Page 35 - Applied Numerical Methods Using MATLAB

24 MATLAB USAGE AND COMPUTATIONAL ERRORS
>>u_noise1 = 2*u_noise-1 %a 1000x1 noise vector with U(-1,1)
>>subplot(222), hist(u_noise1,20) %histogram

2. Random Number with Normal (Gaussian) Distribution
The numbers in a matrix generated by the MATLAB function randn(M,N) have
2
normal (Gaussian) distribution with average m = 0 and variance σ = 1, as
described by N(0,1). The random number x generated by rand() has the prob-
ability density function
1 −x /2
2
f X (x) = √ e (1.1.5)
2π
If you want another Gaussian number y with a general normal distribution
2
N(m, σ ), transform the standard Gaussian number x as follows:
y = σx + m (1.1.6)

The probability density function of the new Gaussian number generated by this
transformation is obtained by substituting x = (y − m)/σ into Eq. (1.1.5) and
dividing the result by the scale factor σ (which can be seen in dx = dy/σ)
so that the integral of the density function over the whole interval (−∞, +∞)
amounts to 1.
1 −(y−m) /2σ 2
2
f Y (y) = √ e (1.1.7)
2πσ
For practice, we make a vector consisting of 1000 standard Gaussian numbers,
transform it to make a vector of numbers having normal distribution N(1,1/4),
2
with mean m = 1 and variance σ = 1/4, and then draw the histograms for the
two Gaussian number vectors (Fig. 1.7c,d).

>>g_noise = randn(1000,1) %a 1000x1 noise vector with N(0,1)
>>subplot(223), hist(g_noise,20) %histogram having 20 divisions
>>g_noise1 = g_noise/2+1 %a 1000x1 noise vector with N(1,1/4)
>>subplot(224), hist(g_noise1,20) %histogram

1.1.9 Flow Control

1. if-end and switch-case-end Statements
An if-end block basically consists of an if statement, a sequel part, and an end
statement categorizing the block. An if statement, having a condition usually
based on the relational/logical operator (Table 1.4), is used to control the program
flow—that is, to adjust the order in which statements are executed according to
whether or not the condition is met, mostly depending on unpredictable situa-
tions. The sequel part consisting of one or more statements may contain else or
elseif statements, possibly in a nested structure containing another if statement
inside it.
The switch-case-end block might replace a multiple if-elseif-..-end
statement in a neat manner.