Tuples and Nested Lists

Transcription

1 stored in hash 1 2 stored in hash 3 and 4 MCS 507 Lecture 6 Mathematical, Statistical and Scientific Software Jan Verschelde, 2 September 2011

2 and stored in hash 1 2 stored in hash 3 4

3 stored in hash tuples are composite structures; e.g, a pair: >>> b = (3, a ) (3, a ) >>> type(b) <type tuple > Tuple assignment is nice for swapping: >>> x = 3; y = 4 >>> (x,y) = (y,x) >>> x 4 >>> y 3 page 3

4 stored in hash tuples have fixed length are good for storing coordinates of points, for example triplets for points in 3-space: >>> A (3, 2, 1) Some operations on tuples: >>> 3 in A True >>> len(a) 3 >>> str(a) (3, 2, 1) >>> B = (A[1],A[2], go ); B (2, 1, go ) page 4

5 stored in hash type conversions There is no append on a tuple, but we may convert a tuple to a list, append and then convert back. Converting string list tuple: >>> s = hello >>> L = [c for c in s] >>> L [ h, e, l, l, o ] >>> tuple(l) ( h, e, l, l, o ) >>> list(l) [ h, e, l, l, o ] >>> reduce(lambda x,y:x+y,l) hello page 5

6 stored in hash Instead of >>> x = 1; y = 2; z = 3 alternative assigments we can store names and values as tuples: >>> names = ( x, y, z ) >>> values = (1,2,3) >>> T = zip(names,values) >>> T [( x, 1), ( y, 2), ( z, 3)] Pairs of names and values give an alternative to the assignment operation. page 6

7 and stored in hash 1 2 stored in hash 3 4

8 stored in hash >>> names = ( x, y, z ) >>> values = (1,2,3) >>> L = zip(names,values); L [( x, 1), ( y, 2), ( z, 3)] >>> D = dict(l) >>> D { y : 2, x : 1, z : 3} dictionaries A dictionary is a set of key:value pairs. The type of the key needs to admit an order. >>> D[ x ] 1 >>> D[ y ] = 5.4; D { y : , x : 1, z : 3} page 8

9 stored in hash hash >>> units = {} >>> units[ kilo ] = 10**3 The initialization as {} is important. Alternative: units = { kilo :10**3 }. >>> units[ mega ] = 10**6 >>> units { mega : , kilo : 1000} To convert dictionaries to lists: >>> units.values() [ , 1000] >>> units.keys() [ mega, kilo ] are like hash. The order is determined internally to allow for fast lookup. page 9

10 stored in hash Some rules for differentiation: rule based programming storing rules in dictionaries >>> D = { sin(x) : cos(x), \... cos(x) : -sin(x) } To prevent evaluation, the keys and values are strings. Applying the rules = consulting the dictionary. >>> D[ sin(x) ] cos(x) >>> D[ cos(x) ] -sin(x) page 10

11 stored in hash differentiation and integration For differentiation and integration, using sympy: >>> from sympy import * >>> var( x ) x >>> diff(sin(x),x) cos(x) >>> integrate(cos(x),x) sin(x) >>> integrate(cos(x),(x,0,pi/2)) 1 For the definite integral, the 2nd argument is a tuple. page 11

12 stored in hash symbols in sympy After var( x ) we can do >>> x x >>> type(x) <class sympy.core.symbol.symbol > >>> x.name x >>> x.is_symbol True We can see the namespace with vars(): >>> vars()[ x ] x With var( x ) we unassign a variable. page 12

13 stored in hash Differentiation and integration in Sage: using Sage sage: var( x ) x sage: diff(cos(x),x) -sin(x) sage: integrate(cos(x),x) sin(x) sage: integrate(cos(x),(x,0,pi/2)) 1 Variables are stored in a dictionary: sage: vars <built-in function vars> sage: help(vars) page 13

14 and stored in hash 1 2 stored in hash 3 4

15 plotting a saddle stored in hash page 15

16 stored in hash lists of lists >>> s = lambda x,y: (x-5)**2 - (y-5)**2 >>> A = [[s(i,j) for j in xrange(10)]... for i in xrange(10)] >>> import pprint # for pretty printing >>> pprint.pprint(a) [[0, 9, 16, 21, 24, 25, 24, 21, 16, 9], [-9, 0, 7, 12, 15, 16, 15, 12, 7, 0], [-16, -7, 0, 5, 8, 9, 8, 5, 0, -7], [-21, -12, -5, 0, 3, 4, 3, 0, -5, -12], [-24, -15, -8, -3, 0, 1, 0, -3, -8, -15], [-25, -16, -9, -4, -1, 0, -1, -4, -9, -16], [-24, -15, -8, -3, 0, 1, 0, -3, -8, -15], [-21, -12, -5, 0, 3, 4, 3, 0, -5, -12], [-16, -7, 0, 5, 8, 9, 8, 5, 0, -7], [-9, 0, 7, 12, 15, 16, 15, 12, 7, 0]] >>> A[5][5] 0 page 16

