MaplePrimes - comments on Post, ImageTools for complex (argument ) plot

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    <title>MaplePrimes - comments on Post, ImageTools for complex (argument ) plot</title>
    <link>http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot</link>
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    <itunes:summary />
    <description>The latest comments added to the Post, ImageTools for complex (argument ) plot</description>
    <image>
      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - comments on Post, ImageTools for complex (argument ) plot</title>
      <link>http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot</link>
    </image>
    <item>
      <title>making it more like a "plot"</title>
      <link>http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot?ref=Feed:MaplePrimes:ImageTools for complex (argument ) plot:Comments#comment124207</link>
      <itunes:summary>&lt;p&gt;A natural followup here is to try and make the resulting exported image file show as more like a Maple plot, with axes or text or labels, etc.&lt;/p&gt;
&lt;p&gt;This can be done by creating an empty plot with all the desired text and axes, exporting that to an image, reading the image back in, and then using that to mask the density image (which pretty much amounts to overlaying them, if the text is black).&lt;/p&gt;
&lt;p&gt;An exported empty plot has a blank border, as the axes don't lie right at the image boundary. This can be accomodated by either fitting the density image to the axes-bounded portion of the empty plot's image, or vice-versa by chopping off the blank border or a slightly larger empty plot. I take the second approach, below. (I suspect the first would be a better choice, if one were aiming to produce a good, fully fledged plot exporter or plot driver replacement.) The boder size also varies with the choice of Maple interface, eg, commandline or Standard GUI.&lt;/p&gt;
&lt;p&gt;This calls `ArgPlot` as coded in the Post. This is rough, top-level stuff, but ideally it could be made into a more general procedure.&lt;/p&gt;
&lt;pre&gt;F:=z-&amp;gt;`if`(z=0,Pi,exp(1/z)):
hsize,vsize:=300,300:

st,str,ba,bu:=time(),time[real](),kernelopts(bytesalloc),kernelopts(bytesused):
  Q:=ArgPlot(F,-0.25,0.25,vsize,hsize):
time()-st,time[real]()-str,kernelopts(bytesalloc)-ba,kernelopts(bytesused)-bu;

st,str,ba,bu:=time(),time[real](),kernelopts(bytesalloc),kernelopts(bytesused):
_Env_plot_warnings:=false:
tempfile:=cat(kernelopts('homedir'),"/temp.jpg"):
# The Standard GUI's plot driver pads the plot with whitespace.
# So we increment the target size for export, and then later chop.
# The padding seems to be absolute in size, rather than relative
# to the dimensions, at least for the GUI's jpeg plot device. Certainly the
# padding can be much greater for jpeg export using the commandline interface's
# jpeg plot driver. Adjust accordingly.
plotsetup('jpeg','plotoutput'=tempfile,'plotoptions'=cat("height=",vsize+6+4,
                                                         ",width=",hsize+5+5));
plot(I,-0.25..0.25,'view'=[-0.25..0.25,-0.25..0.25]);
plotsetup('default'):
try fflush(tempfile); catch: end try:
fclose(tempfile);
# Why doesn't the GUI plot driver flush before returning control?!
# The timing is affected by a delay (YMMV, on NFS or a network drive)
# to wait for the image file to be written. If the `Read` below fails
# and claims the file does not exist, the delay may need increasing.
Threads:-Sleep(1): # 1 second
_Env_plot_warnings:='_Env_plot_warnings':
T:=ImageTools:-Read(tempfile,'format'='JPEG'):
correctedT:=rtable_redim(T[1+6..-1-4,1+5..-1-5,1..-1],1..vsize,1..hsize,1..3):
