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Basics Copyright © Software Carpentry 2010 This work is licensed under the Creative Commons Attribution License See http://software-carpentry.org/license.html for more information. Matrix Programming
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MatricesBasics NumPy (http://numpy.scipy.org) Provides MATLAB-style arrays for Python And many other things A data parallel programming model –Write x*A*x.T to calculate xAx T –The computer takes care of the loops All encapsulated in special objects called arrays
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MatricesBasics Create an array from a list >>> import numpy >>> vals = [1, 2, 3] >>> arr = numpy.array(vals) >>> arr array([1, 2, 3])
![MatricesBasics Create an array from a list >>> import numpy >>> vals = [1, 2, 3] >>> arr = numpy.array(vals) >>> arr array([1, 2, 3])](http://images.slideplayer.com/27/9064235/slides/slide_3.jpg "MatricesBasics Create an array from a list >>> import numpy >>> vals = [1, 2, 3] >>> arr = numpy.array(vals) >>> arr array([1, 2, 3])")
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MatricesBasics Arrays are homogeneous –I.e., all values have the same type Allows values to be packed together –Saves memory –Faster to process 7 3 5 valsarr 3 5 7 int1×3
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MatricesBasics So what does this do? >>> arr = numpy.array([1, 2.3]) >>> arr array([1., 2.3]) A float, not an int
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MatricesBasics You can specify at creation time: >>> array([1, 2, 3, 4], dtype=float32) array([ 1., 2., 3., 4.])
![MatricesBasics You can specify at creation time: >>> array([1, 2, 3, 4], dtype=float32) array([ 1., 2., 3., 4.])](http://images.slideplayer.com/27/9064235/slides/slide_6.jpg "MatricesBasics You can specify at creation time: >>> array([1, 2, 3, 4], dtype=float32) array([ 1., 2., 3., 4.])")
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MatricesBasics You can specify at creation time: >>> array([1, 2, 3, 4], dtype=float32) array([ 1., 2., 3., 4.]) Why would you want to specify a type?
![MatricesBasics You can specify at creation time: >>> array([1, 2, 3, 4], dtype=float32) array([ 1., 2., 3., 4.]) Why would you want to specify a type](http://images.slideplayer.com/27/9064235/slides/slide_7.jpg "MatricesBasics You can specify at creation time: >>> array([1, 2, 3, 4], dtype=float32) array([ 1., 2., 3., 4.]) Why would you want to specify a type")
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MatricesBasics You can also specify the data type later >>> a = array([1, 2, 3, 4], dtype=float32) >>> a.astype(int) array([ 1, 2, 3, 4]) >>> a.dtype = int >>> a array([1065353216, 1073741824, 1077936128, 1082130432])
![MatricesBasics You can also specify the data type later >>> a = array([1, 2, 3, 4], dtype=float32) >>> a.astype(int) array([ 1, 2, 3, 4]) >>> a.dtype = int >>> a array([ , , , ])](http://images.slideplayer.com/27/9064235/slides/slide_8.jpg "MatricesBasics You can also specify the data type later >>> a = array([1, 2, 3, 4], dtype=float32) >>> a.astype(int) array([ 1, 2, 3, 4]) >>> a.dtype = int >>> a array([ , , , ])")
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MatricesBasics booluint[8,16,32,64 ] intfloat int8float[32,64,128 ] int16complex int32complex[64,126] int64 Basic data types (in increasing order) are:
![MatricesBasics booluint[8,16,32,64 ] intfloat int8float[32,64,128 ] int16complex int32complex[64,126] int64 Basic data types (in increasing order) are:](http://images.slideplayer.com/27/9064235/slides/slide_9.jpg "MatricesBasics booluint[8,16,32,64 ] intfloat int8float[32,64,128 ] int16complex int32complex[64,126] int64 Basic data types (in increasing order) are:")
