Comments for Justin Domke's Weblog http://justindomke.wordpress.com Sun, 08 Nov 2009 21:15:07 +0000 http://wordpress.com/ hourly 1 Comment on About by John Barnett http://justindomke.wordpress.com/about/#comment-194 John Barnett Sun, 08 Nov 2009 21:15:07 +0000 #comment-194 Justin, Your Father gave a sermon at his church today. I was impressed. While I am not a religious person, I can understand people who are. Fred did a good job. I hope you and Masao (?spelling) are doing okay. Congratulations on your new position. John Barnett Justin,

Your Father gave a sermon at his church today. I was impressed. While I am not a religious person, I can understand people who are. Fred did a good job.

I hope you and Masao (?spelling) are doing okay.

Congratulations on your new position.

John Barnett

]]> Comment on Completing the square in N dimensions by david http://justindomke.wordpress.com/completing-the-square-in-n-dimensions/#comment-192 david Mon, 02 Nov 2009 23:26:10 +0000 http://justindomke.wordpress.com/?page_id=828#comment-192 I like this. Seems like all of numerics is reducing nonlinear problems to linear ones. Always wondered if there was a generalization of the quadratic equation to operators but never got this far.. I like this. Seems like all of numerics is reducing nonlinear problems to linear ones. Always wondered if there was a generalization of the quadratic equation to operators but never got this far..

]]> Comment on Mandelbrot in Scala by Ewald http://justindomke.wordpress.com/2008/11/29/mandelbrot-in-scala/#comment-191 Ewald Sun, 01 Nov 2009 10:54:41 +0000 http://justindomke.wordpress.com/?p=138#comment-191 http://wiki.cython.org/tutorials/numpy Look here for info on how to use numpy arrays effciently inside a cython routine. I mailed the code. cython -a yourfile.pyx makes an html file that highlights the slow (python calls) bits. Double click the lines to see the generated code. http://wiki.cython.org/tutorials/numpy

Look here for info on how to use numpy arrays effciently inside a cython routine. I mailed the code.

cython -a yourfile.pyx makes an html file that highlights the slow (python calls) bits. Double click the lines to see the generated code.

]]> Comment on Mandelbrot in Scala by Justin http://justindomke.wordpress.com/2008/11/29/mandelbrot-in-scala/#comment-189 Justin Sun, 01 Nov 2009 00:25:39 +0000 http://justindomke.wordpress.com/?p=138#comment-189 Very cool. Actually, since writing this post, I have basically abandoned Scala for python, so that is encouraging. (Python's libraries are 1000x better, which outweighs everything in the end) I am frankly amazed you got such good performance out of regular python! I've been using weave, rather than cython for performance, but I should probably take another look at that. I would appreciate looking at the code ((myfirstname).(mylastname).rit.edu, or just post it as a comment). I remember having a hard time figuring out how to get cython to run quickly. Very cool. Actually, since writing this post, I have basically abandoned Scala for python, so that is encouraging. (Python’s libraries are 1000x better, which outweighs everything in the end) I am frankly amazed you got such good performance out of regular python! I’ve been using weave, rather than cython for performance, but I should probably take another look at that. I would appreciate looking at the code ((myfirstname).(mylastname).rit.edu, or just post it as a comment). I remember having a hard time figuring out how to get cython to run quickly.

]]> Comment on Mandelbrot in Scala by Ewald http://justindomke.wordpress.com/2008/11/29/mandelbrot-in-scala/#comment-188 Ewald Sat, 31 Oct 2009 19:29:07 +0000 http://justindomke.wordpress.com/?p=138#comment-188 Hi, Not sure if this is relevant anymore. Just for fun I coded your second example in python and cython (the calculation bit). Using your numbers, n=2048 level=100 I get: Python Mandelbrot with n=2048 and level=100 in 58.295 seconds Cython Mandelbrot with n=2048 and level=100 in 1.218 seconds Same answer? : True Speedup: 47.8744235634 Laptop has Core 2 Duo T9300 with 3GB ram on Ubuntu 8.10 64bit. I can send you the code if you'd like. Using python/cython/scipy/numpy/matplotlib/f2py is probably a better way than more obscure (for number crunching and real world problems) languages. Cheers Hi,

Not sure if this is relevant anymore. Just for fun I coded your second example in python and cython (the calculation bit).

