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This is awesome. I can't wait until the future when we'll get more informal blog posts from programmers about even more abstract subjects which thus far are dominated in exposition by academics (who very rarely innovate in how they present the material). The day I see a good engineer-style post on HN about sheaf theory or algebraic geometry will be amazing.
Now the real tough question is how do you pronounce Cholesky? I had a Polish math prof who was mad at the American pronunciation, but Cholesky was actually French, so should we actually pronounce it in the francophone style?
Since LAPACK is an excellent library for these matrix functions, why not use it, and translate it to Clojure instead of reinventing the wheel? (There's also a translator from Fortran to C).
Because JVM does not have access to the hardware features needed to execute this efficiently. Also, the power of lapack comes from existing highly tuned implementations , not the interface itself. Reference BLAS and LAPACK are actually quite slow.
Earlier quoted context omitted.
Because JVM does not have access to the hardware features needed to execute this efficiently. Also, the power of lapack comes from existing highly tuned implementations , not the interface itself. Reference BLAS and LAPACK are actually quite slow.
In fact, you can access the hardware through native calls via JNI (or JNA). Or course, then, you have to embedded multiplatform libraries and manage the associated issues. Also, the OpenBLAS implementation is very well optimized for several Intel and AMD processors (you can compile it so that it autodetects which one you're using). It can even reach the efficiency of the Intel's MKL implementation in mono-threaded mo…
OpenBLAS's huge drawback is that it only supports BLAS without LAPACK, sparse, tensors, FFT etc.
Anyway, regarding the OP's comment, I guess that they meant to suggest implementing all that in pure Java, not Java + FFI, since then the native code has to be written in non-Java.
Now the real tough question is how do you pronounce Cholesky? I had a Polish math prof who was mad at the American pronunciation, but Cholesky was actually French, so should we actually pronounce it in the francophone style?
Thus, I'm sticking with ko-LESS-key.
Also seeking opinions on: Weiner (as in the process), and Jensen (as in the inequality), Fourier (as in the series).
Just skimmed and now my eyes are hurt.
Computation cost of calculating the Cholesky factorization of the original second derivative matrix is comparable to cost of calculating the inverse factorization.
Since LAPACK is an excellent library for these matrix functions, why not use it, and translate it to Clojure instead of reinventing the wheel? (There's also a translator from Fortran to C).
Because JVM does not have access to the hardware features needed to execute this efficiently. Also, the power of lapack comes from existing highly tuned implementations , not the interface itself. Reference BLAS and LAPACK are actually quite slow.
Earlier quoted context omitted.
Because JVM does not have access to the hardware features needed to execute this efficiently. Also, the power of lapack comes from existing highly tuned implementations , not the interface itself. Reference BLAS and LAPACK are actually quite slow.
What about correctness? Numerical linear algebra is very difficult and bugs are hard to test for and weed out.
Now the real tough question is how do you pronounce Cholesky? I had a Polish math prof who was mad at the American pronunciation, but Cholesky was actually French, so should we actually pronounce it in the francophone style?
The sophisticated linear algebra practitioners I learned from all said "ko-LESS-key". People who ask me naive questions about the decomposition ("wait, is it upper triangular or lower triangular?") say "choe-LESS-key", or "CHOLES-key", or mutter something even farther off the mark. Thus, I'm sticking with ko-LESS-key. Also seeking opinions on: Weiner (as in the process), and Jensen (as in the inequality), Fourier (as…
I've always heard this pronounced like "for-e-ay" (or "for-e-eh" where the last part is the Canadian "eh?").
Earlier quoted context omitted.
The sophisticated linear algebra practitioners I learned from all said "ko-LESS-key". People who ask me naive questions about the decomposition ("wait, is it upper triangular or lower triangular?") say "choe-LESS-key", or "CHOLES-key", or mutter something even farther off the mark. Thus, I'm sticking with ko-LESS-key. Also seeking opinions on: Weiner (as in the process), and Jensen (as in the inequality), Fourier (as…
Fourier I've always heard this pronounced like "for-e-ay" (or "for-e-eh" where the last part is the Canadian "eh?").
I say "WEE-ner" (since he was American, but, open to correction on that one) and "YEN-sen" (that's how I was taught).