1. Electrical and Computer Engineering Department SUNY – New Paltz
Computer Simulation
“Lecture 6”
Electrical and Computer Engineering Department
SUNY – New Paltz
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2. Logical vectors objectives Logical operators Logical vectors
Logical functions
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3. Logical Operators r = 1; r <= 0.5 ans= 0 r = 0; r <= 0.5 ans= 1
b = [ ];
a == b
ans=
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4. Exercise
Prompt the user to enter a vector of numbers between 1 and 10. Your program should print the total number of elements that are less than 5.
Hint: No for loop are required.
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5. Logical Operators
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6. Be Careful! 0 < r < 1 Wrong! (0 < r) & (r < 1) Correct!
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7. Operator Precedence
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8. Exercise
Prompt the user to enter a vector of numbers between 1 and 10. Your program should print the total number of elements that lie between 1 and 5.
Hint: No for loop are required.
Repeat the above program but this time print out the number of elements between 3 and 7.
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9. Subscripting with logical vectors
ans:
a(logical([ ]))
ans: 0 5
a = a(a > 0)
ans: 1 5 9
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10. Exercise
Prompt the user to enter a vector of numbers between -10 and 10. Your program should separate the input vector into 2 vectors:
1- a vector containing the positive and zero numbers.
2- anther vector containing the negative numbers.
Hint: No for loop are required.
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11. Exercise
Prompt the user to enter a vector (no zeros in the vector). Then change the values of the elements with odd indices to 0.
Hint: use an array of indices
Prompt the user to enter a vector (no zeros in the vector). Then change the values of the elements with negative values to 0.
Hint: use a logical vector of zeros and ones
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12. Verifying Logical Vectors
b= a > 0
islogical(a)
ans: 0
islogical(b)
ans: 1
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13. Subscripting with logical vectors Exercise
Prompt the user to enter a vector of a set of numbers between 0 and 9 of any length.
Your program should use a for loop to iterate through the vector and print the total number of elements that lie between 4 and 7 (inclusive).
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14. Subscripting with logical vectors Exercise
Repeat the same program using logical vectors.
Hint: generate a logical vector out of the user input vector and use the sum() function to get the total.
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15. Application of Logical Vectors
1-form vector 0<x<3*pi
2- form a vector such that if y > 0 then it is one
Multiply y by this vector
x = 0 : pi/20 : 3 * pi;
y = sin(x);
y = y .* (y > 0);
plot(x, y)
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16. Logical functions any(x) all(x) exist(’a’) find(x)
returns the scalar 1 (true) if any element of x is non-zero (true).
returns the scalar 1 if all the elements of x are non-zero.
returns 1 if a is a workspace variable.
returns a vector containing the subscripts of the non-zero (true) elements of x
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17. Examples a=[0 2 1 2 3 4] a = a( find(a) ) x = [8 1 -4 8 6];
find(x >= max(x))
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18. Logical functions Exercises
Prompt the user to enter a vector of numbers between 0 and 9.
Your program should analyze the input vector and respond by printing either:
The vector has no zeros.
The vector has XX non-Zero elements. The first non-zero is at location YY
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19. Logical functions isempty(x) isinf(x) isnan(x)
returns 1 if x is an empty array and 0 otherwise.
returns 1’s for the elements of x which are +Inf or −Inf, and 0’s otherwise
returns 1’s where the elements of x are NaN and 0’s otherwise.
Example: x(isnan(x)) = [ ]
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20. Using ‘any’ and ‘all’ if any(a ~= b) statement end if all(a >= 1)
do something
end
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21. Exercise
Write a program that initially generates 2 random vectors of size 3 (having numbers 1 through 3) – use the randi() function.
Then compare the vectors and respond as:
The vectors are equal or
The vectors have x elements in common or
The vectors have nothing in common
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22. Matrices Objectives • ways of creating and manipulating matrices;
• matrix operations.
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23. Creating matrices a = [1 2; 3 4]; b = a’ x = [5 6]; b= a = [a; x]
1 3 5
2 4 6
a =
1 2
3 4
5 6
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24. Subscripts x = [0:30:180]’; trig(:,1) = x; trig(:,2) = sin(pi/180*x);
a =
1 2 3
4 5 6
7 8 9
x = [0:30:180]’;
trig(:,1) = x;
trig(:,2) = sin(pi/180*x);
trig(:,3) = cos(pi/180*x);
a(3,3)
a(2:3,1:2)
a(3,:)
a(1:2,2:3) = ones(2)
trig =
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25. ‘:’ Operator a = 1 2 3 4 b = a(:) b= 1 3 2 4 b = 1 2 3 4 5 6 a = 0 0
1 5
4 3
2 6
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26. Duplicating rows and columns: tiling
repmat(a, [3 1]) or repmat(a, 3, 1)
ans =
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27. Exercise
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28. Exercise Generate a vector that represents a square waive and plot it.
Hits: use ones() and zeros() along with repmat().
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29. Deleting rows and columns
a(:, logical([1 0 1]))
ans =
1 3
4 6
7 9
a(:,2) = [ ]
a(1,2) = [ ]
a(2:2:6) = [ ]
a =
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30. Elementary matrices eye(3) ans = 1 0 0 0 1 0 0 0 1 pascal(4) ans =
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31. Using MATLAB functions with matrices
1 0 1
1 1 1
0 0 1
all(a)
any(a)
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32. Manipulating matrices
diag
fliplr
flipud
rot90
tril
extracts or creates a diagonal.
flips from left to right.
flips from top to bottom.
Rotate 90 egrees
Extract Lower Triangle
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33. Array (element-by-element) operations on matrices
1 2 3
4 5 6
a .^ 2
ans =
a =
1 2 3
4 5 6
7 8 9
for v = a
disp(v’)
end
1 4 7
2 5 8
3 6 9
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34. Eliminate for loops! r = [0.1:0.01:0.2]’ r = repmat(r, [1 3])
k = 15:5:25
k = repmat(k, [11 1])
temp = (1 + r/n) .^ (n * k);
P = r * A .* temp / n ./ (temp - 1)
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35. Multi-dimensional arrays
1 2
3 4
a(:,:,2) =
5 6
7 8
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36. Matrix operations
Matrix multiplication
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37. Solution to Exercises clc clear all if(any(v) == 0) disp('No Zeros!');
else
w = find(v);
disp(['has ''' num2str(length(w)) ''' zeros']);
end
disp(['first zero index = ' num2str(w(1))])
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38. Solution to Exercises clc clear all % for loop approach sum=0;
v = input('Enter a vector of integers betwwen 0 and 9: ');
for i=v
if(i >= 4 & i <= 7)
sum=sum+1;
end
disp(['total = ' num2str(sum)])
% logical vector approach
disp(sum(v >= 4 & v<=7))
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