complex-numbers

The Matlab documentation says that For speed and improved robustness, you can replace complex i and j by 1i. For example, instead of using a = i; use a = 1i; The robustness part is clear, as there might be variables called i or j . However, as for speed , I have made a simple test in Matlab 2010b and I obtain results which seem to contradict the claim: >>clear all >> a=0; tic, for n=1:1e8, a=i; end, toc Elapsed time is 3.056741 seconds. >> a=0; tic, for n=1:1e8, a=1i; end, toc Elapsed time is 3.205472 seconds. Any ideas? Could it be a version-related issue? After comments by @TryHard and

I have run across some confusing behaviour with square roots of complex numbers in python. Running this code: from cmath import sqrt a = 0.2 b = 0.2 + 0j print(sqrt(a / (a - 1))) print(sqrt(b / (b - 1))) gives the output 0.5j -0.5j A similar thing happens with print(sqrt(-1 * b)) print(sqrt(-b)) It appears these pairs of statements should give the same answer? tzaman Both answers ( +0.5j and -0.5j ) are correct, since they are complex conjugates -- i.e. the real part is identical, and the imaginary part is sign-flipped. Looking at the code makes the behavior clear - the imaginary part of the

I am currently trying to write a program that deals with complex numbers. I have to use classes and methods. I am trying to be able to add, subtract, multiply etc., complex numbers, as well as compare them to one another. I think I have gotten a good start but have some issues. I have started each method, and I think I just need to fill in the gaps. In the method, I used self.x as a placeholder. I'm not really sure what goes there. First off, the program needs to create it's own complex numbers. I'm new to making methods and functions and I'm not sure if I used (self) in the correct places. I

I am working on a project that needs vector math and complex numbers. I am looking a for a good open source API that supports C/C++ and hopefully has decent performance. I can write these functions myself but it will be ugly and slow. You can use the C++ complex numbers library Also, Boost provides linear Algebra package I regularly use Sony Vector Math library bundled with bullet physics . It's fast has many linear algebra algorithms. For complex numbers you can simply use std::complex I haven't used any of these packages personally, but head over to Object-Oriented Numerics for a great

I have build a rudimentary kernel in CUDA to do an elementwise vector-vector multiplication of two complex vectors. The kernel code is inserted below ( multiplyElementwise ). It works fine, but since I noticed that other seemingly straightforward operations (like scaling a vector) are optimized in libraries like CUBLAS or CULA, I was wondering if it is possible to replace my code by a library call? To my surprise, neither CUBLAS nor CULA have this option, I tried to fake it by making one of the vectors the diagonal of a diagonal matrix-vector product, but the result was really slow. As a

if A matrix has complex element and I want to transpose A to A' using the command >>A' Why it is design that a+bi be transformed into a-bi ? What it use for? From here : for complex matrices, it is almost always the case that the combined operation of taking the transpose and complex conjugate arises in physical or computation contexts and virtually never the transpose in isolation ( Strang 1988 , pp. 220-221). In matlab if you want to transpose without conjugating use .' . Actually I'd argue that there are deep reasons why the transpose IS the conjugate . Consider a matrix representation of