Applied numerical methods with MATLAB for engineers and scientists / Steven C. Chapra. — 3rd ed. p. cm. ISBN (alk. paper). Hello, I just pushed an update to the a release. Some things have changed: The PKGBUILD is based on the one VictriD kindly provided here.
Vectors are called lists or arrays in other programming languages. MATLAB handles vectors and matrices in the same way, but since vectors are easier to think about than matrices, we will look at them first. We will also use the term array generally, with vector and matrix referring to the one-dimensional 1D and two-dimensional 2D array forms. These are all examples of the explicit list method of initializing vectors. Exercises 2. Make sure to leave out the semicolon so that you can see the list.
Also, make sure you hit Enter to execute the command. Under the heading Size you will see that x is 1 by 5, which means 1 row and 5 columns. You will also see that the total number of elements is 5. Take the space between the minus sign and 15 to see how the assignment of x changes. This means x is defined and can be used where an array is appropriate without causing an error; however, it has no size or value.
An empty array may be used to remove elements from an array see Section 2. The function logspace can be used to generate logarithmically spaced data. It is a logarithmic equivalent of linspace. If the last number in this function call is omit- ted, the number of values of y computed is by default What is the interval between the numbers 1 and in this example? Thus, the logspace function produces a set of points with an interval between them that increases linearly with y.
The vari- able yy was introduced for two reasons. The first was to generate a vector of the same length as dy. The second was to examine the increase in the interval with increase in y that is obtained with the implementation of logspace. Each has one row and several columns. To generate the column vectors that are often needed in mathematics, you need to transpose such vectors—that is, you need to interchange their rows and columns.
Note that x itself remains a row vector. Try the following: 1. This gives you a row vector of seven random numbers. Enter r 3. This will display the third element of r. The numeral 3 is the subscript. Enter r This should give you the second, third, and fourth elements.
What about r and r [1 7 2 6]? You cre- ate a matrix just as you do a vector, except that a semicolon is used to indicate the end of a row. Generate the table of angles and sines as shown above. You can then edit the output, for example, by inserting text headings above each column this is easier than trying to get headings to line up over the columns with a disp statement.
The edited output can in turn be pasted into a report or printed as is the File menu has a number of printing options. Another way of capturing output is with the diary command. The command: diary filename copies everything that subsequently appears in the Command Window to the text file filename. Stop recording the session with: diary off Note that diary appends material to an existing file—that is, it adds new infor- mation to the end of it.
It is typically written in what is called pseudo-code— that is, statements in English, mathematics, and MATLAB describing in detail how to solve a problem. A structure plan may be written at a number of levels, each of increasing complexity, as the logical structure of the program is developed. A first-level structure plan might be a simple statement of the problem: 1. Initialize Fahrenheit temperature 2. Calculate and display Celsius temperature 3.
Step 1 is pretty straightforward. Step 2 needs elaborating, so the second-level plan could be something like this: 1. Initialize Fahrenheit temperature F 2. Display the value of C 4. The essential point is to cultivate the mental discipline of getting the problem logic clear before attempting to write the program.
The top-down approach of structure plans means that the overall structure of a program is clearly thought out before you have to worry about the details of syntax coding. This reduces the number of errors enormously. A script to implement this is as follows: Two checks of the tool were done. The results were found to be correct and hence this simple script is, as such, validated. The essense of any structure plan and, hence, any computer program can be summarized as follows: 1.
Input: Delclare and assign of input variables. Operations: Solve expressions that use the input variables. Output: Display in graphs or tables the desired results. Air resistance is ignored. We would like to compute the value of s over a period of about The structure plan for this problem is as follows: This plan may seem trivial and a waste of time to write down.
It is well worth developing the mental discipline of structure-planning your program first. Paste a second copy of the plan directly below the first. Finally, paste all the translated MATLAB statements into the Command Window and run them or you can just click on the green triangle in the toolbar of the Editor to execute your script. If necessary, go back to the Editor to make corrections and repaste the cor- rected statements to the Command Window or save the program in the Editor as an M-file and execute it.
This is called an array operation and is different from squaring the vector itself, which is a matrix operation, as we will see later. You might want to save the program under a helpful name, like throw. This way, the plan reminds you what the program does when you look at it again after some months.
After you block selected text, right-click to see the context menu. To comment the text, scroll down to Comment, point, and click. Expressions are constructed from a variety of things, such as numbers, variables, and operators. First we need to look at numbers. For example, 1. This is also called floating-point notation. The number has two parts: The mantissa, which may have an optional decimal point 1. Mantissa and exponent must be separated by the letter e or E.
The mantissa is multiplied by the power of 10 indicated by the exponent. Note that the following is not scientific notation: 1. On computers using standard floating-point arithmetic, numbers are repre- sented to approximately 16 significant decimal digits. The relative accuracy of numbers is given by the function eps, which is defined as the distance between 1. Enter eps to see its value on your computer.
As an exercise, enter the following numbers at the command prompt in scien- tific notation answers follow in parentheses : 1. More information on data types can be found in the Help index. MATLAB also supports signed and unsigned integer types and single-precision floating-point, by means of functions such as int8, uint8, single, and the like. However, before mathematical operations can be performed on such types, they must be converted to double precision using the double function.
The arithmetic operations on two scalar constants or variables are shown in Table 2. Operators operate on operands a and b in the table. Left division seems a little curious: Divide the right operand by the left oper- and. However, matrix left division has an entirely different meaning, as we will see later.
The precedence rules for the operators in Table 2. Note that parentheses have the highest precedence. Note also the difference between parentheses and square brackets. The former are used to alter the precedence of operators and to denote subscripts, while the latter are used to create vectors. When operators in an expression have the same precedence, the operations are carried out from left to right. Table 2. The value 1 is added to each element of the vector In this con- text, the addition is called an array operation because it operates on each ele- ment of the vector array.
Array operations are discussed below. Try: ' The 5 is transposed first into itself since it is a scalar , and then a row vector is formed. They are sometimes called array or element-by-element operations because they are per- formed element-by-element. For example, a. You will have seen that a. Now try [2 3 4].
