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Matlab Programming for Numerical Computation

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The course will be covered in eight modules. Various aspects of MATLAB programming for numerical computation will be covered in these modules, with each module dedicated to on equivalent numerical topic. Each module will be covered in one week, with 2–2.5 hours lectures per week. There will be self-study problems at the end of several of these lectures. Assignments will also be posted periodically.

Module 1: Introduction to MATLAB Programming

Module 2: Approximations and Errors

Module 3: Numerical Differentiation and Integration

Module 4: Linear Equations

Module 5: Nonlinear Equations

Module 6: Regression and Interpolation

Module 7: Ordinary Differential Equations (ODE) – Part 1

Module 8: Ordinary Differential Equations (ODE) – Practical aspects

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assignment with matlab

Prof. Niket Kaisare

Prof. Niket Kaisare is a Professor of Chemical Engineering in IIT-Madras. He works in the area of modeling, design and control for energy applications. He has over ten years of research/teaching experience in academia, and three-year experience in Industrial R&D. He uses computational software, including MATLAB, FORTRAN, Aspen and FLUENT extensively in his research and teaching. Faculty web-page:   http://www.che.iitm.ac.in/~nkaisare/

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  • Date and Time of Exams: 29th March 2020 , Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
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CRITERIA TO GET A CERTIFICATE:

  • Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments
  • Exam score = 75% of the proctored certification exam score out of 100
  • Final score = Average assignment score + Exam score

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  • Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras. It will be e-verifiable at  nptel.ac.in/noc .
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How do I do multiple assignment in MATLAB?

Here's an example of what I'm looking for:

I'd expect something like this afterwards:

But instead I get errors like:

I thought deal() might do it, but it seems to only work on cells.

How do I solve my problem? Must I constantly index by 1 and 2 if I want to deal with them separately?

  • variable-assignment

gnovice's user avatar

  • 3 Deal works only if foo is a cell. You have defined foo as a standard array. That's why you got the ??? Cell contents reference from a non-cell array object. error message. –  Justin Peel Commented Feb 25, 2010 at 20:17

9 Answers 9

You don't need deal at all (edit: for Matlab 7.0 or later) and, for your example, you don't need mat2cell ; you can use num2cell with no other arguments::

If you want to use deal for some other reason, you can:

Ramashalanka's user avatar

  • 3 Just a side note, I think you can only get away with not using deal( as in the first example) in Matlab 7+. –  Justin Peel Commented Feb 25, 2010 at 20:59
  • Interesting. I didn't know that deal is unnecessary nowadays. However, I used mat2cell on purpose, since I assume that the OP might want to separate columns from each other. –  Jonas Commented Feb 25, 2010 at 21:07
  • 3 This is really good. But is there any way to have it all on one line? Maybe something like: [x y] = num2cell(foo){:} (Sorry, still confused by Matlab quite often.) –  Benjamin Oakes Commented Feb 25, 2010 at 21:34
  • @Justin: good point, you need version 7.0 (2004) or later. @Jonas: true, mat2cell is good if you want to split up in different ways. @Benjamin: I'm not aware of a one line method, unless you use a cell to begin with; you can use deal(88,12) if you are starting from scalars. It'd be good if we stuff like num2cell(foo){:} for many Matlab commands. –  Ramashalanka Commented Feb 25, 2010 at 23:26

Note that deal accepts a "list" as argument, not a cell array. So the following works as expected:

The syntax c{:} transforms a cell array in a list, and a list is a comma separated values , like in function arguments. Meaning that you can use the c{:} syntax as argument to other functions than deal . To see that, try the following:

Jonas Heidelberg's user avatar

To use the num2cell solution in one line, define a helper function list :

Sander Evers's user avatar

  • won't the example [a1,a2,a3,a4] = list(1:4) cause Too many output arguments error? –  zhangxaochen Commented Apr 6, 2015 at 12:16

What mtrw said. Basically, you want to use deal with a cell array (though deal(88,12) works as well).