17 stored in hash numpy arrays >>> from numpy import * >>> B = array(a) >>> print B [[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]] >>> B[5,5] 0 >>> B[5] array([-25, -16, -9, -4, -1, 0, -1, -4, -9, -16]) page 17

18 stored in hash numpy.fromfunction >>> from numpy import * >>> s = lambda x,y: (x-5)**2 - (y-5)**2 >>> C = fromfunction(s,(10,10)) >>> print C [[ [ [ [ [ [ [ [ [ [ >>> type(c[0,0]) <type numpy.float64 > page 18

19 stored in hash transpose of lists of lists Rows in the list of lists A become columns: >>> At = [[A[j][i] for j in xrange(len(a[i]))]... for i in xrange(len(a))] >>> pprint(at) [[0, -9, -16, -21, -24, -25, -24, -21, -16, -9], [9, 0, -7, -12, -15, -16, -15, -12, -7, 0], [16, 7, 0, -5, -8, -9, -8, -5, 0, 7], [21, 12, 5, 0, -3, -4, -3, 0, 5, 12], [24, 15, 8, 3, 0, -1, 0, 3, 8, 15], [25, 16, 9, 4, 1, 0, 1, 4, 9, 16], [24, 15, 8, 3, 0, -1, 0, 3, 8, 15], [21, 12, 5, 0, -3, -4, -3, 0, 5, 12], [16, 7, 0, -5, -8, -9, -8, -5, 0, 7], [9, 0, -7, -12, -15, -16, -15, -12, -7, 0]] page 19

20 stored in hash A saddle point in a A is 1 maximal in its row; and computing saddle points 2 minimal in its column. The index of the maximum in reach row: >>> M = [row.index(max(row)) for row in A] >>> M [5, 5, 5, 5, 5, 5, 5, 5, 5, 5] The index of the minimum in each column (transpose of A): >>> m = [col.index(min(col)) for col in At] >>> m [5, 5, 5, 5, 5, 5, 5, 5, 5, 5] We find one saddle point at (5,5). page 20

21 and stored in hash 1 2 stored in hash 3 4

22 stored in hash DBM are standard in the Python library. >>> import anydbm >>> libdb = anydbm.open( library, c ) opened a new dbm with read-write access (flag = c ) >>> d = { author : Lantangen, title : A Primer \... on Scientific Programming with Python } >>> libdb[ 0 ] = str(d) >>> libdb.keys() [ 0 ] keys and values must be of type string >>> libdb.keys() [ 0 ] >>> D = eval(libdb[ 0 ]) >>> type(d) <type dict > >>> D[ author ] Lantangen page 22

23 stored in hash adding and selecting >>> import anydbm >>> mylib = anydbm.open( library, c ) >>> mylib.keys() [ 0 ] >>> mylib[ 1 ] = str({ author : Miller & Ranum,... title : Python Programming }) >>> eval(mylib[ 1 ])[ author ] Miller & Ranum Some other operations: >>> len(mylib) 2 >>> mylib.has_key( 1 ) 1 >>> mylib.has_key( 2 ) 0 page 23

24 DBM file operations stored in hash Python code import anydbm f = anydbm.open( n, c ) f[ key ] = value value = f[ key ] count = len(f) found = f.has_key( key ) del f[ key ] f.close() description load module anydbm create or open dbm file with name n assign value for key load value for key number of entries stored see if entry for key remove entry for key close dbm file Typical use: every record in base has unique key values are dictionaries, stored as strings page 24

25 stored in hash Summary + Exercises We ended chapter 2 of the text book. Exercises: 1 A plateau in a list is the longest sequence of the same elements that occur in the list. Write a Python script that reads a list and prints the start and end index of a plateau in a given list. 2 Make a dictionary D for the ASCII code of the upper case letters, for A to Z, e.g.: D[ R ] == Use a dictionary to write numbers in words (as needed to write a check). Write a script that prompts the user for a dollar amount and that prints the corresponding value in words. page 25

26 more exercises stored in hash 4 Store the information 1 US dollar = euros in a dictionary D and show how to use D for currency conversion. Use a nested dictionary E (dictionary of dictionaries) to store conversion rates, e.g.: E[ US dollar ][ euro ] stores Give Python commands to use anydbm to store antiderivation rules for common trigonometric functions. The first homework is due on Wednesday 7 September. Bring to class your answers to exercise 3 of Lecture 1; exercises 1, 2 of Lecture 2; and exercises 1, 3 of Lecture 3. page 26