Work with Complex Numbers on a GPU

Conditions for Working With Complex Numbers on a GPU

If the output of a function running on a GPU could potentially be complex, you must explicitly specify its input arguments as complex using the complex function. This applies to functions operating on gpuArray objects directly and to functions operating on gpuArray data using arrayfun.

When creating a gpuArray that has negative elements, use G = gpuArray(complex(x)), then you can successfully execute sqrt(G). For example,

x = [-1 0 1];
G = gpuArray(complex(x));
rootG = sqrt(G)

   0.0000 + 1.0000i   0.0000 + 0.0000i   1.0000 + 0.0000i

If the result is a gpuArray of complex data and all the imaginary parts are zero, these parts are retained and the data remains complex. This could result in unnecessary calculations being performed when operating on the data using, for example, sort and isreal.

If using arrayfun, the function input can be specified as complex within the arrayfun call. For example,

x = [-1 0 1];
G = gpuArray(x);
A = arrayfun(@(p) sqrt(complex(p)), G)

   0.0000 + 1.0000i   0.0000 + 0.0000i   1.0000 + 0.0000i

Functions That Return Complex Data

This table lists the functions that might return complex data, along with the input range over which the output remains real.

Function	Input Range for Real Output
acos(x)	abs(x) <= 1
acosh(x)	x >= 1
acoth(x)	abs(x) >= 1
acsc(x)	abs(x) >= 1
asec(x)	abs(x) >= 1
asech(x)	0 <= x <= 1
asin(x)	abs(x) <= 1
atanh(x)	abs(x) <= 1
log(x)	x >= 0
log1p(x)	x >= -1
log10(x)	x >= 0
log2(x)	x >= 0
power(x,y)	x >= 0
reallog(x)	x >= 0
realsqrt(x)	x >= 0
sqrt(x)	x >= 0