS*(cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*((cos(x7/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + cos(x5/2)*cos(x6/2)*sin(x7/2))*((cos(x7/2)*sin(x5/2) + cos(x4/2)*cos(x5/2)*sin(x7/2))*(x3/2 - sin(x5/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4) + BASE_ORIGIN_Z*cos(x4/2)*cos(x5/2) - cos(x5/2)*sin(x4/2)*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2)) + (sin(x7/2)*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) - cos(x5/2)*cos(x6/2)*cos(x7/2))*(x1/2 + BASE_ORIGIN_Z*(sin(x4/2)*sin(x6/2) + cos(x4/2)*cos(x6/2)*sin(x5/2)) + (cos(x4/2)*sin(x6/2) - cos(x6/2)*sin(x4/2)*sin(x5/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + cos(x5/2)*cos(x6/2)*(BASE_ORIGIN_X - BASE_LINK_EXTENTS_X/4)) - (sin(x7/2)*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) + cos(x5/2)*cos(x7/2)*sin(x6/2))*(x2/2 - BASE_ORIGIN_Z*(cos(x6/2)*sin(x4/2) - cos(x4/2)*sin(x5/2)*sin(x6/2)) - (cos(x4/2)*cos(x6/2) + sin(x4/2)*sin(x5/2)*sin(x6/2))*(BASE_LINK_EXTENTS_Y/2 - BASE_ORIGIN_Y + LEG_LINK_EXTENTS_Y/2) + [...] ... Output truncated.  Text exceeds maximum line length of 25,000 characters for Command Window display.

（实际输出被截断以适应 SO 的 30k 字符限制，但你得到了交易）

我敢打赌，解析器matlabFunction不适合这种规模的输入。里面还有一些奇怪的东西：比如 . 顺序的整数字符串文字8e33。

所以我仔细研究了你的功能。幸运的是，您可以将函数转换为字符串，然后处理这些字符串，这只会占用 CPU 时间而不占用内存。

预处理：

for k=1:24
   fstring2{k}=char(inp.f(k));
end

函数长度：

>> cellfun(@length,fstring2)

ans =

  Columns 1 through 12

          11          11          11          11          11          11          11          11          11          11          11          11

  Columns 13 through 24

     2301006     2300241     2299996     8425640     8416273     8424306     1375443     1305245     1302440     1237876     1381084     1310884

休斯顿，我们遇到了问题。

这些符号函数的巨大野兽破坏了解析器matlabFunction，或者更有可能的是，您在操作过程中耗尽了内存。当我尝试这样做时，我确实做到了simplify f(13)，在几秒钟内丢失了 8 GB 的一半。

就像概念验证一样，我试图模拟您的函数中涉及的计算工作。我检查f(13)了（第一只野兽）。有关所涉及操作的一些信息：

>> length(strfind(char(inp.f(13)),'*'))

ans =

      134710

>> length(strfind(char(inp.f(13)),'+'))

ans =

       36932

>> length(strfind(char(inp.f(13)),'-'))

ans =

       26855

>> length(strfind(char(inp.f(13)),'/'))

ans =

      183380

>> length(strfind(char(inp.f(13)),'ln'))

ans =

     0

>> length(strfind(char(inp.f(13)),'exp'))

ans =

     0

>> length(strfind(char(inp.f(13)),'cos'))

ans =

       78700

>> length(strfind(char(inp.f(13)),'sin'))

ans =

       84142

我试图对涉及类似数量的操作的模拟计算进行计时：

x=zeros(36000,1);
tic;
for k=1:36000
   x(k)=(((sin(sin(((cos(cos(3.1+2.1)*3.1)*6.1)*5.1)*9.1)/4.1)/3.1)/6.1)/5.1)/8.1;
end
toc;

Elapsed time is 0.010895 seconds.

这涉及到36000加法、144000乘法、180000除法以及对and的72000调用。sincos

现在，如果我们假设这是一个正确的大致数字，并且如果我们假设您的函数具有类似的操作分布，那么您正在查看40080434函数的字符，即 17 个等效f(13)单位。这表明即使您可以转换为适当的 matlab 函数，您的运行时仅调用f（我们根本没有查看df）至少需要 0.1-0.2 秒。

由于您的问题的性质，我不确定是否有解决方法。我可能会尝试使用sympyin做同样的事情，在python那里您也可以转换为 a lambda（匿名函数的 python 等效项）以用于数值计算。如果那会成功，那么至少您可以尽快使用您的功能。

更新

在发布了我不太乐观的答案后，我相信我已经成功地将您的函数转换为匿名函数。它很脏，但它似乎工作。

首先，如上所述将函数转换为字符串，然后用于symvar提取变量名。然后使用这些函数名创建一个函数定义；不幸的是，我只能使用eval. 应该有一种更优雅的方式，但无论如何我们对可实现的运行时感兴趣。

varcell=symvar(fstring2{13}); %variables of inp.f(13)
vars2=strcat(varcell,','); %add a comma to each var
vars3=[vars2{:}]; %put them into a single string
vars3=vars3(1:end-1); %remove trailing comma

f13=eval(['@(' v3 ') ' fstring2{13}]); %this is your numeric function

转换很麻烦，但匿名函数的实际构造很快，而且不会太占用内存。虚拟运行时：

>> tic; ftry(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58), toc

ans =

   1.1417e+06

Elapsed time is 0.069252 seconds.

它可以变得更加用户友好，例如通过允许函数中的数组操作，或将所有 58 个输入作为单个数组输入传递。但是你的运行时间是一样的。这只是一个功能，您大约有 17 个。你可能永远不会得到你希望的加速。

（无论如何，我确实开始得到

线程“AWT-EventQueue-0”java.lang.OutOfMemoryError 中的异常：Java 堆空间

整个磨难之后的错误，所以它的成功也可能取决于你对“成功”的定义；）

于 2015-10-20T11:46:44.513 回答