# The mask could likely be done more efficiently in-place on Q ("by hand"),
# with saving on allocation and thus subsequent collection.
newQ:=ImageTools:-Mask(Q,correctedT):
ImageTools:-Write(cat(kernelopts('homedir'),"/arg_expinv.jpg"),newQ,'quality'=95):
time()-st,time[real]()-str,kernelopts(bytesalloc)-ba,kernelopts(bytesused)-bu;

ImageTools:-View(newQ);
&lt;/pre&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=124207/417979/arg_expinv.jpg"&gt;&lt;img src="/view.aspx?sf=124207/417979/arg_expinv.jpg" alt=""&gt;&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;This can be compared with less attactive results using `densityplot`. (I understand that densityplot's `grid` option is not the same as the width/height of an image. But increasing the `grid` values, for densityplot or complexplot3d, can be prohibitive in terms of time &amp;amp; memory resources and the performance of the plot driver/exporter and of the GUI itself. These aspects were the original motivation. The usual plotting commands cannot match the image creation method here, especially at higher or publication quality resolutions.)&lt;/p&gt;
&lt;pre&gt;restart:

F:=z-&amp;gt;`if`(z=0,Pi,exp(1/z)):
hsize,vsize:=300,300:
plots:-densityplot(-argument(exp(1/(a+b*I))),a=-0.25..0.25,b=-0.25..0.25,
                   colorstyle=HUE, style=patchnogrid,scaletorange=-Pi..Pi,
                   grid=[hsize,vsize],axes=normal);
&lt;/pre&gt;
&lt;p&gt;Exporting using context-menus (right-click, takes a long time...) produces this,&lt;/p&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=124207/417983/dens_expinv.jpg"&gt;&lt;img src="/view.aspx?sf=124207/417983/dens_expinv.jpg" alt=""&gt;&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;And using the GUI's plot driver with the plotsetup command produces this,&lt;/p&gt;
&lt;pre&gt;plotsetup('jpeg','plotoutput'="driv_expinv.jpg",'plotoptions'=cat("height=",300,
                                                                  ",width=",300));
&lt;/pre&gt;
&lt;p&gt;&lt;a href="/view.aspx?sf=124207/417983/driv_expinv.jpg"&gt;&lt;img src="/view.aspx?sf=124207/417983/driv_expinv.jpg" alt=""&gt;&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;acer&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, ImageTools for complex (argument ) plot</description>
      <guid>124207</guid>
      <pubDate>Thu, 28 Jul 2011 00:58:20 Z</pubDate>
      <itunes:author>acer</itunes:author>
      <author>acer</author>
    </item>
    <item>
      <title>Maple 15 and Windows</title>
      <link>http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot?ref=Feed:MaplePrimes:ImageTools for complex (argument ) plot:Comments#comment126972</link>
      <itunes:summary>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot#comment124207"&gt;@acer&lt;/a&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;thanks for a very stimulating post. I'm a couple of months late, but let me nevertheless report my experience with your code. It's worked great except for Zeta, where it got nowhere after nearly an hour. The output I got was similar to the one you report, beautiful plots, but the performance on my machine not as good, I think:&lt;/p&gt;
&lt;p&gt;my specs:&lt;br&gt;i-7 CPU, Q720 @1.60GHz, 4GB RAM, WIN7Prox64 SP1, Maple 15 Standard GUI,&lt;/p&gt;
&lt;p&gt;my stats (worksheet closed and re-opened before each run):&lt;/p&gt;
&lt;pre&gt;F:=z-&amp;gt;`if`(z=0,Pi,exp(1/z)):&lt;br&gt;st,bu:=time(),kernelopts(bytesalloc):&lt;br&gt;&amp;nbsp; Q:=ArgPlot(F,-0.25,0.25,600,600):&lt;br&gt;time()-st,kernelopts(bytesalloc)-bu;&lt;br&gt;&lt;br&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 11.887, 97041044&lt;br&gt;&lt;br&gt;&lt;/pre&gt;
&lt;pre&gt;F:=unapply(convert(convert(taylor(1/(1-z),z=0,100),polynom),horner,z),z):&lt;br&gt;st,bu:=time(),kernelopts(bytesalloc):&lt;br&gt;&amp;nbsp; Q:=ArgPlot(F,-1.5,1.5,600,600):&lt;br&gt;time()-st,kernelopts(bytesalloc)-bu;&lt;br&gt;&lt;br&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 31.388, 100382768&lt;/pre&gt;
