2.2 Creating & Initializing Variables in MATLAB

Transcription

1 2.2 Creating & Initializing Variables in MATLAB Slide 5 of 27 Do-It-Yourself (DIY) EXERCISE 2-1 Answer the followings: (a) What is the difference between an array, a matrix, and a vector? (b) Let: c = (b-1) What is the size of c? (b-2) What is the value of c(2,3)? (b-3) List the subscripts of all elements containing the value 0.6. (a) In MATLAB, an array is a collection of data values organized into rows (m) & columns (n) with a given single name. The array is the fundamental unit of data in any MATLAB program. A MATLAB array can be categorized into vector (1-D array) or matrix (2-D array). (b) exercise_2_1b.m exercise_2_1b.m >> exercise_2_1b c = c = [ ; ; ] b_1 = 3 4 b_1 = size(c) b_2 = c(2,3) b_2 = c_1_1 = c(1,1) c_1_1 = c_1_2 = c(1,2) c_1_2 = c_1_3 = c(1,3) c_1_3 = c_1_4 = c(1,4) c_1_4 = c_2_1 = c(2,1) c_2_1 = c_2_2 = c(2,2) c_2_2 = c_2_3 = c(2,3) c_2_3 = c_2_4 = c(2,4) c_2_4 = ) c_3_1 = c(3,1) c_3_1 = c_3_2 = c(3,2) c_3_2 = c_3_3 = c(3,3) c_3_3 = c_3_4 = c(3,4) c_3_4 = 0 c(1,4), c(2,1), and c(3,2) are the elements containing the value of 0.6

2 2.2 Creating & Initializing Variables in MATLAB Slide 6 of 27 Do-It-Yourself (DIY) EXERCISE 2-2 Determine the size of the following arrays, using MATLAB. Check your answers by entering the arrays into MATLAB and using whos command (or checking the Workspace Browser). Note that the later arrays may depend on the definitions of arrays defined earlier in this exercise. (a) u = [10 20*i 10+20]; (b) v = [-1; 20; 3]; (c) w = [1 0-9; 2-2 0; 1 2 3]; (d) x = [u v]; (e) y(3,3) = -7; (f) z = [zeros(4,1) ones(4,1) zeros(1,4) ]; (g) v(4) = x(2,1); exercise_2_2_var.m

3 2.2 Creating & Initializing Variables in MATLAB Slide 7 of 27 Do-It-Yourself (DIY) EXERCISE 2-2 (continued) exercise_2_2_var.m u = [10 20*i 10+20]; v = [-1; 20; 3]; w = [1 0-9; 2-2 0; 1 2 3]; x = [u v]; y(3,3) = -7; z = [zeros(4,1) ones(4,1) zeros(1,4) ]; v(4) = x(2,1); Create a MATLAB script (M-File: exercise_2_2_var.m) and execute a series of commands above. Answer the following questions: (a) What is the value of w(2,1)? (b) What is the value of x(2,1)? (c) What is the value of y(2,1)? (d) What is the value of v(3)? exercise_2_2_var.m exercise_2_2_var.m >> exercise_2_2_var u = [10 20*i 10+20]; w_2_1 = 2 v = [-1; 20; 3]; w = [1 0-9; 2-2 0; 1 2 3]; x_2_1 = 0 20i x = [u v]; y(3,3) = -7; y_2_1 = 0 z = [zeros(4,1) ones(4,1) zeros(1,4) ]; v_3 = 3 v(4) = x(2,1); w_2_1 = w(2,1) x_2_1 = x(2,1) y_2_1 = y(2,1) v_3 = v(3)

4 Slide 10 of Special Values Do-It-Yourself (DIY) EXERCISE 2-3 Determine the contents of the following subarrays: 1. Let: c = (a) c(2,:) (b) c(:,end) (c) c(1:2,2:end) (d) c(6) (e) c(4:end) (f) c(1:2,2:4) (g) c([1 3],2) (h) c([2 2],[3 3]) exercise_2_3_1.m >> exercise_2_3_1 exercise_2_3_1.m c_a = c = [ ; ; c_b = ]; c_a = c(2,:) c_c = c_b = c(:,end) c_c = c(1:2,2:end) c_d = c_e = c_d = c(6) c_e = c(4:end) c_f = c_f = c(1:2,2:4) c_g = c_g = c([1 3],2) c_h = c([2 2],[3 3]) c_h = (d): c(6) = c(3,2) WHY??? Since MATLAB (in fact) stores data in column major order, one can (actually) treat a multidimensional array as though it were a 1-D array whose length is equal to the number of elements in the multidimensional array... (NOTE) under normal circumstance, you should never use this feature of MATLAB!

