Least Squares
17 сент. 2013 г. The MAtlAB function polyfit computes least squares polynomial fits by setting up the design matrix and using backslash to find the ...
Magic Squares
2 окт. 2011 г. Write a MAtlAB function ismagic(A) that checks if A is a magic square. 10.2 Magic sum. Show that. 1 n n2. ∑ k=1 k = n3 + n. 2 . 10.3 durerperm ...
Some important Built-in function in MATLAB 1. Square root b=sqrt(x
14 мар. 2020 г. Some important Built-in function in MATLAB. 1. Square root b=sqrt(x) b=sqrt(4). 2. 2. Remainder of dividing x/y a=rem(xy) a=rem(10
Objective 1 Triangular Wave 2 Square Wave 3 Discrete Time
2 Square Wave. MATLAB has a built-in function square to generate a periodic square waveform. Following example will help you draw such a waveform. 2.1
- 1 - Some MATLAB Built-in Functions Function Description sqrt(x
Some MATLAB Built-in Functions. Function. Description sqrt(x). Square root of x nthroot(xn) nth root of x abs(x). Absolute value of x exp(x). Exponential (ex).
Eigenvalues and Singular Values
16 сент. 2013 г. The Matlab function condeig computes eigenvalue condition numbers. ... The qr function in Matlab factors any matrix real or complex
Quadrature
area—plot the function on graph paper and count the number of little squares that The function functions in Matlab itself usually expect the first argument to.
Iteration
2 окт. 2011 г. Matlab responds with x = 3. Next enter this statement x = sqrt(1 + x). The abbreviation sqrt is the Matlab name for the square root function.
Total Least Squares Approach to Modeling: A Matlab Toolbox
In this section we show some applications of the TLS method in static and dynamical modeling by using the created Matlab functions [14]. 3.1 Linear regression
Implementing the 2D square lattice Boltzmann method in Matlab
23 февр. 2023 г. In contrast to LGA. LBM deals with distribution function values instead of single particles. The exact denomination for the following described ...
General Linear Least-Squares and Nonlinear Regression
Applied Numerical Methods with MATLAB for Engineers Chapter 15 & Teaching The least-squares ... function that returns the sum of the squares of the.
Objective 1 Triangular Wave 2 Square Wave 3 Discrete Time
MATLAB has a built-in function sawtooth to generate a periodic triangular waveform. Following example will help you draw such a waveform. 1.1 Example. Generate
Magic Squares
2011?10?2? An n-by-n magic square is an array containing the integers from 1 to n2 ... squares of order n but the MAtlAB function magic(n) generates a ...
Least Squares
2013?9?17? The MAtlAB function polyfit computes least squares polynomial fits by setting up the design matrix and using backslash to find the ...
Some important Built-in function in MATLAB 1. Square root b=sqrt(x
2020?3?14? Some important Built-in function in MATLAB. 1. Square root b=sqrt(x) b=sqrt(4). 2. 2. Remainder of dividing x/y a=rem(xy) a=rem(10
Eigenvalues and Singular Values
2013?9?16? A singular value and pair of singular vectors of a square or ... qr function in Matlab factors any matrix real or complex
Iteration
2011?10?2? The abbreviation sqrt is the Matlab name for the square root function. The quantity on the right. /. 1 + x
DEPARTMENTS OF MATHEMATICS
1999?1?4? MAtlAB has included since at least version 3 a function sqrtm for computing a square root of a matrix. The function works by reducing the ...
INTRODUCTION TO MATLAB FOR ENGINEERING STUDENTS
The function diary is useful if you want to save a complete MATLAB session. of vectors in MATLAB are enclosed by square brackets and are separated by ...
