MATLAB Tutorial Chapter 2 Programming Structures 2 1 for loops Programs for numerical simulation often involve repeating a set of commands many times In MATLAB we instruct the computer to repeat a block of code by using a for loop A simple example of a for loop is for i 1 10 repeats code for i 1 2 10 i print out the value of the loop counter end This ends the section of code that is repeated The counter can be incremented by values other than 1 for i 1 2 10 disp i end This example shows that the counter variables takes on the values 1 3 5 7 9 After 9 the code next tries i 11 but as 11 is greater than 10 is not less than or equal to 10 it does not perform the code for this iteration and instead exits the for loop for i 10 1 1 disp i end As the value of the counter integer is changed from one iteration to the next a common use of for blocks is to perform a given set of operations on different elements of a vector or a matrix This use of for loops is demonstrated in the example below Complex structures can be made by nesting for loops within one another The nested for loop structure below multiplies an m x p matrix with a p x n matrix A 1 2 3 4 11 12 13 14 21 22 23 24 A is 3 x 4 matrix B 1 2 3 11 12 13 21 22 23 31 32 33 B is 4 x 3 matrix im size A 1 m is number of rows of A ip size A 2 p is number of columns of A in size B 2 n is number of columns of B C zeros im in allocate memory for m x n matrix containing 0 s now we multiply the matrices for i 1 im iterate over each row of C for j 1 in iterate over each element in row for k 1 ip sum over elements to calculate C i j C i j C i j A i k B k j end end end C print out results of code A B MATLAB s routine does the same thing clear all 2 2 if case structures and relational operators In writing programs we often need to make decisions based on the values of variables in memory This requires logical operators for example to discern when two numbers are equal Common relational operators in MATLAB are eq a b returns 1 if a is equal to b otherwise it returns 0 eq 1 2 eq 1 1 eq 8 7 8 7 eq 8 7 8 71 When used with vectors or matrices eq a b returns an array of the same size as a and b with elements of zero where a is not equal b and ones where a equals b This usage is demonstrated for the examples below u 1 2 3 w 4 5 6 v 1 2 3 z 1 4 3 eq u w eq u v eq u z A 1 2 3 4 5 6 7 8 9 B 1 4 3 5 5 6 7 9 9 eq A B this operation can also be called using 1 2 1 1 8 7 8 7 8 7 8 71 ne a b returns 1 if a is not equal to b otherwise it returns 0 ne 1 2 ne 1 1 ne 8 7 8 7 ne 8 7 8 71 ne u w ne u v ne u z ne A B another way of calling this operation is to use 1 2 1 1 8 7 8 7 8 7 8 71 lt a b returns 1 if a is less than b otherwise it returns 0 lt 1 2 lt 2 1 lt 1 1 lt 8 7 8 71 lt 8 71 8 7 lt 8 7 8 7 another way of performing this operation is to use 1 2 1 1 2 1 le a b returns 1 if a is less than or equal to b otherwise 0 le 1 2 le 2 1 le 1 1 le 8 7 8 71 le 8 71 8 7 le 8 7 8 7 this operation is also performed using 1 1 1 2 2 1 gt a b returns 1 if a is greater than b otherwise 0 gt 1 2 gt 2 1 gt 1 1 gt 8 7 8 71 gt 8 71 8 7 gt 8 7 8 7 this operation is also performed using 1 2 1 1 2 1 ge a b returns 1 if a is greater than or equal to b otherwise 0 ge 1 2 ge 2 1 ge 1 1 ge 8 7 8 71 ge 8 71 8 7 ge 8 7 8 7 this operation is also performed using 1 1 1 2 2 1 These operations can be combined to perform more complex logical tests logic1 logic2 returns 0 unless both logic1 and logic2 are not equal to zero 1 1 8 7 8 7 1 2 8 7 8 7 1 2 8 71 8 7 1 2 8 7 8 71 1 2 8 7 8 71 i1 1 i2 0 i3 1 i1 i1 i1 i2 i2 i1 i2 i2 i1 i3 1 1 8 7 8 7 1 2 1 1 8 7 8 7 1 2 This operation can be extended to multiple operations more easily by using the command all vector1 that returns 1 if all of the elements of vector1 are nonzero otherwise it returns 0 all i1 i2 i3 all i1 i1 i3 or logic1 logic2 returns 1 if one of either logic1 or logic2 is not equal to zero or if they are both unequal to zero or i1 i2 or i1 i3 or i2 i2 This operation can be extended to more than two logical variables using the command any vector1 that returns 1 if any of the elements of vector1 are nonzero otherwise it returns 0 any i1 i2 i3 any i2 i2 i2 any i1 i2 i2 i2 Used less often in scientific computing is the exclusive or construction xor logic1 logic2 that returns 1 only if one of logic1 or logic2 is nonzero but not both xor i1 i1 xor i2 i2 xor i1 i2 We use these relational operations to decide whether to perform a block of code using an if structure that has the general form logictest1 0 logictest2 1 logictest3 0 if logictest1 disp Executing block 1 elseif logictest2 disp Executing block 2 elseif logictest3 disp Executing block 3 else disp Execute end block end The last block of code is executed if none of the ones before it has been performed logictest1 0 logictest2 0 logictest3 0 if logictest1 disp Executing block 1 elseif logictest2 disp Executing block 2 elseif logictest3 disp Executing block 3 else disp Execute end block end An if loop will not execute 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