Find Error Function
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 = 1×4 -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 = 2×2 0.3183 -0.1236 1.0000 -1.0000
Find Cumulative Distribution Function of Normal Distribution
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')
Calculate Solution of Heat Equation with Initial Condition
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')
x — Input
real number | vector of real numbers | matrix of real numbers | multidimensional array of real numbers
Input, specified as a real number, or a vector, matrix, or multidimensional
array of real numbers.
x cannot be sparse.
The error function erf of x is
You can also find the standard normal probability distribution using the function
normcdf(Statistics and Machine Learning Toolbox). The relationship between the error function
For expressions of the form
1 - erf(x), use the complementary error function
erfcinstead. This substitution maintains accuracy. When
erf(x)is close to
1 - erf(x)is a small number and might be rounded down to
0. Instead, replace
1 - erf(x)with
Calculate with arrays that have more rows than fit in memory.
This function fully supports tall arrays. For more information, see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Strict single-precision calculations are not supported. In the generated code, single-precision inputs produce single-precision outputs. However, variables inside the function might be double-precision.
Run code in the background using MATLAB®
backgroundPool or accelerate code with Parallel Computing Toolbox™
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).