Updated to beta d again... still can’t use JHS- similar to my previous error report. Sorry, no time to give further details now as Liz wants to move on from this WiFi spot. Thanks, Mike
Please reply to [email protected]. Sent from my iPad > On 26 Apr 2019, at 15:35, jonghough via Programming > <[email protected]> wrote: > > The erorr is in the L-BFGS test, which is unrelated to conv nets. In fact > just remove all tests from the init.ijs file and that error can be ignored. > These lines at teh bottom of init.ijs > NB. test > require jpath '~Projects/jlearn/test/testbase.ijs' > require jpath '~Projects/jlearn/test/testgmm.ijs' > require jpath '~Projects/jlearn/test/testknn.ijs' > require jpath '~Projects/jlearn/test/testnnopt.ijs' > require jpath '~Projects/jlearn/test/testoptimize.ijs' > require jpath '~Projects/jlearn/test/testrunner.ijs' > > can be deleted. On Friday, April 26, 2019, 10:39:32 PM GMT+9, Devon > McCormick <[email protected]> wrote: > > Hi Jon - > I came up with a work-around by changing the "beta" parameter to 1e_7 > instead of 0.0001 (in the call to "minBFGS" in "test4") but have no idea > what this means in the larger scheme of things. Your helpful error message > gave me the clue I needed: > > Error attempting line search. The input values to the function may be too > extreme. > Function input value (xk): _9.65977e27 _6.73606e6 > Search direction value (pk): 2.06573e27 3.10187e6 > A possible solution is to reduce the size of the initial inverse hessian > scale, beta. > Beta is currently set to 0.0001, which may be too large/small. > |uncaught throw.: minBFGS_BFGS_ > |minBFGS_BFGS_[0] > > Thanks again. I look forward to exploring this code. > > Regards, > > Devon > > >> On Fri, Apr 26, 2019 at 9:16 AM Devon McCormick <[email protected]> wrote: >> >> Hi Jon - >> I got your example CIFAR-10 code running on one of my machines but got the >> following error when running "init.ijs" on another one (perhaps with a >> different version of J 8.07): >> Test success AdaGrad Optimizer test 1 >> 1 >> Test success 1 >> 1 >> Test success 2 >> 1 >> Test success 3 >> |value error: minBFGS_BFGS_ >> | k=. u y >> |assertThrow[2] >> >> It looks like "minBFGS_BFGS_" was not defined, so I pasted in the >> definition before loading "init.ijs" and got a little further only to hit >> this error: >> Test success 3 >> |NaN error: dot >> |dot[:0] >> 13!:1'' >> |NaN error >> *dot[:0] >> | Hk=.(rhok*(|:sk)dot sk)+(I-rhok*(|:sk)dot yk)dot Hk >> dot(I-rhok*(|:yk)dot sk) >> |minBFGS_BFGS_[0] >> | k=. u y >> |assertThrow[2] >> | ( minBFGS_BFGS_ assertThrow(f f.`'');(fp f.