Total Least Squares Approach to Modeling: A Matlab Toolbox
In this section we show some applications of the TLS method in static and dynamical modeling by using the created Matlab functions [14]. 3.1 Linear regression
MATLAB Basic Functions Reference - MathWorks
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
Chapter 10 Magic Squares - MathWorks
Ann-by-nmagic square is an array containing the integers from 1 ton2arranged so that each of the rows each of the columns and the two principaldiagonals have the same sum For eachn >2 there are many di?erent magicsquares of ordern but theMatlabfunctionmagic(n)generates a particular one Matlabcan generate Lo Shu with = magic(3) which produces
MATLAB Function Example Handout - University of Wyoming
ical function libraries The Matlab Optimization and Curve Fitting Toolboxes include functions for one-norm and in?nity-norm problems We will limit ourselves to least squares in this book 5 3 censusgui The NCM program censusgui involves several di?erent linear models The data
Chapter 1 Iteration - MathWorks
In Matlab and most other programming languages the equals sign is the assignment operator It says compute the value on the right and store it in the variable on the left So the statement x = sqrt(1 + x) takes the current value of x computes sqrt(1 + x) and stores the result back in x
Functions and Scripts - Electrical Engineering and Computer
Many functions are programmed inside MATLAB as built-in functions and can be used in mathematical expressions simply by typing their name with an argument; examples are sin(x) cos(x) sqrt(x) and exp(x) MATLAB has a plethora of built-in functions for mathematical and scientific computations
Chapter 1 Introduction to MATLAB - MathWorks
MATLAB An introduction to MATLAB through a collection of mathematical and com-putational projects is provided by Moler’s free online Experiments with MATLAB [6] A list of over 1500 Matlab-based books by other authors and publishers in several languages is available at [12] Three introductions to Matlab are of par-
MATLAB Getting Started Guide - Massachusetts Institute of
The load function reads binary files containing matrices generated by earlier MATLAB sessions or reads text files containing numeric data The text file should be organized as a rectangular table of numbers separated by blanks with one row per line and an equal number of elements in each row
MATLAB Function Tips - Michigan State University
function [xsqrd xcubd] = square(x) xsqrd = x^2 xcubd = x^3 There are two possible places to position this code If you are using MATLAB 5 0 or later this function code can be placed at the end of the main program in the same file as the main program It could also be placed in its own file which must use the function name or for our example
Matlab Introduction - California State University Long Beach
The batch commands in a file are then executed by typing the name of the file at the Matlab command prompt The advantage to using a ' m' file is that you can make small changes to your code (even in different Matlab sessions) without having to remember and retype the entire set of commands
6057 Introduction to MATLAB Homework 2 - MIT OpenCourseWare
Use magenta square symbols of marker size 10 and line width 4 and no line connecting them You may have to change the x limits to see all 6 symbols (xlim) If the relationship really is exponential it will look linear on a log plot 2 Subplot and axis modes Make a new Square Tight 100 100 200 figure that has a 2x2 grid of axes () subplot 200
MATLAB Commands and Functions - College of Science and
MATLAB Commands – 11 M-Files eval Interpret strings containing Matlab expressions feval Function evaluation function Creates a user-defined function M-file global Define global variables nargin Number of function input arguments nargout Number of function output arguments script Script M-files Timing cputime CPU time in seconds
Searches related to function square matlab filetype:pdf
MATLAB is installed on the engineering instructional facility You can find it in the Start>Programs menu You can also install MATLAB on your own computer This is a somewhat involved process –you need to first register your name at mathworks then wait until they create an account for you there then download MATLAB and activate it
What are the functions of MATLAB?
- MATLAB Function Example Handout. MatLab is a high performance numeric computing environment, which includes numerical analysis, matrix computation, signal processing, and graphics to provide answers to the most troubling of mathematical problems. This handout provides different examples to show the different aspects of MatLab.
How to generate unit step function in MATLAB?
- function [x]=unitstep (x) %This is a unit step "function". The vector keeping track of time is the %input. If time is negative then a zero is returned. If time is zero than %0.5 is returned.
How to generate square wave in MATLAB?
- Square wave is generated using “square” function in Matlab. The command sytax – square (t,dutyCycle) – generates a square wave with period for the given time base. The command behaves similar to “ sin ” command (used for generating sine waves), but in this case it generates a square wave instead of a sine wave.
