Vectors
What is a vector?
Traditionally...
a vector is an object that has both magnitude and direction
Or
an organism, typically a biting insect or tick, that transmits a disease or parasite from one animal or plant to another.
Vector Usage
So what are Arrays?
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Are Vectors = Arrays?
All vectors are arrays but not all arrays are vectors
Creating Vectors
Row Vectors (note capital letter notation)
Column Vectors
Vectorization
How to quickly build large arrays
Linspace
Tools
Functions and Operations
X = [1 5 2 4] |
Y = [3 2 2 6] |
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3 * X |
[3 15 6 12] |
X .* X |
[1 25 4 16] |
Y .^ 2 |
[9 4 4 36] |
X + Y |
[4 7 4 10] |
cos(X) |
[0.5403 0.2837 -0.4161 -0.6536] |
exp(Y) |
[20.0855 7.3891 7.3891 403.4288] |
log(X) |
[0 1.6094 0.6931 1.3863] |
Preallocation
Which to choose?
| zeros() | You will be adding or subtracting datasets |
| ones() | You will be multiplying or dividing datasets |
| rand() | You need a sample dataset |
| nan() | You are overwriting cells with values that may be zero |
Index
This is the address of your values
Four score and seven...
Wait...not that address
Vector Manipulation
M = [7 3 2 9 1]
| M(1:3) | displays first 3 elements in M |
| M(3:5) | displays last 3 elements in M |
| N = M(1:3) | create new array N that is a subset of M |
| P = [M(1) M(3) M(4)] | create new array N that is a subset of M |
| M(1:3) + P | [14 5 11] |
| M(1) + M(4) | 16 |
| M(7) | Does not exist - Index exceeds matrix dimensions. |
| M(7) = 7 | [7 3 2 9 1 0 7] |
| V = 1:1000 | V(20:4:850) |
Strings
Remember that strings are arrays?
| A = ['J' 'a' 'n' 'e' ' ' 'S' 'a' 'y' 's'] |
| A = 'Jane Says' |
| B = ['I' '''m' ' ' 'd' 'o' 'n' 'e' ' ' 'w' 'i' 't' 'h' ' ' 'S' 'e' 'r' 'g' 'i' 'o'] |
| B = 'I''m done with Sergio' (note 2 single quotes) |
| A(1:4) = 'Dave' |
Examples
start = input('Enter the first value of your vector:');
stop = input('Enter the last value of your vector:');
dx = input('Enter the jump value:');
vector = start:dx:stop
lengthOnes = input('Enter the length of the ones vector:');
onesVector = ones(1,lengthOnes)
lengthZeros = input('Enter the length of the zeros vector:');
zerosVector = zeros(1,lengthZeros)
lengthRand = input('Enter the length of the rand vector:');
randVector = rand(1,lengthRand)
lengthNan = input('Enter the length of the NaN vector:');
nanVector = nan(1,lengthNan)
display('Now you can change the length of your rand vector.');
addRand = input('How many more values would you like to add?');
newLength = lengthRand + addRand;
randVector(newLength) = rand
display('Until we learn to use loops and if statements, we will have the extra zeros in our vector.');
fprintf('Now we will create a new rand vector with length %d',newLength);
newRandVector = rand(1,newLength)
Algorism and Bushism of the Day
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"They misunderestimated me." |
"We're going to have the best-educated American people in the world." |
Lesson of the Day
Don't wish it were easier, wish you were better
‘Responsibility is the price of greatness.’ — Winston Churchill
Freedom doesn't mean no responsibility. In fact, it requires extra responsibility. Freedom is the ability to make a choice, and responsibility is required once you make that choice.
Fairness isn't a handout. Fairness is the willingness to offer dignity to others. The dignity of being seen and heard, and having a chance to make a contribution.
And equality doesn't mean equal. Equality doesn't guarantee me a starting position on the Knicks. Equality means equality of access, the opportunity to do my best without being disqualified for irrelevant reasons.