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جميع معادلات ماتلاب الأساسية في ملف واحد فقط
MATLAB Basic Functions Reference
MATLAB Environment
clc Clear command window
help fun Display in-line help for fun
doc fun Open documentation for fun
uiimport(“filename”) Open interactive import tool
save(“filename”,”vars”) Save variables to file
clear item Remove items from workspace
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
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
‘Hello’ 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 2×3 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:end) 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
ones(m,n) Create m x n matrix of ones
eye(n) Create a n x n identity matrix
A=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), randi Create uniformly distributed random
numbers or integers
randn(m,n) Create normally distributed random
numbers
Special Variables and Constants
pi 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
real(z) Real part of complex number
imag(z) Imaginary part of complex number
conj(z) Element-wise complex conjugate
isreal(z) Determine whether array is realmathworks.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
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
Tables
table(var1,…,varN) Create table from data in variables
var1, …, varN
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 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, marker, and
color as a string.
Example: “-r”
= red solid line without markers
legend(“1st”, “2nd”) Add legend to axes
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/zlim Get or set x/y/z axis range
axis(lim), axis style Set axis limits and style
grid on/off Show axis grid
hold on/off Retain the current plot when
subplot(m,n,p),
tiledlayout(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
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 Datamathworks.com/help/matlab
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
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));
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
Other product or brand names may be trademarks or registered trademarks of their respective holders.
mathworks.com/help/matlab
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
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
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 triangular part of matrix
linsolve(A,B) Solve linear system of the form AX=B
lsqminnorm(A,B) Least-squares solution to linear equation
qr(A), lu, chol Matrix decompositions
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 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
simplify(expr) 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
diff(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
Descriptive Statistics
sum(A), prod Sum or product (along columns)
max(A), min, bounds Largest and smallest element
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
detrend(x) Remove polynomial trend
isoutlier(A) Find outliers in data
*requires Symbolic Math Toolbox

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