MATLAB Basic Functions Reference

MATLAB Environment
`clc`	Clear command window
`help fun`	Display in-line help for `fun`
`doc fun`	Open documentation for `fun`
`load("filename","vars")`	Load veriables from .`mat` file
`uiimport("filename")`	Openinteractive important tool
`save("filename","vars")`	Save variables to file
`clear item`	Remove items from worksapce
`examplescript`	Run the script file named `examplescript`
`format style`	Set output display format
`ver`	Get list of installed toolboxes
`tic, toc`	Start and stop timer
`Ctrl+C`	Abort the current calculation

Defining and Changing Array Variables
`a = 5`	Define a variable a with value 5
`A = [1 2 3; 4 5 6]` `A = [1 2 3` `4 5 6]`	Define A as a 2x3 matrix “space” separates columns “;” or new line separates rows
`[A,B]`	Concatenate arrays horizontally
`[A;B]`	Concatenate arrays vertically
`x(4) = 7`	Change fourth element of x to 7
`A(1,3) = 5`	Change A(1,3) to 5
`x(5:10)`	Get fifth to tenth elements of x
`x(1:2:end)`	Get every send element of x (first to last)
`x(x>6)`	List elements greater than 6
`x(x==10)=1`	Change lements using condition
`A(4,:)`	Get fourth row of A
`A(:,3)`	Get third column of A
`A(6, 2:5)`	Get second to fifth element in sixth row of A
`A(:,[1 7])=A(:,[7 1])`	Swap the first and seventh column
`a:b`	[a, a+1, a+2 ..., a+n] with a+n≤b
`a:ds:b`	Create regularly spaced vector with spacing ds
`linspace(a,b,n)`	Create vector of n equally spaced values
`logspace(a,b,n)`	Create vector of n logarithmically spaced values
`zeros(m,n)`	Create m x n matrix of zeroes
`ones(m,n)`	Create m x n identity matrix
`eye(n)`	Create a n x n identity matrix
`A-diag(x)`	Create diagonal matrix from vector
`x=diag(A)`	Get diaonal elements of matrix
`meshgrid(x,y)`	Create 2D and 3D grids
`rand(m,n), randi`	Create uniformly distributed random numbers of integers
`randn(m,n)`	Create normally distributed random numbers

Operators and Special Characters
`+, -, *, /`	Matrix math operations
`.*, ./`	Array multiplication and division (element-wise operation)
`^, .^`	Matrix and array power
`\`	Left division or linear optimization
`.', '`	Normal and complex conjugate transpose
`==, ~=, <, >, <=, >=`	Relational operators
`&&, \|\|, ~, xor`	Logical operations (AND, NOT, OR, XOR)
`;`	Suppress output display
`...`	Connect lines (with break)
`% Description`	Comment
`'Hello'`	Definition of a character vector
`"This is a string"`	Definition of a string
`str1 + str2`	Append strings

Special Variables and Constants
`ans`	Most recent answer
`pi`	π=3.141592654…
`i, j, li, lj`	Imaginary unit
`NaN, nan`	Not a number (i.e., division by zero)
`Inf, inf`	Infinity
`eps`	Floating-point relative accuracy

Complex Numbers
`i, j, li, lj`	Imaginary unity
`real(z)`	Real part of complex number
`image(z)`	Imaginary part of complex number
`angle(z)`	Phase angle in radians
`conj(z)`	Element-wise complex conjugate
`isreal(z)`	Determine whether array is real

Elementary Functions
`sin(x), asin`	Sine and inverse (argument in radians)
`sind(x), asind`	Sine and inverse (argument in degrees)
`sinh(x), asinh`	Hyperbolic sine and inverse (argument in radians)
Analogous for the other trigonometric functions: `cos`, `tan`, `csc`, `sec`, and `cot`
`abs(x)`	Absolute value of x, complex magnitude
`exp(x)`	Exponential of x
`sqrt(x), nthroot(x,n)`	Square root, real nth root of real numbers
`log(x)`	Natural logarithm of x
`log2(x), log10`	Logarithm with base 2 and 10, respectively
`factorial(n)`	Factorial of n
`sign(x)`	Sign of x
`mod(x,d)`	Remainder after division (modulo)
`ceil(x), fix, floor`	Round toward +inf, 0, -inf
`round(x)`	Round to nearest decimal or integer

