1. EE 194/BIO 196: Modeling,simulating and optimizing biological systems
Spring 2018
Tufts University
Instructor: Joel Grodstein
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))
[0]
[1]
[2] 90 99 60 90
[0] [1] [2] [3]
EE 194/Bio 196 Joel Grodstein

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

8. Modify one element Assume we’ve set HW[2,:]=[89,80,99,93] HW[1,2]=90
error
[0]
[1]
[2] 90 99 60 90 91 80 55 90 93 50 89 80 99 93
[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 91 80 55 93 80 55 93 89 80 99 93
[0] [1] [2] [3]
[0]
[1]
[2] 90 90 99 91 80 89 99 60 90 91 80 55 93 89 80 99 93
[0] [1] [2] [3]
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) a2 = np.array ([2,4,6]) 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])
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]])
What if you want to loop through every element of a 2D array?
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] 90 99 70 60 90 91 80 65 55 93 89 80 99 93
[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 may be 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 [[ ] [ ][ ] ...]. Then double every element and print it.
Prints the odd columns of a 2D array
EE 194/Bio 196 Joel Grodstein