Assuming you start with an array foo that is n-by-2, and you want to assign the first column to x and the second to y, you do the following:

Community's user avatar

DEAL is really useful, and really confusing. foo needs to be a cell array itself, I believe. The following seems to work in Octave, if I remember correctly it will work in MATLAB as well:

mtrw's user avatar

I cannot comment other answers, so separate addition.

you can use deal(88,12) if you are starting from scalars

deal can be used as a one-liner for non-scalars as well, of course if you already have them in separate variables, say:

and now you deal them with one line:

However, if they are packed in one variable, you can only deal them if they are in a cell or structure array - with deal(X{:}) for cell array and deal(S.field) for structure array. (In the latter case only one field is dealt, but from all structures in array.) With Matlab v.7+ you can use X{:} and S.field without deal , as noted in other answers.

Victor K's user avatar

Create a function arr2vars for convenience

You can use it then like this

Tigliottu's user avatar

You might be looking for

resulting in

So you have a working one-liner.

luckydonald's user avatar

There is an easier way.

Full documentation at Mathworks.

0x1000001's user avatar

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Coursera Course: Introduction to Programming 👩‍💻 with MATLAB ~by Vanderbilt University 🎓

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Introduction to programming with matlab ~ vanderbilt university.

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Introduction to matlab programming.

Screenshot of MATLAB’s command prompt and a series of for basic mathematical operations.

MATLAB’s command prompt can be used for quick and easy calculations.

In this unit, you will learn how to use the MATLAB® command prompt for performing calculations and creating variables. Exercises include basic operations, and are designed to help you get familiar with the basics of the MATLAB interface. One of MATLAB’s conveniences is its ability to work with lists of numbers. You will have the opportunity to practice constructing and manipulating lists, vectors, and matrices. Since the unit also serves as an introduction to programming, you will receive guidance on defining variables, storing values in variables, and changing the values of variables.

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  • Ace Your Simulink Assignments with MATLAB

Tips and Tricks for Writing Simulink Assignments

John Doe

Simulink is a powerful software programme that is frequently used for the design and simulation of dynamic systems. Engineering, physics, and economics are just a few of the many fields in which it has applications. The programming language MATLAB, on the other hand, is widely used for numerical analysis, data processing, and visualisation tasks. Your ability to simulate and analyse complex systems can be significantly improved by combining these two tools. Simulink's simulation capabilities and MATLAB's analytical capabilities can be combined to create models that are not only highly accurate but also extremely efficient. We'll walk you through the steps of writing assignments on Simulink using MATLAB in this blog post, giving you a step-by-step manual to help you master this potent tool. Your work will benefit greatly from the knowledge and skills you learn from this tutorial, whether you are a professional or a student.

Understand the Problem Statement

Understanding the problem statement in its entirety is crucial before beginning the Simulink modelling process. Spend some time carefully reading the assignment and identifying its main goals and requirements. Knowing the problem statement will help you design your Simulink model in a clear direction and ensure that you take into account all the pertinent aspects of the issue.

When examining the problem statement, bear the following in mind:

  • Name the system: Find out what kind of system you are required to model. Is it a system of command, a system of communication, or something else entirely? It will be easier for you to select the appropriate Simulink blocks and methods if you are aware of the system's behaviour and intended use.
  • Specify inputs and outputs: List the system's inputs and outputs. You can use this as a guide when choosing the right sources and sinks in Simulink.
  • Be aware of restrictions: Any restrictions or limitations mentioned in the problem statement should be taken into consideration. These might be concerned with system settings, signal ranges, or computational capabilities. For your Simulink model to be feasible, adherence to these constraints is essential.

You can create a Simulink model that is more precise and efficient if you fully comprehend the problem statement.

Break Down the Problem into Subsystems

It is frequently beneficial to divide a complex Simulink assignment into more manageable, smaller subsystems. This strategy makes the entire modelling process easier and enables you to concentrate on one particular aspect at a time. A Simulink model that has been broken down into smaller systems is more reusable and modular.