`'');(4 >> 3);100000;0.0001;0.0001) >> |test4[2] >> | res=. u'' >> |testWrapper[0] >> | test4 testWrapper 4 >> |run__to[5] >> | run__to'' >> |[-180] >> c:\users\devon_mccormick\j64-807-user\projects\jlearn\test\testoptimize.ijs >> | 0!:0 y[4!:55<'y' >> |script[0] >> |fn[0] >> | fn fl >> |load[:7] >> | 0 load y >> |load[0] >> | load fls >> |require[1] >> | require jpath'~Projects/jlearn/test/testoptimize.ijs' >> |[-39] c:\Users\devon_mccormick\j64-807-user\projects\jlearn\init.ijs >> | 0!:0 y[4!:55<'y' >> |script[0] >> |fn[0] >> | fn fl >> |load[:7] >> | 0 load y >> |load[0] >> | >> load'c:\Users\devon_mccormick\j64-807-user\projects\jlearn\init.ijs' >> >> The arguments to "dot" appear to be extreme values: >> (I-rhok*(|:yk)dot sk) >> 1 0 >> _ 0 >> Hk >> _ _4.62371e38 >> _4.62371e38 2.76904e_78 >> >> Any idea what might cause this? >> >> Thanks, >> >> Devon >> >> >> >> >> On Thu, Apr 25, 2019 at 9:55 PM Devon McCormick <[email protected]> >> wrote: >> >>> That looks like it did the trick - thanks! >>> >>> On Thu, Apr 25, 2019 at 9:23 PM jonghough via Programming < >>> [email protected]> wrote: >>> >>>> Hi Devon. >>>> Did you run the init.ijs script. If you run that initially, everything >>>> should be setup, and you should have no problems. >>>> On Friday, April 26, 2019, 9:54:55 AM GMT+9, Devon McCormick < >>>> [email protected]> wrote: >>>> >>>> Hi - so I tried running the code at " >>>> https://github.com/jonghough/jlearn/blob/master/adv/conv2d.ijs"; but get >>>> numerous value errors. >>>> >>>> Is there another package somewhere that I need to load? >>>> >>>> Thanks, >>>> >>>> Devon >>>> >>>> On Fri, Apr 19, 2019 at 10:57 AM Raul Miller <[email protected]> >>>> wrote: >>>> >>>>> That's the same thing as a dot product on ravels, unless the ranks of >>>>> your arguments are ever different. >>>>> >>>>> Thanks, >>>>> >>>>> -- >>>>> Raul >>>>> >>>>> On Thu, Apr 18, 2019 at 8:13 PM jonghough via Programming >>>>> <[email protected]> wrote: >>>>>> >>>>>> The convolution kernel function is just a straight up elementwise >>>>> multiply and then sum all, it is not a dot product or matrix product. >>>>>> Nice illustration is found here: >>>> https://mlnotebook.github.io/post/CNN1/ >>>>>> >>>>>> so +/@:,@:* works. I don't know if there is a faster way to do it. >>>>>> >>>>>> Thanks, >>>>>> Jon On Friday, April 19, 2019, 5:54:24 AM GMT+9, Raul Miller < >>>>> [email protected]> wrote: >>>>>> >>>>>> They're also not equivalent. >>>>>> >>>>>> For example: >>>>>> >>>>>> (i.2 3 4) +/@:,@:* i.2 3 >>>>>> 970 >>>>>> (i.2 3 4) +/ .* i.2 3 >>>>>> |length error >>>>>> >>>>>> I haven't studied the possibilities of this code base enough to know >>>>>> how relevant this might be, but if you're working with rank 4 arrays, >>>>>> this kind of thing might matter. >>>>>> >>>>>> On the other hand, if the arrays handled by +/@:,@:* are the same >>>>>> shape, then +/ .*&, might be what you want. (Then again... any change >>>>>> introduced on "performance" grounds should get at least enough >>>> testing >>>>>> to show that there's a current machine where that change provides >>>>>> significant benefit for plausible data.) >>>>>> >>>>>> Thanks, >>>>>> >>>>>> -- >>>>>> Raul >>>>>> >>>>>> On Thu, Apr 18, 2019 at 4:16 PM Henry Rich <[email protected]> >>>> wrote: >>>>>>> >>>>>>> FYI: +/@:*"1 and +/ . * are two ways of doing dot-products fast. >>>>>>> +/@:,@:* is not as