EDUCBA

EDUCBA

MENUMENU
  • Free Tutorials
  • Free Courses
  • Certification Courses
  • 360+ Courses All in One Bundle
  • Login
Home Data Science Data Science Tutorials Matlab Tutorial Matlab Gradient
Secondary Sidebar
Matlab Tutorial
  • Advanced
    • MATLAB Class
    • Arrays in MATLAB
    • Matlab find value in array
    • MATLAB Grader
    • Power Spectral Density MATLAB
    • Matlab Textscan
    • String Array in MATLAB
    • MATLAB Random Numbers
    • Matlab Dot
    • MATLAB 2D Array
    • MATLAB? zero padding
    • MATLAB sort matrix
    • MATLAB Plot Function
    • 2D Plots in MATLAB
    • 3D Plots in MATLAB
    • MATLAB Fread
    • Spectrogram MATLAB
    • MATLAB Average
    • MATLAB exponent
    • MATLAB not enough input arguments
    • MATLAB comment
    • MATLAB zpk
    • Scatter Plots in MATLAB
    • MATLAB 3d scatter plot
    • Bar Graph in MATLAB
    • Bar Plot MATLAB
    • Log Plot MATLAB
    • Polar Plot in MATLAB
    • Surface Plot in MATLAB
    • MATLAB Plot Circle
    • Boxplot in MATLAB
    • MATLAB Plot Multiple Lines
    • Linspace MATLAB
    • Histogram in MATLAB
    • Plot Vector MATLAB
    • MATLAB Legend
    • MATLAB Plot Legend
    • MATLAB ezplots
    • Column Vector MATLAB
    • MATLAB Plot Marker
    • MATLAB LineWidth
    • MATLAB Line Style
    • Contour plot in MATLAB
    • MATLAB Sine Wave
    • Reshape in MATLAB
    • Natural Log in MATLAB
    • Random Number Generator in MATLAB
    • Complex Numbers in MATLAB
    • MATLAB Figure
    • Heatmap in MATLAB
    • MATLAB Technical Computing
    • Colors in MATLAB
    • Colormap in MATLAB
    • MATLAB Plot Colors
    • MATLAB fplot()
    • MATLAB Stacked Bar
    • MATLAB sphere()
    • MATLAB cylinder()
    • MATLAB mesh()
    • Pie Chart in MATLAB
    • MATLAB Gradient
    • Grid on MATLAB
    • Repmat in MATLAB
    • dlmread in MATLAB
    • Meshgrid in MATLAB
    • MATLAB Struct
    • MATLAB Cross Product
    • MATLAB colorbar Label
    • MATLAB Save Variable
    • MATLAB Saveas
    • MATLAB Cell Array
    • Polynomial in MATLAB
    • ismember MATLAB
    • Heaviside MATLAB
    • MATLAB rref
    • MATLAB polyfit()
    • MATLAB xlim
    • MATLAB Variance
    • Optimset MATLAB
    • Quiver MATLAB
    • Newton Raphson MATLAB
    • Mat2cell MATLAB
    • Magnitude MATLAB
    • format long MATLAB
    • Dot Product MATLAB
    • Jacobian MATLAB
    • What is Matlab?
    • Convolution MATLAB
    • Moving Average MATLAB
    • Fourier Series MATLAB
    • Gaussian Fit MATLAB
    • Bisection Method MATLAB
    • Laplace Transform MATLAB
    • Fourier Transform MATLAB
    • Signal Processing MATLAB
    • MATLAB Forms
    • Complex Conjugate MATLAB
    • MATLAB Write to File
    • uigetfile MATLAB
    • MATLAB Toolbox
    • MATLAB Errorbar
    • MATLAB Index Exceeds Matrix Dimensions
    • Nyquist MATLAB
    • Impulse Response MATLAB
    • xlsread MATLAB
    • MATLAB xlswrite
    • Matplotlib Scatter
    • MATLAB Import Data
    • MATLAB Export Data
    • MATLAB Read CSV
  • Basic
    • MATLAB Area Under Curve
    • MATLAB not equal
    • MATLAB max
    • MATLAB exist
    • MATLAB Table
    • MATLAB regression
    • MATLAB Lists
    • MATLAB quantile
    • MATLAB Round
    • MATLAB readtable
    • MATLAB disp
    • MATLAB Standard Deviation
    • MATLAB quadprog
    • MATLAB Transpose
    • Introduction to MATLAB
    • Advantages of MATLAB
    • MATLAB Features
    • Taylor Series MATLAB
    • MATLAB Z Transform
    • fsolve in MATLAB
    • MATLAB QR
    • Career in MATLAB
    • Uses Of MATLAB
    • MATLAB Free
    • How to Install MATLAB
    • How to Use MATLAB?
    • MATLAB Version
    • MATLAB Compiler
    • MATLAB Commands
    • MATLAB Block Comment
    • MATLAB? sprintf
    • MATLAB fprintf
    • Data Types in MATLAB
    • MATLAB Integral
    • MATLAB Double Integral
    • MATLAB boolean
    • MATLAB vpa
    • MATLAB Object
    • MATLAB Annotation
    • MATLAB Variables
    • MATLAB Global Variables
    • MATLAB Operators
    • MATLAB Logical Operators