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MatricesBasics Many other ways to create arrays >>> z = numpy.zeros((2, 3)) >>> z array([[0., 0., 0.], [0., 0., 0.]]) Type is float unless something else specified
![MatricesBasics Many other ways to create arrays >>> z = numpy.zeros((2, 3)) >>> z array([[0., 0., 0.], [0., 0., 0.]]) Type is float unless something else specified](http://images.slideplayer.com/27/9064235/slides/slide_10.jpg "MatricesBasics Many other ways to create arrays >>> z = numpy.zeros((2, 3)) >>> z array([[0., 0., 0.], [0., 0., 0.]]) Type is float unless something else specified")
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MatricesBasics Many other ways to create arrays >>> z = numpy.zeros((2, 3)) >>> z array([[0., 0., 0.], [0., 0., 0.]]) Type is float unless something else specified What do these do? >>> block = numpy.ones((4, 5)) >>> mystery = numpy.identity(4)
![MatricesBasics Many other ways to create arrays >>> z = numpy.zeros((2, 3)) >>> z array([[0., 0., 0.], [0., 0., 0.]]) Type is float unless something else specified What do these do.](http://images.slideplayer.com/27/9064235/slides/slide_11.jpg ">>> block = numpy.ones((4, 5)) >>> mystery = numpy.identity(4).")
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MatricesBasics Can create arrays without filling in values >>> x = numpy.empty((2, 2)) >>> x array([[3.82265e-297, 4.94944e+173], [1.93390e-309, 1.00000e+000]]) "Values" will be whatever bits were in memory Should not be used without being initialized
![MatricesBasics Can create arrays without filling in values >>> x = numpy.empty((2, 2)) >>> x array([[ e-297, e+173], [ e-309, e+000]]) Values will be whatever bits were in memory Should not be used without being initialized](http://images.slideplayer.com/27/9064235/slides/slide_12.jpg "MatricesBasics Can create arrays without filling in values >>> x = numpy.empty((2, 2)) >>> x array([[ e-297, e+173], [ e-309, e+000]]) Values will be whatever bits were in memory Should not be used without being initialized")
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MatricesBasics Can create arrays without filling in values >>> x = numpy.empty((2, 2)) >>> x array([[3.82265e-297, 4.94944e+173], [1.93390e-309, 1.00000e+000]]) "Values" will be whatever bits were in memory Should not be used without being initialized When is this useful?
![MatricesBasics Can create arrays without filling in values >>> x = numpy.empty((2, 2)) >>> x array([[ e-297, e+173], [ e-309, e+000]]) Values will be whatever bits were in memory Should not be used without being initialized When is this useful](http://images.slideplayer.com/27/9064235/slides/slide_13.jpg "MatricesBasics Can create arrays without filling in values >>> x = numpy.empty((2, 2)) >>> x array([[ e-297, e+173], [ e-309, e+000]]) Values will be whatever bits were in memory Should not be used without being initialized When is this useful")
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MatricesBasics Assigning creates alias: does not copy data >>> first = numpy.ones((2, 2)) >>> first array([[1., 1.], [1., 1.]]) >>> second = first >>> second[0, 0] = 9 >>> first array([[9., 1.], [1., 1.]])
![MatricesBasics Assigning creates alias: does not copy data >>> first = numpy.ones((2, 2)) >>> first array([[1., 1.], [1., 1.]]) >>> second = first >>> second[0, 0] = 9 >>> first array([[9., 1.], [1., 1.]])](http://images.slideplayer.com/27/9064235/slides/slide_14.jpg "MatricesBasics Assigning creates alias: does not copy data >>> first = numpy.ones((2, 2)) >>> first array([[1., 1.], [1., 1.]]) >>> second = first >>> second[0, 0] = 9 >>> first array([[9., 1.], [1., 1.]])")