fast. >>>>>>> >>>>>>> Henry Rich >>>>>>> >>>>>>>> On 4/18/2019 10:38 AM, jonghough via Programming wrote: >>>>>>>> >>>>>>>> Regarding the test network I sent in the previous email, it will >>>> not >>>>> work. This one should: >>>>>>>> >>>>>>>> NB. >>>>> >>>> ========================================================================= >>>>>>>> >>>>>>>> >>>>>>>> NB. 3 classes >>>>>>>> NB. horizontal lines (A), vertical lines (B), diagonal lines (C). >>>>>>>> NB. each class is a 3 channel matrix 3x8x8 >>>>>>>> >>>>>>>> >>>>>>>> A1=: 3 8 8 $ 1 1 1 1 1 1 1 1, 0 0 0 0 0 0 0 0, 0 0 0 0 0 0 0 0, >>>> 1 1 >>>>> 1 1 1 1 1 1, 0 0 0 0 0 0 0 0, 1 1 1 1 1 1 1 1, 1 1 1 1 1 1 1 1, 0 0 0 >>>> 0 0 0 >>>>> 0 0, 0 0 0 0 0 0 0 0 >>>>>>>> >>>>>>>> A2=: 3 8 8 $ 1 1 1 1 1 1 1 1, 0 0 0 0 0 0 0 0, 1 1 1 1 1 1 1 1, >>>> 1 1 >>>>> 1 1 1 1 1 1, 0 0 0 0 0 0 0 0 >>>>>>>> >>>>>>>> A3=: 3 8 8 $ 1 1 1 1 1 1 1 1, 0 0 0 0 0 0 0 0, 0 0 0 0 0 0 0 0 >>>>>>>> >>>>>>>> A4=: 3 8 8 $ 1 1 1 1 1 1 1 1, 0 0 0 0 0 0 0 0, 0 0 0 0 0 0 0 0, >>>> 1 1 >>>>> 1 1 1 1 1 1, 1 1 1 1 1 1 1 1, 0 0 0 0 0 0 0 0 >>>>>>>> >>>>>>>> A5=: 2 |. A4 >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> B1=: |:"2 A1 >>>>>>>> >>>>>>>> B2=: |:"2 A2 >>>>>>>> >>>>>>>> B3=: |:"2 A3 >>>>>>>> >>>>>>>> B4=: |:"2 A4 >>>>>>>> >>>>>>>> B5=: |:"2 A5 >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> C1=: 3 8 8 $ 1 0 0 0 0 0 0 1, 0 1 0 0 0 0 1 0, 0 0 1 0 0 1 0 0, >>>> 0 0 >>>>> 0 1 1 0 0 0, 0 0 0 1 1 0 0 0, 0 0 1 0 0 1 0 0, 0 1 0 0 0 0 1 0, 1 0 0 >>>> 0 0 0 >>>>> 0 1 >>>>>>>> >>>>>>>> C2=: 3 8 8 $ 1 0 0 0 0 0 0 0, 0 1 0 0 0 0 0 0, 0 0 1 0 0 0 0 0, >>>> 0 0 >>>>> 0 1 0 0 0 0, 0 0 0 0 1 0 0 0, 0 0 0 0 0 1 0 0, 0 0 0 0 0 0 1 0, 0 0 0 >>>> 0 0 0 >>>>> 0 1 >>>>>>>> >>>>>>>> C3=: 3 8 8 $ 1 0 1 0 1 0 0 0, 0 1 0 1 0 1 0 0, 0 0 1 0 1 0 1 0, >>>> 0 0 >>>>> 0 1 0 1 0 1, 1 0 0 0 1 0 1 0, 0 1 0 0 0 1 0 1, 1 0 1 0 0 0 1 0, 0 1 0 >>>> 1 0 0 >>>>> 0 1 >>>>>>>> >>>>>>>> C4=: |."1 C3 >>>>>>>> >>>>>>>> C5=: 3 8 8 $ 1 1 1 1 0 0 0 0, 0 0 1 1 1 1 0 0, 0 0 0 0 1 1 1 1, >>>> 1 1 >>>>> 0 0 0 0 1 1, 1 1 1 1 0 0 0 0, 0 0 1 1 1 1 0 0, 0 0 0 0 1 1 1 1, 1 1 0 >>>> 0 0 0 >>>>> 1 1 >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> A=: 5 3 8 8 $, A1, A2, A3, A4, A5 >>>>>>>> >>>>>>>> B=: 5 3 8 8 $, B1, B2, B3, B4, B5 >>>>>>>> >>>>>>>> C=: 5 3 8 8 $, C1, C2, C3, C4, C5 >>>>>>>> >>>>>>>> INPUT=: A,B,C >>>>>>>> >>>>>>>> OUTPUT=: 15 3 $ 1 0 0, 1 0 0, 1 0 0, 1 0 0, 1 0 0, 0 1 0, 0 1 0, >>>> 0 1 >>>>> 0, 0 1 0, 0 1 0, 0 0 1, 0 0 1, 0 0 1, 0 0 1, 0 0 1 >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> pipe=: (10;10;'softmax';1;'l2';0.0001) conew 'NNPipeline' >>>>>>>> >>>>>>>> c1=: ((10 3 4 4);2;'relu';'adam';0.01;0) conew 'Conv2D' >>>>>>>> >>>>>>>> b1=: (0; 1 ;0.0001;10;0.01) conew 'BatchNorm2D' >>>>>>>> >>>>>>>> a1=: 'relu' conew 'Activation' >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> c2=: ((12 10 2 2); 1;'relu';'adam';0.01;0) conew 'Conv2D' >>>>>>>> >>>>>>>> b2=: (0; 1 ;0.0001;5;0.01) conew 'BatchNorm2D' >>>>>>>> >>>>>>>> a2=: 'relu' conew 