    • MATLAB nan
    • MATLAB Patch
    • MATLAB AND Operator
    • MATLAB OR Operator
    • Vectors in MATLAB
    • What is Simulink in MATLAB
    • MATLAB Interpolation
    • MATLAB Imread
    • fscanf MATLAB
    • Euler Method MATLAB
    • Root Locus MATLAB
    • MATLAB return
    • Bode Plot MATLAB
    • Nargin MATLAB
    • MATLAB Matrix Inverse
    • MATLAB String to Number
    • MATLAB string
    • MATLAB ColorBar
    • MATLAB Surfc
    • MATLAB Concatenate
    • NUMEL MATLAB
    • MATLAB? File Extension
    • MATLAB File
    • MATLAB Smooth
    • MATLAB ones
    • Exponential in MATLAB
    • MATLAB ksdensity
    • MATLAB log
    • MATLAB Append
    • MATLAB hold on
    • MATLAB Magnitude of Vector
    • Heatmap in MATLAB
    • MATLAB xticks
    • MATLAB randn
  • Control Statements
    • IF-Else Statement in MATLAB
    • If Statement in MATLAB
    • Loops in MATLAB
    • For Loop in MATLAB
    • While Loop in MATLAB
    • do while loop in MATLAB
    • Nested Loop in MATLAB
    • Switch Statement in MATLAB
    • Break in MATLAB
  • Functions
    • MATLAB Functions
    • MATLAB user defined function
    • Calling Functions in MATLAB
    • Transfer Functions in MATLAB
    • Anonymous Functions in MATLAB
    • Inline Functions in MATLAB
    • Bessel Functions in MATLAB
    • Mean Function in MATLAB
    • Find Function MATLAB
    • Filter Function in MATLAB
    • IIR Filter MATLAB
    • Piecewise Function in MATLAB
    • Sum Function in MATLAB
    • Simulink MATLAB Function
    • MATLAB Create Function
    • MATLAB Inverse Function
    • MATLAB Count
    • Step Function MATLAB
    • MATLAB limit
    • Fminsearch in MATLAB
    • Covariance in MATLAB
    • Summation in MATLAB
    • Linear Fit MATLAB
    • MATLAB?linear regression
    • MATLAB Derivative
    • MATLAB Derivative of Function
    • MATLAB Comet()
    • Fzero MATLAB
    • xlabel MATLAB
    • Matplotlib Legend
    • Matplotlib Subplots
    • Plot graph MATLAB
    • MATLAB Format
    • MATLAB plot title
    • Multiple Plots in MATLAB
    • MATLAB Indexing
    • Ceil MATLAB
    • Curve Fitting MATLAB
    • MATLAB trapz()
    • MATLAB Normalize
    • MATLAB diff
    • MATLAB sym()
    • MATLAB Syms
    • Absolute Value MATLAB
    • MATLAB Exponential
    • Kalman Filter MATLAB
    • Low Pass Filter MATLAB
    • Bandpass Filter MATLAB
    • MATLAB Unique
    • Trapezoidal Rule MATLAB
    • MATLAB Root Finding
    • MATLAB stem()
    • MATLAB loglog()
    • MATLAB Autocorrelation
    • MATLAB Sort
    • Simplify MATLAB
    • Cumsum MATLAB
    • Eval Function MATLAB
    • Polyval MATLAB
    • MATLAB Colon
    • MATLAB Eigenvalues
    • MATLAB fit
    • Delta Function MATLAB
    • MATLAB Remainder
    • Differentiation in MATLAB
    • Permute MATLAB
    • isempty MATLAB
    • MATLAB text()
    • MATLAB Display Text
    • Varargin in MATLAB
    • MATLAB gca
    • MATLAB fill()
    • MATLAB pcolor()
    • MATLAB min
    • MATLAB xcorr
    • MATLAB? color codes
    • Semilogy MATLAB
    • MATLAB? eye
    • feval MATLAB
    • num2str in MATLAB
    • MATLAB Images
    • MATLAB Image? Segmentation
    • Imagesc MATLAB
    • MATLAB Image Processing
    • MATLAB Image Resize
    • MATLAB Flag
    • MATLAB fopen
    • Strcmp MATLAB
    • MATLAB fwrite
    • MATLAB fft()
    • MATLAB zeros()
    • MATLAB textread
    • Arctan MATLAB
    • MATLAB Scripts
    • Butterworth filter MATLAB
    • MATLAB Findpeaks
    • MATLAB find Index
    • MATLAB Cell
    • MATLAB Unit Step Function
    • MATLAB Backslash
    • MATLAB Mod
    • Size Function in MATLAB
    • Secant MATLAB
  • Matrix
    • Matrix in MATLAB
    • 3D Matrix in MATLAB
    • Transpose Matrix MATLAB
    • Sparse Matrix in MATLAB
    • Matrix Multiplication in MATLAB
    • Identity Matrix in MATLAB
    • MATLAB?writematrix
  • Programs
    • Square Root in MATLAB
    • Square Wave MATLAB
    • Squeeze MATLAB
    • Factorial in MATLAB
    • Cell to String MATLAB
  • Interview Questions
    • MATLAB Interview Questions

