Short A Tutorial on Matlab ( by T. Co, 2003,2004 ) Part I. BASICS
I. Assigning Values to Variables, Vectors and Matrices Use the equality symbol, e.g. A=3 Variables are case sensitive: temperature is not the same as Temperature To check values, just type the variable name There are special constants already available, e.g. pi, Inf For complex numbers, either use 3+2i or 3+2j Vectors and matrices are enclosed with square brackets: a) Elements of rows are separated by commas: A=[1,2,3] b) Elements of columns are separated by semicolons: B=[1;2;3] c) Matrices can be seen as columns of row vectors, C=[1,2,3;4,5,6] Alternatively, use spaces to separate row elements and return keys for column elements: B = [ 1 2 3 4 5 6 1 0 1] To get size information, a) size(A) yields [# rows, # cols] b) size(A,1) yields # rows c) size(A,2) yields # cols d) length(v) yields # elements in vector v Some shortcuts are available: a) A = 1:0.1:2 yields a row vector [1, 1.1, 1.2, ... , 1.9, 2] b) diag([1,2,3]) yields a diagonal matrix [1,0,0 ; 0,2,0 ; 0,0,3] c) diag([1,2,3],1) yields a matrix [ 0,1,0,0 ; 0,0,2,0 ; 0,0,0,3 ; 0,0,0,0 ] d) eye(4) yields an identity matrix of size 4x4 e) zeros(3) yields a matrix of zeros of size 3x3 f) zeros(size(A)) yields a matrix of zeros having the same size as A g) ones(3), ones(2,5), ones(size(A)) works the same as zeros() except it produces a matrix of ones h) rand(m,n) matrix of uniformly distributed random numbers of size m by n i) randn(m,n) matrix of normally distributed random numbers of size m by n j) linspace(a,b,n) creates a vector of n elements linearly spaced from a to b
k) logspace(a,b,n)
creates a vector of n elements logarithmically spaced from 10a to 10b
Vectors and matrices can be appended to build larger matrices, e.g. E=[A,B;C,D] To disable the echoing results you could include a semicolon after each command line. To check existing list, you could type who or whos To extract elements: a) A(1,2) gives the element at row 1 and column 2 b) A(3,:) gives the third row of A c) A(:,4) gives the fourth column of A d) A([3,2],[2,1]) extracts rows 3 and 2, and columns 2 and 1 To remove rows and columns: a) A(2,:)=[] removes the 2nd row b) A(:,1)=[] removes the 1st column Reshaping and vectorization a) A(:) b) reshape(A,m,n)
yields a vectorized column [a11 ; a21 ; ...;an1 ; ...; a1n; ...;ann] yields a matrix of size m by n by building it column-wise
II. Matrix Operations and other operations matrix operations 1. addition 2. multiplication 3. determinant 3. inverse 4. right division 5. left division 6. transpose 7. exponentiation 8. matrix exponentiation 9. rank 10. eigenvalue/eigenvectors 11. characeristic polynomial 12 Kronecker product 14. trace 15. pseudo-inverse
C=A+B C=A*B c=det(A) inv(A) or A^(-1) C=B/A (same as C=B*inv(A) ) C=A\B (same as C= inv(A)*B ) C=A.' ( Note: C=A' is conjugate transpose) B=A^3 B=expm(A) R=rank(A) [Eigenvals,Eigenvecs] = eig(A) p = poly(A) C=kron(A,B) t=trace(A) M = pinv(A)
polynomials 16. roots of polynomial 17. polynomial, given roots 18. polynomial multiplication
R = roots([ 1, 4, 2] ) ( = roots of s2+4s+2=0 ) p=poly([r1,r2]) p=conv( [1, 4, 2],[-2, 3] ) ( = (s2 + 4s + 2)(-2s+3) )
column-wise operation 19. column-wise sum 20. column-wise product
s=sum([1,2,3;4,5,6]) ( = [ 5,7,9] ) p=prod([1,2,3;4,5,6]) ( = [ 4, 10, 18] ) V = sort(A) if A = [ 5, 3 ] then V= [ 1, 3 ] [ 1, 4 ] [5, 4 ] [V,K] = sort(A)
sorting 21. sort cols in ascending order
22. sorting and getting indices
Elementwise operation: precede operator by a dot, e.g. A.*B, A./B, A.^2
III. Plotting 2D plots plot(x,y) plot(x,y,x,z) plot(x,y,'-',x,z,'--')