'Activation' >>>>>>>> >>>>>>>> p1=: 2 conew 'PoolLayer' >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> fl=: 3 conew 'FlattenLayer' >>>>>>>> >>>>>>>> fc=: (12;3;'softmax';'adam';0.01) conew 'SimpleLayer' >>>>>>>> >>>>>>>> b3=: (0; 1 ;0.0001;2;0.01) conew 'BatchNorm' >>>>>>>> >>>>>>>> a3=: 'softmax' conew 'Activation' >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> addLayer__pipe c1 >>>>>>>> >>>>>>>> addLayer__pipe p1 >>>>>>>> >>>>>>>> NB.addLayer__pipe b1 >>>>>>>> >>>>>>>> addLayer__pipe a1 >>>>>>>> >>>>>>>> addLayer__pipe c2 >>>>>>>> >>>>>>>> NB.addLayer__pipe b2 >>>>>>>> >>>>>>>> addLayer__pipe a2 >>>>>>>> >>>>>>>> addLayer__pipe fl >>>>>>>> >>>>>>>> addLayer__pipe fc >>>>>>>> >>>>>>>> NB.addLayer__pipe b3 >>>>>>>> >>>>>>>> addLayer__pipe a3 >>>>>>>> >>>>>>>> require 'plot viewmat' >>>>>>>> NB. check the input images (per channel) >>>>>>>> NB. viewmat"2 A1 >>>>>>>> NB. viewmat"2 B1 >>>>>>>> NB. viewmat"2 C1 >>>>>>>> >>>>>>>> >>>>>>>> OUTPUT fit__pipe INPUT NB. <--- should get 100%ish accuracy after >>>>> only a few iterations. >>>>>>>> NB. >>>>> >>>> ========================================================================= >>>>>>>> >>>>>>>> >>>>>>>> Running the above doesn't prove much, as there is no training / >>>>> testing set split. It is just to see *if* the training will push the >>>>> networks parameters in the correct direction. Getting accurate >>>> predictions >>>>> on all the A,B,C images will at least show that the network is not >>>> doing >>>>> anything completely wrong. It is also just useful as a playground to >>>> see if >>>>> different ideas work. >>>>>>>> >>>>>>>> You can test the accuracy with >>>>>>>> OUTPUT -:"1 1 (=>./)"1 >{: predict__pipe INPUT >>>>>>>> On Thursday, April 18, 2019, 11:36:35 AM GMT+9, Brian >>>> Schott < >>>>> [email protected]> wrote: >>>>>>>> >>>>>>>> I have renamed this message because the topic has changed, but >>>>> considered >>>>>>>> moving it to jchat as well. However I settled on jprogramming >>>>> because there >>>>>>>> are definitely some j programming issues to discuss. >>>>>>>> >>>>>>>> Jon, >>>>>>>> >>>>>>>> Your script code is beautifully commented and very valuable, >>>> imho. >>>>> The lack >>>>>>>> of an example has slowed down my study of the script, but now I >>>> have >>>>> some >>>>>>>> questions and comments. >>>>>>>> >>>>>>>> I gather from your comments that the word tensor is used to >>>>> designate a 4 >>>>>>>> dimensional array. That's new to me, but it is very logical. >>>>>>>> >>>>>>>> Your definition convFunc=: +/@:,@:* works very well. However, for >>>>> some >>>>>>>> reason I wish I could think of a way to defined convFunc in >>>> terms of >>>>> X=: >>>>>>>> dot=: +/ . * . >>>>>>>> >>>>>>>> The main insight I have gained from your code is that (x u;.