Related Courses

MATLAB Certification Course

R Programming Course

All in One Data Science Courses

Matlab Gradient

By Priya PedamkarPriya Pedamkar

Matlab Gradient

Introduction to Matlab Gradient

The gradient is defined as the slope of any feature in general terms. In mathematics, it is defined as the partial derivative of any function. It is the collection of all the partial derivatives that are defined as part of the function into a vector. The field generated by it is known as gradient field and it can be in two dimensions or three-dimension. The resultant gradient in terms of x, y and z give the rate of change in x, y and z directions respectively. iN this topic, we are going to learn about Matlab Gradient.

Working of Gradient in Matlab with Syntax

In Matlab, we use the numerical gradient to represent the derivatives of the function. The function used while working with gradient is denoted by “gradient”. We can perform several operations using gradient function in Matlab. Please find the below syntaxes which can be used to perform various operations:

  • X= gradient[a]: This function returns a one-dimensional gradient which is numerical in nature with respect to vector ‘a’ as the input. Here X is the output which is in the form of first derivative da/dx where the difference lies in the x-direction.
  • [X, Y] = gradient[a]: This function returns two-dimensional gradients which are numerical in nature with respect to vector ‘a’ as the input. Here X and Y are the outputs that are in the form of first derivatives da/dx and da/dy where the difference lies in the x and y direction respectively.
  • [X, Y, Z…. N] =gradient(a): This syntax returns the numerical gradient of the number of components present in the input array.
  • [___] = gradient (a, h): This syntax returns the gradient with the number of spacing points mentioned in the input argument ‘h’ which can be used in any direction.
  • [__] = gradient (a, hb, hc, hd, he….hn): This syntax returns n number of spacing points in every dimension as given in a.

Examples of Matlab Gradient

Below are the examples for Matlab Gradient

All in One Data Science Bundle(360+ Courses, 50+ projects)
Python TutorialMachine LearningAWSArtificial Intelligence
TableauR ProgrammingPowerBIDeep Learning
Price
View Courses
360+ Online Courses | 50+ projects | 1500+ Hours | Verifiable Certificates | Lifetime Access
4.7 (86,584 ratings)

Example #1

To calculate the gradient of a vector.

Start Your Free Data Science Course

Hadoop, Data Science, Statistics & others

A = 11:15

11   12  13  14  15

Output

x = gradient(a)

11111

  • In the above example, the function calculates the gradient of the given numbers. The input arguments used in the function can be vector, matrix or a multidimensional array and the data types that can be handled by the function are single, double. It also supports the use of complex numbers in Matlab. “h” in the syntax is used to define the spacing between the points in the respective directions which is uniform in nature and it is denoted as a scalar quantity.
  • The data types that can be handled by the function are single, double. It also supports the use of complex numbers in Matlab. “hb,” hc”,” hd” denote the unique spacing between the points in each direction and they can be scalar or vector in nature. The number of input arguments that we specify while declaring the function, it should always match the dimension of the array used.
  • If the input is scalar in nature, then it means the spacing used between the points is constant in the respective dimension. If the input is the vector in nature, then it represents the coordinates with the respective dimension and vector’s length should always match the dimension size which is used. The data types that are accepted are single and double in nature. It also supports the use of complex numbers.
  • The output arguments which are returned by the gradient function have the same nature as that of input arguments used and are known as Numerical Gradients. X represents gradient in the second dimension which is columns, Y represents the gradient in the first dimension which is the rows and the rest of the outputs follow in the same directions. If we want to use gradient function multiple times then instead of calling it many times, we can use “diff” function.

