MATLAB Fundamentals Cheat Sheet

MATLAB Fundamentals - Cheat Sheet Basics Workspace ans clc clear var clf close all ctrl-c doc fun disp(’text’) format short—long help fun load filename {vars} save {-append} file {vars} addpath path iskeyword arg % This is a comment ... ";" (after command) scriptname tic, toc ver MATLAB Documentation: Most recent answer clear command window clear variables Workspace Clear all plots Close all plots Kill the current calculation open documentation Print text Set output display format open in-line help load variables from .mat file save var to file include path to .. Check if arg is keyword Comments connect lines (with break) suppresses output runs scriptname.m start and stop timer List of installed toolboxes mathworks.com/help/matlab/ Defining and Changing Variables a = 5 Define variable a to be 5 A = [1, 2, 3, 4; Set A to be a 3 × 4 matrix 5, 6, 7, 8; ”,” separates columns 9, 10, 11, 12] ”;” separates rows [A,B], horzcat(A,B) Concatenate arrays horizontally [A;B], vertcat(A,B) Concatenate arrays vertically x(2) = 7 Change 2nd element of x to 7 A(2,1) = 0 Change A2,1 to 0 x(2:12) The 2nd to the 12th elem. of x x(1:3:end) Every 3rd elem. of x (1st to last) x(x>6) List elements > 6. x(x>8)=8 change elements using condition A(4,:) Get the 4th row of A A(:,3) Get the 3rd column of A A(6, 1:3) Get 1st to 3rd elem in 6th row zeros(9, 5) Make a 9 × 5 matrix of zeros ones(9, 5) Make a 9 × 5 matrix of ones eye(7) Make a 7 × 7 identity matrix diag(x) Create diagonal matrix diag(A) Get diagonal elements of matrix meshgrid(x) 2-D and 3-D grids 7:15 Row vector of 7, 8, . . . , 14, 15 a:ds:b lin. spaced vector with spacing ds linspace(1,20,35) Lin. spaced vector (35 elements) logspace(1, 1e5, 50) Log. spaced vector (50 elements) Arithmetics +, A*B A.*B A./B B.\A / \ A∧ n A.∧ n sum(X) prod(X) Numerics and Linear Algebra Addition, Subtraction (elementwise) Matrix multiplication elementwise multiplication elementwise division Left array division Solve xA = B for x Solve Ax = B for x normal/(square) matrix power Elementwise power of A Sum of elements (along columns) Product of elements (along columns) Elementary Functions sin(A) Sine of argument in radians sind(A) Sine of argument in degrees asin(A) Inverse sine in radians sinh(A) Hyperbolic sine there are analogous elementwise trigonometric functions for cos, tan and cot abs(A) sqrt(x) log(x) log10(x) sign(x) exp(x) Compute |x| √ Compute x Compute ln(x) Compute log10 (x) sign of x exponential of x Complex Numbers abs(z) Absolute value and complex magnitude angle(z) Phase angle complex(a,b) Create complex numbers conj(z) Elementwise complex conjugate i or j Imaginary unit imag(z) Imaginary part of complex number isreal(z) Determine whether array is real real(z) Real part of complex number ctranspose(Z) Complex conjugate transpose Constants pi NaN Inf eps realmax realmin π = 3.141592653589793 Not a number (i.e. 0/0) Infinity Floating-point relative accuracy Largest positive floating-point number Smallest positive floating-point number Numerical Integration and integral(f,a,b) integral2(f,a,b,c,d) integral3(f,a,b,..,r,s) trapz(x,y) cumtrapz(x,y) diff(X) gradient(X) Differentiation Numerical integration 2D num. integration 3D num. integration Trapezoidal integration Cumulative trapez integration Differences (along columns) Numerical gradient Matrix Functions/ Linear Algebra A’ Transpose of matrix or vector inv(A) inverse of A (use with care!) det(A) determinant of A eig(A),eigs(A) eigenvalues of A (subset) cross(A,B) Cross product dot(A,B) Dot product kron(A,B) Kronecker tensor product norm(x) Vector and matrix norms linsolve(A,B) Solve linear system of equations rank(A) Rank of matrix trace(A) Sum of diagonal elements curl(X,Y,Z,U,V,W) Curl and angular velocity divergence(X,..,W) Compute divergence of vector field null(A) Null space of matrix orth(A) Orthonormal basis for matrix range mldivide(A,B) Solve linear system Ax = B for x mrdivide(B,A) Solve linear system xA = B for x decomposition(A) Matrix decomposition lsqminnorm(A,B) Least-squares solution to linear eq. rref(A) Reduced row echelon form balance(A) Diagonal scaling (improve eig. vec.) svd(A) Singular value decomposition gsvd(A,B) Generalized svd chol(A) Cholesky factorization Matrix manipulation cat(dim,A,B) ndims(A) flip(A) fliplr(A) flipud(A) squeeze(A) reshape(A,sz) size(A) sort(A) sortrows(A) length(A) Concatenate arrays Number of array dimensions Flip order of elements Flip array left to right Flip array up to down Remove