Using your numbers, n=2048 level=100 I get:

Python Mandelbrot with n=2048 and level=100 in 58.295 seconds
Cython Mandelbrot with n=2048 and level=100 in 1.218 seconds
Same answer? : True
Speedup: 47.8744235634

Laptop has Core 2 Duo T9300 with 3GB ram on Ubuntu 8.10 64bit. I can send you the code if you’d like. Using python/cython/scipy/numpy/matplotlib/f2py is probably a better way than more obscure (for number crunching and real world problems) languages.

Cheers

]]> Comment on Convex Functions by justindomke http://justindomke.wordpress.com/convex-functions/#comment-185 justindomke Mon, 19 Oct 2009 21:27:39 +0000 http://justindomke.wordpress.com/convex-functions/#comment-185 Well... OK. First, assume $latex f$ is convex, and let's prove $latex g$ is convex. We have that $latex g(\alpha t + \beta s)$ $latex = f(x + (\alpha t + \beta s)v)$ $latex = f(\alpha (x + t v) + \beta (x + s v))$ $latex \leq \alpha f(x + t v) + \beta (x + s v)$ $latex = \alpha g(t) + \beta g(s)$. Now, instead assume $latex g$ is convex for all choices of $latex x,v$. Then, $latex f(\alpha x + \beta y)$ $latex = f(x + \beta(y-x))$ $latex = g(\beta)$ (where $latex v=y-x$ in the definition of $latex g$). $latex \leq (1-\beta)g(0) + \beta g(1)$ $latex = \alpha f(x) + \beta f(y)$ In all honesty that wasn't as trivial as I remembered it being... Well… OK. First, assume f is convex, and let’s prove g is convex. We have that

g(\alpha t + \beta s)
= f(x + (\alpha t + \beta s)v)
= f(\alpha (x + t v) + \beta (x + s v))
\leq \alpha f(x + t v) + \beta (x + s v)
= \alpha g(t) + \beta g(s).

Now, instead assume g is convex for all choices of x,v. Then,
f(\alpha x + \beta y)
= f(x + \beta(y-x))
= g(\beta) (where v=y-x in the definition of g).
\leq (1-\beta)g(0) + \beta g(1)
= \alpha f(x) + \beta f(y)

In all honesty that wasn’t as trivial as I remembered it being…

]]> Comment on Convex Functions by Lee Jae won http://justindomke.wordpress.com/convex-functions/#comment-184 Lee Jae won Mon, 19 Oct 2009 00:33:06 +0000 http://justindomke.wordpress.com/convex-functions/#comment-184 I read the book. Also I attended the lecture. But he had assigned proving the upper definition to their students so I coudln't find the reason I wanted to know. Could you please prove the upper definition again for me? Thank you. I read the book.

Also I attended the lecture.

But he had assigned proving the upper definition to their students so I coudln’t find the reason I wanted to know.

Could you please prove the upper definition again for me?

Thank you.

]]> Comment on Convex Functions by justindomke http://justindomke.wordpress.com/convex-functions/#comment-183 justindomke Sun, 18 Oct 2009 22:39:12 +0000 http://justindomke.wordpress.com/convex-functions/#comment-183 I highly recommend Boyd and Vandenberghe's book: http://www.stanford.edu/~boyd/cvxbook/ I highly recommend Boyd and Vandenberghe’s book:

http://www.stanford.edu/~boyd/cvxbook/

]]> Comment on Convex Functions by Lee Jae won http://justindomke.wordpress.com/convex-functions/#comment-182 Lee Jae won Sun, 18 Oct 2009 18:09:13 +0000 http://justindomke.wordpress.com/convex-functions/#comment-182 A function is convex if any only if the restriction to a line is always convex. This follows pretty easily from the definition: is convex if and only if is convex for any and Would you please explain why this definition is formed to me? I want to know origin of this definition please send e-mail to me.. A function is convex if any only if the restriction to a line is always convex. This follows pretty easily from the definition:

is convex if and only if is convex for any and

Would you please explain why this definition is formed to me?

I want to know origin of this definition

please send e-mail to me..

]]> Comment on Fitting an inference algorithm instead of a model by john zheng http://justindomke.wordpress.com/2009/08/18/fitting-an-inference-algorithm-instead-of-a-model/#comment-174 john zheng Mon, 05 Oct 2009 22:47:46 +0000 http://justindomke.wordpress.com/?p=741#comment-174 I guess this is a bit similar to Vapnik's philosophy of "empirical inference science"... in short, the end justifies the means. I guess this is a bit similar to Vapnik’s philosophy of “empirical inference science”… in short, the end justifies the means.

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