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CPET 190

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CPET 190

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  1. CPET 190 Lecture 5 Problem Solving with MATLAB http://www.etcs.ipfw.edu/~lin Lecture 5 - By Paul Lin

  2. Lecture 5: More On MATLAB Arrays 5.1 More MATLAB Functions 5.2 Array Operators 5.3 Array Arithmetic Operations 5.4 Sub-arrays Lecture 5 - By Paul Lin

  3. 5.1 More MATLAB Functions size(this_array) • returns the two values specifying the number of rows and columns in this_array length(this_array) • returns the length of a vector, or the longest dimension of a 2-D array zeros(n) • built-in MATLAB function for creating an n-by-n array with all elements are initialized to zero zeros(n, m) • for creating an n-by-m all-zero array Lecture 5 - By Paul Lin

  4. 5.1 More MATLAB Functions(continue) ones(n) • built-in MATLAB function for creating an n-by-n array with all elements are initialized to one ones(n, m) • for creating an n-by-m all-one array eye(n) • for creating an n-by-n identity matrix in which all elements in the main diagonal are ones eye(n, m) • for creating an n-by-m identity matrix Lecture 5 - By Paul Lin

  5. 5.1 More MATLAB Functions(continue) >> help rand RAND Uniformly distributed random numbers. RAND(N) is an N-by-N matrix with random entries, chosen from a uniform distribution on the interval (0.0,1.0). RAND(M,N) and RAND([M,N]) are M-by-N matrices with random entries. RAND(M,N,P,...) or RAND([M,N,P,...]) generate random arrays. RAND with no arguments is a scalar whose value changes each time it is referenced. RAND(SIZE(A)) is the same size as A. Lecture 5 - By Paul Lin

  6. 5.1 More MATLAB Functions(continue) >> help fix FIX Round towards zero. FIX(X) rounds the elements of X to the nearest integers towards zero. See also FLOOR, ROUND, CEIL. Lecture 5 - By Paul Lin

  7. 5.1 More MATLAB Functions(continue) A1 = 1 1 1 1 1 1 1 1 1 B1 = 1 1 1 1 1 1 A_eye = 1 0 0 0 1 0 0 0 1 Example 5.1: Creating arrays using array functions n = 3; m = 2; % an 3 x 3 all-zero array A0 = zeros(3) % an 3 x 2 all zero array B0 = zeros(3, 2) % an 3 x 3 all-one array A1 = ones(3) % an 3 x 2 all-zero array B1 = ones(3,2) %An identify array A_eye = eye(n) A0 = 0 0 0 0 0 0 0 0 0 B0 = 0 0 0 0 0 0 Lecture 5 - By Paul Lin

  8. 5.2 Array Operators Transpose operator ( ' ) • swap the rows and columns of an array Colon operator (: ) • one of the most useful operator in MATLAB. We can use it to create regularly spaced vectors, subscript matrices, and specify for iterations Lecture 5 - By Paul Lin

  9. 5.2 Array Operators array_r1 = 0.2722 0.1988 0.0153 0.7468 array_r2 = 0.4451 0.9318 0.4660 0.4186 array_c1 = 0.2722 0.1988 0.0153 0.7468 array_c2 = 0.4451 0.9318 0.4660 0.4186 Example 5.2: Vector Transpose Example • rand() – random number generation function >> % Generate an array using rand() function array_r1 = rand(1, 4) array_r2 = rand(1, 4) % Convert row vector to column vector array_c1 = array_r1' array_c2 = array_r2' Lecture 5 - By Paul Lin

  10. 5.2 Array Operators (continue) Example 5.3: Using rand(), fix() functions and array transpose operator >> A = rand(1,4) *10 A = 0.5789 3.5287 8.1317 0.0986 >> A = fix(A) A = 0 3 8 0 >> B = fix(rand(1,4)*10) B = 1 2 1 6 >> C = [A' B'] C = 0 1 3 2 8 1 0 6 Lecture 5 - By Paul Lin

  11. 5.2 Array Operators(continue) R_1 = 0 1 R_2 = 3 2 R_3 = 8 1 R_4 = 0 6 C_1 = 0 3 8 0 C_2 = 1 2 1 6 • Example 5.4: Using colon operator to pick-up selected rows or columns • A(: , j) – extracts j-th column of A • A(i, :) – extracts the i-th row of A C = 0 1 3 2 8 1 0 6 C_1 = C(:,1) C_2 = C(:, 2) R_1 = C(1,:) R_2 = C(2, :) R_3 = C(3, :) R_4 = C(4, :) Lecture 5 - By Paul Lin

  12. 5.2 Array Operators(continue) • Example 5.5: This problem solving example uses the colon operator with integers to generate a regularly spaced temperature vector from 0 to 100 in degree C.We will also print all data to show that C to F Temperature Conversion holding a linear relationship. • Analysis (identified equations and MATLAB equations, and using plot function to show the linear relationship) F = 9/5 C + 32 C = 0:10:100; F = 9/5 * C + 32; plot(C, F) Lecture 5 - By Paul Lin

