This example shows how to use GPU-enabled MATLAB functions to operate with gpuArrays. You can check the properties of your GPU using the gpuDevice function.

gpuDevice

ans = 
  CUDADevice with properties:

                      Name: 'GeForce GTX 1080'
                     Index: 1
         ComputeCapability: '6.1'
            SupportsDouble: 1
             DriverVersion: 10.1000
            ToolkitVersion: 10.1000
        MaxThreadsPerBlock: 1024
          MaxShmemPerBlock: 49152
        MaxThreadBlockSize: [1024 1024 64]
               MaxGridSize: [2.1475e+09 65535 65535]
                 SIMDWidth: 32
               TotalMemory: 8.5899e+09
           AvailableMemory: 6.9012e+09
       MultiprocessorCount: 20
              ClockRateKHz: 1733500
               ComputeMode: 'Default'
      GPUOverlapsTransfers: 1
    KernelExecutionTimeout: 1
          CanMapHostMemory: 1
           DeviceSupported: 1
            DeviceSelected: 1

Create a row vector that repeats values from -15 to 15. To transfer it to the GPU and create a gpuArray, use the gpuArray function.

X = [-15:15 0 -15:15 0 -15:15];
gpuX = gpuArray(X);
whos gpuX

  Name      Size            Bytes  Class       Attributes

  gpuX      1x95                4  gpuArray              

To operate with gpuArrays, use any GPU-enabled MATLAB function. MATLAB automatically runs calculations on the GPU. For more information, see Run MATLAB Functions on a GPU. For example, use a combination of diag, expm, mod, round, abs, and fliplr.

gpuE = expm(diag(gpuX,-1)) * expm(diag(gpuX,1));
gpuM = mod(round(abs(gpuE)),2);
gpuF = gpuM + fliplr(gpuM);

Plot the results.

imagesc(gpuF);
colormap(flip(gray));

If you need to transfer the data back from the GPU, use gather. Gathering back to the CPU can be costly, and is generally not necessary unless you need to use your result with functions that do not support gpuArray.

result = gather(gpuF);
whos result

  Name         Size            Bytes  Class     Attributes

  result      96x96            73728  double              

In general there can be differences in the results if you run the code on the CPU, due to numerical precision and algorithmic differences between GPU and CPU. Answers on CPU and GPU are both equally valid floating point approximations to the true analytical result, having been subjected to different roundoff during computation. In this example, the results are integers and round eliminates the roundoff errors.

This example shows how to use MATLAB functions and operators with gpuArrays to compute the integral of a function, using the Monte Carlo integration method.

Define the number of points to sample. Sample points in the domain of the function, the interval [-1,1] in both x and y coordinates, by creating random points with the rand function. To create a random array directly on the GPU, use the rand function and specify 'gpuArray'. For more information, see Establish Arrays on a GPU.

n = 1e6;
x = 2*rand(n,1,'gpuArray')-1;
y = 2*rand(n,1,'gpuArray')-1;

Define the function to integrate, and use the Monte Carlo integration formula on it. This function approximates the value of $$\pi$$ by sampling points within the unit circle. Because the code uses GPU-enabled functions and operators on gpuArrays, the computations automatically run on the GPU. You can perform binary operations such as element-wise multiplication using the same syntax as MATLAB arrays use. To learn more about GPU-enabled functions, see Run MATLAB Functions on a GPU.

f = x.^2 + y.^2 <= 1;
result = 4*1/n*f'*ones(n,1,'gpuArray')

result =

    3.1403

This example shows how to use GPU-enabled MATLAB functions to compute a well-known mathematical construction: the Mandelbrot set. Check your GPU using the gpuDevice function.

Define the parameters. The Mandelbrot algorithm iterates over a grid of real and imaginary parts. The following code defines the number of iterations, grid size, and grid limits.

maxIterations = 500;
gridSize = 1000;
xlim = [-0.748766713922161, -0.748766707771757];
ylim = [ 0.123640844894862,  0.123640851045266]; 

You can use the gpuArray function to transfer data to the GPU and create a gpuArray, or you can create an array directly on the GPU. gpuArray provides GPU versions of many functions that you can use to create data arrays, such as linspace. For more information, see Create GPU Arrays Directly.

x = gpuArray.linspace(xlim(1),xlim(2),gridSize);
y = gpuArray.linspace(ylim(1),ylim(2),gridSize);
whos x y

  Name      Size              Bytes  Class       Attributes

  x         1x1000                4  gpuArray              
  y         1x1000                4  gpuArray              

Many MATLAB functions support gpuArrays. When you supply a gpuArray argument to any GPU-enabled function, the function runs automatically on the GPU. For more information, see Run MATLAB Functions on a GPU. Create a complex grid for the algorithm, and create the array count for the results. To create this array directly on the GPU, use the ones function, and specify 'gpuArray'.

[xGrid,yGrid] = meshgrid(x,y);
z0 = complex(xGrid,yGrid);
count = ones(size(z0),'gpuArray');

The following code implements the Mandelbrot algorithm using GPU-enabled functions. Because the code uses gpuArrays, the calculations happen on the GPU.

z = z0;
for n = 0:maxIterations
    z = z.*z + z0;
    inside = abs(z) <= 2;
    count = count + inside;
end
count = log(count);

When computations are done, plot the results.

imagesc(x,y,count)
colormap([jet();flipud(jet());0 0 0]);
axis off