The ith element of the first vector is raised to the power of the ith element of the second vector. The period dot is necessary for the array operations of multiplication, division, and exponentiation because these operations are defined differently for matrices; they are then called matrix oper- ations see Chapter 6.
When array operations are applied to two vectors, both vectors must be the same size! Array operations also apply between a scalar and a nonscalar. Check this with 3. This property is called scalar expansion. Multiplication and division operations between scalars and nonscalars can be written with or without the period i.
A common application of element-by-element multiplication is finding the scalar product also called the dot product of two vectors x and y, which is defined as: Table 2. Add 1 to each element of the vector [2 3 -1]. Multiply each element of the vector [1 4 8] by 3. Answer: [0 -2 3] 2. Square each element of the vector [2 3 1]. If an expression is terminated with a semicolon ; , its value is not displayed, although it is still returned by ans.
Assignment always works in this direction. This is useful for suppressing irritating output of intermedi- ate results or large matrices. Statements may involve array operations, in which case the variable on the left- hand side may become a vector or a matrix. However, it is helpful to think of commands as changing the general environment in some way, for example, load, save, and clear. Statements do the sort of thing we usually associate with programming, such as evaluating expressions and car- rying out assignments, making decisions if , and repeating for.
Let us again consider, as an example, the calculation of compound interest. The following program comp. The operation in the statement described in bullet item 1 is such that every element in the vector B is deter- mined by operating on every element of vector A all at once, by interpreting once a single command line. See if you can adjust the program comp.
Hint: use a vector for n: [1 5 10 15 20]. The numerical answers are in parentheses. Can you spot the errors in the following expression? You need to think through the process carefully. The best approach is to develop a formula to convert x acres to hectares.
Convert 6. You can also use disp to display a message enclosed in apostrophes called a string. Apostrophes that are part of the message must be repeated: disp 'Pilate said, ''What is truth? If we want to display a string, we create it; that is, we type a message between apostrophes. This we have done already in the above example by defining the string 'The answer is '. Note that the last space before the second apostrophe is part of the string.
This is very useful when displaying large matrices, for example, rand ,7 see help more for details. You can begin your search for infor- mation by clicking the question mark at the top of the desktop to open the help documents. Then search for fopen, a utility which allows you to open a file. Scroll to the bottom of the page in the help manual on this topic and find the following list of functions: fclose, feof, ferror, fprintf, fread, fscanf, fseek, ftell, fwrite.
Click on fprintf, which is a formatted output utility that is popular if you are a C-language programmer. Of course, the simplest input of data is the assignment of values to variables in a program of commands. How- ever, if the integer is too large, it is displayed in scientific notation with five significant digits— is displayed as 1.
Check this by first entering at the command line and then If the value x is in the range 0. Check this by entering the following numbers at the prompt on separate lines : 0. You can change from the default with variations on the format command, as follows. If you want values displayed in scientific notation floating-point form whatever their size, enter the command: format short e All output from subsequent disp statements will be in scientific notation, with five significant digits, until the next format command is issued.
Enter this com- mand and check it with the following values: 0. If you want more accurate output, you can use format long e. This also gives scientific notation but with 15 significant digits. Use format long to get fixed-point notation with 15 significant digits. Use format bank for financial calculations; you get fixed point with two deci- mal digits for cents. Suppress irritating line feeds with format compact, which gives a more compact display.
Use format hex to get hexadecimal display. Use format rat to display a number as a rational approximation ratio of two integers. Note that even this is an approximation! Try out format rat on 2 and e exp 1. In certain appli- cations this is a convenient way of displaying matrices. The command format by itself reverts to the default format. In this example, the common scale factor is , so the elements displayed must all be multiplied by it to get their proper value—for example, for the second element 1.
Taking a factor of out of the third element 1e-4 leaves 1e-7, which is represented by 0. In this section we look at a new feature: repetition. This is implemented by the extremely power- ful for construct. We will first look at some examples of its use, followed by explanations. The disp statement is repeated five times, three times, and not at all. This is an iterative repetitive procedure that refines an initial guess. Here is the structure plan: 1. Initialize a 2.
Most computers and calculators use a similar method internally to compute square roots and other standard mathematical functions. Run the following program to generate a list of n and n! You had better leave out the disp statement! Or you can move it from above the end command to below it. The following example also highlights a problem that sometimes occurs when computing a limit.
The question is this: What is the limit of this sequence as n gets indefinitely large? If we try to compute xn directly, we can get into trou- ble, because n! Each time through the loop it will contain the next element of the vector j:k or j:m:k, and statements there may be one or more are carried out for each of these values. This value is called the iteration or trip count.
Note that if the iteration count is negative, the loop is not executed. It is basically a counter. In fact, if the index does appear explicitly in statements, the for can often be vectorized more details on this are given in Section 2. A simple example of a more efficient faster program is as follows. In this case i is assigned as a vector hence, this change vectorizes the original program.
You may have noticed that the Editor does this for you auto- matically with a feature called smart indenting. If you leave them out you will get an error message. Nothing will happen until you do so. The index moves through each element of the vector in turn, providing a neat way of processing each item in a list.
Other forms of the for loop as well as the while loop will be discussed in Chapter 8. There are situations where a for loop is essential, as in many of the examples in this section so far. If you have written a for loop that involves the index of the loop in an expression, it may be pos- sible to vectorize the expression, making use of array operations where neces- sary, as the following examples show. Thus, t0 records when the calculation starts.
The function etime returns the time in seconds elapsed between its two argu- ments, which must be vectors as returned by clock. If you have a faster PC, it should take less time. Now try to vectorize this calculation before looking at the solution. Here it is: This way takes only 0.
Once again, try to vectorize the sum: The same PC gives a time of about 0. Of course, the computation time in these examples is small regardless of the method applied. However, learning how to improve the effi- ciency of computation to solve more complex scientific or engineering prob- lems will be helpful as you develop good programming skills. More details on good problem-solving and program design practices are introduced at the end of this chapter and dealt with, in more detail, in the next.
