gibson:teaching:fall-2012:math445:review_diary
Diary of review session
x = 1:3 % 1 to 3 by increments of 1
x =
1 2 3
x = 1:3:10 % 1 to 10 by increments of 3
x =
1 4 7 10
x = [ 3 8 12 14 ] % specify elements of a vector manually
x =
3 8 12 14
x = [ 3 8 12 14 ]' % ' means transpose: turns a row vector into a col vector
x =
3
8
12
14
x = [ 3 ; 8 ; 12 ; 14 ] % semicolons inside [] delimit rows, produces col vector
x =
3
8
12
14
A = [ 4 2 1 ; 3 4 5; 7 2 9] % semicolons delimit rows, produces matrix
A =
4 2 1
3 4 5
7 2 9
A = [ 4 2 1 ; 3 4 5; 7 2 9]' % ' means transpose, interchange A(i,j) and A(j,i)
A =
4 3 7
2 4 2
1 5 9
3 + 4*i % this is how you enter a complex number
ans =
3.0000 + 4.0000i
i % i is the unit imaginary number
ans =
0 + 1.0000i
i^2 % i == sqrt(-1), i^2 == -1
ans =
-1
z = 3 + 4*i % assign complex number to z
z =
3.0000 + 4.0000i
A = [ 4 2 1 ; 3 4 5; 7 2 9+2*i] % a matrix with a complex element
A =
4.0000 2.0000 1.0000
3.0000 4.0000 5.0000
7.0000 2.0000 9.0000 + 2.0000i
1.3e-03 % compact scientific notation, means 1.3 times 10^(-3)
ans =
0.0013
4e14 % means 4 x 10^14
ans =
4.0000e+14
4*10^(+14) % same thing
ans =
4.0000e+14
% A floating point number has sixteen digits of accuracy.
% That means sixteen digits in the MANTISSA (here 1.4)
1.4e75
ans =
1.4000e+75
% The EXPONENT can go up to +308 or -324
1e308 % this is ok
ans =
1.0000e+308
1e309 % this is not ok
ans =
Inf
1/0 % infinity, infinity, how can I reach infinity?
ans =
Inf
-1/0 % another way, downwards
ans =
-Inf
Inf-Inf % this is undefined, so the answer is Not a Number
ans =
NaN
0/0 % this is undefined, so the answer is Not a Number
ans =
NaN
tan(pi/2) % might guess Inf, but Matlab's pi is rounded to sixteen digits
ans =
1.6331e+16
format long
pi
ans =
3.141592653589793
4 + 7^4 + 0/0*(4+3) % a single NaN in an expression with make the result NaN
ans =
NaN
% elementwise calculations
x = [2 1 3];
x =
2 1 3
y = [4 6 9];
y =
4 6 9
x + y % + on vectors means elementwise addtion
ans =
6 7 12
x - y % - on vectors means elementwise subtraction
ans =
-2 -5 -6
% but * on vectors is the innerproduct!
x = [2 1 3]
x =
2 1 3
y = [4 6 9]'
y =
4
6
9
x*y % innerproduct for 3-vectors is x(1)*y(1) + x(2)*y(2) + x(3)*y(3)
ans =
41
2*4 + 1*6 + 3*9
ans =
41
% to get component wise multiplication of vectors, use .* sytnax
x = [2 1 3]
x =
2 1 3
y = [4 6 9]
y =
4 6 9
x.*y % componentwise multiplication: ans(i) = x(i)*y(i)
ans =
8 6 27
x = [2 1 3];
x.^2 % componentwise square
ans =
4 1 9
x./y % componentwise division
ans =
0.500000000000000 0.166666666666667 0.333333333333333
0 == 0 && 1 == 1 % true AND true => true
ans =
1
0 == 0 && 1 == 0 % true AND false => false
ans =
0
0 == 0 || 1 == 0 % true OR false => true
zeros(4,5) % makes a 4 x 5 matrix of zeros
ans =
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
ones(4,5) % makes a 4 x 5 matrix of ones
ans =
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
eye(5) % makes a 5 x 5 identity matrix, I
ans =
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
% rand(4,5) makes a 4 x 5 matrix of random numbers
% uniformly distributed btwn 0 and 1
rand(4,5)
ans =
0.6557 0.6787 0.6555 0.2769 0.6948
0.0357 0.7577 0.1712 0.0462 0.3171
0.8491 0.7431 0.7060 0.0971 0.9502
0.9340 0.3922 0.0318 0.8235 0.0344
randi(10, 3,2) % makes a 3 x 2 matrix of random integers btwn 1 and 10
ans =
5 8
7 3
8 7
% makes a 3 x 2 matrix of random numbers with a Guassian or normal distrib.
randn(3,2)
ans =
0.6007 -0.0068
-1.2141 1.5326
-1.1135 -0.7697
x = randn(1000,1); % make a vector of 1000 random numbers in Gaussian dist
hist(x) % plot a histogram of x
xlabel('value of x')
ylabel('number of occurences')
title('Histogram of Gaussian distribution')
x = rand(1000,1); % make a vector of 1000 random numbers in uniform distrib
figure(2) ; % open a new figure window
hist(x)
title('Histogram of uniform distribution')
ylabel('number of occurences')
xlabel('valiue of x')
% size function
A = rand(4,5)
A =
0.8844 0.6198 0.1962 0.7985 0.7022
0.4390 0.2606 0.3039 0.9875 0.3755
0.7817 0.4457 0.4833 0.1590 0.9737
0.1485 0.8440 0.3378 0.2369 0.9723
size(A)
ans =
4 5
[M N] = size(A)
M =
4
N =
5
size(A,1) % return the number of rows in A
ans =
4
size(A,2) % return the number of cols in A
ans =
5
x = input('please type in a number: ')
please type in a number: 34
x =
34
disp('hello, world!') % simple print of input
hello, world!
% fprintf is for more complicated printing
x = 12; y = 3;
% print the string argument, substituting the values of x,y in place of %d's
% %d marker means decimal variable
fprintf('x == %d, y == %d\n', x, y);
x == 12, y == 3
x = 'z'
x =
z
% %c marker means character variable
fprintf('x == %c\n', x);
x == z
gibson/teaching/fall-2012/math445/review_diary.txt · Last modified: 2012/09/25 10:22 by gibson
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