matlab-basic-functions-reference.pdf

mathworks.com/help/matlab

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 variables from .mat file

uiimport("filename")

Open interactive import tool

save("filename","vars")

Save variables to file

clear ite m

Remove items from workspace

examplescript

Run the script file named

examplescript

format style

Set output display format

ver

Get list of installed toolboxes

tic, t oc

Start and stop timer

Ctrl+C

Abort the current calculation

Operators and Special Characters

+, -, *, /

Matrix math operations

.*, ./

Array multiplication and division

(element-wise operations)

^, .^

Matrix and array power

Left division or linear optimization

.', '

Normal and complex conjugate

transpose

==, ~=, <, >, <=, >=

Relational operators

&&, ||, ~, xor

Logical operations

(AND, OR, NOT, XOR)

;

Suppress output display

...

Connect lines (with break)

% Description

Comment

'H ello'

Definition of a character vector

"This is a string"

Definition of a string

str1 + str2

Append strings

Defining and Changing Array Variables

a = 5

Define 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 4th element of x to 7

A(1,3) = 5

Change A(1,3) to 5

x(5:10)

Get 5th to 10th elements of x

x(1:2:e n d)

Get every 2nd element of x (1st to last)

x(x>6)

List elements greater than 6

x(x==10)=1

Change elements using condition

A(4,:)

Get 4th row of A

A(:,3)

Get 3rd column of A

A(6, 2:5)

Get 2nd to 5th element in 6th row of A

A(:,[1 7 ])= A(:,[ 7 1])

Swap the 1st and 7th 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 zeros

o n e s(m,n)

Create m x n matrix of ones

eye(n)

Create a n x n identity matrix

A= d iag(x)

Create diagonal matrix from vector

x= d ia g(A)

Get diagonal elements of matrix

m e s h g r i d(x,y)

Create 2D and 3D grids

rand(m,n), randi

Create uniformly distributed random

numbers or integers

ra nd n(m,n)

Create normally distributed random

numbers

Special Variables and Constants

ans

Most recent answer

π=3.141592654…

i, j, 1i, 1j

Imaginary unit

NaN, nan

Not a number (i.e., division by zero)

Inf, inf

Infinity

eps

Floating-point relative accuracy

Complex Numbers

i, j, 1i, 1j

Imaginary unit

r e a l(z)

Real part of complex number

i m a g(z)

Imaginary part of complex number

a ngle(z)

Phase angle in radians

conj(z)

Element-wise complex conjugate

is r e a l(z)

Determine whether array is real

mathworks.com/help/matlab

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 (arg. in

radians)

Analogous for the other trigonometric functions:

cos, tan, csc, sec, and cot

a bs(x)

Absolute value of x, complex magnitude

ex p(x)

Exponential of x

sq rt(x), nt h root(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

sig n(x)

Sign of x

mod(x,d)

Remainder after division (modulo)

ceil(x), fix, floor

Round toward +inf, 0, -inf

rou n d(x)

Round to nearest decimal or integer

Tables

t a b l e( v a r 1,...,v a r N )

Create table from data in variables

var1, ..., varN

readtable("file")

Create table from file

array2table(A)

Convert numeric array to table

T.v a r

Extract data from variable var

T( r o w s , c o l u m n s ),

T(rows,["col1","coln"])

Create a new table with specified

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

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, m arker, 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/zla b el("la b e l")

Add x/y/z axis label

x/y/zticks(ticksvec)

Get or set x/y/z axis ticks

x/y/ztic kla b els(la b els)

Get or set x/y/z axis tick labels

x/y/ztic k a ngle(a ngle)

Rotate x/y/z axis tick labels

x/y/zli m

Get or set x/y/z axis range

axis(lim), axis style

Set axis limits and style

text(x,y,"txt")

Add text

grid o n/off

Show axis grid

hold on/off

Retain the current plot when

adding new plots

s u b p l o t( m , n , p ),

tile d layo ut(m,n)

Create axes in tiled positions

yyaxis left/right

Create second y-axis

figure

Create figure window

gcf, gca

Get current figure, get current axis

clf

Clear current figure

close all

Close open figures

Common Plot Types

Plot Gallery: mathworks.com/products/matlab/plot-gallery

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 • Clean Outlier

• Find Change Points • Find Local Extrema

• Remove Trends • Smooth Data

mathworks.com/help/matlab

Integration and Differentiation

integral(f,a,b)

Numerical integration

(analogous functions for 2D and 3D)

t ra p z(x,y)

Trapezoidal numerical integration

d iff(X)

Differences and approximate derivatives

gra d ient(X)

Numerical gradient

c u r l( X,Y,Z,U,V,W )