Series with alternating signs are a little more challenging. You should get 0. Not bad. For example, prod 1:n will find n! Time both versions in each case. Repeat a few times—cut and paste from the Command History window make sure that a new r is generated each time. The if construct, which is fundamental to all comput- ing languages, is the basis of such decision making.
The simplest form of if in a single line is: if condition; statements; end Note the following points: n condition is usually a logical expression i. The relational operators are shown in Table 2. If the expression evaluates to 0, it is regarded as false; any other value is true.
This is not generally recommended; the if statement is easier to understand for you or a reader of your code , if condition is a logical expression. The value 1 for true is therefore assigned to x. After executing these commands type the command whos to find that the variable x is in the class of logical variables. What about g? Finally, if you try: if 79 disp 'true' , else disp 'false' , end do you get true?
Try other values, including 0 and some negative values. Most banks offer differential interest rates. The Random Bank goes one step further and gives you a random amount in your account to start with! Run the following program a few times: Display the values of bal and rate each time from the command line to check that MATLAB has chosen the correct interest rate.
The basic form of if-else for use in a program file is: Note that: n statementsA and statementsB represent one or more statements. It works as follows: 1. If it is true, statementsB are executed, followed by the statement after end. In this way, all conditions are tested until a true one is found. If none of the conditions is true, statements after else are executed. Arrange the logic so that not more than one of the conditions is true. There can be any number of elseifs, but at most one else.
It is good programming style to indent each group of statements as shown. Note the double equal sign in the test for equality; see Chapter 5 for more on logical operators. This saves a lot of computing time and is easier to read if the if construct is in a loop that is repeated often. Using this form, instead of the elseif ladder, you can make the following common mistake: Can you see why you get the wrong answer instead of if bal has the value ?
When designing the logic, you need to make sure that one and only one of the conditions will be true at any one time. However, whatever the value of bal, this condition will always be true. Can you see why? This is called nesting and should not be confused with the elseif ladder. You have to be careful with elses. In general, else belongs to the most recent if that has not been ended. The correct positioning of end is therefore very important, as the next example demonstrates.
Suppose you want to compute the solution to a quadratic equation. Your program could contain the following nested ifs: The else belongs to the second if by default, as intended. The result is that else belongs to the firstif instead of to the second one. Division by zero is therefore guaranteed instead of prevented!.
You may be wondering if for statements enclosing ifs can be vectorized. The answer is yes, courtesy of logical arrays. Discussion of this rather interesting topic is postponed until Chapter 5. In this example it is used to decide whether a random integer is 1, 2, or 3 see Section 5. However, it is useful to know what they are since the square root of a negative number may come up as a mistake if you are trying to work only with real numbers.
The imaginary part of a complex number may also be entered without an asterisk, 3i. Some functions are specific to complex numbers. If z is a complex number, real z , imag z , conj z , and abs z all have the obvious meanings.
Try the following: Note these points: n If y is complex, the statement plot y is equivalent to plot real y , imag y n The statement axis 'equal' is necessary to make circles look round; it changes what is known as the aspect ratio of the monitor. For complex matrices, the operations ' and. It can be accessed through the Help button? In other words, it is a program. The statements are carried out when the script file name is entered at the prompt in the Command Window.
A script file name must have the. Script files are therefore also called M-files. The output from the script will then appear in the Command Window. Only the first 63 characters are significant. All variables created during a session remain in the workspace until removed with clear. The command who lists the variables in the workspace; whos gives their sizes.
Clicking a variable in it invokes the Array Editor, which may be used to view and change variable values. Elements are sepa- rated by spaces or commas. Rows are separated by semicolons. The colon operator is used to generate vectors, with elements increasing decreasing by regular increments decrements. Vectors are row vectors by default. Use the apostrophe transpose operator ' to change a row vector into a column vector. A subscript may itself be a vector. Subscripts always start at 1.
The default numeric type is double precision. All mathematical operations are carried out in double precision. They operate according to rules of precedence. A semicolon after an expression suppresses display of its value. The array operations of multiplication, right and left division, and exponentiation are indicated by. They may be used to evaluate a formula repeatedly for some or all of the elements of a vector. This is called vectorization of the formula.
If the index of a for statement is used in the expression being repeated, the expression can often be vectorized, saving a great deal of computing time. Any expression that evaluates to zero is regarded as false. Any other value is true. The elseif ladder is a good way to choose between a number of options, only one of which should be true at a time. Write a script that inputs this volume in gallons and pints and converts it to liters. Answer: Now try to add tangents in the fourth column.
Try some variations of the format command. Answer: 10, 2. The marks are out of Try it on the following: Hint: Use the mean function. Can you do even better by vectorizing the code? Can you figure out what it is? Now rewrite the script using vectors and array operations. Draw up a table of the values of i, j, and m to show how they change while the script executes.
Compute the value of I. Answer: 0. Write a program that enters the following five consumptions into a vector and uses a for loop to calculate and display the total charge for each one: , , , , Write a program to compute and print the balance each month for a year.
Write a program that uses a for loop to compute the balance after a year of compounding interest in this way. Chapter exercises 81 2. Answer: Values in the last row of output should be 12, 0. Write a program to compute and display the population every ten years from to Try to plot a graph of the population against time as well Figure 7. Use the built-in function log for the natural logarithm ln. This is a big advantage of MATLAB and tools like it ; it allows you to customize your working environment to meet your own needs.
In the first part of this chapter we discuss the design process. In the second part we examine the structure plan—the detailed description of the algorithm to be implemented. We will consider relatively simple programs. However, the pro- cess described is intended to provide insight into what you will confront when you deal with more complex engineering, scientific, and mathematical prob- lems during the later years of your formal education, your life-long learning, and your continuing professional education.
In the third part we introduce the basic construct of a MATLAB function to help you develop more sophisticated programs. To be sure, the examples examined so far have been logically simple. To de- sign a successful program you need to understand a problem thoroughly and break it down into its most fundamental logical stages.
