Getting started with Matlab Numerical Methods Appendix B

Getting started with Matlab Numerical Methods Appendix B http: //www. mathworks. com/access/helpdesk/ help/techdoc/learn_matlab. html

What Is MATLAB? n n n n Math and computation Algorithm development Data acquisition Modeling, simulation, and prototyping Data analysis, exploration, and visualization Scientific and engineering graphics Application development, including graphical user interface building

The MATLAB System n n n Development Environment. The MATLAB Mathematical Function Library. The MATLAB Language. n n n a high-level matrix/array language Graphics. The MATLAB External Interfaces (API).

MATLAB Online Help n n n n Desktop Tools and Development Environment Mathematics Programming Graphics 3 -D Visualization Creating Graphical User Interfaces External Interfaces/API

Matrices and Arrays n To enter Dürer's matrix, simply type in the Command Window >>A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1] n A = n 16 3 2 13 n 5 10 11 8 n 9 6 7 12 n 4 15 14 1 n

sum, transpose, and diag n sums of the columns of A n >>sum(A) n n >>sum(A')' n n n ans = 34 34 sum(diag(A)) n ans = 34 The transpose operation is denoted by an apostrophe or single quote, '.

Subscripts n >>A(1, 4) + A(2, 4) + A(3, 4) + A(4, 4) n n n ans = 34 >>X = A; >>X(4, 5) = 17 n n n X = 16 3 2 13 0 5 10 11 8 0 9 6 7 12 0 4 15 14 1 17

The Colon Operator n n n n n >> 1: 10 ans = 1 2 3 4 5 6 7 8 9 10 >> 100: -7: 50 ans = 100 93 86 79 72 65 58 51 >> 0: pi/4: pi ans = 0 0. 7854 1. 5708 2. 3562 3. 1416 In subscript >> A(1, 1: 4) ans = 16 3 2 13

The magic Function n n n n >> B = magic(4) B = 16 2 3 13 5 11 10 8 9 7 6 12 4 15 1 To make this B into Dürer's A, swap the two middle columns: A = B(: , [1 3 2 4])

Expressions n Variables n n Numbers n n 3 -99 0. 0001 9. 6397238 1. 60210 e-20 6. 02252 e 23 1 i -3. 14159 j 3 e 5 i Operators n num_students = 25 +-*/^ Left division Functions n n n help elfun help specfun help elmat

Working with Matrices

Generating Matrices n n zeros All zeros ones All ones rand Uniformly distributed random elements randn Normally distributed random elements

ones(n, m) n >> ones(3, 4) n ans = n n n 1 1 1

zeros(n, m) n >> zeros(3, 4) n ans = n n n 0 0 0

rand(n, m) n >> rand(3, 4) n ans = n n n 0. 9501 0. 4860 0. 4565 0. 4447 0. 2311 0. 8913 0. 0185 0. 6154 0. 6068 0. 7621 0. 8214 0. 7919

randn(3, 4) n >> randn(3, 4) n ans = n n n -0. 4326 0. 2877 1. 1892 0. 1746 -1. 6656 -1. 1465 -0. 0376 -0. 1867 0. 1253 1. 1909 0. 3273 0. 7258

Load and Save. mat n >> A = [1 2 3] >> B = [4 5 6] >> save mydata. mat >> clear n >> load mydata. mat n n n

eye(n), eye(size(A)) n >> eye(3) n >> eye(size(A)) n ans = n n n 1 0 0 0 1 n n n 1 0 0 0 0 1 0

Load and save ASCII file n n n n >> a = magic(4); b = ones(2, 4) * -5. 7; c = [8 6 4 2]; >> save >> clear -ascii mydata. dat >> load mydata. dat >> mydata = 16. 0000 2. 0000 3. 0000 13. 0000 5. 0000 11. 0000 10. 0000 8. 0000 9. 0000 7. 0000 6. 0000 12. 0000 4. 0000 15. 0000 1. 0000 -5. 7000 -5. 7000 8. 0000 6. 0000 4. 0000 2. 0000

Building Tables n n n n >> n = (0: 9)'; pows = [n n. ^2 2. ^n] pows = 0 0 1 1 1 2 2 4 4 3 9 8 4 16 5 25 32 6 36 64 7 49 128 8 64 256 9 81 512 MATLAB uses a dot, or decimal point, as part of the notation for multiplicative array operations.

Multivariate Data n >>D = [ n n n n to obtain the mean and standard deviation of each column, use >>mu = mean(D), sigma = std(D) n n 72 134 3. 2 81 201 3. 5 69 156 7. 1 82 148 2. 4 75 170 1. 2 ] mu = 75. 8 161. 8 3. 48 sigma = 5. 6303 25. 499 2. 2107 >>help datafun >>help stats

Matlab Graphics

plot(x, y) n n n t=[0: 5: 100] y=t. ^0. 34 -log 10(t)+1. /t plot(t, y) title(‘Plot of y versus t’) grid

3 D graphics n n n n [x, y]=meshgrid(-4. 0: 0. 2: 4. 0, -4. 0: 0. 2: 4. 0); z=(-20*x. ^2+x)+(-15*y. ^2+5. *y); surfl(x, y, z); axis([-4 4 -800 0]) xlabel('x-axis'); ylabel('y-axis'); zlabel('z-axis');

Try yourself, and have fun!