+_3 >>>> y) >>>>> can be >>>>>>>> used with x of shape 2 n where n>2 (and not just 2 2). This is >>>> great >>>>>>>> information. And that you built the convFunc directly into cf is >>>>> also very >>>>>>>> enlightening. >>>>>>>> >>>>>>>> I have created a couple of examples of the use of your function >>>> `cf` >>>>> to >>>>>>>> better understand how it works. [The data is borrowed from the >>>> fine >>>>> example >>>>>>>> at http://cs231n.github.io/convolutional-networks/#conv . Beware >>>>> that the >>>>>>>> dynamic example seen at the link changes everytime the page is >>>>> refreshed, >>>>>>>> so you will not see the exact data I present, but the shapes of >>>> the >>>>> data >>>>>>>> are constant.] >>>>>>>> >>>>>>>> Notice that in my first experiments both `filter` and the RHA of >>>>> cf"3 are >>>>>>>> arrays and not tensors. Consequently(?) the result is an array, >>>> not a >>>>>>>> tensor, either. >>>>>>>> >>>>>>>> i=: _7]\".;._2 (0 : 0) >>>>>>>> 0 0 0 0 0 0 0 >>>>>>>> 0 0 0 1 2 2 0 >>>>>>>> 0 0 0 2 1 0 0 >>>>>>>> 0 0 0 1 2 2 0 >>>>>>>> 0 0 0 0 2 0 0 >>>>>>>> 0 0 0 2 2 2 0 >>>>>>>> 0 0 0 0 0 0 0 >>>>>>>> 0 0 0 0 0 0 0 >>>>>>>> 0 2 1 2 2 2 0 >>>>>>>> 0 0 1 0 2 0 0 >>>>>>>> 0 1 1 1 1 1 0 >>>>>>>> 0 2 0 0 0 2 0 >>>>>>>> 0 0 0 2 2 2 0 >>>>>>>> 0 0 0 0 0 0 0 >>>>>>>> 0 0 0 0 0 0 0 >>>>>>>> 0 0 0 1 2 1 0 >>>>>>>> 0 1 1 0 0 0 0 >>>>>>>> 0 2 1 2 0 2 0 >>>>>>>> 0 1 0 0 2 2 0 >>>>>>>> 0 1 0 1 2 2 0 >>>>>>>> 0 0 0 0 0 0 0 >>>>>>>> ) >>>>>>>> >>>>>>>> k =: _3]\".;._2(0 :0) >>>>>>>> 1 0 0 >>>>>>>> 1 _1 0 >>>>>>>> _1 _1 1 >>>>>>>> 0 _1 1 >>>>>>>> 0 0 1 >>>>>>>> 0 _1 1 >>>>>>>> 1 0 1 >>>>>>>> 0 _1 0 >>>>>>>> 0 _1 0 >>>>>>>> ) >>>>>>>> >>>>>>>> $i NB. 3 7 7 >>>>>>>> $k NB. 3 3 3 >>>>>>>> >>>>>>>> filter =: k >>>>>>>> convFunc=: +/@:,@:* >>>>>>>> >>>>>>>> cf=: 4 : '|:"2 |: +/ x filter&(convFunc"3 3);._3 y' >>>>>>>> (1 2 2,:3 3 3) cf"3 i NB. 3 3$1 1 _2 _2 3 _7 _3 1 0 >>>>>>>> >>>>>>>> My next example makes both the `filter` and the RHA into >>>> tensors. And >>>>>>>> notice the shape of the result shows it is a tensor, also. >>>>>>>> >>>>>>>> filter2 =: filter,:_1+filter >>>>>>>> cf2=: 4 : '|:"2 |: +/ x filter2&(convFunc"3 3);._3 y' >>>>>>>> $ (1 2 2,:3 3 3) cf2"3 i,:5+i NB. 2 2 3 3 >>>>>>>> >>>>>>>> Much of my effort regarding CNN has been studying the literature >>>> that >>>>>>>> discusses efficient ways of computing these convolutions by >>>>> translating the >>>>>>>> filters and the image data into flattened (and somewhat sparse} >>>>> forms that >>>>>>>> can be restated in matrix formats. These matrices accomplish the >>>>>>>> convolution and deconvolution as *efficient* matrix products. >>>> Your >>>>>>>> demonstration of the way that j's ;._3 can be so effective >>>>> challenges the >>>>>>>> need for such efficiencies. >>>>>>>> >>>>>>>> On the other hand, I could use some help understanding how the 1 >>>> 0 2 >>>>> 3 |: >>>>>>>> transpose you apply to `filter` is effective in the >>>> backpropogation >>>>> stage. >>>>>>>> Part of my confusion is that I would have thought the transpose >>>>> would have >>>>>>>> been 0 1 3 2 |:, instead. Can you say more about that? >>>>>>>> >>>>>>>> I have yet to try to understand your verbs `forward` and >>>> `backward`, >>>>> but I >>>>>>>> look forward to doing so. >>>>>>>> >>>>>>>> I could not find definitions for the following functions and >>>> wonder >>>>> if you >>>>>>>> can say more about them, please? >>>>>>>> >>>>>>>> bmt_jLearnUtil_ >>>>>>>> setSolver >>>>>>>> >>>>>>>> I noticed that your definitions of relu and derivRelu were more >>>>> complicated >>>>>>>> than mine, so I attempted to test yours out against mine as >>>> follows. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> relu =: 0&>. >>>>>>>> derivRelu =: 0&< >>>>>>>> (relu -: 0:`[@.>&0) i: 4 >>>>>>>> 1 >>>>>>>> (derivRelu -: 0:`1:@.>&0) i: 4 >>>>>>>> 1 >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Sun, Apr 14, 2019 at 8:31 AM jonghough via Programming < >>>>>>>> [email protected]> wrote: >>>>>>>> >>>>>>>>> I had a go writing conv nets in J. >>>>>>>>> See >>>>>>>>> https://github.com/jonghough/jlearn/blob/master/adv/conv2d.ijs >>>>>>>>> >>>>>>>>> This uses ;.3 to do the convolutions. Using a version of this , >>>>> with a >>>>>>>>> couple of fixes/, I managed to get 88% accuracy on the cifar-10 >>>>> imageset. >>>>>>>>> Took several days to run, as my algorithms are not optimized in >>>> any >>>>> way, >>>>>>>>> and no gpu was used. >>>>>>>>> If you look at the references in the above link, you may get >>>> some >>>>> ideas. >>>>>>>>> >>>>>>>>> the convolution verb is defined as: >>>>>>>>> cf=: 4 : 0 >>>>>>>>> |:"2 |: +/ x filter&(convFunc"3 3);._3 y >>>>>>>>> ) >>>>>>>>> >>>>>>>>> Note that since the input is an batch of images, each 3-d >>>> (width, >>>>> height, >>>>>>>>> channels), we are actually doing the whole forward pass over a >>>> 4d >>>>> array, >>>>>>>>> and outputting another 4d array of different shape, depending on >>>>> output >>>>>>>>> channels, filter width, and filter height. >>>>>>>>> >>>>>>>>> Thanks, >>>>>>>>> Jon >>>>>>>>> >>>>>>>> Thank you, >>>>>>>> >>>>>>> >>>>>>> >>>>>>> --- >>>>>>> This email has been checked for viruses by AVG. >>>>>>> https://www.avg.com >>>>>>> >>>>>>> >>>> ---------------------------------------------------------------------- >>>>>>> For information about J forums see >>>> http://www.jsoftware.com/forums.htm >>>>>> >>>> ---------------------------------------------------------------------- >>>>>> For information about J forums see >>>> http://www.jsoftware.com/forums.htm >>>>>> >>>> ---------------------------------------------------------------------- >>>>>> For information about J forums see >>>> http://www.jsoftware.com/forums.htm >>>>> ---------------------------------------------------------------------- >>>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>>> >>>> >>>> -- >>>> >>>> Devon McCormick, CFA >>>> >>>> Quantitative Consultant >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>> >>> >>> -- >>> >>> Devon McCormick, CFA >>> >>> Quantitative Consultant >>> >>> >> >> -- >> >> Devon McCormick, CFA >> >> Quantitative Consultant >> >> > > -- > > Devon McCormick, CFA > > Quantitative Consultant > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