In other words, you have to develop a systematic procedure or algorithm for solving it. There are a number of methods that may assist in algorithm development. In this chapter we look at one, the structure plan. Its development is the primary part of the software or code design process because it is the steps in it that are translated into a language the computer can understand—for example, into MATLAB commands.
There are numerous toolboxes available through MathWorks among others on a variety of engi- neering and scientific topics. A great example is the Aerospace Toolbox, which provides reference standards, environmental models, and aerodynamic coef- ficients which can be imported for advanced aerospace engineering designs. Certainly, you want to be sure that the tools you save are reasonably well writ- ten i.
What does it mean to create well-written programs? The goals in designing a software tool are that it works, it can easily be read and understood, and, hence, it can be systematically modified when required. For programs to work well they must satisfy the requirements associated with the problem or class of problems they are intended to solve.
The specifications i. That is, all options should be usable without error within the limits of the specifications see Figures 3. The program must be readable and hence clearly understandable. Thus, it is useful to decompose major tasks or the main program into subtasks or subprograms that do specific parts of it.
Each subtask should be designed so that it can be evaluated independently before it is imple- mented in the larger scheme of things i. A well written code, when it works, is much more easily evaluated in the testing phase of the design process. If changes are necessary to correct sign mistakes and the like, they can be easily implemented. One thing to keep in mind when you add comments to describe the process programmed is this: Add enough comments and references so that a year from the time you write the program you know exactly what was done and for what purpose.
Note that the first few comment lines in a script file are displayed in the Command Window when you type help followed by the name of your file file naming is also an art. The design process1 is outlined next. The steps may be listed as follows: Step 1: Problem analysis. The context of the proposed investigation must be established to provide the proper motivation for the design of a computer program. The designer must fully recognize the need and must develop an understanding of the nature of the problem to be solved.
Develop a detailed statement of the mathematical problem to be solved with a computer program. Step 3: Processing scheme. Define the inputs required and the outputs to be produced by the program. Step 4: Algorithm. This list of tasks is the structure plan and is written in pseudo-code i. The goal is a plan that is understandable and easily translated into a computer language. Step 5: Program algorithm.
Translate or convert the algorithm into a computer language e. Step 6: Evaluation. Test all of the options and conduct a validation study of the program. For example, compare results with other programs that do similar tasks, compare with experimental data if appropriate, and compare with theoretical predictions based on theoretical methodology related to the problems to be solved.
The objective is to determine that the subtasks and the overall program are correct and accurate. The additional debugging in this step is to find and correct logical errors e. Step 7: Application. Solve the problems the program was designed to solve. If the program is well designed and useful, it can be saved in your working directory i. Let us consider the projectile problem examined in first-semester physics. It is assumed that engineering and science students understand this problem if it is not familiar to you, find a physics text that describes it or search the Web; the formulas that apply will be provided in step 2.
In this example we want to calculate the flight of a projectile e. We want to determine the trajectory of the flight path and the horizontal distance the projectile or object travels before it hits the ground. Let us assume zero air resistance and a constant gravitational force acting on the object in the op- posite direction of the vertical distance from the ground.
We want to determine the time it takes the projectile, from the start of motion, to hit the ground, the horizontal distance traveled, and the shape of the trajec- tory. In addition, we want to plot the speed of the projectile versus the angular direction of this vector. We need, of course, the theory or mathematical ex- pressions that describes the solution to the zero-resistance projectile problem in order to develop an algorithm to obtain solutions to it.
Step 2. The mathematical formulas that describe the solution to the projectile problem are provided in this step. Then the maximum values of the altitude and the range are computed along with their respective arrival times.
Vx We must keep in mind when we study the solutions based on these formulas that the air resistance was assumed negligible and the gravitational accelera- tion was assumed constant. Step 3. The outputs are the range and time of flight, the maximum altitude, and the time it is reached, and the shape of the trajectory in graphical form.
Steps 4 and 5. The algorithm and structure plan developed to solve this prob- lem are given next as a MATLAB program, because it is relatively straightforward and the translation to MATLAB is well commented with details of the approach applied to its solution i. This plan, and M-file, of course, is the summary of the results developed by trying a number of approaches during the design process, and thus discarding numerous sheets of scratch paper before summarizing the results! There are more explicit examples of structure plans for your review and investigation in the next section of this chapter.
Keep in mind that it was not difficult to enumerate a list of steps associated with the general design process, that is, the technical problem solving. However, it is certainly not so easy to imple- ment the steps because they draw heavily on your technical-solution design experience.
Hence, we must begin by studying the design of relatively simple programs like the one described in this section. The program was evaluated by executing a number of values of the launch angle and launch speed within the required specifications. This is well known for the zero air re- sistance case in a constant g force field.
How can you find additional examples of MATLAB programs good ones or otherwise to help develop tools to solve your own problems? There are also many examples of use- ful scripts that are placed on the Web for anyone interested in them. This responsibility holds for all tools applied by the engineer and the scientist. Hence, it is very important just as in using a laboratory apparatus that users prove to themselves that the tool they are using is indeed valid for the problem they are trying to solve.
To check that it works, type each line in the Command Window followed by Enter. Note the position of each graphic; location is determined by the three integers in the subplot function list of arguments. Search Help via the question mark? Exercise In this example a structure plan to solve the quadratic equation is given. A structure plan of the complete algorithm for finding the solution s x, given any values of a, b, and c, is shown in Figure 3.
Figure 3. Use cut and paste to make another copy of the plan below the first one, and translate the second copy into MATLAB state- ments. If it is a good structure plan, it should translate line for line. A function M-file is similar to a script file in that it also has a. However, a function M-file differs from a script file in that a function M-file communicates with the MATLAB workspace only through specially designated input and output argu- ments.
Functions are indispensable tools when it comes to breaking a problem down into manageable logical pieces. Short mathematical functions may be written as one-line inline objects. This capa- bility is illustrated by example in the next subsection.