When breaking your issue down into smaller components, take into account the following steps:

  • List the independent parts: To find any independent components or functional blocks that can be isolated, analyse the problem statement. These components' inputs and outputs ought to be clearly defined.
  • Create individual subsystems for each independent component: After identifying the independent components, create individual subsystems for each of them in Simulink. These auxiliary systems can be created as independent models and then incorporated into the primary model.
  • Establish subsystem communication: Plan how the subsystems will communicate with one another. Use the proper Simulink signals and blocks to create data flow and communication between subsystems.

Your Simulink model will be more organised, simpler to debug, and enable better teamwork if you divide the issue into smaller systems.

Validate and Test your Simulink Model

One of the most important steps in the assignment writing process is validating and testing your Simulink model. It guarantees that your model behaves as you would expect and complies with the requirements. Before submitting the assignment, you can find any mistakes or discrepancies in your model by conducting exhaustive validation and testing.

When validating and testing your Simulink model, take into account the following methods:

  • Unit testing: Test each component of your model separately to ensure it is operational. Utilise the proper test inputs, then compare the outputs to what was anticipated. This aids in locating any problems with specific subsystems.
  • Simulation case studies: To assess your Simulink model's general behaviour, create various simulation scenarios. Change the inputs, look at the results, and evaluate how the system reacts in various scenarios. By doing so, you can evaluate the model's effectiveness and make sure the specifications are being met.
  • Boundary testing: Evaluate how the model responds to changes in input ranges or parameter values. This is crucial to determine whether the model correctly handles edge cases and responds to extreme scenarios.
  • Compare the results of your Simulink model against known analytical solutions or theoretical calculations, if at all possible. This will ensure that your model is accurate and that it adheres to accepted theories or principles.
  • Sensitivity analysis: To conduct a sensitivity analysis, change the model's parameters within predetermined limits. This makes it easier to see how changing a parameter affects how the system behaves and can highlight any unforeseen sensitivities or instabilities.

Throughout the assignment writing process, regularly validating and testing your Simulink model will guarantee the dependability and accuracy of your results. It also aids in troubleshooting and improving your model so that it effectively satisfies the assignment's requirements.

Writing Assignments on Simulink using MATLAB

It's time to dive into writing assignments with MATLAB and Simulink now that you have a firm grasp of their fundamentals. While MATLAB is a high-level programming language used for data analysis, visualisation, and algorithm development, Simulink is a graphical programming environment that enables the creation of complex models and simulations. These resources work as a whole to provide a thorough method for addressing challenging engineering and scientific issues. Simulink and MATLAB are vital tools that will help you accomplish your goals successfully and efficiently, regardless of whether you're working on a project in the area of control systems, signal processing, or any other field that calls for modelling and simulation. The steps are as follows:

Step 1: Create a Simulink Model

Making a Simulink model is the first step in using MATLAB to write assignments using Simulink. Follow these steps to accomplish this:

  • Launch MATLAB and select the Simulink toolbar icon.
  • To create a new model, select "Blank Model" in the Simulink window.
  • To create the system you want to simulate, drag and drop blocks from the Simulink Library Browser onto the model canvas in the Simulink Editor.
  • To define the input-output relationships of the system, connect the blocks using lines.
  • The Simulink model can be saved by selecting "File" and then "Save As."

Step 2: Define System Parameters

Defining the system parameters comes after creating the Simulink model. This entails specifying the model parameters, defining the system inputs and outputs, and choosing the appropriate solver settings. Follow these steps to accomplish this:

  • To set a block's parameters in the Simulink model, double-click on it.
  • Define the characteristics of the input and output signals, such as their amplitude, frequency, and time duration.
  • Specify the parameters for the simulation, including the step size, solver type, and simulation time.

Step 3: Run the Simulation

Running the simulation is the next step after defining the system parameters. This will simulate the system's behaviour over time. Follow these steps to accomplish this:

  • To begin the simulation, click the "Run" button in the Simulink window.
  • The Simulation Data Inspector window will show the simulation results. This window allows you to examine the simulation results and see how the system behaves.

Tips for Writing Assignments on Simulink

Anyone wishing to explore the world of engineering and scientific simulations must have a solid understanding of how to write assignments on Simulink using MATLAB. After going over the fundamentals, it's time to put your knowledge to the test. Learning Simulink and MATLAB will give you a strong toolkit to build simulations and designs that can solve challenging problems, whether you are an engineering student or a seasoned professional. Let's look at some tips to make the process simpler and more effective. If you keep practising and exploring the many features and capabilities of Simulink and MATLAB, you will soon find yourself producing high-quality simulations that can help make a significant impact in your field.

