Find the error function of a value.
ans = 0.7175
Find the error function of the elements of a vector.
V = [-0.5 0 1 0.72]; erf(V)
ans = -0.5205 0 0.8427 0.6914
Find the error function of the elements of a matrix.
M = [0.29 -0.11; 3.1 -2.9]; erf(M)
ans = 0.3183 -0.1236 1.0000 -1.0000
The cumulative distribution function (CDF) of the normal, or Gaussian, distribution with standard deviation and mean is
Note that for increased computational accuracy, you can rewrite the formula in terms of
erfc . For details, see Tips.
Plot the CDF of the normal distribution with and .
x = -3:0.1:3; y = (1/2)*(1+erf(x/sqrt(2))); plot(x,y) grid on title('CDF of normal distribution with \mu = 0 and \sigma = 1') xlabel('x') ylabel('CDF')
Where represents the temperature at position and time , the heat equation is
where is a constant.
For a material with heat coefficient , and for the initial condition for and elsewhere, the solution to the heat equation is
k = 2,
a = 5, and
b = 1, plot the solution of the heat equation at times
t = 0.1,
x = -4:0.01:6; t = [0.1 5 100]; a = 5; k = 2; b = 1; figure(1) hold on for i = 1:3 u(i,:) = (a/2)*(erf((x-b)/sqrt(4*k*t(i)))); plot(x,u(i,:)) end grid on xlabel('x') ylabel('Temperature') legend('t = 0.1','t = 5','t = 100','Location','best') title('Temperatures across material at t = 0.1, t = 5, and t = 100')
The error function erf of x is
You can also find the standard normal probability
distribution using the Statistics and Machine Learning Toolbox™ function
normcdf. The relationship between the error
For expressions of the form
1 - erf(x),
use the complementary error function
This substitution maintains accuracy. When
1 - erf(x) is
a small number and might be rounded down to
1 - erf(x) with