On Wed, May 20, 2009 at 14:46, dmitrey <dmitrey.kros...@scipy.org> wrote: > On May 20, 10:34 pm, Robert Kern <robert.k...@gmail.com> wrote: >> On Wed, May 20, 2009 at 14:24, dmitrey <dmitrey.kros...@scipy.org> wrote: >> > hi all, >> >> > suppose I have A that is numpy ndarray of floats, with shape n x n. >> >> > I want to obtain dot(A, b), b is vector of length n and norm(b)=1, but >> > instead of exact multiplication I want to approximate b as a vector >> > [+/- 2^m0, ± 2^m1, ± 2^m2 ,,, ± 2^m_n], m_i are integers, and then >> > invoke left_shift(vector_m) for rows of A. >> >> You don't shift floats. You only shift integers. For floats, >> multiplying by an integer power of 2 should be fast because of the >> floating point representation (the exponent just gets incremented or >> decremented), so just do the multiplication. >> >> > So, what is the simplest way to do it, without cycles of course? Or it >> > cannot be implemented w/o cycles with current numpy version? >> >> It might help if you showed us an example of an actual b vector >> decomposed the way you describe. Your description is ambiguous. >> >> -- >> Robert Kern > > For the task involved (I intend to try using it for speed up ralg > solver) it doesn't matter essentially (using ceil, floor or round), > but for example let m_i is > floor(log2(b_i)) for b_i > 1e-15, > ceil(log2(-b_i)) for b_i < - 1e-15, > for - 1e-15 <= b_i <= 1e-15 - don't modify the elements of A related > to the b_i at all.
I strongly suspect that a plain dot(A, b) will be faster than doing all of that. With a little bit of work with frexp() and ldexp(), you could probably do those floor(log2())'s cheaply, but ultimately, you will still need to do a dot(A, b_prime) at the end. There is no bit-shift operation available for floats (anywhere, not just numpy); you have to form the float corresponding to +-2**m and multiply. If you had many A-matrices and a static b-vector, you might see a tiny improvement because all of the b_prime elements were exactly of the form +-2**m, but I doubt it. -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
