جميع معادلات ماتلاب الأساسية في ملف واحد فقط – MATLAB Basic Functions Reference

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
load(“filename”,”vars”) Load variables from .mat file
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
ans Most recent answer
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
angle(z) Phase angle in radians
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
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
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 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
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/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-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 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
  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));
  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© 2024 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See mathworks.com/trademarks for a list of additional trademarks.
  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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