Curl and angular velocity

d iv e r g e n c e( X,..,W )

Compute divergence of

vector field

o d e45(o d e,t s p a n,y 0)

Solve system of nonstiff ODEs

ode15s(o de,tspan,y0)

Solve system of stiff ODEs

deval(sol,x)

Evaluate solution of differential equation

pdepe(m,pde,ic,...

b c,x m,t s)

Solve 1D partial differential equation

p d e v a l( m,x m e s h ,...

usol,x q)

Interpolate numeric PDE solution

Numerical Methods

fz er o(f u n,x0)

Root of nonlinear function

f m i n s earc h(f u n,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

Interpolation and Polynomials

interp1(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

p oly(x)

Polynomial with specified roots x

p o l y e i g( A 0, A 1,..., A p)

Eigenvalues for polynomial eigenvalue

problem

p o ly f it(x,y,d)

Polynomial curve fitting

re sid u e(b,a)

Partial fraction expansion/decomposition

ro ot s( p)

Polynomial roots

polyval(p,x)

Evaluate poly p at points x

polyint(p,k)

Polynomial integration

p oly d er(p)

Polynomial differentiation

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 ar gs. possi ble

cavg=cu msum(vec)./(1:lengt h(vec));

end

Anonymous Functions

% defined via function handles

fun = @(x) cos(x.^2)./abs(3*x);

Control Structures

if, elseif Conditions

if n<10

d isp("n smaller 10")

elseif n<=20

d isp("n between 10 and 20")

else

d isp("n larger than 20")

Switch Case

n = input("Enter an integer: ");

switch n

case -1

d isp("negative one")

case {0,1,2,3} % check four cases together

d isp("integer between 0 and 3")

otherwise

d isp("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

d isp("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

t r y, c a t c h

Execute statements and catch errors

Other product or brand names may be trademarks or registered trademarks of their respective holders.

mathworks.com/help/matlab

Matrices and Arrays

le n g t h(A)

Length of largest array dimension

size(A)

Array dimensions

n u m e l(A)

Number of elements in array

sort(A)

Sort array elements

sor t ro w s(A)

Sort rows of array or table

flip(A)

Flip order of elements in array

sq u e eze(A)

Remove dimensions of length 1

re shap e(A,sz)

Reshape array

rep mat(A,n)

Repeat copies of array

a n y( A ), a l l

Check if any/all elements are nonzero

n n z(A)

Number of nonzero array elements

fi nd(A)

Indices and values of nonzero elements

Linear Algebra

ra n k(A)

Rank of matrix

trac e(A)

Sum of diagonal elements of matrix

d et(A)

Determinant of matrix

p oly(A)

Characteristic polynomial of matrix

eig(A), eigs

Eigenvalues and vectors of matrix (subset)

inv(A), pinv

Inverse and pseudo inverse of matrix

nor m(x)

Norm of vector or matrix

e x p m ( A ), l o g m )

Matrix exponential and logarithm

c r oss(A,B)

Cross product

d ot(A,B)

Dot product

kron(A,B)

Kronecker tensor product

n u l l(A)

Null space of matrix

or t h(A)

Orthonormal basis for matrix range

tril(A), triu

Lower and upper triangular part of matrix

linsolve(A,B)

Solve linear system of the form AX=B

lsq m innor m(A,B)

Least-squares solution to linear equation

qr(A), lu, chol

Matrix decompositions

sv d(A)

Singular value decomposition

gsvd(A,B)

Generalized SVD

r r ef(A)

Reduced row echelon form of matrix

Symbolic Math*

sym x, syms x y z

Declare symbolic variable

eqn = y == 2*a + b

Define a symbolic equation

solve(eqns,vars)

Solve symbolic expression

for variable

subs(expr,var,val)

Substitute variable in expression

expand(expr)

Expand symbolic expression

factor(expr)

Factorize symbolic expression

si m plif y(e x pr)

Simplify 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 expressions

d i ff(e x p r,va r,n)

Differentiate symbolic expression

dsolve(deqn,cond)

Solve differential

equation symbolically

i nt(e x p r,v a r,[a, b])

Integrate symbolic expression

taylor(fu n,var,z0)

Taylor expansion of function

Descriptive Statistics

sum(A), prod

Sum or product (along columns)

max(A), min, bounds

Largest and smallest element

mean(A), median, mode

Statistical operations

s t d ( A ), v a r

Standard deviation and variance

movsum(A,n), movprod,

movmax, movmin,

mov m ean, m ov me dia n,

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

det re n d(x)

Remove polynomial trend

isoutlier(A)

Find outliers in data

*requires Symbolic Math Toolbox