MATLAB examples - introduction

A = [ 16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1 ]
A
A'
sum(A)      (matlab tends to operate on columns -> returns row vector)
sum(A')
sum(A')'    (returns a column vector of row sums)

A(4,2)      (row first, then column, just like in normal matrix notation)
A(2,4)
A(4,5)      (should give error message)
X = A
X(4,5) = 17    (assignment always works, though, even if have to expand)

1:10        (returns row vector of integer range)
100:-7:50
0:pi/4:pi
A(1:4,4)    (select 4th column)
A(:,4)      (shorthand for selecting all of available range)
A(:,end)    (refers to last column)

A(:,[1 3 2 4])     (swap rows - think of this as matlab making a
                    reasonable interpretation of a vector being used
                    in place of a scalar)

(more accurately, matlab thinks "naturally" in terms of matrices.
A scalar is simply a 1x1 matrix)

A(8)        (8th element - equivalent to A(4,2))

variables:
  created automatically as needed - no typing (like C has).
  this means you have to be a bit more careful about typos.
  also consider that names are unique up to a user-defined length:

    namelengthmax

  clear <name>             (delete name - CHECK)

numbers:
  3
  -99
  0.01
  1.6e-20
  6.022e23
  1i
  -3.14j    (also complex - i or j the same)
  3e5i

  internal format is 64-bit IEEE format:  ~16 digits, exponent 10^+-308

operators:
  + - * /    (as you'd expect)
  \          (left division)
  ^          (power)
  '          (complex conjugate transpose)
  ( )

functions:
  help elfun
  help specfun
  help elmat

  (many functions as you'd expect)

  pi
  i
  j
  Inf
  NaN

  rho = (1+sqrt(5))/2
  a = abs(3+4i)
  huge = exp(log(realmax))
  toobig = pi * huge

matrix generation:
  zeros
  ones
  rand     (uniformly distributed random numbers)
  randn    (normally distributed)

  load

  (m-files - scripts)

matrix manipulation:

  B = [ A A+32; A+48 A+16];         (concatenation by []'s)

  X = A;
  X(:,2) = []         (deletes 2nd column)
  X

  X(1,2) = []      (error - trying to delete a single element,
                    but other elements in row/column are left)
  X(2:2:10) = []   (single dimension - so considered as a row vector.
                    now deletion is valid)

  (but you could change values of elements individually.  also a range)
  X(1:2,2:3) = 0

  det(A)
  eig(A)

other operators:

  .*             (element-by-element multiplication)
  ./
  .\
  .^
  .'             (unconjugated array transpose)

  n = (0:9)';
  pows = [n n.^2 2.^n]

  x = (1:0.1:2)';
  logs = [x log10(x)]

logical subscripting (different from reordering rows - apparently need a matrix of
0 and 1 exactly the same size as the matrix):

  x = [ 2.1 1.7 1.6 1.5 NaN 1.9 1.8 1.5 5.1 1.8 1.4 28 1 ];
  x = x(isfinite(x))

  (gets rid of NaN; isfinite() gives 0 only in column position of NaN)

  x = x(abs(x-mean(x)) <= 3*std(x))

  (removes outliers, > 3 sigma from mean)

  A(~isprime(A)) = 0

  (zeros non-prime elements of matrix)

suppressing output:  end with a semicolon
  (especially useful in loops where you don't need the intermediate values)

entering long statements:  ...

basic plots:

  x = -1:.1:1;
  y = x.^3;
  plottools

  (click on both x and y using shift-click in variable workspace.
  then right-click for menu, select plot(x,y))

  (get m-code from File menu)



  x = 0:pi/100:2*pi;
  y = sin(x);
  plot(x,y)

  y2 = sin(x-0.25);
  y3 = sin(x-0.5);
  plot(x,y,x,y2,x,y3)

  [x,y,z] = peaks           (example of 3-valued function)
  pcolor(x,y,z)
  shading interp
  hold on                   (continue plotting in same space)
  contour(x,y,z,20,'k')
  hold off

reset figure properties:

  clf reset

subplots:

  t = 0:pi/10:2*pi;
  [X,Y,Z] = cylinder(4*cos(t));
  subplot(2,2,1); mesh(X)
  subplot(2,2,2); mesh(Y)
  subplot(2,2,3); mesh(Z)
  subplot(2,2,4); mesh(X,Y,Z)

3D plots

  [X,Y] = meshgrid(-8:.0.5:8);
  R = sqrt(X.^2 + Y.^2) + eps;
  Z = sin(R)./R;                   (eps prevents divide by 0)
  mesh(X,Y,Z,'EdgeColor','black')

  surf(X,Y,Z)
  colormap hsv
  colorbar

  surf(X,Y,Z)
  colormap hsv
  alpha(.4)

  surf(X,Y,Z,'FaceColor','red','EdgeColor','none')
  camlight left; lighting phong

View -> Camera Toolbar
select Rotate3D tool


other examples:  look up "animate" in the online help

chaos example