Further details on writing functions are provided in Chapter 7. For example: Note that the input values of x and y can be arrays and, hence, the output f1 will be an array of the same size as x and y. The construction of a function file starts with the dec- laration of a function command. This is followed by the formula that is the function of interest that you wish to substitute a particular value of x to get the corresponding value of y.
The structure plan for the evaluation of a particular algebraic function is as follows: The function M-file created based on this plan is as follows: It was saved as f. After saving it, it was used as follows in the Command Window. Try the following example: Let us create a function that takes as input the three coefficients of the qua- dratic equation.
We want the output to be the two roots of the quadratic equa- tion, i. One way of dealing with the known solutions of the quadratic equation is to create a function file based on the structure plan already described. The two roots in this case are real.
It is a useful exercise to test all possibilities to evaluate whether or not this function successfully deals with all quadratic equations with constant coefficients. The purpose of this example was to il- lustrate how to construct a function file. Note that the only variables in the Workspace are the coefficients a b c. The variables defined and needed in the function are not included in the Workspace. Carry out the plan by sketching the construction: 1. Draw two perpendicular x- and y-axes 2.
Display M 4. Give the output. Test it on the data in Exercise 2. Chapter exercises 99 3. Use the structure plan in Figure 3. Your script should be able to handle all possible values of the data a, b, and c. The structure plan in Figure 3. Adjust your script so that it can also find complex roots. The program should input the coefficients a, b, c, d, e, and f. However, it is good for the development of your programming skills to do it the long way, as in this exercise.
Plot y versus t for t from 0 to 10 in increments of 0. This shape is called a uniform catenary. However, more interesting problems in science and engineering are likely to involve special mathematical functions like sines, cosines, loga- rithms, and so on. In addition, you may wish to import data to be plotted or operated on mathematically, and export data for future use.
It also discusses the exporting of data to files in your work directory for later use with MATLAB or with other software tools. A short list of some of the more common ones follows. Alternatively, go to the Help browser by clicking the Help icon? Search for Alphabetical List of Functions. Note that if the argument of a function is an array, the function is applied ele- ment by element to all the values in the array, e. It is also, to some extent, expected that you already know, from your first courses in mathematics and science, something about these functions.
One way to examine these functions is to plot them. For example, do the following exercise for all functions of the assigned variable x, as illustrated next. You should get an illustration that looks like a V.
Note how the hours, minutes, and seconds are left-filled with zeros if necessary. Let us consider the arc-cosine, the arc-sine, and the arc- tangent functions, i. If you specify x, i. To provide an answer, the following M-file script was created and executed. The graphical comparison of the computed results is illustrated in Figure 4. The process of moving data between MATLAB and disk files is called import- ing from disk files and exporting to disk files.
Binary format is more efficient in terms of storage space required. Also search for the topic import wizard or type, in the Command Window, help uiimport. You can use tabs instead of spaces by specifying the -tabs qualifier instead of -ascii. If you save character arrays strings in this way, the ASCII codes of the characters are written to the file. If the array A has been saved in myData. You can cre- ate it in a text editor, or it could be created by any other program that exports data in ASCII format.
Note: n If no variables are listed the entire workspace is saved. Chapter exercises 4. Write a script to input a length in metres which may have a decimal part and convert it to yards, feet, and inches. Check: 3. The program displays every member xn computed. Adjust it to display only every 10th value of xn. Hint: the expression rem n, 10 will be zero only when n is an exact multiple of Use this in an if statement to display every 10th value of xn.
Write a script which inputs a number of minutes and converts it to hours and minutes. Now write a script to convert seconds into hours, minutes, and seconds. The plan must specify the number and type of all notes and coins in the change, and should in all cases give as few notes and coins as possible. If you are not familiar with dollars and cents, use your own monetary system.
The topic is so useful and, hence, important that it deserves vectors Subscripting with Try these exercises on the command line: logical vectors Enter the following statements: Using any and all It should return the value 1. Can you see why 0 0 0 1 0 is returned? When a vector is involved in a logical expression, the comparison is carried out element by element as in an arithmetic operation.
If the comparison is true for a particular element of the vector, the resulting vector, which is called a logical vector, has a 1 in the corresponding position; otherwise it has a 0. The same applies to logical expressions involving matrices. You can also compare vectors with vectors in logical expressions. The following script plots the graph, shown in Figure 5. Element-by-element multiplication by y with. A neat way around this problem is to use a logical vector to replace the zero with eps.
If you are not too hot at trig graphs, perhaps you should sketch the graph roughly with pen and paper before you run the script! The scale on the MATLAB plot is therefore very large about , making it impos- sible to see the structure of the graph anywhere else. Work out the following problem on the command line: 1. Now use a similar statement to count how many elements of r are greater than or equal to 0.
Since rand generates uniformly distributed random numbers, you would expect the number of random numbers which are less than 0. Generate a vector of a few thousand random numbers suppress display with a semi-colon this time and use a logical vector to count how many are less than 0. Repeat a few times with a new set of random numbers each time. Because the numbers are random, you should never get quite the same answer each time.
Here is the program: It also takes a lot longer. Compare times for the two methods on your computer. Discarding the decimal part of this expression with floor gives an integer in the required range. Verify your result by displaying d. Estimate the probability of throwing a six by dividing the number of sixes thrown by Using random numbers like this to mimic a real situation based on chance is called simulation.
Repeat with more random numbers in the vector d. The more you have, the closer the proportion of sixes gets to the theoretical expected value of 0. Can you see why it would be incorrect to use round instead of floor? The problem is that round rounds in both directions, whereas floor rounds everything down.
Table 5. The OR operator is technically an inclusive OR, because it is true when either or both of its operands are true. See Help on ops. The precedence levels of the logical operators, among others, are shown in Table 5. As usual, precedences may be overridden with brackets, e. It is surprising because: a. If you have got this far you deserve to be let into a secret. MATLAB is based on the notorious language C, which allows you to mix different types of operators in this way Pascal, for example, would never allow such flexibility!