Tip 1: Plan Your Model

The success of a Simulink model depends on careful planning. This entails specifying model parameters, choosing appropriate blocks, and defining the system's inputs and outputs. You can ultimately save time and avoid mistakes by doing this. You'll have a much smoother experience building your Simulink model if you take the time to plan it out before getting started.

Tip 2: Use Simulink Libraries

Simulink's pre-built blocks and libraries make it simpler than ever to create models. You can save time and effort while also ensuring the precision and dependability of your model by utilising these libraries. Simulink gives users of all skill levels a wide range of options with its extensive selection of pre-built blocks and libraries. You can streamline your modelling process and generate excellent results by utilising these features.

Tip 3: Optimize Your Model

Optimising your Simulink model for accuracy and speed is crucial as you build it. This entails lowering the number of blocks and lines, utilising effective solver settings, and whenever possible, simplifying the system. You can run simulations faster and more accurately by optimising your model.

Tip 4: Test Your Model

It's crucial to thoroughly test your model before submitting your Simulink assignment. This entails checking that the inputs and outputs are accurate, putting the model through its paces, and contrasting the simulation's findings with what is anticipated. You can find errors in your model and fix them before they grow into bigger issues by testing it.

Common Mistakes to Avoid

Students frequently make mistakes when using MATLAB to complete Simulink assignments, which can reduce the accuracy and effectiveness of their work. These mistakes might involve using Simulink blocks incorrectly, providing inadequate or inaccurate inputs, or failing to pay attention to the system's overall structure and design. Students can produce high-quality Simulink assignments that satisfy their academic requirements by being aware of these common pitfalls and taking precautions to avoid them. Here are some errors to avert:

Mistake 1: Not Understanding the System

When using Simulink to complete assignments, one of the biggest mistakes students make is not fully comprehending the system they are simulating. Make sure you have a solid understanding of the system's inputs, outputs, and behaviour before you begin building your Simulink model.

Mistake 2: Using Too Many Blocks

A common mistake is using too many blocks in your Simulink model. All necessary building blocks must be present in order for the model to accurately replicate the system, but including too many can slow down simulation and make it more difficult to understand the model. Therefore, it's crucial to strike a balance between having all the necessary building blocks and making sure the model is still effective and easy to understand.

Mistake 3: Not Optimizing the Model

If you want to run simulations quickly and reliably, you must optimise your Simulink model. Simulations may run more slowly and with lower precision if optimisation is neglected. To make the most of your simulation efforts, it is crucial to take the time to optimise your Simulink model. By doing this, you can make sure that your simulations run more quickly and generate accurate results that can be applied to guide decision-making.

Mistake 4: Not Testing the Model

To find errors and ensure accurate simulation results, you must thoroughly test your Simulink model. Failure to conduct model testing could lead to errors in your assignments and lower grades. Therefore, take the time to thoroughly test your Simulink model to ensure that it is operating as intended and to prevent any future costly mistakes. In the long run, a well-tested Simulink model can save you time and headaches.

If you are willing to put in the time to study and practise, writing assignments on Simulink using MATLAB can be a rewarding experience. Simulink and MATLAB are effective programmes for modelling and analysing dynamic systems. They can be used in a variety of industries, including engineering, business, and biology.

Remember to stay organised, plan your model carefully, use Simulink libraries, optimise your model for speed and accuracy, and test your model thoroughly as you work on your Simulink assignments. Never be afraid to ask for assistance from your professors, teaching assistants, or online resources if you run into problems along the way.

You will excel in your assignments and gain important skills that will benefit your future career if you master MATLAB and Simulink. So continue to practise and learn, and take pleasure in the process of developing Simulink models that can aid in the comprehension and resolution of complex systems.