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MatricesBasics Assigning creates alias: does not copy data >>> first = numpy.ones((2, 2)) >>> first array([[1., 1.], [1., 1.]]) >>> second = first >>> second[0, 0] = 9 >>> first array([[9., 1.], [1., 1.]]) Not second[0][0]
![MatricesBasics Assigning creates alias: does not copy data >>> first = numpy.ones((2, 2)) >>> first array([[1., 1.], [1., 1.]]) >>> second = first >>> second[0, 0] = 9 >>> first array([[9., 1.], [1., 1.]]) Not second[0][0]](http://images.slideplayer.com/27/9064235/slides/slide_15.jpg "MatricesBasics Assigning creates alias: does not copy data >>> first = numpy.ones((2, 2)) >>> first array([[1., 1.], [1., 1.]]) >>> second = first >>> second[0, 0] = 9 >>> first array([[9., 1.], [1., 1.]]) Not second[0][0]")
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MatricesBasics Use the array.copy method >>> first array([[1., 1.], [1., 1.]]) >>> second = first.copy() >>> second[0, 0] = 9 >>> first array([[1., 1.], [1., 1.]])
![MatricesBasics Use the array.copy method >>> first array([[1., 1.], [1., 1.]]) >>> second = first.copy() >>> second[0, 0] = 9 >>> first array([[1., 1.], [1., 1.]])](http://images.slideplayer.com/27/9064235/slides/slide_16.jpg "MatricesBasics Use the array.copy method >>> first array([[1., 1.], [1., 1.]]) >>> second = first.copy() >>> second[0, 0] = 9 >>> first array([[1., 1.], [1., 1.]])")
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MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3)
![MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3)](http://images.slideplayer.com/27/9064235/slides/slide_17.jpg "MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3)")
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MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3) Not a method
![MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3) Not a method](http://images.slideplayer.com/27/9064235/slides/slide_18.jpg "MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3) Not a method")
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MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3) Consistent
![MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3) Consistent](http://images.slideplayer.com/27/9064235/slides/slide_19.jpg "MatricesBasics Arrays also have properties >>> first array([[1., 1.], [1., 1.]]) >>> first.shape (2, 2) >>> block = numpy.zeros((4, 7, 3)) >>> block.shape (4, 7, 3) Consistent")
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MatricesBasics array.size is the total number of elements >>> first.size 4 >>> block.size 84 2×2 4×7×3
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MatricesBasics Reverse on all axes with array.transpose >>> first = numpy.array([[1, 2, 3], [4, 5, 6]]) >>> first.transpose() array([[1, 4], [2, 5], [3, 6]]) >>> first array([[1, 2, 3], [4, 5, 6]])
![MatricesBasics Reverse on all axes with array.transpose >>> first = numpy.array([[1, 2, 3], [4, 5, 6]]) >>> first.transpose() array([[1, 4], [2, 5], [3, 6]]) >>> first array([[1, 2, 3], [4, 5, 6]])](http://images.slideplayer.com/27/9064235/slides/slide_21.jpg "MatricesBasics Reverse on all axes with array.transpose >>> first = numpy.array([[1, 2, 3], [4, 5, 6]]) >>> first.transpose() array([[1, 4], [2, 5], [3, 6]]) >>> first array([[1, 2, 3], [4, 5, 6]])")
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MatricesBasics Flatten arrays using array.ravel >>> first = numpy.zeros((2, 2, 2)) >>> second = first.ravel() >>> second.shape (8,)
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MatricesBasics Think about the 2×4 array A: >>> A array([[1, 2, 3, 4], [5, 6, 7, 8]]) A looks 2-dimensional But computer memory is 1-dimensional Must decide how to lay out values
![MatricesBasics Think about the 2×4 array A: >>> A array([[1, 2, 3, 4], [5, 6, 7, 8]]) A looks 2-dimensional But computer memory is 1-dimensional Must decide how to lay out values](http://images.slideplayer.com/27/9064235/slides/slide_23.jpg "MatricesBasics Think about the 2×4 array A: >>> A array([[1, 2, 3, 4], [5, 6, 7, 8]]) A looks 2-dimensional But computer memory is 1-dimensional Must decide how to lay out values")
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MatricesBasics 12345678 1234 5678 Logical Physical Row-major order concatenates the rows Used by C and Python
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MatricesBasics 15263748 1234 5678 Logical Physical Column-major order concatenates the columns Used by Fortran and MATLAB
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MatricesBasics No difference in usability or performance… …but causes headaches when passing data from one language to another (Just like 0-based vs. 1-based indexing)
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MatricesBasics No difference in usability or performance… …but causes headaches when passing data from one language to another (Just like 0-based vs. 1-based indexing) What order are 3-dimensional arrays stored in?