5 Slide 11 of Special Values Do-It-Yourself (DIY) EXERCISE 2-3 (continued) 2. Determine the contents of array a after the following statements are executed : (a) a = [1 2 3; ; 7 8 9]; a([3 1],:) = a([1 3],:); (b) a = [1 2 3; ; 7 8 9]; a([1 3],:) = a([2 2],:); (c) a = [1 2 3; ; 7 8 9]; a = a([2 2],:); 3. Determine the contents of array a after the following statements are executed : (a) (b) (c) b = [1 2 3]; a(2,:) = b; b = []; a(:,3) = b ; b = [7 8 9]; a(3,:) = b([3 1 2]); exercise_2_3_2.m / exercise_2_3_3.m exercise_2_3_2.m >> exercise_2_3_2 a_a = a = [1 2 3; ; 7 8 9]; a([3 1],:) = a([1 3],:); a_a = a a_b = a = [1 2 3; ; 7 8 9]; a([1 3],:) = a([2 2],:); a_b = a a_c = a = [1 2 3; ; 7 8 9]; a_c = a([2 2],:) exercise_2_3_3.m >> exercise_2_3_3 a_a = b = [1 2 3]; a(2,:) = b; a_a = a a_b = b = []; a(:,3) = b'; a_c = a_b = a b = [7 8 9]; a(3,:) = b([3 1 2]); a_c = a

6 Slide 14 of Data Files Do-It-Yourself (DIY) EXERCISE 2-4 Answer the followings: 1. How would you tell MATLAB to display all real values in exponential format with 15 significant digits? 2. What do the following sets of statements do? What is the output from them? (a) (b) radius = input( Enter circle radius:\n ); area = pi * radius^2; str = [ The area is num2str(area)]; disp(str); value = int2str(pi); disp([ The value is value! ]); 3. What do the following sets of statements do? What is the output from them? value = e2; fprintf( value = e\n,value); fprintf( value = f\n,value); fprintf( value = g\n,value); fprintf( value = 12.4f\n,value); 1. format long e will display all real values in exponential format with 15 significant digits. 2. exercise_2_4_2.m exercise_2_4_2.m >> exercise_2_4_2 (a) radius = input('enter circle radius:\n'); Enter circle radius: area = pi*radius^2; 25 str = ['The area is ' num2str(area)]; The area is disp(str); disp(' '); Hit Enter to continue... disp('hit Enter to continue...'); disp(' '); The value is 3! pause (b) value = int2str(pi); disp(['the value is ' value '!']); 3. exercise_2_4_3.m exercise_2_4_3.m >> exercise_2_4_3 value = e2; value = e+04 fprintf('value = e\n',value); value = fprintf('value = f\n',value); value = fprintf('value = g\n',value); value = fprintf('value = 12.4f\n',value);

7 Slide 19 of Hierarchy of Operations Do-It-Yourself (DIY) EXERCISE 2-5 Assume that the following variables are defined as: 2 1 a b 3 1 Evaluate the following MATLAB assignment statements, showing the details of hierarchy of operations. (a) result = a.* c; (b) result = a * [c c]; (c) result = a.* [c c]; (d) result = a + b * c; (e) result = a + b.* c; 1 c 2 d 3 exercise_2_5.m exercise_2_5.m >> exercise_2_5 a = [2 1; -1 2]; result_b = b = [0-1; 3 1]; 4 4 c = [1 2]'; 3 3 d = -3; result_c = result_a = a.* c <= CANNOT DO THIS! result_b = a * [c c] result_c = a.* [c c] result_d = a + b * c <= CANNOT DO THIS! result_e = a + b.* c <= CANNOT DO THIS!

8 Slide 20 of Hierarchy of Operations Do-It-Yourself (DIY) EXERCISE 2-6 Solve for x in the equation Ax = B, where: A B Understand that you are solving a set of simultaneous linear equations: a x a x a x b a x a x a x b a x a x a x b a11 a12 a13 b1 x1 Ax B A a21 a22 a 23 B b x x 2 2 a 31 a32 a33 b 3 x 3 This can be solved by a multiplication of Matrix Inverse of A and B, as: 1 x A B In MATLAB, the Matrix Left Division will do the job... A \ B <= which is defined as: inv(a) * B exercise_2_6.m exercise_2_6.m >> exercise_2_6 Simultaneous Linear Equations Solver x = A = [1 2 1; 2 3 2; ]; B = [1 1 0]'; x = A \ B; x x1 = x2 = x = inv(a)*b x3 = x x1 = x(1) x2 = x(2) x3 = x(3)

9 Slide 23 of Introduction to Plotting Do-It-Yourself (DIY) EXERCISE 2-7 Starting from the Example 1-1 (plot of sin(x) function), modify this plot as shown below: Modify: line color/style and marker style Add: title, axis labels, and grid exercise_2_7_sin_x.m exercise_2_7_sin_x.m Based on: example_1_1_sin_x.m clc close all clear all x = 0:0.1:6; y = sin(x); plot(x,y,'k-',x,y,'bo'); title('plot of f(x)=sin(x)'); xlabel('x'); ylabel('sin(x)'); grid on axis equal

10 Slide 24 of Introduction to Plotting Do-It-Yourself (DIY) EXERCISE 2-8 Starting from the Example 1-2 (plot of sin(x) and cos(x) function), modify this plot as shown below: Modify: line color/style Add: title, axis labels, legend, and grid exercise_2_8_cos_x.m exercise_2_8_cos_x.m Based on: example_1_2_cos_x.m clc clear all close all x = 0:0.1:6; y1 = sin(x); y2 = cos(x); plot(x,y1,'b-',x,y2,'r--'); title('plot of sin(x) and cos(x)'); xlabel('x'); ylabel('f(x)'); legend ('f(x)=sin(x)','f(x)=cos(x)') grid on axis equal