The explanation is due partly to the resolution of surprise a. The complete operator precedence is given in Table 5. It simply churns through the expression accord- ing to its rules which may not be what you expect. Suppose r has the value 0.
Mathematically, the inequality is true for this value of r since it lies in the required range. The script in Section 5. In general, if x and v are vectors, where v has n elements, then x v means: [x v 1 , x v 2 , The function logical v returns a logical vector, with elements which are 1 or 0 according as the elements of v are non-zero or 0. A summary of the rules for the use of a logical vector as a subscript are as follows: n A logical vector v may be a subscript of another vector x.
What will: a logical [1 1 1 0 0] return? And what about a logical [0 0 0 0 0]? Logical vector subscripts provide an elegant way of removing certain elements from a vector, e. However, the numeric vector [0 0 1 1 1] is not a logical vector; the statement: islogical [0 0 1 1 1] returns 0. Examples are given in the following list where x is a vector unless otherwise stated. See Help on logical functions. If you don't want to compile gcc8 on every machine, just compile it once and then install it on all the machines.
There should be clear instructions for those who want to disable GCC from the pkgbuild. Otherwise toolboxes cannot be installed using the Add-on Explorer. I have discovered a bug using kernel Restarting the app allows me to use it again however clicking out of it again replicates the bug. Let me know what further details you would need.
The following changes since commit db1 :. Added instructions on how to download the license file and installation key if the license is provided by an organization and MATLAB is being installed for the first time on a PC. You can get gcc8 binaries by adding the arch4edu repository.
This is not a minimal package; if you don't want gcc integration, you can install matlab through other methods. I ran this on an i7 desktop with 16GB RAM and it choked the machine trying to compile gcc8 for over an hour, but it did complete successfully. I then tried on a lower spec laptop and it aborted with gcc compile errors after about 20 minutes.
Could you say what are the advantages of using gcc8? I will edit this comment once I resolve these issues, and what I did. I am able to start matlab with zero problems now provided I use the -softwareopengl flag when running matlab. Please note that I can reproduce the error by not including the flag - I will add this as an alias so I dont need to type it every time. Building any AUR package requires the dependencies installed.
That is what dependency is. For this package; it's not enough that you have all the dependencies installed locally, but you need to provide the three aforementioned files in the README in the build directory. I can start matlab without a desktop environment so I will look into what is going on there, thanks.
I suggest getting acquainted, but there should be no issues installing gcc8 using an aur helper. Try running matlab -nodesktop from a terminal; and if you get to the console that means it has something to do with your graphical desktop. I don't know how to resolve your issue, never encountered it. That or install matlab locally in your home folder using only the mathworks installer and see if it works. The build seemed successful however once I run the matlab file I get an empty grey text box with the window title "Error Starting Desktop", not even the only button I'm assuming says close has text.
I am not very sure what you mean by "in the presence of either or both llvm-libs and gcc-libs would solve the problem" since I don't think it's quite possible to remove package "llvm-libs" or even "gcc-libs". Perhaps I misunderstood your words. But I do not know whether this will affect matlab loading gcc8 libs. If that was an issue; I would have the same issue, but I don't. I assume the presence of either or both llvm-libs and gcc-libs would solve the problem?
On the PC that the built installable pkgbuild won't work; first install llvm-libs, try to open, then remove llvm-libs and install gcc-libs, try to open, then install llvm-libs again and try to open. Then could you report? If you give it green light; I'll add the necessary packages as dependencies. I also encountered billypilgrim's problem. Or, in other words, the current version of llvm-libs requires a higher version of gcc-libs than gcc8-libs to properly function.
I think the problem could be fixed if the updated lib path can be excluded for OpenGL, but I do not know how to achieve this. I don't have issues with amdgpu and this pkgbuild. And here's the error message I get within the matlab GUI once it's loaded: com. Read the readme. Rename your installer dir to something else, download to a folder called matlab and tar it there. I managed to make it work using this.
Edit: I have my license. Do I need any other files from somewhere before this package will work? Cloning matlab build files Checking matlab dependencies Resolving dependencies Checking inter-conflicts Building matlab Failed to build matlab. I'm on a zen2 microarchitecture AMD Ryzen 7 x and it works fine. It probably is something else related specifically to your desktop.
If you are not using it already; I suggest installing amd-microcode and making sure your bootloader loads the related ramdisk before loading initrd. Either way; you can build the package on your server; copy the tar. Please post this in mathworks forums; as anyone else on other linux distros having the same problem can benefit from your experience; or help diagnose what exactly is going wrong. Strangely enough, I copied exact same files to my arch server and it runs. I guess that architecture issue still persists on this version and I'm running my desktop on AMD zen2.
I've installed the latest update and it seemed to go without any hitches apart from having to re-activate Matlab afterwards. Many thanks bbaserdem! Everything I've tested works fine apart from Matlab's built-in updater which notifies me about an update but always fails during the installation with the message "Something unexpected occured".
I'm guessing it's some kind of permissions error but not really sure. Has anybody else managed to use it successfully? I would check mathworks forums for a fix; as if the provided installer is not working on your system it's an issue on the installer end. I can't replicate your issue so I don't know how to help you. Seems to be a matlab installer issue. Cannot install even with their default installer. Generate a "archive is not a ZIP archive" error but last one has this issue is way back to a.
No idea what's going wrong there. Not really, I created the tar bar exactly as the md instructed. However, the downloaded matlab folder does not have that file in the first place. I assume this is a problem with the way you created the tar file; did you follow the instructions as exactly stated in the README provided by the repo?
I would delete the one you have and recreate the needed files. Do you have this file in your downloaded matlab folder? What is that installer? I can't help if you are not being specific. There should be some installer log somewhere; but I don't know where the installer puts it. Your problem is not due to python; because anything to do with python is printed on stdout when you run makepkg.
That is the thing, I don't actually know whats wrong with that installer, it does not have any log. I don't even know how to debug this, I might need to do some chroot to mimic makepkg and go through build steps one by one. I built this package just fine; with the up to date versions of dependencies. And everything works. So curious as to what is not working.