  13. 5.2 Array Operators (continue) • Example 5.5: Solution % CtoF_plot.m % Author: M. Lin % Date: 9/6/04 % Description: C = 0:10:100; F = (9/5)* C + 32; plot(C, F), grid on xlabel('Degree C'), ylabel('Degree F') title(' C vs F') Lecture 5 - By Paul Lin

  14. 5.2 Array Operators(continue) % sine60hz_2d.m % Author: M. Lin % Date: 9/6/04 % Description: f = 60; T = 1/f; Vm = 10; dt = 0.001*T; t = 0:dt: 5*T; e = Vm*sin(2*pi*f*t); sine60 = [t' e']; save sine60.mat sine60 clear load sine60.mat plot(sine60(:,1), sine60(:,2)) • Example 5.6: Reconstruct the sine 60Hz signal and its time vector as a 2-D array and save it as sine60hz.mat file. Verify result by reloading the program and plot the sine wave using colon operator. • Solution: f = 60 Hz, T = 1/f Vm = 10 volts, dt = 0.001*T, t = 0:dt: 5*T e = Vm*sin(2*pi*f*t) Lecture 5 - By Paul Lin

  15. 5.2 Array Operators (continue) • Example 5.6: MATLAB Solution Lecture 5 - By Paul Lin

  16. 5.3 Array Arithmetic Operations + Addition • A + B adds A and B arrays of the same dimension, unless one is a scalar. A scalar can be added to a matrix of any dimension. • An Example: both A and B are 2-by-2 array, A + B is | (a11 + b11) (a12 + b12) | | (a21 + b21) (a22 + b22) | Lecture 5 - By Paul Lin

  17. 5.3 Array Arithmetic Operations(continue) - Subtraction. • A - B subtracts B from A. A and B arrays must have the same dimension, unless one is a scalar. A scalar can be subtracted from a matrix of any dimension. • An Example: both A and B are 2-by-2 array, A - B is | (a11 - b11) (a12 - b12) | | (a21 - b21) (a22 - b22) | Lecture 5 - By Paul Lin

  18. 5.3 Array Arithmetic Operations (continue) .* Array Multiplication • A .* B is the element-by-element product of the arrays A and B. A and B must have the same dimension, unless one is a scalar. A scalar can be multiplied to a matrix of any dimension. • An Example: both A and B are 2-by-2 array, A .* B is | (a11 * b11) (a12 * b12) | | (a21 * b21) (a22 * b22) | Lecture 5 - By Paul Lin

  19. 5.3 Array Arithmetic Operations (continue) ./ Array Right Division • A ./B is the element-by-element division of the arrays A and B. A and B must have the same dimension, unless one is a scalar. A scalar can be divided by a matrix of any dimension. • An Example: both A and B are 2-by-2 array, A ./ B is | (a11 / b11) (a12 / b12) | | (a21 / b21) (a22 / b22) | Lecture 5 - By Paul Lin

  20. 5.3 Array Arithmetic Operations (continue) >> A = fix(rand(2)*10) B = fix(rand(2)*10) W = A - B X = A + B Y = A .* B Z = A./ B A = 9 6 2 4 B = 8 4 7 0 Example 5.7: Element-by-element array arithmetic operations A = fix(rand(2)*10) B = fix(rand(2)*10) W = A - B X = A + B Y = A .* B Z = A./ B Lecture 5 - By Paul Lin

  21. 5.3 Array Arithmetic Operations (continue) Example 5.7: continue W = A - B X = A + B Y = A .* B Z = A./ B A = 9 6 2 4 B = 8 4 7 0 >> A - B W = 1 2 -5 4 >> A + B X = 17 10 9 4 >> A .* B Y = 72 24 14 0 >> A./B Warning: Divide by zero. (Type "warning off MATLAB: divideByZero" to suppress this warning.) Z = 1.1250 1.5000 0.2857 Inf Lecture 5 - By Paul Lin

  22. 5.4 SubArrays Subarrays can be formed by using colon (: ) operator to select a portion of an array Example 5.9: Subarray Examples array4 = [10 20 30; -20 -30 -40; 30 40 50] array5 = array4(1, : ) % [10 20 30] array6 = array4(: ,1: 2: 3) % [first column third column] array6 = 10 30 -20 -40 30 50 array1 = [1 2 3 4 5]; array7 = array1(3: end) array 7 = 3 4 5 array1(end) ans = 5 Lecture 5 - By Paul Lin

  23. Summary 5.1 More MATLAB Functions 5.2 Array Operators 5.3 Array Arithmetic Operations 5.4 Subarrays Lecture 5 - By Paul Lin