Numpy. Luis Pedro Coelho. October 22, Programming for Scientists. Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (1 / 26)

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1 Numpy Luis Pedro Coelho Programming for Scientists October 22, 2012 Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (1 / 26)

2 Historical Numeric (1995) Numarray (for large arrays) scipy.core (briefly, around 2005) numpy (2005) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (2 / 26)

3 Currently numpy 1.6 de facto standard very stable Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (3 / 26)

4 Basic Type numpy.array or numpy.ndarray. Multi-dimensional array of numbers. Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (4 / 26)

5 numpy example import numpy a s np A = np. array ( [ [ 0, 1, 2 ], [ 2, 3, 4 ], [ 4, 5, 6 ], [ 6, 7, 8 ] ] ) p r i n t A[ 0, 0 ] p r i n t A[ 0, 1 ] p r i n t A[ 1, 0 ] Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (5 / 26)

6 Some Array Properties import numpy a s np A = np. array ( [ [ 0, 1, 2 ], [ 2, 3, 4 ], [ 4, 5, 6 ], [ 6, 7, 8 ] ] ) p r i n t A. shape p r i n t A. s i z e Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (6 / 26)

7 Some Array Functions... p r i n t A. max( ) p r i n t A. min ( ) max(): maximum min(): minimum ptp(): spread (max - min) sum(): sum std(): standard deviation Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (7 / 26)

8 Other Functions np.exp np.sin All of these work element-wise! Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (8 / 26)

9 Arithmetic Operations import numpy a s np A = np. array ( [ 0, 1, 2, 3 ] ) B = np. array ( [ 1, 1, 2, 2 ] ) p r i n t A + B p r i n t A * B p r i n t A / B Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (9 / 26)

10 Broadcasting Mixing arrays of different dimensions import numpy a s np A = np. array ( [ [ 0, 0, 1 ], [ 1, 1, 2 ], [ 1, 2, 2 ], [ 3, 2, 2 ] ] ) B = np. array ( [ 2, 1, 2 ] ) p r i n t A + B p r i n t A * B Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (10 / 26)

11 Broadcasting Special case: scalar. import numpy a s np A = np. arange ( 100 ) p r i n t A + 2 A += 2 Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (11 / 26)

12 Data Types numpy.ndarray is a homogeneous array of numbers. Types Boolean integers floating point numbers Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (12 / 26)

13 Object Construction import numpy a s np A = np. array ( [ 0, 1, 1 ], f l o a t ) A = np. array ( [ 0, 1, 1 ], bool ) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (13 / 26)

14 Reduction A = np. array ( [ [ 0, 0, 1 ], [ 1, 2, 3 ], [ 2, 4, 2 ], [ 1, 0, 1 ] ] ) p r i n t A. max( 0 ) p r i n t A. max( 1 ) p r i n t A. max( ) prints [2,4,3] [1,3,4,1] 4 The same is true for many other functions. Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (14 / 26)

15 Slicing import numpy a s np A = np. array ( [ [ 0, 1, 2 ], [ 2, 3, 4 ], [ 4, 5, 6 ], [ 6, 7, 8 ] ] ) p r i n t A[ 0 ] p r i n t A[ 0 ]. shape p r i n t A[ 1 ] p r i n t A[ :, 2 ] Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (15 / 26)

16 Two minute break Talk to your neighbours Play around in Python Ask questions Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (16 / 26)

17 Slices Share Memory! import numpy a s np A = np. array ( [ [ 0, 1, 2 ], [ 2, 3, 4 ], [ 4, 5, 6 ], [ 6, 7, 8 ] ] ) B = A[ 0 ] B[ 0 ] = - 1 p r i n t A[ 0, 0 ] Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (17 / 26)

18 Pass is By Reference def double (A) : A *= 2 A = np. arange ( 20 ) double (A) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (18 / 26)

19 Pass is By Reference def double (A) : A *= 2 A = np. arange ( 20 ) double (A) A = np. arange ( 20 ) B = A. copy ( ) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (18 / 26)

20 Logical Arrays A = np. array ( [ - 1, 0, 1, 2, - 2, 3, 4, - 2 ] ) p r i n t (A > 0 ) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (19 / 26)

21 Logical Arrays II A = np. array ( [ - 1, 0, 1, 2, - 2, 3, 4, - 2 ] ) p r i n t ( (A > 0 ) & (A < 3 ) ). mean( ) What does this do? Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (20 / 26)

22 Logical Indexing A[A < 0 ] = 0 or A *= (A > 0 ) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (21 / 26)

23 Logical Indexing p r i n t Mean o f p o s i t i v e s, A[A > 0 ]. mean( ) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (22 / 26)

24 Some Helper Functions Constructing Arrays A = np. z e r o s ( ( 10, 10 ), i n t ) B = np. ones ( 10 ) C = np. arange ( 100 ). reshape ( ( 10, 10 ) )... Multiple Dimensions img = np. z e r o s ( ( 1024, 1024, 3 ) ) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (23 / 26)

25 Documentation Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (24 / 26)

26 Matplotlib Matplotlib is a plotting library for Python. import pylab import numpy a s np X = np. l i n s p a c e ( - 4,+4, 1000 ) pylab. p l o t (X, np. exp ( -X**2 ) ) pylab. x l a b e l ( r $x$ ) pylab. y l a b e l ( r $\exp ( - x^{2} ) $ ) pylab. s a v e f i g ( gaussian. pdf ) Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (25 / 26)

27 Matplotlib Example exp( x 2 ) x Luis Pedro Coelho (Programming for Scientists) Numpy October 22, 2012 (26 / 26)