Plotting
`plot(x,y,LineSpec)` Line styles: `-, --, :, -.` Markers: `+, o, *, ., x, s, d` Colors: `r, g, b, c, m, y, k, w`	Plot y vs. x (`LineSpec` is optional) `LineSpec` is a combination of `linestyle`, `marker`, and `color` as a string. Example: "`-r`" = red solid line without markers
`title("Title")`	Add plot title
`legend("1st", "2nd")`	Add legend to axes
`x/y/zlabel("label")`	Add x/y/z axis label
`x/y/zticks(ticksvec)`	Get or set x/y/z axis ticks
`x/y/ztickangle(angle)`	Rotate x/y/z axis tick labels
`x/y/zlim`	Get or set x/y/z axis range
`axis(lim), axis style`	Set axis limits and style
`text(x,y,"txt")`	Add text
`grid on/off`	Show axis grid
`hold on/off`	Retain the current plot when adding new plots
`subplot(m,n,p), tiledlayout(m,n)`	Create axes in tiled positions
`yyaxis left/right`	Create second y-axi
`figure`	Create figure window
`gcf, gca`	Get current figure, get current axis
`clf`	Clear current figure
`close all`	Close open figures

Tables
`table(var1,...,varN)`	Create table from data in variables var1, ..., varN
`readtable("file")`	Create table from file
`array2table(A)`	Convert numeric array to table
`T.var`	Extract data from variable var
`T(rows,columns), T(rows,["col1","coln"])`	Create a new table with specificed rows and columns from T
`T.varname=data`	Assign data to (new) column in T
`T.Properties`	Access properties of T
`categorical(A)`	Create a categorical array
`summary(T), groupsummary`	Print summary of table
`join(T1, T2)`	Join tables with common variables

Tasks (Live Editor)
Live Editor tasks are apps that can be added to a live script to interactively perform a specific set of operations. Tasks represent a series of MATLAB commands. To see the commands that the task runs, show the generated code.
Common tasks available from the Live Editor tab on the desktop toolstrip: Clean Missing Data Find Change Points Remove Trends Clean Outlier Find Local Extrema Smooth Data

Programming Methods
Functions
% Save your function in a function file or at the end % of a script file. Function files must have the % same name as the 1st function function cavg = cumavg(x) %multiple args. possible cavg=cumsum(x)./(1:length(x)) ; end
Anonymous Functions
% defined via function handles fun = @(x) cos(x.^2)./abs(3*x);
Control Structures
`if`, `elseif`, Conditions
if n<10 disp("n smaller 10") elseif n<=20 disp("n between 10 and 20") else disp("n larger than 20")
Switch Case
n = input("Enter an integer: "); switch n case -1 disp("negative one") case {0,1,2,3} % check four cases together disp("integer between 0 and 3") otherwise disp("integer value outside interval [-1,3]") end % control structures terminate with end
For-Loop
% loop a specific number of times, and keep % track of each iteration with an incrementing % index variable for i = 1:3 disp("cool"); 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/control commands
`break`	Terminate execution of for- or while-loop
`continue`	Pass control to the next iteration of a loop
`try, catch`	Execute statements and catch errors

Numerical Methods
`fzero(fun,x0)`	Root of nonlinear function
`fminsearch(fun,x0)`	Find minimum of function
`fminbnd(fun,x1,x2)`	Find minimum of fun in [x1, x2]
`fft(x), ifft(x)`	Fast Fourier transform and its inverse
Integration and Differentiation
`integral(f,a,b)`	Numerical integration (analogous functions for 2D and 3D)
`trapz(x,y)`	Trapezoidal numberical integration
`diff(X)`	Differences and approximate derivatives
`gradient(X)`	Numerical gradient
`curl(X,Y,Z,U,V,W)`	Curl and angular velocity
`divergence(X,...,W)`	Compute divergence of vector field
`ode45(ode,tspan,y0)`	Solve system of nonstiff ODEs
`ode15s(ode,tspan,y0)`	Solve system of stiff ODEs
`deval(sol,x)`	Evaluate solution of differential equation
`pdepe(m,pde,ic,...bc,xm,ts)`	Solve 1D partial differential equation
`pdeval(m,xmesh,...usol,xq)`	Interpolate numeric PDE solution
Interpolation and Polynomials
`interpl(x,v,xq)`	1D interpolation (analogous for 2D and 3D)
`pchip(x,v,xq)`	Piecewise cubic Hermite polynomial interpolation
`spline(x,v,xq)`	Cubic spline data interpolation
`ppval(pp,xq)`	Evaluate piecewise polynomial
`mkpp(breaks, coeffs)`	Make piecewise polynomial
`unmkpp(pp)`	Extract piecewise polynomial details
`poly(x)`	Polynomial with specified roots x
`polyeig(A0,A1,...Ap)`	Eigenvalues for polynomial eigenvalue problem
`polyfit(x,y,d)`	Polynomial curve fitting
`residue(b,a)`	Partial fraction expansion/decomposition
`roots(p)`	Polynomial roots
`polyval(p,x)`	Evaluate poly p at points x
`polyint(p,k)`	Polynomial integration
`polyder(p)`	Polynomial differentiation

