Using logical operators and conditional statements

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See the previous section for that. Because arithmetic and logical binary operations in matlab operations are so similar to the equivalent mathematical operations, a basic knowledge of linear algebra is mandatory to use matlab effectively.

However, we won't be as precise as in mathematics when using the terms vector and matrix. However, there are special functions just for vectors; see the vector module for an explanation of how to use these. Now that you know how to define a simple array, you should know how to access its elements. Accessing the content of an array is done through the operatorwith the index inside the parenthesis; the indexing of the first element is To access a single matrix element, you can use the i,j subscript, where i is the index in the row, and j in the column:.

You can also access a matrix element through a unique index; in this case, the order is column arithmetic and logical binary operations in matlab, meaning you first go through all elements of the first column, then the 2d column, etc The column major mode is the same as in Fortran, and the contrary of the order in the C language. It is also possible to access blocks of matrices using the colon: This operator is like a arithmetic and logical binary operations in matlab it tells MATLAB that you want all elements of a given dimension or with indices between two given values.

For example, say you want to access the entire first row of matrix a above, but not the second row. Then you can write:. Now say you only want the first two elements in the first row. To do this, use the following syntax:. Finally, if you do not know the size of an array but wish to access all elements from a certain index until the end of the array, use the end operator, as in.

In addition to index addressing, you can also access only elements of an array that satisfy some logical criterion. Then you can achieve this arithmetic and logical binary operations in matlab two ways. The first is to use the find function to find the indices of all numbers between 2 and 4 in the array, and then address the array with those indices:.

The second method is to use logical addressing, which first changes a into a logical array, with value 1 if the logical expression is true and 0 if it is false. It then finds and returns all values in the a which are true. The syntax for this is as follows:. The interesting part is of course applying some operations on those arrays. Multiplication and division are more problematic: It makes sense only in the matrix context.

If you desire to multiply or divide two matrices or vectors component-wise, or to raise all components of one matrix to the same power, rather than using matrix definitions arithmetic and logical binary operations in matlab these operators, you can use the dot. The two matrices must have the same dimensions. For example, for multiplication. As matlab is a numerical computing language, you should keep in mind that a matrix which is theoretically invertible may lead to precision problems and thus giving imprecise results or even totally wrong results.

The message above "matrix is singular to working precision" should appear in those cases, meaning the results cannot be trusted. This is especially useful in least square problems. The same boolean operators that can arithmetic and logical binary operations in matlab used for point values can also be used to compare arrays. To do this, MATLAB compares the elements componentwise and returns them in a logical array of the same size as the two arrays being compared. The two arrays must have the same size.

You must be careful when using comparisons between arrays as loop conditions, since they clearly do not return single values and therefore can cause ambiguous results. The loop condition should be reducable to a single boolean value, T or F, not an array. Two common ways of doing this are the "any" and the "all" functions. A function call any array will return true if array contains any nonzero values and false if all values are zero.

It does the comparisons in one direction first then the other, so to reduce a matrix you must call the any function twice. The function allsimilarly, returns true if and only if all elements in a given row or column are nonzero.

Horizontal concatenation is done by treating an array as if it were a variable included in a row. Vertical concatenation is done by treating an array as if it were a variable included in a column.

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Another key concept in programming is the ability to test a conditional statement and make decisions about the flow of the program based on the truth value of the statement. Examples of such statements are "Is A equal to B?

To formulate the above questions, we will use binary operators that take two arguments 'A' and 'B' in the above examples and returns a value of "true" or "false". In Matlab, "true" is integer 1 and "false" is the integer 0. The binary operators that we will find use in comparing numeric values are called "relational operators", and are given here. Matlab interprets this by evaluating from left to right. Writing the same expression using parenthesis, it is perhaps clearer how Matlab is evaluating this expression.

The expression in the parenthesis evaluates to true , which Matlab stores are the integer value 1. The next conditional statement checks to see if m is less than 0, and of course it is not. These relational tests, when used with Matlab arrays, produce another array whose entries are '0' where the relational test is false, and '1' where the relational statement is true. These arrays in turn can be used to index into the original array and mask certain elements. For example, we can pull out only the positive entries of x:.

We can use this array to selectively set entries in x to different values depending on the masking array. Where these logical statements become useful is when they can be used to control the flow of a program. For example, suppose you wanted to divide one number by another number. You might first check to see that the divisor is not equal to 0. As a more complex example, we determine whether a quadratic polynomial has 0, 1 or two real roots, and whether the parabola opens up or down.

In the above, we had conditional statements checking to see whether a real number is equal to 0. In general, it is not a good idea to check for exact equality when compare the values of two real numbers.

Consider the following example. In finite precision arithmetic, we cannot compute the exact value of the function cos x. We can also use conditional statements in arrays. In this case, we have to come up with a single truth value for the logical array, and as a result, we must be very careful about how we use logical arrays in conditional statements.

For example, consider the following code fragment:. You might think that this sets negative entries in x to and positive entries to But in fact, all it does is set the array x to the scalar value The first statement x will only be true if all entries of x are negative. Since we probably have a mix of both positive and negative entries, the code will set x to the scalar value Sometimes, you may want to know the indices of the entries in an array that meet some criteria. For example, suppose we wanted to know where the first non-zero number in an array occurs.

The Matlab find function will return for us an array of indices at which some logically array is set to true. The array idx contains the indices of the positive entries. If no entries are found meeting the criteria, then find returns an empty array. In this lab, you will practice using conditional statements. Use a mask to find all the entries in the vector x that are between Plot the following discontinuous function over the interval [-5,5].

Be sure to include any end point conditions. Use only an array 'mask' to select points to include in each piece. Do you want to try the above code fragments on your own? Download the Matlab script that produces this page here.

Back to tutorial index Using logical operators and conditional statements Topics in this lab Logical operators Using logical operators with arrays Conditional statements Using arrays in conditional statements Using the Matlab 'find' function Lab exercises.

Logical operators Another key concept in programming is the ability to test a conditional statement and make decisions about the flow of the program based on the truth value of the statement. A Here are some simple examples illlustrating the use of relational or "logical" operators.

Back to the top Using logical operators with arrays These relational tests, when used with Matlab arrays, produce another array whose entries are '0' where the relational test is false, and '1' where the relational statement is true. For example, we can pull out only the positive entries of x: Or, we can pull out only the negative entries of x: Back to the top Conditional statements Where these logical statements become useful is when they can be used to control the flow of a program.

The real roots are: Back to the top Using arrays in conditional statements We can also use conditional statements in arrays. For example, consider the following code fragment: Back to the top Using the Matlab 'find' function Sometimes, you may want to know the indices of the entries in an array that meet some criteria. Back to the top Lab exercises In this lab, you will practice using conditional statements.