&lt;pre&gt;st,bu:=time(),kernelopts(bytesalloc):&lt;br&gt;Q:=ArgPlot(Zeta,-40.0,2.0,300,300):&lt;br&gt;time()-st,kernelopts(bytesalloc)-bu;&lt;br&gt;&lt;br&gt;Warning,&amp;nbsp; computation interrupted&lt;br&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 1435.474, 125281888&lt;/pre&gt;
&lt;pre&gt;F:=z-&amp;gt;Beta(z,1.1-1.7*I): Digits:=7:&lt;br&gt;st,bu:=time(),kernelopts(bytesalloc):&lt;br&gt;Q:=ArgPlot(F,-10.0,10.0,300,300):&lt;br&gt;time()-st,kernelopts(bytesalloc)-bu;&lt;br&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 503.649, 54057300&lt;/pre&gt;
&lt;pre&gt;&amp;nbsp;&lt;/pre&gt;
&lt;pre&gt;# Adding axes:&lt;br&gt;&lt;br&gt;F:=z-&amp;gt;`if`(z=0,Pi,exp(1/z)):&lt;br&gt;st,str,ba,bu:=time(),time[real](),kernelopts(bytesalloc),kernelopts(bytesused):&lt;br&gt;&amp;nbsp; Q:=ArgPlot(F,-0.25,0.25,vsize,hsize):&lt;br&gt;time()-st,time[real]()-str,kernelopts(bytesalloc)-ba,kernelopts(bytesused)-bu;&lt;br&gt;&lt;br&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 2.995, 3.073, 35645056, 43740452&lt;br&gt;&lt;br&gt;newQ:=ImageTools:-Mask(Q,correctedT):&lt;br&gt;ImageTools:-Write(cat(currentdir(),kernelopts(dirsep),"arg_expinv_new.jpg"),newQ,quality=95):&lt;br&gt;time()-st,time[real]()-str,kernelopts(bytesalloc)-ba,kernelopts(bytesused)-bu;&lt;br&gt;&lt;br&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; 0.187, 8.518, 2358864, 7682788&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;/pre&gt;</itunes:summary>
      <description>The latest comments added to the Post, ImageTools for complex (argument ) plot</description>
      <guid>126972</guid>
      <pubDate>Sat, 22 Oct 2011 23:47:07 Z</pubDate>
      <itunes:author>PatrickT</itunes:author>
      <author>PatrickT</author>
    </item>
    <item>
      <title>performance</title>
      <link>http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot?ref=Feed:MaplePrimes:ImageTools for complex (argument ) plot:Comments#comment126979</link>
      <itunes:summary>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot#comment126972"&gt;@PatrickT&lt;/a&gt; I'm glad if you found it worthwhile.&lt;/p&gt;
&lt;p&gt;Forgive me, please, if I belabor a few points. The speedup of the approach was (to me) an incidental benefit. what I was originally striving for was a way to get very high resolution (high pixel count and fidelity of the image therein) without consuming vast memory resources. Or, in short, to get what might otherwise be unattainable in practice using `plot` and plot-export drivers.&lt;/p&gt;
&lt;p&gt;It can be important to carefully watch the MS-Windows Task Manager's report of total memory in use by both Maple kernel and GUI. I have found that 3D plotting and gif export can cause the GUI to consume huge amounts of memory that go unreported by `kernelopts`. And it can be difficult to get the resolution and quality as good by plotting as by these techniques of constructing the image directly.&lt;/p&gt;
&lt;p&gt;I believe you'd find that, even if you timings are not quite matching my own as posted, the speed and memory performance to attain comparable quality images would still far outstrip the best possible by plotting and exporting.&lt;/p&gt;
&lt;p&gt;I tried to include some examples where the expression was Compile'able, and some which may be evalhf'able or not. That's why some examples are much faster than others.&lt;/p&gt;
&lt;p&gt;Out of curiosity, may I ask, is the &lt;a href="http://www.maplesoft.com/support/help/AddOns/view.aspx?path=Compiler"&gt;Compiler&lt;/a&gt; package functional and tested on your described 32bit Maple 15? if not, then the posted code should hopefully fall back to the evalhf interpreter.&lt;/p&gt;
&lt;p&gt;Be sure to install (some version number, but certainly the 64bit version of) the free MSVC++ for 64bit Windows when you decide to install 64bit Maple 15 on your Windows 7 system. It'll be a PITA to &lt;a href="http://www.maplesoft.com/support/help/AddOns/view.aspx?path=Compiler/Setup"&gt;configure&lt;/a&gt;, but worth it. (When and if you have problems getting the Maple Compiler package functioning for that installation,be sure to Post to this site.)&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, ImageTools for complex (argument ) plot</description>
