1 / 12

Review

Review. Define a matrix: m = [ 1 3 4; 5 7 9 ] Join A & B horizontally: C = [ A B ] Join A & B vertically: C = [ A ; B ] Colon operator: 1:10 1:2:10 Transpose rows ↔ columns: A’ Initialization: zeros(n,m) ones(n,m) eye(n) size(A)

awena
Télécharger la présentation

Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Review • Define a matrix: m = [ 1 3 4; 5 7 9 ] • Join A & B horizontally: C = [ A B ] • Join A & B vertically: C = [ A ; B ] • Colon operator: 1:10 1:2:10 • Transpose rows ↔ columns: A’ • Initialization: zeros(n,m) ones(n,m) eye(n) size(A) • N-dims: c(:,:,1) = [1:3 ; 4:6]; c(:,:,2) = [7:9 ; 10:12]; • Linear indexing (column major): m(2,3) m(6) • Subarrays: A([1 3],1:2) = [ 1 2 ; 3 4 ]; • end is highest value taken by subscript: m(2:end,:)

  2. Exercises • Create the following matrix c using the colon operator: Now display the following subarrays: • (a) the 2nd row • (b) the last column • (c) 1st and 2nd rows from the 2nd column onwards • (d) the 6th element (using single subscript) • (e) all elements from the 4th onwards • (f) 1st and 2nd rows (2nd and 4th columns only) • (g) 1st and 3rd rows, 2nd column only • (h) a new 2x4 matrix with row 3 on both of its rows c(2,:) c(:,end) c(1:2,2:end) c(6) c(4:end) c(1:2,[2 4]) c([1 3],2) c([3 3],:)

  3. Displaying output The simplest way to display output is simply to omit the semi-colon at the end of the line Another way is to use disp(), possibly in combination with num2str() or int2str() • disp(pi) • str = [‘The value of pi = ’,num2str(pi)] • disp(str) For more tailored output use the fprintf function: • General syntax is fprintf(format,data), e.g. • fprintf(‘The value of pi is %f \n’,pi) • fprintf(‘The value of pi is %6.2f \n’,pi) • You can also use: • %d Display as an integer • %e Display in exponential format • %g Either floating point of exponential format (the shorter) • \t , \n Tab separator and new line

  4. Data files using load/save Probably the easiest way to import data into a Matlab program is from a tab delimited file. Excel can export tables in tab-delimited format. These can be read using the load function with the -ascii option Example: Create a table as follows using an Open Office Calc spreadsheet and save it as tab-delimited Open Office:File – Save as – Format CSV. Tick Edit Filter settings and change delimiter to <TAB> Excel: File – Save As Type “Text (Tab delimited) (*.txt)“ If you open the file in Text Editor, it should look like this: 12 23 34 45 56 67 78 89

  5. Data files using load/save • x = load(‘-ascii’,’my.tab.delimited.file.csv’) • x = • 12 23 34 45 • 56 67 78 89 • Similarly, one can use the save function to store in ascii format (we will look at other I/O later): • x = [1:3;4:6]; • save(‘-ascii’,’xout.dat’,’x’) • The resulting file looks like this: 1.00000000e+000 2.00000000e+000 3.00000000e+000 4.00000000e+000 5.00000000e+000 6.00000000e+000

  6. Scalar arithmetic Assigment statements are of the form • variable_name = expression • Scalar operators: • Addition, subtraction: a+b a-b • Multiplication, division: a*b a/b • Exponentiation: a^b When many operations are combined into a single expression, it is important to know in what order Matlab will evaluate the terms.

  7. Scalar arithmetic Matlab has a series of rules governing the hierarchy (or order) in which operations are evaluated within an expression, as follows • 1. Expressions in parentheses (innermost to outermost) • 2. Exponentials (left to right) • 3. Multiplications and divisions (left to right) • 4. Additions and subtractions (left to right) Thus, the expression • distance = 0.5 * accel * time ^ 2 • is equivalent to • distance = 0.5 * accel * (time ^ 2) • but not equivalent to • distance = (0.5 * accel * time) ^ 2

  8. Exercise • Declare: a=3; b=2; c=5; d=3 and calculate the following expressions:

  9. Array and Matrix operations • Matlab has two types of operations between arrays: • (a) element-by-element operations where the two operands have the same number of rows and columns, for example • A = [1 2 ; 3 4]; B=[-1 3; -2 1] • Addition, Subtraction: A+B A-B • Multiplication, Division: A .* B A ./ B • Exponentiation: A .^ B • One operand can be scalar, the other a matrix • e.g. 2 .^ A • Although for multiplication,divsion A * 2 = A .* 2 and A/2 = A./2 • (b) Matrix operations • Ordinary matrix multiplication: A * B • Matrix exponent: A^2 (scalar exponent) • Matrix left division: A \ B = inv(A) * b

  10. Exercise • If a= ,b= ,c= • Calculate: • a + b • a X c • c X a (should give error!) • Elementwise a X b • Matrix multiplication: a X b • a X a X a X a • If x = 1:10 and y=ones(1,10) • Calculate (remember that z x zT = )

  11. Common built-in functions • Mathematical functions: • sum(x): sum of elements of a vector or columns of a matrix • mean(x): mean, similarly columnwise for matrix • rand, rand(m), rand(m,n): random numbers (uniform, interval [0,1]) • abs(x) • sin(x), cos(x), tan(x) • exp(x), log(x), log10(x) • [value,index] = max(x), [value,index] = min(x) • sqrt(x) • Rounding • ceil(x), floor(x): to +∞ and -∞ respectively • fix(x): nearest integer towards zero • round(x): to nearest integer • String conversion • int2str, num2str, str2num

  12. Exercises • Assign n=100, then compute • Compute: • Compute (using sum then without sum) • if x=3, calculate cosh (using exp) • Generate a vector r of means for 1000 random number vectors of length 50. See your results with the command: hist(r,40)

More Related