MATLAB
Basic Functions Reference
MATLAB Environment
clcClear command window
help funDisplay in-line help for fun
doc funOpen 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 itemRemove items from workspace
examplescriptRun the script file named
examplescript format styleSet output display format
verGet list of installed toolboxes
tic, tocStart and stop timer
Ctrl+C
Abort the current calculationOperators and Special CharactersMatrix math operations
Array multiplication and division
(element-wise operations)Matrix and array power
Left division or linear optimization
Normal and complex conjugate
transposeRelational operators
&&, ||, ~, xorLogical operations
(AND, NOT, OR, XOR)Suppress output display
Connect lines (with break)
% DescriptionComment'Hello'
Definition of a character vector
"This is a string"Definition of a string
str1 + str2 Append stringsDefining and Changing Array Variables a = 5Define 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) = 7Change 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:end)Get every 2nd element of x (1st to last)x(x>6)
List elements greater than 6
x(x==10)=1Change 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:ds:bCreate regularly spaced vector with
spacing ds linspace(a,b,n)Create vector o equally spaced values
logspace(a,b,n)Create vector o logarithmically spaced
values zeros(m,n)Create m x n matrix of zeros
ones(m,n)Create m x n matrix of ones
eye(n) Create a n x n identity matrixA=diag(x)
Create diagonal matrix from vector
x=diag(A)Get diagonal elements of matrix
meshgrid(x,y)Create 2D and 3D grids
rand(m,n), randiCreate uniformly distributed random
numbers or integers randn(m,n)Create normally distributed random
numbersSpecial Variables and Constants
ansMost recent answer
piπ=3.141592654...
i, j, 1i, 1jImaginary unitNaN, nan
Not a number (i.e., division by zero)
Inf, inf
Infinity
epsFloating-point relative accuracy
Complex Numbers
i, j, 1i, 1jImaginary unit
real(z)Real part of complex number
imag(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), asinSine and inverse (argument in radians)
sind(x), asindSine and inverse (argument in degrees)
sinh(x), asinhHyperbolic sine and inverse (arg. 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), log10Logarithm with base 2 and 10, respectively
factorial(n)Factorial o
sign(x)Sign of x
mod(x,d)Remainder after division (modulo)
ceil(x), fix, floorRound toward +inf, 0, -inf
round(x)Round to nearest decimal or integer
Tables
tab le(var1,...,varN)Create table from data in variables
var1, ..., varN readtable("file")Create table from file
array2table(A)Convert numeric array to table
T.varExtract data from variable var
T(row s, co lumns),
T(rows,["col1","coln"])
Create a new table with specified
rows and columns from TT.varname=data
Assign data to (new) column in T
T.Properties
Access properties of T
categorical(A)Create a categorical array
summary(T), groupsummaryPrint summary of table
join(T1, T2)Join tables with common variables
Plotting
plot(x,y,LineSpec)Line styles:
Markers:
+, o, *, ., x, s, dColors:
r, g, b, c, m, y, k, wPlot 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/zticklabels(labels)Get or set x/y/z axis tick labels
x/y/ztickangle(angle)Rotate x/y/z axis tick labels
x/y/zlimGet or set x/y/z axis range
axis(lim), axis styleSet axis limits and style
text(x,y,"txt")Add text
grid on/offShow axis grid
hold on/offRetain the current plot when
adding new plots s ub pl ot(m,n,p), tiledlayout(m,n)Create axes in tiled positions
yyaxis left/rightCreate second y-axis
figureCreate figure window
gcf, gcaGet current figure, get current axis
clfClear current figure
closeClose open figures
Common Plot Types
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
Integration and Differentiation
integral(f,a,b)Numerical integration
(analogous functions for 2D and 3D) trapz(x,y)Trapezoidal numerical 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
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
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
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
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(vec)./(1:length(vec)); endAnonymous 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 endFor-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 endWhile-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 endFurther programming/control commands
breakTerminate execution of for- or while-loop
continuePass control to the next iteration of a loop
try, catchExecute statements and catch errors
© 2021 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See for a list of additional trademarks.
Other product or brand names may be trademarks or registered trademarks of their respective holders.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)Remove dimensions of length 1
reshape(A,sz)Reshape array
repmat(A,n)Repeat copies of array
a ny(A), allCheck if any/all elements are nonzero
nnz(A)Number of nonzero array elements
find(A)Indices and values of nonzero elements
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), eigsEigenvalues and vectors of matrix (subset)
inv(A), pinvInverse and pseudo inverse of matrix
norm(x)Norm of vector or matrix
e x p m A l o g mMatrix exponential and logarithm
cross(A,B)Cross product
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