Introduction to Matlab: Features and Program Structure
Matlab offers a simple calculator-like syntax with a strong library of functions for numerical analysis and extensive toolboxes for various fields. It is a universally recognized language in engineering with open-source options available. The program structure includes functions, conditionals, looping, and mathematical functions like trigonometry, hyperbolic, and special functions.
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L02-Introduction to Matlab Christopher Crawford PHY 404G 2020-08-17
Features of Matlab Simple calculator-like syntax with minimum boilerplate Almost everything is a matrix of complex doubles Powerful library of builtin functions for numerical analysis Extensive toolbox for application-specific fields Universally recognized language of engineering Open-source clones and cloud versions available 2020-08-17 2/27
Punctuation [ a, b; c, d] a(1,2) f(x,y) S={1,'s'}; S{1,2} 1:2:10 a(:,2) end .*'.' x.a x.('a') @(x)x^2 fn1, fn2 fn1; fn2; 'str'"str" 1.6e-19 pi, e, i, j, eps ans % comment !pwd Matrix concatenation (space=',' and newline=';') Matrix indexing, function evaluation Cell array and indexing (heterogenous elements) Range, [whole] subrange, largest index value Element operation, transpose, structure member Anonymous (unnamed) function Command separator, ; silences output Command continuation to next line String constants (either ' or " ) Numeric constant in scientific notation Numeric constants: 3.14.., 2.71.., sqrt(-1), 2e-52 Result of previous calculation First comment block used for 'help' documentation Shell (system) command 2020-08-17 3/27
Operator precedence () .' .^ ' ^ + - ! * / \ + - : < <= > >= == ~= Comparison & | && || Parentheses (manual precedence) Transpose, Power, Hermitian transpose, Matrix power Sign, Negative, Logical negation Multiplication, Right division, Left division Addition, Subtraction Colon operator (range) Element-wise AND Element-wise OR Short-circuit AND Short-circuit OR 2020-08-17 4/27
Program structure function [y1 y2 ] = myfun (x1, x2, ) nargin/out, varargin/out{} z=x1+x2 y1=z; y2=z^2 end SUBROUTINE % variable # of arguments % local variable % output variables % saved in file myfun.m CONDITIONAL if a==b a=a+1 elseif a>b a=a-1 end LOOPING for k=1:5 a(k)=2*k end switch k case 1 a=a+1 case 2 a=a+2 otherwise a=0 end k=5 while k>0 k=k-1 end break, continue 2020-08-17 5/27
Functions Mathematics cos(x), sin, tan, acos, asin, atan - trig atan2(y,x) - knows the quadrant cosd(x), - angles in degrees cosh(x), - hyperbolic functions exp(x), log(x), log10(x), log2(x) - exponent sqrt(x) - square root abs(x) - magnitude (absolute val.) sign(x) - x/abs(x) airy(n,x) - Airy function besselX(n,x) - Bessel func. X=j,y,i,k,h erf, erfc, erfcx, erfinv gamma(x) - ? = ? 1 ! expint(x) - exponential integral legendre(n,x) - Legendre polynomials factorial(x) - factorial Matrices eye, zeros, ones, diag, magic - constructor rand, randn, randperm - random, normal size, length, numel, rows, cols, ndims reshape, squeeze - repack matrix flipud, fliplr, circshift, shiftdim - elements dot, cross, kron - products, (Kronecker) norm, vecnorm - magnitude (cols) inv, det, trace - inverse, determinant, trace [v,d]=eig(a) - eigenvectors, eigenvalues [u,v,d]=svd(a) - singular value decomp QR, LU, rref, rcond, cond - other decomp fft, ifft - fast Fourier transform, inverse conv , deconv, xcor - convolution (+poly) sum, max, min, median, mean, std stats is{matrix,vector,scalar,empty,column,row} - error functions 2020-08-17 6/27
Functions Conversion, Text I/O ceil, floor, round, fix - real to integer real, imag, angle, abs, conj - complex clear , cls, clf - clear vars, screen, figure load, save, {csv,dlm,xls}read/write - files fread/fwrite - raw binary file I/O printf, fprintf, disp - print output input, textscan - read input char - convert ASCII to char strfind, strsplit, strjoin, strcat, replace, contains, cellstr, regexp - string fns num2string, int2str, mat2str, str2num cell2struct, struct2cell - conversions cell2mat, mat2cell - partitioned matrix num2cell - matrix/rows/cols to cell array Plotting, Analysis meshgrid, ndgrid, linspace - domain X,Y plot, plot3, hist, bar, pie, area, contour, quiver, scatter, compass, rose, semilogx, loglog, stem, stairs, image, imagesc - plots axis, title, x/y/zlabel, legend, view - format figure, subplot, clf, saveas - plot window line, fill, text, rectangle - annotations sort, issorted, sortrows - sort array find - find elements of array fminsearch - find minimum of function fzero - find the zeros of function interp1 - interpolate X,Y arrays diff, gradient, trapz, quad - calculus ode{23,45,113,23s,15s} - ODE integrator 2020-08-17 7/27
