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Array Operations

Array Operations. ENGR 1181 MATLAB 04. Array Operations In The Real World.

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Array Operations

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  1. Array Operations ENGR 1181 MATLAB 04

  2. Array Operations In The Real World Aerospace Engineers use turbulence data to calculate how close other planes can fly near the wake of a larger plane. These vortices can cause unstable flight conditions for smaller planes approaching the wake of a commercial jetliner. Thus this turbulent flow data is important in airspace management and stall design.

  3. Today's Learning Objectives • Scalar Math • Vector Math • Scalar – Vector Math • Vector – Vector Math • Vector Functions

  4. Scalar math review For scalar variables a and b: >> a = 6; >> b = 2; MATLAB has scalar math operations: >> a + b >> a – b >> a * b >> a / b >> a ^ b

  5. Scalar–vector addition Define the vector v and the scalar c: >> v = [ 10 20 30 40 ] ; >> c = 4 ; Add them: >> v + c >> c + v ans = 14 24 34 44

  6. Vector–vector addition Define the vector v and the vector c: >> v = [ 10 20 30 40 ] ; >> c = [ 2 4 6 8] ; Add them: >> v + c >> c + v v and c must be the same length! ans = 12 24 36 48

  7. Scalar-vector multiplication For the vector x and the scalar c: >> v = [ 10 20 30 40 ] ; >> c = 4 ; Multiply them:>> c * v>> v * c ans = 40 80 120 160

  8. Vector-vector multiplication x = [ 10 20 30 40 ] y = [ 2 4 6 8 ] Now multiply: >> z = x * y ??? Error using ==> mtimes Inner matrix dimensions must agree!!!

  9. Vector-vector multiplication x = [ 10 20 30 40 ] y = [ 2 4 6 8 ] To multiply to arrays element by element we need to use the following syntax: >> z = x .* y z = 20 80 180 320

  10. Scalar-vector division >> v = [ 10 20 30 40 ] >> c = 4 Divide them: >> v / c ans = 2.50 5.00 7.50 10.00

  11. Scalar-vector division >> v = [ 10 20 30 40 ] >> c = 4 Divide them: >> c / v >> c./v Error using / Matrix dimensions must agree. ans = 0.400 0.200 0.133 0.100

  12. Vector-vector division x = [ 10 20 30 40 ] y = [ 2 4 6 8 ] Divide them: >> x . / y Also, try >> y . / x ans = 5 5 5 5 ans = 0.20 0.20 0.20 0.20

  13. Scalar-vector exponents >> v = [ 10 20 30 40 ] >> c = 4 Try instead: >> v .^ c Try: >> v ^ c Error using ^ Inputs must be a scalar and a square matrix. To compute elementwise POWER, use POWER (.^) instead.

  14. Vector-vector exponents x = [ 2 2 2 2 ] ; y = [ 2 4 6 8 ] ; Also try >> y .^ x Try this: >> x .^ y ans = 4 16 64 256 ans = 4 16 36 64

  15. Scalar-vector math summary For a scalar c and a vector v: Addition v + c or c + v Subtraction v – c or c – v Multiplication v * c or c * v or v.*c or c.*v Division v / c or c./v or v ./ c Exponent v .^ c or c .^ v

  16. Vector-vector math summary For two vectors x and y : Addition x + y or y + x Subtraction x – y or y – x Multiplication x .* y or y .* x Division x ./ y or y ./ x Exponent x .^ y or y .^ x You must alwaysuse the dot operator for Multiplication, Division, andExponent

  17. Example 1 Calculate y = 4x2for x = 1,2,3 and 4. First define x >> x = [1 2 3 4]; Then calculate y >> y = 4.*x.^2Which ‘.’ is required here? y = 4 16 36 64

  18. Example 2 Calculate y = (4a2 + a)/(2+a) for a = 1,2,3 and 4. First define a = [ 1 2 3 4 ] >> a = [1 2 3 4]; a = 1 2 3 4 >> y = ((4*a.^2)+a)./(2+a) y = 1.6667 4.5000 7.8000 11.3333

  19. Built-in vector functions MATLAB has built-in functions for vectorsWhen v is a vector: max(v) Returns the largest element in v min(v) Returns the smallest element in v mean(v) Returns the average value of the elements in v sum(v) Returns the sum of the elements of v length(v) Returns the number of elements in v sort(v) Sorts the elements of v

  20. Important Takeaways • Know when to use a DOT Operator for Multiplication, Division, and Exponents. • Only use a dot operator when appropriate and understand what you are trying to accomplish before you use it. • Vector functions operate on an entire set of numbers located inside of an array, or matrix.

  21. Preview of Next Class • Inputs and outputs with script files • Inputting data into and out of programs • GPA calculator example • With and without use of vectors • Inputting to a script file • Output to command window

  22. Tasks to Complete • Review today’s Quiz #04. • Open the in-class activity from the EEIC website and we will go through it together. • Then, start working on MAT-04 homework. • Before next class, you will read more detail about script files including global variables. There is also information on input and output (I/O) commands in MATLAB.

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