Arrays, Matrices

Many Matlab commands (e.g., those creating graphs) accept the variables as arrays.

Numerical array operations are simple to perform. Here are some examples:

• create the array [1 1.2 1.4 1.6 1.8 2]
  (related commands are linspace, logspace)

  x=1:.2:2

• compute the function x->2*x^4+x*sin(x)/4/(1+x) for these values
  (note that when we have to multiply, divide etc. two arrays element-by-element,
  we use the operation preceded by a period: .*, ./ and .^ for powers).

  y=2*x.^4+x.* sin(x)/4./(1+x)

• graph the points (x(i),y(i)), i=1,2,3,4,5,6   (and interpolate)

  plot(x,y)

• define an array, check its length

  x=[1 3 4 6 8 2]
len=length(x)

• select the third entry

  y=x(3)

• select the sub-array consisting of the middle 4 terms, respectively the last three terms, or any sequence of terms

  z=x(2:5)
s=x(end-2:end)
r=x([1 3 3 2 4 2])

• reverse the array

  t=x(6:-1:1)

• logical subscripting
  
  One can select values of an array (could be multi-dimensional too) and their location with logical operations. These are much faster then using a loop to check/select each entry.
  
  To see more about this, look in the "Getting started" guide, under "More About Matrices and Arrays", "Logical Subscripting". Part of that is here.
  
  Here are a few examples. Read the documentation for find for more uses (e.g., locating the 'first' or 'last' match).

      
  
  >> x=[2,3,4,3,5,2]
  
  x =
       2     3     4     3     5     2
  
  >> x(x>3)               % subarray of entries > 3
  
  ans =
       4     5
  
  >> find(x>3)          % indexes of entries > 3
  
  ans =
       3     5
  
  >> x(x==4)            % subarray of entries equal to 4
  
  ans =
       4
  
  >> x(x==2)            % subarray of entries equal to 2
  
  ans =
       2     2
  
  >> x(isprime(x))        % subarray of prime entries
  
  ans =
       2     3     3     5     2
  
  >> find(isprime(x))     % indexes of prime entries in x
  
  ans =
       1     2     4     5     6
  
  >> x(find(isprime(x)))     % same as x(isprime(x))
  
  ans =
       2     3     3     5     2
      
    

• add two more entries to the array t from above, which had 6 entries:

  t(7:8)=[9 20]

• delete the third enty:

  t(3)=[]

• Commands that create matrices with certain initial values are zeros, ones, eye, diag, rand, randn, magic, etc.
• create a 50 x 100 x 10 "matrix" (with initial entries zero); do not display it!

  M=zeros(50,100,10);

• create a 2 x 3 matrix

  U=	1 2 5 3 4 0

  U=[1 2 5; 3 4 0]

• replace the first row of U with ones

  U(1,:)=ones(1,3)

• take the first two columns of U to form a new matrix

  A=U(:,1:2)

• compute the conjugate transpose of A

  B=A'

  (the non-conjugate transpose is given by .'; it differs from the above only if the matrix has non-real entries)
• multiply the two matrices

  C=A * B

• divide C by A on the left; should obtain B

  A\C

• divide C by B on the right; should obtain A

  C/B

• compute the third power of C

  D=C^3

• compute the inverse of C and check the result

  E=C^(-1)

E*C