How to learn these matlab statements?

Question

I've been informed what statements we need to know and here are my answers to what they do. Please correct me if I'm mistaken somewhere and please tell me how I learn more advanced statement that I might need e.g. the .* and .^ for element-wise operation I did not yet learn.

%  Mini-Matlab:
%  =============
% 
%  Find out what these statements do!
%  Then you can write a Matlab-program.

% "%" starts a Matlab comment

x=[2 3]

The above is like an array, a vector that resides in memory after the statement.

y=[4 5]'

This is a column vector.

A=[x; y']

The semicolon separates the rows of a matrix.

B=sin(A)

This is like a regular mathematical function.

z=x.*y'

This too is just like a function in the classic math / CS.

c=A\y

This is important and solves an equation system but which? How is the original equation stated? Does the above solve Ay=c? Please specify.

a='Hej'

The above is just a variable like in any other computer language.

a(2)='a'

The above sets the second element of the vector a to the string 'a'.

v=3:2:9

The above constructs a vector from 3 to 9 with the step 2.

w=5:3:15

The above constructs a vector from 5 to 15 with the step 3.

t=0:0.05:10;

t becomes a vector between 0 and 10 with increments of 0.05.

f=t.*exp(2*t);

This is just like a regular function definition.

plot(t,f)

This plots the function on the y-axis and the t on the x-axis.

title('Fin kurva');

This just sets the title of the graph.

g=3*t.*sin(t);

This is a more comlex function definition, still easy to understand what it does.

k=cos(t+2)+sin(t.^2);

Another simple function definition.

help XXX % XXX=sin, cos, plot, disp

Accessing the online help system.

if CONDITION
  STATEMENTS...
end;

Self-explanatory.

if CONDITION
  STATEMENTS...
else
  STATEMENTS...
end;

Also self-explanatory.

for VARIABLE = VECTOR
  SATSER...
end;

A regular for-loop

while VILLKOR
  SATSER...
end;

Easy to understand if you ever programmed.

So I think I understand most of the statement but from this list it appears that the most relevant to study is the equation solver c=A\y that I need to practice how to use.

Answer 1

x=[2 3]

The above is like an array, a vector that resides in memory after the statement.

[ ... ] creates a matrix of everything you put inside the brackets. A matrix can be scalar (1x1), row-vector (1xN), column-vector (Nx1) or full blown 2d matrix (MxN). Matlab knows also higher dimensional matrices, but you can't input them using the bracket notation (inputting slices (which themselves are 2d) of a higher dimensional matrix is possible however).

y=[4 5]'

This is a column vector.

[4 5] creates a 1x2 vector, the ' is the transpose operator, which transforms it to a 2x1 vector.

A=[x; y']

The semicolon separates the rows of a matrix.

indeed, and because x is 1x2 and y' also, A is 2x2 with its first row x and 2nd row y'.

B=sin(A)

This is like a regular mathematical function.

sin: Y = sin(X) returns the circular sine of the elements of X. So you can input either a scalar, vector, or even a matrix. Output is same size as input.

z=x.*y'

This too is just like a function in the classic math / CS.

.* is the element-wise multiplication operator. It is important that x and y are same size, else this will error! each element of x is multiplied with the corresponding element of y, in this case, the result will be: [2*4 3*5]

c=A\y

This is important and solves an equation system but which? How is the original equation stated? Does the above solve Ay=c? Please specify.

Documentation: Backslash or matrix left division. If A is a square matrix, A\B is roughly the same as inv(A)*B, except it is computed in a different way.

So it is equal to c=inv(A)*y, hence it solves A*c=y. Those slash-and-backslash are always tricky if you don't use them all the time.

a='Hej'

The above is just a variable like in any other computer language.

Incorrect, any text specified within ' symbols, is interpreted as text, so a will be a character array, you can see this using the whos function.

a(2)='a'

The above sets the second element of the vector a to the string 'a'.

Correct, this is only feasible because a is of type char, and 'a' (rhs) is a 1x1 char. The resulting a will contain 'Haj'.

v=3:2:9

The above constructs a vector from 3 to 9 with the step 2.

Correct, so the result is: v = [3 5 7 9]. Notice that 3:2:10 produces the same vector!

w=5:3:15

The above constructs a vector from 5 to 15 with the step 3.

Correct

t=0:0.05:10;

t becomes a vector between 0 and 10 with increments of 0.05.

from 0 to 10, including!

f=t.*exp(2*t);

This is just like a regular function definition.

same thing as with the sine function plus there is a element-wise multiplication of t with exp(...)

plot(t,f)

This plots the function on the y-axis and the t on the x-axis.

This plots the vector f on the y-axis and t on the x-axis, so resulting plot will consist of datapoints (t(ii), f(ii)) with ii ranging from 1 to the length of the vectors. t and f must be of same length!

title('Fin kurva');

This just sets the title of the graph.

Correct

g=3*t.*sin(t); k=cos(t+2)+sin(t.^2);

Simple functions.

Correct

help XXX % XXX=sin, cos, plot, disp

Accessing the online help system.

correct, but it's not online, it's builtin. For example: 'help sin' will give you some help on using the sin function.

if CONDITION STATEMENTS... end;

Self-explanatory.

if CONDITION STATEMENTS... else STATEMENTS... end;

Also self-explanatory.

for VARIABLE = VECTOR SATSER... end;

A regular for-loop

yes, VARIABLE will take all values in VECTOR sequentially. You can pass VECTOR either as a variable, or directly as 1:2:10. Examples: here

The online matlab documentation usually can give all the information you need, and for everything else there is SO.

Answer 2

c=A\y is matrix left division to solve the equation Ac=y.

If A is a square matrix, then A\y is equivalent to inv(A)*y, pinv(A)*y or mldivide(A,y), but they are computed in different ways.

If A is a rectangular matrix, then inv is not applicable, so A\y is equivalent topinv(A)*y and mldivide(A,y). They are the least squares solutions of Ac=y but in different sense.

More info here