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 thevpaanddigitsfunctions in Symbolic Math Toolbox™. When you reduce precision, you are gaining performance by reducing accuracy. For details, seeChoose Numeric or Symbolic Arithmetic.

For example, finding the Riemann zeta function of the large matrixCtakes a long time. First, initializeC.

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

Then, find the time taken to calculatezeta(C).

tic zeta(C); toc

Elapsed time is 340.204407 seconds.

Now, repeat this operation with a lower precision by usingvpa. First, change the precision used byvpato a lower precision of10digits by usingdigits. Then, usevpato reduce the precision ofCand findzeta(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 the1001-by-301matrixC.

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

Runningzeta(vpa(C))with 10-digit precision takes 15 minutes, while runningzeta(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.