Increase Speed by Reducing Precision

Increase MATLAB^®’s speed by reducing the precision of your calculations. Reduce precision by using variable-precision arithmetic provided by the vpa and digits functions in Symbolic Math Toolbox™. When you reduce precision, you are gaining performance by reducing accuracy. For details, see Choose Numeric or Symbolic Arithmetic.

For example, finding the Riemann zeta function of the large matrix C takes a long time. First, initialize C.

[X,Y] = meshgrid((0:0.0025:.75),(5:-0.05:0));
C = X + Y*i;

Then, find the time taken to calculate zeta(C).

tic
zeta(C); 
toc

Elapsed time is 340.204407 seconds.

Now, repeat this operation with a lower precision by using vpa. First, change the precision used by vpa to a lower precision of 10 digits by using digits. Then, use vpa to reduce the precision of C and find zeta(C) again. The operation is significantly faster.

digits(10)
vpaC = vpa(C);
tic
zeta(vpaC);
toc

Elapsed time is 113.792543 seconds.

For larger matrices, the difference in computation time can be even more significant. For example, consider the 1001-by-301 matrix C.

[X,Y] = meshgrid((0:0.0025:.75),(5:-0.005:0));
C = X + Y*i;

Running zeta(vpa(C)) with 10-digit precision takes 15 minutes, while running zeta(C) takes three times as long.

digits(10)
vpaC = vpa(C);
tic
zeta(vpaC);
toc

Elapsed time is 886.035806 seconds.

tic
zeta(C);
toc

Elapsed time is 2441.991572 seconds.