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MatricesBasics Can reshape arrays in many other ways >>> first = numpy.array([1, 2, 3, 4, 5, 6]) >>> first.shape (6,) >>> second = first.reshape(2, 3) >>> second array([[1, 2, 3], [4, 5, 6]]) Also aliases the data Tuple with 1 element Not packed into a tuple
![MatricesBasics Can reshape arrays in many other ways >>> first = numpy.array([1, 2, 3, 4, 5, 6]) >>> first.shape (6,) >>> second = first.reshape(2, 3) >>> second array([[1, 2, 3], [4, 5, 6]]) Also aliases the data Tuple with 1 element Not packed into a tuple](http://images.slideplayer.com/27/9064235/slides/slide_28.jpg "MatricesBasics Can reshape arrays in many other ways >>> first = numpy.array([1, 2, 3, 4, 5, 6]) >>> first.shape (6,) >>> second = first.reshape(2, 3) >>> second array([[1, 2, 3], [4, 5, 6]]) Also aliases the data Tuple with 1 element Not packed into a tuple")
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MatricesBasics New shape must have same size as old >>> first = numpy.zeros((2, 2)) >>> first.reshape(3, 3) ValueError: total size of new array must be unchanged Cannot possibly work because it is just creating an alias for the existing data
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MatricesBasics Change physical size using array.resize >>> block array([[ 10, 20, 30], [110, 120, 130], [210, 220, 230]]) >>> block.resize(2, 2) >>> block array([[ 10, 20], [110, 120]])
![MatricesBasics Change physical size using array.resize >>> block array([[ 10, 20, 30], [110, 120, 130], [210, 220, 230]]) >>> block.resize(2, 2) >>> block array([[ 10, 20], [110, 120]])](http://images.slideplayer.com/27/9064235/slides/slide_30.jpg "MatricesBasics Change physical size using array.resize >>> block array([[ 10, 20, 30], [110, 120, 130], [210, 220, 230]]) >>> block.resize(2, 2) >>> block array([[ 10, 20], [110, 120]])")
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MatricesBasics Change physical size using array.resize >>> block array([[ 10, 20, 30], [110, 120, 130], [210, 220, 230]]) >>> block.resize(2, 2) >>> block array([[ 10, 20], [110, 120]]) What happens when the array grows?
![MatricesBasics Change physical size using array.resize >>> block array([[ 10, 20, 30], [110, 120, 130], [210, 220, 230]]) >>> block.resize(2, 2) >>> block array([[ 10, 20], [110, 120]]) What happens when the array grows](http://images.slideplayer.com/27/9064235/slides/slide_31.jpg "MatricesBasics Change physical size using array.resize >>> block array([[ 10, 20, 30], [110, 120, 130], [210, 220, 230]]) >>> block.resize(2, 2) >>> block array([[ 10, 20], [110, 120]]) What happens when the array grows")
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MatricesBasics Review: –Arrays are blocks of homogeneous data –Most operations create aliases –Can be reshaped (size remains the same) –Or resized
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November 2010 created by Richard T. Guy Copyright © Software Carpentry 2010 This work is licensed under the Creative Commons Attribution License See http://software-carpentry.org/license.html for more information.
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