Matrices and Arrays
`length(A)`	Length of largest array dimension
`size(A)`	Array dimensions
`numel(A)`	Number of elements in array
`sort(A)`	Sort array elements
`sortrows(A)`	Sort rows of array or table
`flip(A)`	Flip order of elements in array
`squeeze(A)`	Remoe dimensions of length 1
`reshape(A,sz)`	Reshape array
`repmat(A,n)`	Repeat copies of array
`any(A), all`	Check if any/all elements are nonzero
`nnz(A)`	Number of nonzero array elements
`find(A)`	Indices and values of nonzero elements

Descriptive Statistics
`sum(A), prod`	Sum or product (along columns)
`max(A), min, bounds`	Largest and smallest elements
`mean(A), median, mode`	Statistical operations
`std(A), var`	Standard deviation and variance
`movsum(A,n), movprod, movmax, movmin, movmean, movmedian, movstd, movvar`	Moving statistical functions n = length of moving window
`cumsum(A), cumprod, cummax, cummin`	Cumulative statistical functions
`smoothdata(A)`	Smooth noisy data
`histcounts(X)`	Calculate histogram bin counts
`corrcoef(A), cov`	Correlation coefficients, covariance
`xcorr(x,y), xcov`	Cross-correlation, cross-covariance
`normalize(A)`	Normalize data
`dtrend(x)`	Remove polynomial trend
`isoutlier(A)`	Find outliers in data

Linear Algebra
`rank(A)`	Rank of matrix
`trace(A)`	Sum of diagonal elements of matrix
`det(A)`	Determinant of matrix
`poly(A)`	Characteristic polynomial of matrix
`eig(A), eigs`	Eigenvalues and vectors of matrix (subset)
`inv(A), pinv`	Inverse and pseudo inverse of matrix
`norm(x)`	Norm of vector or matrix
`expm(A), logm)`	Matrix exponential and logarithm
`cross(A,B)`	Cross product
`dot(A,B)`	Dot product
`kron(A,B)`	Kronecker tensor product
`null(A)`	Null space of matrix
`orth(A)`	Orthonormal basis for matrix range
`tril(A), triu`	Lower and upper triagnular part of matrix
`linsolve(A,B)`	Solve linear system of the form AX=B
`lsqminnorm(A,B)`	Least-squares solution to linear equation
`svd(A)`	Singular value decomposition
`gsvd(A,B)`	Generalized SVD
`rref(A)`	Reduced row echelon form of matrix

Symbolic Math*
sym x, syms x y z	Declare a symbolic variable
eqn = y == 2*a + b	Define a sybmolic equation
solve(eqns,vars)	Solve sybmolic expression for variable
subs(expr,var, val)	Substitute variable in an expression
expand(expr)	Expand symbolic expression
assume(var, assumption)	Make assumption for variable
assumptions(z)	Show assumptions for symbolic object
fplot(expr), fcontour, fsurf, fmesh, fimplicit	Plotting functions for symbolic object
dif(expr,var,n)	Differentiate symbolic expression
dsolve(deqn,cond)	Solve differential equation symbolically
int(expr,var,[a, b])	Integrate symbolic expression
taylor(fun,var,z0)	Taylor expansion of function

Cheat Sheets

MATLAB Basic Functions Reference

Table of Contents

MATLAB Environment

Operators and Special Characters

Complex Numbers

Plotting

Tasks (Live Editor)

Programming Methods

Descriptive Statistics

Symbolic Math

Defining and Changing Array Variables

Special Variables and Constants

Elementary Functions

Tables

Numerical Methods

Matrices and Arrays

Linear Algebra

Control Structures

Further programming/control commands

Integration and Differentiation

Interpolation and Polynomials