uses default combines plot of y vs x and z vs x specifies how each plot is drawn: solid line for x-y and dashed for x-z
Labeling xlabel('Time (sec)') ylabel('Temperature') title('Case 1') text(1.2, 3.0, 'Case 1') gtext('Case 2')
labeling the x-axis labels the y-axis puts title on top of plot puts text on specified location text is place with the aid of the mouse
(or use the menu bar in the figure window) You can use a limited version of TeX formatting for a) greek letters and other symbols (see TeX manual) ' \alpha \nabla T ' yields a text : b) subscript and superscripts: 'T_{surround}^{a+b}' yields a text : Tsurrounda+b
Axis settings axis([0,10,-1,1]) axis('square') axis hold
specifies x-range as 0 to 10, and y-range as -1 to 1 makes the plot square returns to automatic axis mode freezes the previous plot
3D plots [x,y]=meshgrid(-10:0.5:10, -2:0.2:2) initializes x and y matrices ( for the following try z=sin(x/2).*sin(y) ) mesh(x,y,z) mesh plot surface surf(x,y,z) plot surfl(x,y,z) surface plots with lighting shading interp smoothens shading scheme as interpolated colormap(gray) changes coloring scheme to gray scale brighten(-0.5) darkens picture ( if >0 then it brightens) view([10,60]) changes view to azimuth=10o and elevation=60o
IV. Printing print sends plot to printer print h:\sample1.ps saves the plot as a file print -deps h:\sample2.eps specifies format (or you can use the menu in the figure window) V. Workspaces clear clear a, B, Temperature diary h:\case1.dry save h:\assign1.mat save h:\assign1.mat a, B
erases all variables erases only specified variables saves all terminal activity and saves in file case1.dry saves workspace
saves only specified variables save h:\assign1.mat a, B -ascii saves in ascii format load h:\assign1.mat loads workspace load h:\data1.any loads from a file and creates a matrix named data1 ( or you can use menu items for importing data and changing paths)
VI. Some helpful tips help cursor up and down keys VI. Multidimensional Arrays
grabs help information from functions or script files scrolls through previous commands
a) Creating arrays of higher dimensions - Method 1: set using assignments Given: A=[1,2; 3,4] Then type: A(:,:,2)= [11, 22; 33, 44] Method 2: using cat function Given: A=[1,2 ; 3,4] B = [11 , 22; 33, 44] Then type: C=cat(3,A,B) Method 3: using "ones", "zeros" and "repmat"
b) Dimensions and Reshaping arrays ndims(A) size(A) reshape(A,[m,n,p]) gets the number of dimensions of A gets the size of each dimension of A reshapes A into a multidimensional array of size [m,n,p] by first collecting all elements of A in a column and then distributing according to the specified size.
c) Permuting arrays permute(A,[2,1,3]) (where 1,2,3 are the dimensions, not sizes)
changes the dimension indexing, this is essentially like the transpose, except it applies on any dimension.
VII.
Structures Features/Motivation: - helps encapsulate and organize information of different types - uses text fields, instead of numeric fields - can be collected as arrays - can have subfields - most commands require the options to come from structures - most commands can output to structures a) Creating Structures Method 1: Use period to create fields and subfields student.IDNumber=1234; student.Name='Hank Hill'; Method 2: Use the struct command student=struct('IDNumber',1234,... 'Name','Hank Hill'); For building structure arrays, just start numbering student(2)=struct('IDNumber',5678,... 'Name','Robert Plant');
b) Extracting Information: just type the structure name including the fields student(2) student(2).Name c) Removing fields student = rmfield( student , 'IDNumber' )
VIII. Cell Arrays Features/Motivation - Cell ar...