dimensions of length 1 Reshape array size of A Sort array elements Sort rows of matrix or table Length of largest array dimension Graphics Plotting plot(x,y) axis equal title(’A Title’) xlabel(’x axis’) ylabel(’y axis’) legend(’foo’, ’bar’) grid hold on / off xlim /ylim / zlim figure Plot types Plot y vs. x Scale axes equally Add title to the plot Add label to the x axis Add label to the y axis Label 2 curves for the plot Add a grid to the plot Multiple plots on single figure get or set axes range Start a new plot Relational and logical operations == Check equality ∼= > greater than >= < less than <= &, && logical AND ∼ |, | | logical OR xor if, elseif Conditions Check inequality greater or equal to less or equal to logical NOT logical exclusive-OR if n<10 disp('n smaller 10') elseif n<20 disp('n between 10 and 20') else disp('n larger than 20') end % control structures terminate with end Switch Case n = input('Enter a number: '); switch n case -1 disp('negative one') case 0 disp('zero') case {1,2,3} %check three cases together disp('positive one') otherwise disp('other value') end % control structures terminate with end Interpolation and fitting interp1(x,v,xq) interp2(X,Y,V,Xq,Yq) interp3(X,..V,..Zq) pchip(x,v,xq) spline(x,v,xq) ppval(pp,xq) mkpp(breaks,coeffs) unmkpp(pp) 1-D data interpolation (table lookup) 2D interpolation for meshgrid data 3D interpolation for meshgrid data Piecew. cubic Hermite poly interpol Cubic spline data interpolation Evaluate piecewise polynomial Make piecewise polynomial Extract piecewise polynomial details Differential equations ode45(ode,tspan,y0) ode15s(ode,tspan,y0) pdepe(m,pde,ic,bc,xm,ts) pdeval(m,xmesh,usol,xq) Optimization fminbnd(fun,x1,x2) fminsearch(fun,x0) lsqnonneg(C,d) fzero(fun,x0) optimget(opt,’par’) optimset(’opt’,val) Solve system of nonstiff ODE Solve system of stiff ODE Solve 1D PDEs Interpolate num. PDE solution Find minimum of fun(x) in [x1 , x2 ] Find minimum of function Solve non-neg. lin. least-squares prob. Root of nonlinear function Optimization options values Define optimization options For-Loop %loop a specific number of times, and keep track of each ... iteration with an incrementing index variable %parfor might be used to parallelize the execution for i = 1:3 disp('cool'); % comment with some LATEXin it: πx2 end % control structures terminate with end While-Loop %loops as long as a condition remains true n = 1; nFactorial = 1; while nFactorial < 1e100 n = n + 1; nFactorial = nFactorial * n; end % control structures terminate with end Further programming commands break exit the current loop (combine with if) continue go to next iteration (combine with if) try, catch Execute statements and catch errors Plot gallery: mathworks.com/products/matlab/plot-gallery Programming methods Functions % defined in m-file % File must have the same name as the function function output = addNumbers(x, y) output = x + y; %multiple or var nr of args possible end Anonymous Functions % defined via function handles f = @(x) cos(x.ˆ2)./(3*x); Special Topics Polynomials poly(x) poly(A) polyeig(x) polyfit(x,y,d) residue(b,a) roots(x) polyval(p,x) conv(u,v) deconv(u,v) polyint(p,k) polyder(p) Polynomial with roots x Characteristic polynomial of matrix Polynomial eigenvalue problem Polynomial curve fitting Partial fraction expansion/decomposition Polynomial roots Evaluate poly p at points x Convolution and polynomial multiplication Deconvolution and polynomial division Polynomial integration Polynomial differentiation Descriptive Statistics bounds(A) Smallest and largest elements max(A) Maximum elements of an array min(A) Minimum elements of an array mode(A) Most frequent values in array mean(A) Average or mean value of array median(A) Median value of array std(A) Standard deviation var(A) Variance hist(X) calculate and plot histogram corrcoef(A) Correlation coefficients cov(A) Covariance xcorr(x,y) Cross-correlation xcov(x,y) Cross-covariance rand Uniformly distributed random numbers randn Normally distributed random numbers randi Uniformly distributed pseudorandom integers further functions: movmax, movmin, cummax, cummin, movprod, movsum, cumsum, cumprod, movmean, movmedian, movstd, movvar. Discrete Math factor(n) factorial(n gcd(n,m) lcm(n,m) mod(a,m) ceil(X) fix(X) floor(X) round(X) Prime factors Factorial of input Greatest common divisor least common multiple Remainder after division (modulo operation) Round toward positive infinity Round toward zero Round toward negative infinity Round to nearest decimal or integer