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Solve linear assignment problem

Description

M = matchpairs( Cost , costUnmatched ) solves the linear assignment problem for the rows and columns of the matrix Cost . Each row is assigned to a column in such a way that the total cost is minimized. costUnmatched specifies the cost per row of not assigning each row, and also the cost per column of not having a row assigned to each column.

[ M , uR , uC ] = matchpairs( Cost , costUnmatched ) additionally returns indices for unmatched rows in uR and indices for unmatched columns in uC .

[ ___ ] = matchpairs( Cost , costUnmatched , goal ) specifies the goal of the optimization using any of the output argument combinations in previous syntaxes. goal can be 'min' or 'max' to produce matches that either minimize or maximize the total cost.

collapse all

Assign Flights with Minimal Cost

Assign salespeople to flights such that the total cost of transportation is minimized.

A company has four salespeople who need to travel to key cities around the country. The company must book their flights, and wants to spend as little money as possible. These salespeople are based in different parts of the country, so the cost for them to fly to each city varies.

This table shows the cost for each salesperson to fly to each key city.

Dallas Chicago New   York   City St.   Louis Fred $ 6 0 0 $ 6 7 0 $ 9 6 0 $ 5 6 0 Beth $ 9 0 0 $ 2 8 0 $ 9 7 0 $ 5 4 0 Sue $ 3 1 0 $ 3 5 0 $ 9 5 0 $ 8 2 0 Greg $ 3 2 5 $ 2 9 0 $ 6 0 0 $ 5 4 0

Each city represents a sales opportunity. If a city is missed, then the company loses out on an average revenue gain of $2,000.

Create a cost matrix to represent the cost of each salesperson flying to each city.

Use matchpairs to assign the salespeople to the cities with minimal cost. Specify the cost of unassignment as 1000, since the cost of unassignment is counted twice if a row and a column remain unmatched.

matchpairs calculates the least expensive way to get a salesperson to each city.

Dallas Chicago New   York   City St.   Louis Fred $ 6 0 0 $ 6 7 0 $ 9 6 0 $ 560 Beth $ 9 0 0 $ 280 $ 9 7 0 $ 5 4 0 Sue $ 310 $ 3 5 0 $ 9 5 0 $ 8 2 0 Greg $ 3 2 5 $ 2 9 0 $ 600 $ 5 4 0

Unequal Numbers of Rows and Columns

Match rows to columns when you have many more columns than rows in the cost matrix.

Create a 3-by-8 cost matrix. Since you have only three rows, matchpairs can produce at most three matches with the eight columns.

Use matchpairs to match the rows and columns of the cost matrix. To get the maximum number of matches, use a large cost of unassignment (relative to the magnitude of the entries in the cost matrix). Specify three outputs to return the indices of unmatched rows and columns.

Five of the columns in C are not matched with any rows.

Assign Taxis to Maximize Profit

Assign taxis to routes such that the profit is maximized.

A taxi company has several ride requests from across the city. The company wants to dispatch its limited number of taxis in a way that makes the most money.

This table shows the estimated taxi fare for each of five ride requests. Only three of the five ride requests can be filled.

Ride   1 Ride   2 Ride   3 Ride   4 Ride   5 Cab   A $ 5 . 7 0 $ 6 . 3 0 $ 3 . 1 0 $ 4 . 8 0 $ 3 . 5 0 Cab   B $ 5 . 8 0 $ 6 . 4 0 $ 3 . 3 0 $ 4 . 7 0 $ 3 . 2 0 Cab   C $ 5 . 7 0 $ 6 . 3 0 $ 3 . 2 0 $ 4 . 9 0 $ 3 . 4 0

Create a profits matrix to represent the profits of each taxi ride.

Use matchpairs to match the taxis to the most profitable rides. Specify three outputs to return any unmatched rows and columns, and the 'max' option to maximize the profits. Specify the cost of unassignment as zero, since the company makes no money from unfilled taxis or ride requests.

matchpairs calculates the most profitable rides to fill. The solution leaves ride requests 3 and 5 unfilled.

Calculate the total profits for the calculated solution. Since costUnmatched is zero, you only need to add together the profits from each match.

Track Point Positions over Time

Use matchpairs to track the movement of several points by minimizing the total changes in distance.