I ran into the same Python issue and I "backported" the Python 3. Matlab installed and I was able to start a Matlab engine from an iPython shell, so I would suspect it works. I even installed the Update 3 as root after Matlab told me I could do that from the little bell icon menu and it still works. It seems gcc8 was submitted to AUR a month after I installed the package. I'll also change the gcc version when I fix the python issue.
However; the line you are reporting should work; as I installed using the previous version before. I do remember making a few typos that made the package not build but I recall not committing them but perhaps I did? So for that, you are on your own. If you people rather not deal with this; you can remove the matlab-engine-for-python from depends array manually; and remove any build instructions for python integration.
Year and matlab still does not respect a quick version check on their launcher matlab script. Again I apologize for the delay in updating the package; but I'm not going to push any changes until I can confirm that everything works; and I need access to my PC before that. I tried swapping the Build function from the makepkg version bbaserdem mentioned a , which seems to have fixed that error but now I'm getting a different, generic build error:. I change gcc9 to gcc and it just works!
As for the python3. But I use anaconda, and I make it use python provided by anaconda. And I have to use the legacy installation script, or it will fail. I have a fix for the python 3. If you feel confident; you can dig out the fix in the PKGBUILD commit history; i believe either b or a versions were using an outdated version of python and I had the fix for either one of the versions.
If not; I ask for patience until I get back home to make sure the spoofing works before i publish. The installer for matla-engine-for-python doesnt currently support python 3. Any clues where this is installed? Followed the Readme and installation finished without errors. From the supported compiler page, it seems that GCC 8.
X is better supported and the supported gfortran version seems to be only 8. Running the check on the build machine also would require activating MATLAB on the build machine which introduces other problems. That is why I did not include the check function originally when I created the package. I think having an additional script that tests the MATLAB installation on the target machine is probably the way to go. Of course this is extra work but it would resolve questions like the one by rellieberman.
If you install the created package on a machine that is different than the licensed one, you won't be able to run the package. There are absolutely no files distributed through the AUR; this is just an installation script. This is not meant to be portable due to how the EULA works; you are not supposed to port it anywhere. However; what you can do is you can run this package on some computer B; but prepare the outlying package to be installed on computer A.
As long as you keep your copies to yourself; you are fully within the EULA. Robustness wise; this is the recommended installation procedure from the MATLAB website regarding installing without an active internet connection so that I don't agree with; it's the proper way to do so.
The check function is a good suggestion for things like compatible python version and whatnot, I'll see what I can come up with based on your suggestion. Hardware tests would not be good practice; as there is no guarantee that the computer that will run the built package is the same as the one doing the packaging; not to mention the makepkg user usually does not have access to hardware interfaces.
Not to mention not all hardware will support every feature can't run gpu array on one of my PC's, hardware acceleration and audio is disabled on my server, not everyone wants all the features, etc. Maintenance wise; I have seen this package neglected over the past few years.
While i'm working at the lab I'm in for another year and while I actively use Arch as my desktop distribution; I am planning on maintaining this package and won't share maintenance with someone else unless I can trust them. But I will most likely maintain it for another year, a year and a half at most, and then pass it on to someone with motivation to provide.
I think the package would benefit from a check function or an extra script that checks the installation. I would incrementally add dependencies until the package would pass those tests. I do not have a license for newer versions of MATLAB, so can no longer maintain the package or really help with the tests.
I'll run it myself once it's OK for me to do so when i'm not actively using matlab and free time In the meantime; anyone wishing to skip libselinux installation can try removing from the dependency array for now. Thanks for the quick response. I would just point out that the installer ran fine on my system without libselinux. Is there anything I could test to help make sure it works?
I installed very few of matlabs components so maybe it's needed for some other component. You don't need to set it up. It is also listed as a dependency in the docker build images. I can double check if everything works fine without libselinux for b and remove it if it doesnt break less aur dependencies, the better ; but previously with a on arch; the installer would not run without libselinux which was confounding as there was no documentation on that dependence and installer.
Their official supported distro is Ubuntu; and I assume Ubuntu has libselinux by default. Even if the main binary does not need it; you need to run the installer yourself at least once; so i consider that as a dependency. Does anyone know why libselinux is a dependency? I have just installed this package without the selinux dependency and all seems to be working fine. Seem like quite an overhead to have to install selinux just to run matlab. I replaced the name with mcc-matlab so it should not happen.
If you can confirm it works fine that would be great. Matlab version: 9. This is for the latest matlab version b; not a; a does not work with with python 3. Sorry for the message spam; but brought the pkgbuild up to b. It works with all the features I tested with hardware acceleration, jupyter notebook using python engine, gui using bspwm. If anyone is using this PKGBUILD; please let me know if compilation works switched to native libraries Also; gcc6 is let go in favor of gcc9; which is in the community repos so you can drop the aur dependency.
As this is flagged out of date since half a year, I would kindly ask greyltc to add bbaserdem as a comaintainer as proposed below. Would it be possible to add the file type associations and icons to the script? In the installation directory of the Windows version there are 25 icons for different filetypes.
If there is a way of auto-extracting these from the Linux installer that would be great. Even just. I tried matching the dependency list with all the packages in the dockerfile. Most of the debian packages are in the arch repos; or at least AUR, but the versions referanced on the dockerfile are older than arch versions. A lot of these dependencies are probably not needed; but I don't want to test what works and what breaks one-by-one.
Still I can install just fine. Do note that matlab installer does need libselinux to run; and is needed to generate the tar. Echoing what japm48 said, Ra has a new installer which depends on libselinux to run.
Also, I think Mathworks changed some other stuff because, unlike previous versions, once installed I didn't have to change Matlab's glib symlinks to point to system libraries to get the add-ons manager to work. For the record: I found the missing dependency by executing.
Error downloading sources: matlab. Apologies I don't get around to updating this too often. If you'd like to help maintain it, let me know and I can add you as a co-maintainer. The install instructions in the wiki look mostly okay though I haven't followed them to check that , but hopefully you should just be able to get by with reading my notes in the PKGBUILD its self.
