######################################## # A brief introduction to numpy arrays # ######################################## # # Prereqs: Basic python. "import", built-in data types (numbers, lists, # strings), range # # This short tutorial is mostly about introducing numpy arrays, how they're # different from basic python lists/tuples, and the various ways you can # manipulate them. It's intended to be both a runnable python script, and # a step by step tutorial. # # This tutorial does NOT cover # 1) Installing numpy/dependencies. For that see # # http://docs.scipy.org/doc/numpy/user/install.html # # 2) Basic python. This includes getting, installing, running the python # interpreter, the basic python data types (strings, numbers, sequences), # if statements, or for loops. If you're new to python an excellent place # to start is here: # # http://docs.python.org/2/tutorial/ # # 3) Any numpy libraries in depth. It may include references to utility # functions where necessary, but this is strictly a tutorial for # beginners. More advanced documentation is available here: # # (Users guide) # http://docs.scipy.org/doc/numpy/user/index.html # (Reference documentation) # http://docs.scipy.org/doc/numpy/reference/ # # # # ## Lets get started! print "Importing numpy" import numpy as np ## This loads the numpy library and lets us refer to it by the shorthand "np", ## which is the convention used in the numpy documentation and in many ## online tutorials/examples print "Creating arrays" ## Now lets make an array to play around with. You can make numpy arrays in ## a number of ways, ## Filled with zeros: zeroArray = np.zeros( (2,3) ) # [[ 0. 0. 0.] print zeroArray # [ 0. 0. 0.]] ## Or ones: oneArray = np.ones( (2,3) ) # [[ 1. 1. 1.] print oneArray # [ 1. 1. 1.]] ## Or filled with junk: emptyArray = np.empty( (2,3) ) print emptyArray ## Note, emptyArray might look random, but it's just uninitialized which means ## you shouldn't count on it having any particular data in it, even random ## data! If you do want random data you can use random(): randomArray = np.random.random( (2,3) ) print randomArray ## If you're following along and trying these commands out, you should have ## noticed that making randomArray took a lot longer than emptyArray. That's ## because np.random.random(...) is actually using a random number generator ## to fill in each of the spots in the array with a randomly sampled number ## from 0 to 1. ## You can also create an array by hand: foo = [ [1,2,3], [4,5,6]] myArray = np.array(foo) # [[1 2 3] print myArray # [4 5 6]] print "Reshaping arrays" ## Of course, if you're typing out a range for a larger matrix, it's easier to ## use arange(...): rangeArray = np.arange(6,12).reshape( (2,3) ) # [[ 6 7 8] print rangeArray # [ 9 10 11]] ## there's two things going on here. First, the arange(...) function returns a ## 1D array similar to what you'd get from using the built-in python function ## range(...) with the same arguments, except it returns a numpy array ## instead of a list. print np.arange(6,12) # [ 6 7 8 9 10 11 12] ## the reshape method takes the data in an existing array, and stuffs it into ## an array with the given shape and returns it. print rangeArray.reshape( (3,2) ) # [[ 6 7] # [ 8 9] # [10 11]] #The original array doesn't change though. print rangeArray # [[ 6 7 8] # [ 9 10 11] ## When you use reshape(...) the total number of things in the array must stay ## the same. So reshaping an array with 2 rows and 3 columns into one with ## 3 rows and 2 columns is fine, but 3x3 or 1x5 won't work #print rangeArray.reshape( (3,3) ) #ERROR squareArray = np.arange(1,10).reshape( (3,3) ) #this is fine, 9 elements print "Accessing array elements" ## Accessing an array is also pretty straight forward. You access a specific ## spot in the table by referring to its row and column inside square braces ## after the array: print rangeArray[0,1] #7 ## Note that row and column numbers start from 0, not 1! Numpy also lets you ## refer to ranges inside an array: print rangeArray[0,0:2] #[6 7] print squareArray[0:2,0:2] #[[1 2] # the top left corner of squareArray # [4 5]] ## These ranges work just like slices and python lists. n:m:t specifies a range ## that starts at n, and stops before m, in steps of size t. If any of these ## are left off, they're assumed to be the start, the end+1, and 1 respectively print squareArray[:,0:3:2] #[[1 3] #skip the middle column # [4 6] # [7 9]] ## Also like python lists, you can assign values to specific positions, or ## ranges of values to slices squareArray[0,:] = np.array(range(1,4)) #set the first row to 1,2,3 squareArray[1,1] = 0 # set the middle spot to zero squareArray[2,:] = 1 # set the last row to ones print squareArray # [[1 2 3] # [4 0 6] # [1 1 1]] ## Something new to numpy arrays is indexing using an array of indices: fibIndices = np.array( [1, 1, 2, 3] ) randomRow = np.random.random( (10,1) ) # an array of 10 random numbers print randomRow print randomRow[fibIndices] # the first, first, second and third element of # randomRow ## You can also use an array of true/false values to index: boolIndices = np.array( [[ True, False, True], [False, True, False], [ True, False, True]] ) print squareArray[boolIndices] # a 1D array with the selected values # [1 3 0 1 1] ## It gets a little more complicated with 2D (and higher) arrays. You need ## two index arrays for a 2D array: rows = np.array( [[0,0],[2,2]] ) #get the corners of our square array cols = np.array( [[0,2],[0,2]] ) print squareArray[rows,cols] #[[1 3] # [1 1]] boolRows = np.array( [False, True, False] ) # just the middle row boolCols = np.array( [True, False, True] ) # Not the middle column print squareArray[boolRows,boolCols] # [4 6] print "Operations on arrays" ## One useful trick is to create a boolean matrix based on some test and use ## that as an index in order to get the elements of a matrix that pass the ## test: sqAverage = np.average(squareArray) # average(...) returns the average of all # the elements in the given array betterThanAverage = squareArray > sqAverage print betterThanAverage #[[False False True] # [ True False True] # [False False False]] print squareArray[betterThanAverage] #[3 4 6] ## Indexing like this can also be used to assign values to elements of the ## array. This is particularly useful if you want to filter an array, say by ## making sure that all of its values are above/below a certain threshold: sqStdDev = np.std(squareArray) # std(...) returns the standard deviation of # all the elements in the given array clampedSqArray = np.array(squareArray.copy(), dtype=float) # make a copy of squareArray that will # be "clamped". It will only contain # values within one standard deviation # of the mean. Values that are too low # or to high will be set to the min # and max respectively. We set # dtype=float because sqAverage # and sqStdDev are floating point # numbers, and we don't want to # truncate them down to integers. clampedSqArray[ (squareArray-sqAverage) > sqStdDev ] = sqAverage+sqStdDev clampedSqArray[ (squareArray-sqAverage) < -sqStdDev ] = sqAverage-sqStdDev print clampedSqArray # [[ 1. 2. 3. ] # [ 3.90272394 0.31949828 3.90272394] # [ 1. 1. 1. ]] ## Multiplying and dividing arrays by numbers does what you'd expect. It ## multiples/divides element-wise print squareArray * 2 # [[ 2 4 6] # [ 8 0 12] # [ 2 2 2]] ## Addition works similarly: print squareArray + np.ones( (3,3) ) #[[2 3 4] # [5 1 7] # [2 2 2]] ## Multiplying two arrays together (of the same size) is also element wise print squareArray * np.arange(1,10).reshape( (3,3) ) #[[ 1 4 9] # [16 0 36] # [ 7 8 9]] ## Unless you use the dot(...) function, which does matrix multiplication ## from linear algebra: matA = np.array( [[1,2],[3,4]] ) matB = np.array( [[5,6],[7,8]] ) print np.dot(matA,matB) #[[19 22] # [43 50]] ## And thats it! There's a lot more to the numpy library, and there are a few ## things I skipped over here, such as what happens when array dimensions ## don't line up when you're indexing or multiplying them together, so if ## you're interested, I strongly suggest you head over to the scipy wiki's ## numpy tutorial for a more in depth look at using numpy arrays: ## ## http://www.scipy.org/Tentative_NumPy_Tutorial