      <guid>126979</guid>
      <pubDate>Sun, 23 Oct 2011 06:44:33 Z</pubDate>
      <itunes:author>acer</itunes:author>
      <author>acer</author>
    </item>
    <item>
      <title>compiler and 64bit</title>
      <link>http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot?ref=Feed:MaplePrimes:ImageTools for complex (argument ) plot:Comments#comment127020</link>
      <itunes:summary>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot#comment126979"&gt;@acer&lt;/a&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Oh and I'm also primarily interested in high-quality plots, performance being secondary.&lt;/p&gt;
&lt;p&gt;I do have the compiler installed and working. I have installed the &lt;span class="st"&gt;&lt;em&gt;Microsoft Visual C++&lt;/em&gt; 2010 Redistributable Package&lt;/span&gt;, because I needed it for something else. I also have older versions (do I need the older versions as well?). I haven't configured it yet, because I am actually using the 32bit version (on a 64bit machine, because a couple of versions ago I had some installation problem). Will I see a performance improvement with the properly configured 64bit version?&lt;/p&gt;
&lt;p&gt;May I ask a few questions related to exporting high-quality plots.&lt;/p&gt;
&lt;p&gt;1. Can your procedure be used/adapted for other kinds of plots? I'm thinking about combining several 2D plots obtained with commands other than plot, such as plottools:-point and plots:-odeplot.&lt;/p&gt;
&lt;p&gt;Or perhaps I should instead bypass plots:-odeplot altogether and instead use the data from dsolve together with plot?&lt;/p&gt;
&lt;p&gt;2. Is there a simple way to transform a 3D plot into a 2D plot for subsequent printing via your method? For instance, using the viewpoint option. I have in mind creating a 3D plot, selecting 4 viewpoints, transforming to 2D plot and exporting the resulting 4 2D plots in high-quality.&lt;/p&gt;
&lt;p&gt;thanks acer.&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, ImageTools for complex (argument ) plot</description>
      <guid>127020</guid>
      <pubDate>Mon, 24 Oct 2011 12:31:18 Z</pubDate>
      <itunes:author>PatrickT</itunes:author>
      <author>PatrickT</author>
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    <item>
      <title>reason for my asking</title>
      <link>http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot?ref=Feed:MaplePrimes:ImageTools for complex (argument ) plot:Comments#comment127024</link>
      <itunes:summary>&lt;p&gt;&lt;a href="http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot#comment127020"&gt;@PatrickT&lt;/a&gt; I wasn't so much asking about whether you'd installed MSVC++ on your machine, as much as I was asking whether the Maple command Compiler:-Compile is confirmed as functioning in your installed 32bit Maple 15.&lt;/p&gt;
&lt;p&gt;That would entail that the examples on the &lt;a href="http://www.maplesoft.com/support/help/search.aspx?term=Compiler"&gt;?Compiler&lt;/a&gt; help-page would run properly. Whether that functions, or not, was what I was wondering since you'd mentioned timings for this Maple code running on your Intel i7 on Windows.&lt;/p&gt;
&lt;p&gt;The 32bit Maple for Windows returns "IBM INTEL NT" when the command kernelopts('system') is issued in Maple. Typically, the external C compiler that the Maple Compiler:-Compile command uses (internally) for that version is the Watcom compiler that is bundled with Maple part of Maple's own installation process.&lt;/p&gt;
&lt;p&gt;I understand, that you have not yet installed 64bit Maple 15 on your Windows 7 and configured it to use the "free" MSVC++ &amp;amp; 64bit SDK for that platform, which is what is needed to get Compiler:-Compile to function in that version. That'll be another topic, for another day, sure.&lt;/p&gt;
&lt;p&gt;Now, to answer your questions, as best as I know:&lt;/p&gt;
