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‎Examples/Basic/numpy-tutorial.py‎

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

‎dist/QSTK-0.2.5-py2.7.egg‎

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‎dist/QSTK-0.2.5.tar.gz‎

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