02/23/2016 FREEMAT Tutorial

These are the exercises from the FreeMat packet.

 FreeMat v4.2

 Copyright (c) 2002-2008 by Samit Basu

 Licensed under the GNU Public License (GPL)

 Type <help license> to find out more
      <helpwin> for online help
      <pathtool> to set or change your path

 Use <dbauto on/off> to control stop-on-error behavior

 Use ctrl-b to stop execution of a function/script

 JIT is enabled by default - use jitcontrol to change it

 Use <rootpath gui> to set/change where the FreeMat toolbox is installed

--> % Using FREEMAT as a Calculator
--> % Exercise 1
--> 3+4
ans =
 7

--> % Exercise 2
--> 6+3/2
ans =
 7.5000

--> (6+3)/2
ans =
 4.5000

--> 11^2
ans =
 121

--> 2*3+4^3
ans =
 70

--> % Math Functions
--> % Exercise 1
--> sqrt(67)
ans =
 8.1854

--> 2*sin(90)
ans =
 1.7880

--> % sin(90) isn't 0 because the argument is in radians
--> 2*sin(6.28)
ans =
 -0.0064

--> %Redoing Errors
--> %Exercise 1
--> 3=4
Error: Unexpected input
     3=4
      ^

--> 3+4
ans =
 7

--> % Assigning Expressions to Variables
--> % Exercise 1
--> x=2*5
x =
 10

--> x
ans =
 10

--> x=2*5;
--> x
ans =
 10

--> % Creating an Array
--> % Exercise 1
--> C = [1,2,3;4,5,6;7,8,9]

C =
 1 2 3
 4 5 6
 7 8 9

--> % Automatically Creating Vectors
--> % Exercise 1
--> 0:0.5:10
ans =
 Columns 1 to 11
         0    0.5000    1.0000    1.5000    2.0000    2.5000    3.0000    3.5000    4.0000    4.5000    5.0000

 Columns 12 to 21
    5.5000    6.0000    6.5000    7.0000    7.5000    8.0000    8.5000    9.0000    9.5000   10.0000

--> % Transposing Arrays
--> % Exercise 1
--> test1 = [2 3 4 5]
test1 =
 2 3 4 5

--> test2 = test1'
test2 =
 2
 3
 4
 5

--> xx = [1 2 3; 4 5 6]
xx =
 1 2 3
 4 5 6

--> xx'
ans =
 1 4
 2 5
 3 6

--> % Applying Functions to Row Vectors
--> % Exercise 1
--> x = 0:pi/10:2*pi
x =
 Columns 1 to 11
         0    0.3142    0.6283    0.9425    1.2566    1.5708    1.8850    2.1991    2.5133    2.8274    3.1416

 Columns 12 to 21
    3.4558    3.7699    4.0841    4.3982    4.7124    5.0265    5.3407    5.6549    5.9690    6.2832

--> y=sin(x)
y =
 Columns 1 to 11
         0    0.3090    0.5878    0.8090    0.9511    1.0000    0.9511    0.8090    0.5878    0.3090    0.0000

 Columns 12 to 21
   -0.3090   -0.5878   -0.8090   -0.9511   -1.0000   -0.9511   -0.8090   -0.5878   -0.3090   -0.0000

--> z=cos(x)
z =
 Columns 1 to 11
    1.0000    0.9511    0.8090    0.5878    0.3090    0.0000   -0.3090   -0.5878   -0.8090   -0.9511   -1.0000

 Columns 12 to 21
   -0.9511   -0.8090   -0.5878   -0.3090   -0.0000    0.3090    0.5878    0.8090    0.9511    1.0000

--> g=exp(x)
g =
 Columns 1 to 11
    1.0000    1.3691    1.8745    2.5663    3.5136    4.8105    6.5861    9.0170   12.3453   16.9020   23.1407

 Columns 12 to 21
   31.6821   43.3762   59.3867   81.3068  111.3178  152.4060  208.6603  285.6784  391.1245  535.4917

--> h=log10(x)
h =
 Columns 1 to 11
 -Inf   -0.5029   -0.2018   -0.0257    0.0992    0.1961    0.2753    0.3422    0.4002    0.4514    0.4971

 Columns 12 to 21
    0.5385    0.5763    0.6111    0.6433    0.6732    0.7013    0.7276    0.7524    0.7759    0.7982