&lt;p&gt;1) No, this technique does not relate to usual plots in any immediate way that I know of. It was just a technique for generating image of 'plots' that involve showing a value for (almost) every location in the field.&lt;/p&gt;
&lt;p&gt;If one is only plotting a spacecurve, then it doesn't seem to apply. Except &lt;em&gt;maybe&lt;/em&gt; in one way. Some plots don't look smooth enough. Just try plot(sin(x),x=-10..10) for example. One can see that the displayed curve does not look nice and smooth. Raising the number of computed points very high does not help, as that just makes the curve show as being very jagged at a very small grained level. I'm not sure whether this is a problem fixable in the display or export drivers, or whether the adaptive plot data generation or methodology needs adjusting. What I know is that it looks clunky to the naked eye. Now, possibly a "replacement" gif creation utility &lt;em&gt;might&lt;/em&gt; be able to produce a smoother curve in an image. But what an effort, to duplicate all that `plot` does! Really, this is so very basic, and important, that it ought to be fixed in the normal plotting mechanisms.&lt;/p&gt;
&lt;p&gt;2) Not in any direct way, that I can see. I suppose it could be done, but the code for doing so would have to be new, and wouldn't be a direct application of what I've coded here. Also, I've never studied hard the code that lies behind the usual plottools:-project command.&lt;/p&gt;
&lt;p&gt;These are interesting questions (and high quality plotting in general is important) but they don't seem directly related to the application above.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, ImageTools for complex (argument ) plot</description>
      <guid>127024</guid>
      <pubDate>Mon, 24 Oct 2011 13:33:52 Z</pubDate>
      <itunes:author>acer</itunes:author>
      <author>acer</author>
    </item>
    <item>
      <title>compiler</title>
      <link>http://www.mapleprimes.com/posts/123463-ImageTools-For-Complex-argument--Plot?ref=Feed:MaplePrimes:ImageTools for complex (argument ) plot:Comments#comment127030</link>
      <itunes:summary>&lt;p&gt;@acer&lt;/p&gt;
&lt;p&gt;thanks for your help, once again, acer, and sorry for not properly understanding your questions.&lt;br&gt;&lt;br&gt;I have checked and have been able to run the examples the &lt;a href="http://www.maplesoft.com/support/help/search.aspx?term=Compiler"&gt;?Compiler&lt;/a&gt; help-page gives. The watcom compiler seems to be properly installed to work with the 32 bit version. In the sense that it spits out the same output reported in the help page. And yes, I do get the message&amp;nbsp;&lt;span&gt; "IBM INTEL NT"&lt;/span&gt;. But, as you say, I have not set it up to use 64 bit and MSVC++. That shall be my next task, as soon as some urgent things are out of the way.&lt;/p&gt;
&lt;p&gt;&amp;gt; &lt;span&gt;It was just a technique for generating image of 'plots' that involve showing a value for (almost) every location in the field.&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;I understand. &lt;/p&gt;
&lt;p&gt;&lt;span&gt;&amp;gt; &amp;gt; &lt;span&gt;2. Is there a simple way to transform a 3D plot into a 2D plot for subsequent printing via your method? &lt;/span&gt;&lt;br&gt;&amp;gt; I suppose it could be done, but the code for doing so would have to be new, and wouldn't be a direct application of what I've coded here. &lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span&gt;thanks for your answer, my question is misplaced, I shall start a new thread altogether.&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span&gt;thanks acer, I'll report back if I run into difficulties setting up the 64bit/MSVC++ combo.&lt;br&gt;&lt;/span&gt;&lt;/p&gt;</itunes:summary>
      <description>The latest comments added to the Post, ImageTools for complex (argument ) plot</description>
      <guid>127030</guid>
      <pubDate>Mon, 24 Oct 2011 16:26:39 Z</pubDate>
      <itunes:author>PatrickT</itunes:author>
      <author>PatrickT</author>
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