Example #2

To calculate the gradient of the function ae^a2−b2 and plot the contour lines

a = -1:0.3:1;

b = a’;

c = a.* exp (-a.^2 – b.^2);

Output

[pa, pb] = gradient(c)

contour (a,b,c)

We can also use the gradient function if the input argument is a function. It is given by the below syntax:

gradient (a, y): It gives the gradient vector of the function defined in the input argument with respect to the vector mentioned in y. If vector ‘y’ is not mentioned in the input, then it finds the scalar gradient function according to the variables mentioned in the function. Variables used in the vector have an order and it is specified by symvar.

The input arguments can be an expression or a function which can be scalar in nature. y is the vector with respect to which we can find the gradient vector. If y is empty, then it returns an empty gradient object. The gradient vector of function is the collection of all the first partial derivatives with respect to function defined.

Example #3

To calculate the gradient of the function as given:

syms a b c

f = 2*b*c*sin(a) + 3*a*sin(c)*cos(b);

gradient (f, [a, b, c])

Output

3*cos(b)*sin(c) + 2*b*c*cos(a)

2*c*sin(a) – 3*a*sin(b)*sin(c)

2*b*sin(a) + 3*a*cos(b)*cos(c)

There are various properties that are associated with the gradient in Matlab, like its color and transparency level can be adjusted by providing the parameters to the input argument with the required values. Numerical gradients can be calculated for any number of variables since there is no specific limit to it. It can be calculated for every direction by determining the partial derivatives of different values used in the function. If we give spacing between the points, then the gradient approximates the difference accordingly.

Conclusion

There are many applications where the gradient is used like it is used in the field of mathematics and physics to find the maxima and minima points using the algorithm. The algorithm which uses gradient is Gradient Descent Algorithm which is also used in machine learning and data science to optimize various parameters before applying it in the model to get better accuracy. It is also used in regression techniques because computation using this technique is comparatively faster as compared to others.

Recommended Articles

This is a guide to Matlab Gradient. Here we discuss the Working of Gradient in Matlab along with the syntax and examples. You may also have a look at the following articles to learn more –

  1. Matlab Features
  2. Colors in Matlab
  3. Matlab AND Operator
  4. Matlab Compiler
  5. Complete Guide to Matlab Inverse Function
  6. Steps to Use Matlab Comet()
  7. How to Use Matlab?
  8. Vector in Java | Examples
Popular Course in this category
MATLAB Training (3 Courses, 1 Project)
  3 Online Courses |  1 Hands-on Project |  8+ Hours |  Verifiable Certificate of Completion
4.5
Price

View Course

Related Courses

R Programming Training (13 Courses, 20+ Projects)4.9
All in One Data Science Bundle (360+ Courses, 50+ projects)4.8
1 Shares
Share
Tweet
Share
Primary Sidebar
Footer
About Us
  • Blog
  • Who is EDUCBA?
  • Sign Up
  • Live Classes
  • Corporate Training
  • Certificate from Top Institutions
  • Contact Us
  • Verifiable Certificate
  • Reviews
  • Terms and Conditions
  • Privacy Policy
  •  
Apps
  • iPhone & iPad
  • Android
Resources
  • Free Courses
  • Database Management
  • Machine Learning
  • All Tutorials
Certification Courses
  • All Courses
  • Data Science Course - All in One Bundle
  • Machine Learning Course
  • Hadoop Certification Training
  • Cloud Computing Training Course
  • R Programming Course
  • AWS Training Course
  • SAS Training Course

ISO 10004:2018 & ISO 9001:2015 Certified

© 2022 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA
Free Data Science Course

SPSS, Data visualization with Python, Matplotlib Library, Seaborn Package

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA Login

Forgot Password?

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA
Free Data Science Course

Hadoop, Data Science, Statistics & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

Let’s Get Started

By signing up, you agree to our Terms of Use and Privacy Policy.

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Loading . . .
Quiz
Question:

Answer:

Quiz Result
Total QuestionsCorrect AnswersWrong AnswersPercentage

Explore 1000+ varieties of Mock tests View more