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Modeling 2D Arrays for Optimizing Biological Systems

Learn how to manipulate 2D arrays for biological system optimization using Python with Joel Grodstein at Tufts University. Explore array indexing, copying, looping, and advanced techniques.

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Modeling 2D Arrays for Optimizing Biological Systems

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  1. EE 194/BIO 196: Modeling,simulating and optimizing biological systems Spring 2018 Tufts University Instructor: Joel Grodstein joel.grodstein@tufts.edu 2D arrays

  2. Arrays so far • We’ve already used arrays – but just in “1D” • HW1 = np.array([90,99,60,90]) • HW1[0]=90 • HW1[3]=60 • One homework, four students • Next up: add an extra dimension (so, “2D”) • Use an egg carton again 90 99 60 90 [0] [1] [2] [3] EE 194/Bio 196 Joel Grodstein

  3. 2D arrays • Think of a 2D array as a table of numbers • 3 homeworks, 4 students • Each row is a homework • Each column is a student • How do I access it? • HW[0,2] is 60 • HW[1,2] is 55 • HW[2,1] is • How do I build it? • HW = np.array ([[90,99,60,90],[91,80,55,93],[89,80,99,93]]) [0] [1] [2] 90 99 60 90 91 80 55 93 89 80 99 93 [0] [1] [2] [3] 80 EE 194/Bio 196 Joel Grodstein

  4. 2D arrays • Another way to build it: • HW = np.zeros ((3,4)) • HW[0,0:4] = [90,99,60,90] [0] [1] [2] 90 99 60 90 0 0 0 0 0 0 0 0 0 0 0 0 [0] [1] [2] [3] EE 194/Bio 196 Joel Grodstein

  5. 2D arrays • Another way to build it: • HW = np.zeros ((3,4)) • HW[0,0:4] = [90,99,60,90] • HW[1,:] = [91,80,55,93] • (just “:” means the whole row) [0] [1] [2] 90 99 60 90 91 80 55 93 0 0 0 0 0 0 0 0 [0] [1] [2] [3] EE 194/Bio 196 Joel Grodstein

  6. Reading 2D arrays • Read it as usual: • print (HW[0,0:4]) • print (HW[1,:]) • print (HW[2,:]) [0] [1] [2] 90 99 60 90 91 80 55 93 0 0 0 0 [0] [1] [2] [3] [90,99,60,90] [91,80,55,93] [0,0,0,0] EE 194/Bio 196 Joel Grodstein

  7. More slice access • HW[1,1:] • HW[1:3,2] • HW[1:3,2:] [0] [1] [2] 90 99 60 90 80 55 93 91 80 55 93 0 0 0 0 55 [0] [1] [2] [3] 0 55 93 0 0 EE 194/Bio 196 Joel Grodstein

  8. Modify one element • Assume we’ve set HW[2,:]=[89,80,99,93] • HW[1,2]=90 • HW[2,0]=50 • HW[3,0] = 80 • error [0] [1] [2] 90 99 60 90 91 80 93 90 55 89 80 99 93 50 [0] [1] [2] [3] EE 194/Bio 196 Joel Grodstein

  9. Still more slice access • copy a row • HW[2,:] = HW[1,:] • copy two columns • HW[:,2:4] = HW[:,0:2] [0] [1] [2] 90 99 60 90 91 80 55 93 89 80 99 93 [0] [1] [2] [3] [0] [1] [2] 91 80 55 93 90 99 60 90 91 80 55 93 89 80 99 93 90 99 91 80 [0] [1] [2] [3] 89 80 EE 194/Bio 196 Joel Grodstein

  10. Remember our problem with arrays? a1 = np.array ([2,4,6]) a2 = a1 a2[1]=1 print (a2) print (a1) a1 = np.array ([2,4,6]) a2 = np.array ([2,4,6]) a2[1]=1 print (a2) print (a1) We’ll learn more strategies to beat this problem later [2, 4, 6] Now a2=[2, 4, 6] [2, 1, 6] [2, 1, 6] Now we have two different egg cartons [2, 1, 6] “Later” has now arrived [2, 4, 6] EE 194/Bio 196 Joel Grodstein

  11. Copying an array a1 = np.array ([2,4,6]) a2 = np.array ([2,4,6]) a2[1]=1 print (a2) print (a1) • And this works just as well with 2D arrays. • We’ll use it in the Manduca HW Now we have two different egg cartons a1.copy() [2, 1, 6] [2, 4, 6] EE 194/Bio 196 Joel Grodstein

  12. Looping through an array • Remember how we looped through an array? ar = np.array ([1,3,5]) for i in ar: • What happens if we loop through a 2D array? ar = np.array ([[1,3,5],[11,13,15]]) for i in ar: • What if you want to loop through every element of a 2D array? ar = np.array ([[1,3,5],[11,13,15]]) for i in ar.flat: i becomes 1, 3 and then 5 i becomes [1,3,5] and then [11,13,15] i becomes 1, 3, 5, 11, 13 and finally 15 EE 194/Bio 196 Joel Grodstein

  13. Advanced indexing • Python has advanced indexing capabilities that mirror Matlab • HW [ HW<65] += 10 • HW [2, HW[2,:]>90] = 0 [0] [1] [2] 70 90 99 60 90 65 91 80 55 93 89 80 99 93 0 0 [0] [1] [2] [3] EE 194/Bio 196 Joel Grodstein

  14. Advanced indexing Advanced indexing can build a 2D array from elements of a 1D array: ar_1D = np.array ([2,4,6,8]) indices = np.array ([[1,1][2,3]]) ar_2D = ar_1D [indices] It can also do the reverse: ar_1D = ar_2D [ [0,1,1], [0,1,0] ] 4 4 6 8 4 8 6 EE 194/Bio 196 Joel Grodstein

  15. Group exercise • Given: two arrays ar1 and ar2 • Each one is 10 rows and 4 columns • Build an array ar3 that has even rows from ar1, odd from ar2 • Make sure that changing ar3 will not change ar1 or ar2 • Lookahead: this will be similar to a genetic algorithm EE 194/Bio 196 Joel Grodstein

  16. Another group exercise • Given: one 10x4 array ar1 • Pick a random pair of rows (e.g., rows 0&1) • Replicate it forwards (i.e., so rows 2&3 become identical to 0&1) • Make sure not to try to copy, e.g., rows 7&8 to rows 9 & 10 • Since there is no row #10! • (This maybe useful for genetic mutations) EE 194/Bio 196 Joel Grodstein

  17. Follow-up activities • Try the examples from this lecture yourself • Vary them, or even mis-type some to see what happens • More exercises. Write a program that… • Creates an NxN array with 1 on the border and 0 inside • Creates an 8x8 array and fills it with a checkerboard pattern • Finds the indices of the maximum and minimum values in a 2D array • Creates an NxN cyclic matrix [[0 1 2 3 4] [1 2 3 4 0][2 3 4 0 1] ...]. Then double every element and print it. • Prints the odd columns of a 2D array EE 194/Bio 196 Joel Grodstein

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