Error: This folder name is invalid. The destination folder cannot be named "private". You need the complete iso. You can then use those files along with the contents of the. I'm having issues installing this. I got the fik and lic files and the latest zip from Mathworks, but when running makepkg -si it terminates with the following error:. Oct 31, Exiting with status -2 Oct 31, End - Unsuccessful. I am not, I am just creating a local tarball of matlab, so I can distribute it easily on my 4 archlinux installations.
But knowing the file structure for the tarball is a godsent. A typical matlab tarball look like this:. I was wondering if anyone had any issues installing Rb. I'm trying to create the tar file using the installer, but it looks like the toolboxes are installed somewhere i dont know.
I used to install to a directory called faux, and cancelled the moment toolboxes finished, then merged the two directories. Not working this time around, Im getting missisng file warnings on the installer. I tried looking for guides regarding creating the tar but nada.
Can anyone help out? Verificato ncurses And gcc6 in AUR is gcc 6. For non-network installations, installation from a purchased DVD for example, nowhere will provide this matlab. Now gcc6 is removed from the official repositories. It makes the current way, which is the solution 1, is acceptable now.
So you can keep them. License files are really complicated. You can have per user license files and per machine license files. Activation is really stupid, as far as I could determine all it does is download the license file and copy it to the required directory 9it probably tell TMW lots of stuff also. I don't quite understand your point, user just need to provide matlab. As for mex, should I remove the unused library files, and set mex opt? You didn't answer me directly. Why matlab.
How could these users even get this file to run makepkg? About mex. But it is acceptable for matlab since it cannot be re-distributed. It should be left to the user to decide and set via makepkg. Not all of use package and then install. In these cases, the carezy long compression time is worth it to reduce the download bandwidth.
Really wish I had a license for a new version. Trying to get some of the older versions to work is a dependency hell. I would much rather figure out the new dependencies and be done with it. It looks like Darcy Hu made a modification that fixed the issue. As for the mex compiler issues. I have been told by TMW that higher versions are not supported. That said, I could never find a test case that failed with a higher version. As for the dependencies, it is a real nightmare. I spent a lot of time starting with a clean chroot and only the base group installed and slowly added dependencies until I could get MATLAB to start.
Then I tested things like plotting, sound, the doc viewer, opengl, cuda, etc. You still need a license file from you administrator if you use network installation. For non-network installation, we could automate activate after installation. For mex support with libs issue, you could use higher version of compilers, though it's not officially supported.
I think it's clear enough, user need to prepare a tarball matlab. I don't see such problem. Because it will take a lot of time to compress the package and then you will extract it just after the compression. That would leave only a single aur dependency. There is a matlabb package seperately in aur. Either untar into a directory named matlab then tar -cvf matlab.
It behaves almost as same as your current one, except splitting the keys to a new package. Hi all, I create a repo in Github. I remove all dependencies, install all products available by default, and no desktop entry is provided.
I gonna add a desktop entry to wiki. I'm not sure if other activating method would work. So after installation, one still need to activate matlab. I just download it from school website our school buy licenses.
Here we go The full form of Matlab is Matrix Laboratory, which one of the best coding languages that are used for technical and scientific computations. This programming language includes an environment for data visualization, computations, and logic codings. It also includes inbuilt error debugging and editing tools, and it can support the idea of object-oriented programming OOP.
These parameters make Matlab great use and use these tools for academic research and teaching. You might be familiar with the concept of Matlab, and its basic operation, data types, and loops. This post will provide you the details of the switch case in Matlab.
The switch case statement is used to control the flow logic that can be used extensively. You can use several alternatives using the If, If-else statements. This statement can make the code lengthy and debug and not easy to read. Switch case statement helps the programmers to select the number of options that makes the code easy to read, less time-consuming, but the way of implementation can be varied.
Each option is called a case. Here the true statement means the condition must satisfy the statement:. As you have the idea about the syntax of the switch case in Matlab , now the flow diagram will make it easier to understand. If you go through with each statement block, then you can understand the working processor of the switch case statement.
It is the power of the flow diagram and why it is necessary to teach the complications of the programming. Using the flow diagram, you can frame your design and logics of error-free coding before actually writing it on the system. The switch case statement is used to execute the set of the statement s that are based on the criteria of the various choices.
Each of the options is covered with the case statement. The C switch construct allows for execution to go through many case groups before its execution halts. In C, we can use break statements to control the execution. The idea, however, is different in MATLAB, where switch construct executes one case group only and hence it does not need break statements.
This example does a very simple job. The core idea is to pass through a switch statement and print message based on some condition. We create a basic logic of matching the number and providing an output based on the number. In this example of Switch Statement in Matlab, based on the grade obtained, we classify the distinction.
After running, it will display Excellent Performance as the chosen grade in the first line of code is A. Replace that A with B and run again, you will get the output as Well-done Performance. So, based on the grade selected, the distinction comes, and all of this could be done is about 10 lines of code. Imagine doing the same user if-else logic and the code will be much longer and will contain many additional conditional statements.
Students are advised to learn and practice code as much as possible. This shall ensure that concepts are well understood, and students are feeling confident about writing error-free code. If there are any specific questions or if they run into errors while executing code they can comment on this article or get in touch for further clarification.
For more examples and case studies using switch statements, students are advised to use google search or look into the official MATLAB documentation. It is always good to refer to official documentation as it provided comprehensive discussion and a lot of edge cases for relevant scenarios.
This has been a guide to Switch Statement in Matlab. Here we discussed the basic concepts, working, flow diagram with some examples of Switch Statement in Matlab. You can also go through our other suggested articles to learn more —. By signing up, you agree to our Terms of Use and Privacy Policy.
Submit Next Question. Forgot Password? 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.
Popular Course in this category.
Accordingly, you full SQL on the your script, spam lists. Enter your point, eM. Both also offer more XP, max expansions to current functions.
Следующая статья city navigator north america torrent 2016