--> % Array Operations
--> % Exercise 1
--> BB=cos(x)-sin(x)
BB =
 Columns 1 to 11
    1.0000    0.6420    0.2212   -0.2212   -0.6420   -1.0000   -1.2601   -1.3968   -1.3968   -1.2601   -1.0000

 Columns 12 to 21
   -0.6420   -0.2212    0.2212    0.6420    1.0000    1.2601    1.3968    1.3968    1.2601    1.0000

--> CC=cos(x)*sin(x)
Error: Requested matrix multiplication requires arguments to be conformant.
--> DD=cos(x).*sin(x)
DD =
 Columns 1 to 11
         0    0.2939    0.4755    0.4755    0.2939    0.0000   -0.2939   -0.4755   -0.4755   -0.2939   -0.0000

 Columns 12 to 21
    0.2939    0.4755    0.4755    0.2939    0.0000   -0.2939   -0.4755   -0.4755   -0.2939   -0.0000

--> % Addressing Arrays
--> % Exercise 1
--> m = [1 2 3; 4 5 6; 7 8 9]
m =
 1 2 3
 4 5 6
 7 8 9

--> m(1,:)
ans =
 1 2 3

--> m(:,1)
ans =
 1
 4
 7

--> m(1:2,:)
ans =
 1 2 3
 4 5 6

--> m(:,2:3)
ans =
 2 3
 5 6
 8 9

--> % Creating Simple Plots
--> % Exercise 1
--> degree = 0:2*pi/100:2*pi
degree =
 Columns 1 to 11
         0    0.0628    0.1257    0.1885    0.2513    0.3142    0.3770    0.4398    0.5027    0.5655    0.6283

 Columns 12 to 22
    0.6912    0.7540    0.8168    0.8796    0.9425    1.0053    1.0681    1.1310    1.1938    1.2566    1.3195

 Columns 23 to 33
    1.3823    1.4451    1.5080    1.5708    1.6336    1.6965    1.7593    1.8221    1.8850    1.9478    2.0106

 Columns 34 to 44
    2.0735    2.1363    2.1991    2.2619    2.3248    2.3876    2.4504    2.5133    2.5761    2.6389    2.7018

 Columns 45 to 55
    2.7646    2.8274    2.8903    2.9531    3.0159    3.0788    3.1416    3.2044    3.2673    3.3301    3.3929

 Columns 56 to 66
    3.4558    3.5186    3.5814    3.6442    3.7071    3.7699    3.8327    3.8956    3.9584    4.0212    4.0841

 Columns 67 to 77
    4.1469    4.2097    4.2726    4.3354    4.3982    4.4611    4.5239    4.5867    4.6496    4.7124    4.7752

 Columns 78 to 88
    4.8381    4.9009    4.9637    5.0265    5.0894    5.1522    5.2150    5.2779    5.3407    5.4035    5.4664

 Columns 89 to 99
    5.5292    5.5920    5.6549    5.7177    5.7805    5.8434    5.9062    5.9690    6.0319    6.0947    6.1575

 Columns 100 to 101
    6.2204    6.2832

--> output=sin(degree);
--> plot(degree,output)
--> hold on
--> plot(degree,cos(degree))

--> a=2
a =
 2

--> square

Error: Undefined function or variable square
--> % Solving Simultaneous Equations with MATLAB
--> % Exercise 1
--> R = [50 40; 40 60]
R =
 50 40
 40 60

--> V = [10; 20]
V =
 10
 20

--> I = inv(R)*V
I =
   -0.1429
    0.4286

--> % Operations with Complex Numbers
--> % Exercise 1
--> A=2+2j, B=-1+3j, C=2+j
A =
   2.0000 +  2.0000i

B =
  -1.0000 +  3.0000i

C =
   2.0000 +  1.0000i

--> D=(A*B)/C
D =
  -2.4000 +  3.2000i

--> E=(A+B)*C
E =
  -3.0000 + 11.0000i

--> % Functions to convert rectangular to polar
--> % Exercise 1
--> A=3+4j,B=3-2j,C=2*exp(50*phase*j)
A =
   3.0000 +  4.0000i

B =
   3.0000 -  2.0000i

Error: Undefined function or variable phase
-->