Plot a grid of points at time t = 0 in green. At time t = 1 , some of the points move a small amount in a random direction.

assignment with matlab

Use matchpairs to match the points at t = 0 with the points at t = 1 . To do this, first calculate a cost matrix where C(i,j) is the Euclidean distance from point i to point j .

Next, use matchpairs to match the rows and columns in the cost matrix. Specify the cost of unassignment as 1. With such a low cost of unassignment relative to the entries in the cost matrix, it is likely matchpairs will leave some points unmatched.

The values M(:,2) correspond to the original points ( x 0 , y 0 ) , while the values M(:,1) correspond to the moved points ( x 1 , y 1 ) .

Plot the matched pairs of points. The points that moved farther than 2*costUnmatched away from the original point remain unmatched.

assignment with matlab

Input Arguments

Cost — cost matrix matrix.

Cost matrix. Each entry Cost(i,j) specifies the cost of assigning row i to column j .

Data Types: single | double

costUnmatched — Cost of not matching scalar

Cost of not matching, specified as a scalar. matchpairs compares the value of 2*costUnmatched to the entries in Cost to determine whether it is more beneficial for a row or column to remain unmatched. Use this parameter to make matches more or less likely in the algorithm. For more information, see linear assignment problem .

Example: M = matchpairs(C,10) specifies a cost of 10 for not matching a row or column of C .

goal — Optimization goal 'min' (default) | 'max'

Optimization goal, specified as either 'min' or 'max' . The optimization goal specifies whether the total cost should be minimized or maximized.

Example: M = matchpairs(Cost,costUnmatched,'max') specifies that the rows and columns of Cost should be matched together to maximize the total cost.

Output Arguments

M — matches matrix.

Matches, returned as a matrix. M is a p -by- 2 matrix, where M(i,1) and M(i,2) are the row and column indices of a matched pair in the cost matrix. The rows of M are sorted with the second column in ascending order.

Each row and column can be matched a single time only, so each M(i,1) value and each M(i,2) value is unique.

M contains p matches, and p is less than or equal to the maximum number of matches min(size(Cost)) .

The cost of the matches in M is sum([Cost(M(1,1),M(1,2)), Cost(M(2,1),M(2,2)), ..., Cost(M(p,1),M(p,2))]) .

uR — Unassigned rows column vector

Unassigned rows, returned as a column vector of indices. The entries in uR indicate which rows in Cost are unassigned. Each entry in uR and uC contributes to the total cost of the solution according to costUnassigned .

uC — Unassigned columns column vector

Unassigned columns, returned as a column vector of indices. The entries in uC indicate which columns in Cost are unassigned. Each entry in uR and uC contributes to the total cost of the solution according to costUnassigned .

Linear Assignment Problem

The linear assignment problem is a way of assigning rows to columns such that each row is assigned to a column and the total cost of the assignments is minimized (or maximized). The cost of assigning each row to each column is captured in a cost matrix . The entry Cost(i,j) is the cost of assigning row i to column j .

The cost of unassignment assigns a cost to any row or column that is not matched. This practice allows for minimum-cost solutions that do not assign all rows or columns. If a row and column are not matched, this increases the total cost by 2*costUnmatched .

The total cost of a solution M is the sum of the cost of all matched pairs added to the cost of all unmatched pairs:

T C = ∑ i = 1 p Cost ( M ( i , 1 ) , M ( i , 2 ) ) + costUnmatched   ⋅   ( m + n − 2 p )

In code the total cost is

Cost is an m -by- n matrix.

M is a p -by- 2 matrix, where M(i,1) and M(i,2) are the row and column of a matched pair.

(m+n-2*p) is the total number of unmatched rows and columns.

[1] Duff, I.S. and J. Koster. "On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix." SIAM J. Matrix Anal. & Appl. 22(4), 2001. pp 973–996.

Extended Capabilities

C/c++ code generation generate c and c++ code using matlab® coder™..

Usage notes and limitations:

Code generation does not support sparse matrix inputs for this function.

Version History

Introduced in R2019a

equilibrate | sprank | dmperm

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