If c is also a real number the MAT LAB command acb or acb generates a row

If c is also a real number the mat lab command acb or

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(although we can’t imagine why you would want to do it this way). If c is also a real number the MAT- LAB command >> [a:c:b] or >> a:c:b generates a row vector where the difference between successive elements is c . Thus, we can generate num- bers in any arithmetic progression using the colon operator. For example, typing >> [18:-3:2] generates the row vector (18 , 15 , 12 , 9 , 6 , 3). while typing >> [ pi : -.2*pi : 0 ] generates the row vector ( π, . 8 π, . 6 π, . 4 π, . 2 π, 0). Warning: There is a slight danger if c is not an integer. As an oversimplified example, entering >> x = [.02 : .001 : .98] should generate the column vector (0 . 02 , 0 . 021 , 0 . 022 , . . ., 0 . 979 , 0 . 98) T . However, because of round-off errors in storing floating-point numbers, there is a possibility that the last element in x will be 0 . 979. The MATLAB package was written specifically to minimize such a possibility, but it still remains. We will discuss the command linspace which avoids this difficulty in sec- tion 4. An easy “fix” to avoid this possibility is to calculate x by >> x = [20:980] /1000 2.3. Manipulating Matrices For specificity in this subsection we will mainly work with the 5 × 6 matrix E = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 , which can be generated by >> E = [ 1:6 ; 7:12 ; 13:18 ; 19:24 ; 25:30 ] Note: Spaces will frequently be used in MATLAB commands in this subsection for readability. You can use the colon notation to extract submatrices from E . For example, >> F = E( [1 3 5] , [2 3 4 5] ) extracts the elements in the first, third, and fifth rows and the second, third, fourth, and fifth columns of E ; thus, F = 2 3 4 5 14 15 16 17 26 27 28 29 . This possiblity is much more real in the programming language C. For example, the statement for ( i = 0.02; i <= 0.98; i = i + .001 ) generates successive values of i by adding 0 . 001 to the preceding value. It is possible that when i should have the value 0 . 98, due to round-off errors the value will be slightly larger; the condition i <= 0.98 will be false and the loop will not be evaluated when i should be 0 . 98. 21
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2.3. Manipulating Matrices You can generate this submatrix more easily by typing >> F = E( 1:2:5 , 2:5 ) There is an additional shortcut you can use: in a matrix a colon by itself represents an entire row or column. For example, the second column of F is F(:,2) and the second row is F(2,:) . To replace the second column of F by two times the present second column minus four times the fourth column enter >> F(:,2) = 2*F(:,2) - 4*F(:,4) And suppose you now want to double all the elements in the last two columns of F . Simply type >> F(:,3:4) = 2*F(:,3:4) Entering E(:,:) prints out exactly the same matrix as entering E . This is not a very useful way of entering E , but it shows how the colon operator can work. On the other hand, entering >> G = E( : , 6:-1:1 ) generates a matrix with the same size as E but with the columns reversed, i.e., G = 6 5 4 3 2 1 12 11 10 9 8 7 18 17 16 15 14 13 24 23 22 21 20 19 30 29 28 27 26 25 .
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  • Fall '13
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