Would a better graphics card or more cores make Mathematica faster?

Question

In general, can Mathematica automatically (i.e. without writing code specifically for this) exploit GPU hardware and/or parallelize built-in operations across multiple cores?

For example, for drawing a single very CPU-intensive plot or solving a very CPU-intensive equation, would upgrading the graphics hardware result in speed-up? Would upgrading to a CPU with more cores speed things up? (I realize that more cores mean I could solve more equations in parallel but I'm curious about the single-equation case)

Just trying to get a handle on how Mathematica exploits hardware.

Answer 1

I wouldn't say Mathematica does automatically GPU or Paralell-CPU computing, at least in general. Since you need do something with paralell kernels, then you should initialize more kernels and/or upload CUDALink or OpenCLLink and use specific Mathematica functionality to exploit the potential of CPU and/or GPU.

For example, I haven't got very powerful graphics card (NVIDIA GeForce 9400 GT) but we can test how CUDALink works. First I have to upload CUDALink :

Needs["CUDALink`"] 

I am going to test multiplication of large matrices. I choose a random matrix 5000 x 5000 of real numbers in range (-1,1) :

M = RandomReal[{-1,1}, {5000, 5000}];

Now we can check the computing times without GPU support

  In[4]:= AbsoluteTiming[ Dot[M,M]; ]

  Out[4]= {26.3780000, Null}

and with GPU support

In[5]:= AbsoluteTiming[ CUDADot[M, M]; ]

Out[5]= {6.6090000, Null}

In this case we obtained a performance speed-up roughly of factor 4, by using CUDADot instead of Dot.

Edit

To add an example of parallel CPU acceleration (on a dual-core machine) I choose all prime numbers in range [2^300, 2^300 +10^6]. First without parallelizing :

In[139]:= AbsoluteTiming[ Select[ Range[ 2^300, 2^300 + 10^6], PrimeQ ]; ]

Out[139]= {121.0860000, Null}

while using Parallelize[expr], which evaluates expr using automatic parallelization

In[141]:= AbsoluteTiming[ Parallelize[ Select[ Range[ 2^300, 2^300 + 10^6], PrimeQ ] ]; ]

Out[141]= {63.8650000, Null}

As one could expect we've got almost two times faster evaluation.