Download presentation
Presentation is loading. Please wait.
1
Copyright ©2000-9 CRS Enterprises Ltd 1 Python for Scientists by Chris Seddon
3
Copyright ©2000-9 CRS Enterprises Ltd 3 Python for Scientists 1.NumPy 2.Plotting with gnuplot 3.Plotting with matplotlib 4.SciPy
5
Copyright ©2000-9 CRS Enterprises Ltd 5 Chapter 1 1
6
Copyright ©2000-9 CRS Enterprises Ltd 6 NumPy multi-dimensional arrays creating arrays reshaping arrays slicing and iterating stacking arrays splitting arrays shallow and deep copies broadcasting indexing grids matrices
7
Copyright ©2000-9 CRS Enterprises Ltd 7 01 creating arrays a = empty( (3,5) )# create empty 3 x 5 array a = ones( (3,5) )# filled with 1's a = zeros( (3,5) )# filled with 0's a = array( [2,3,5,7,11,13,17] )# from a list # create 1D array using arange a = arange(4,17) # create equally spaced 1D array a = linspace(-50.0,50.0,5) # use a function a = fromfunction(lambda i,j,k: i + j + k, (4,2,3)) a = empty( (3,5) )# create empty 3 x 5 array a = ones( (3,5) )# filled with 1's a = zeros( (3,5) )# filled with 0's a = array( [2,3,5,7,11,13,17] )# from a list # create 1D array using arange a = arange(4,17) # create equally spaced 1D array a = linspace(-50.0,50.0,5) # use a function a = fromfunction(lambda i,j,k: i + j + k, (4,2,3)) several different ways to create an array
![Copyright © CRS Enterprises Ltd 7 01 creating arrays a = empty( (3,5) )# create empty 3 x 5 array a = ones( (3,5) )# filled with 1 s a = zeros( (3,5) )# filled with 0 s a = array( [2,3,5,7,11,13,17] )# from a list # create 1D array using arange a = arange(4,17) # create equally spaced 1D array a = linspace(-50.0,50.0,5) # use a function a = fromfunction(lambda i,j,k: i + j + k, (4,2,3)) a = empty( (3,5) )# create empty 3 x 5 array a = ones( (3,5) )# filled with 1 s a = zeros( (3,5) )# filled with 0 s a = array( [2,3,5,7,11,13,17] )# from a list # create 1D array using arange a = arange(4,17) # create equally spaced 1D array a = linspace(-50.0,50.0,5) # use a function a = fromfunction(lambda i,j,k: i + j + k, (4,2,3)) several different ways to create an array](http://images.slideplayer.com./42/11421439/slides/slide_7.jpg "Copyright © CRS Enterprises Ltd 7 01 creating arrays a = empty( (3,5) )# create empty 3 x 5 array a = ones( (3,5) )# filled with 1 s a = zeros( (3,5) )# filled with 0 s a = array( [2,3,5,7,11,13,17] )# from a list # create 1D array using arange a = arange(4,17) # create equally spaced 1D array a = linspace(-50.0,50.0,5) # use a function a = fromfunction(lambda i,j,k: i + j + k, (4,2,3)) a = empty( (3,5) )# create empty 3 x 5 array a = ones( (3,5) )# filled with 1 s a = zeros( (3,5) )# filled with 0 s a = array( [2,3,5,7,11,13,17] )# from a list # create 1D array using arange a = arange(4,17) # create equally spaced 1D array a = linspace(-50.0,50.0,5) # use a function a = fromfunction(lambda i,j,k: i + j + k, (4,2,3)) several different ways to create an array")
8
Copyright ©2000-9 CRS Enterprises Ltd 8 numpy.reshape(a, newshape, order='C') gives a new shape to an array without changing its data C or Fortran style arrays available Fortran stores arrays in row order with the first subscript increasing most rapidly C/C++ in column order with the last subscript increasing most rapidly 02 reshaping arrays # create array a = ones( (24,) ) # reshape it b = a.reshape(2,3,4) # create array a = ones( (24,) ) # reshape it b = a.reshape(2,3,4)
9
Copyright ©2000-9 CRS Enterprises Ltd 9 03 array types # create array of int a = array( [2,3,5,7,11,13,17] ) # create array of float a = array( [2,3,5,7,11,13,17], dtype="float64" ) # create array of complex a = array( [2,3,5,7,11,13,17], dtype="complex64" ) # create array of int a = array( [2,3,5,7,11,13,17] ) # create array of float a = array( [2,3,5,7,11,13,17], dtype="float64" ) # create array of complex a = array( [2,3,5,7,11,13,17], dtype="complex64" ) dtype defines the type of ndarray bool_ uint8 uint16 uint32 uint64 int8 int16 int32 int64 float32 float64 float96 complex64 complex128 complex192
![Copyright © CRS Enterprises Ltd 9 03 array types # create array of int a = array( [2,3,5,7,11,13,17] ) # create array of float a = array( [2,3,5,7,11,13,17], dtype= float64 ) # create array of complex a = array( [2,3,5,7,11,13,17], dtype= complex64 ) # create array of int a = array( [2,3,5,7,11,13,17] ) # create array of float a = array( [2,3,5,7,11,13,17], dtype= float64 ) # create array of complex a = array( [2,3,5,7,11,13,17], dtype= complex64 ) dtype defines the type of ndarray bool_ uint8 uint16 uint32 uint64 int8 int16 int32 int64 float32 float64 float96 complex64 complex128 complex192](http://images.slideplayer.com./42/11421439/slides/slide_9.jpg "Copyright © CRS Enterprises Ltd 9 03 array types # create array of int a = array( [2,3,5,7,11,13,17] ) # create array of float a = array( [2,3,5,7,11,13,17], dtype= float64 ) # create array of complex a = array( [2,3,5,7,11,13,17], dtype= complex64 ) # create array of int a = array( [2,3,5,7,11,13,17] ) # create array of float a = array( [2,3,5,7,11,13,17], dtype= float64 ) # create array of complex a = array( [2,3,5,7,11,13,17], dtype= complex64 ) dtype defines the type of ndarray bool_ uint8 uint16 uint32 uint64 int8 int16 int32 int64 float32 float64 float96 complex64 complex128 complex192")
10
Copyright ©2000-9 CRS Enterprises Ltd 10 04 operating on arrays # operations are performed on each element c = a * b + 2 # dot and cross product c = dot(a,b) c = cross(a,b) # operations are performed on each element c = a * b + 2 # dot and cross product c = dot(a,b) c = cross(a,b) operations are performed on each and every element arrays are mutable
11
Copyright ©2000-9 CRS Enterprises Ltd 11 05 array methods a = array( random.random(10) * 100, dtype="int" ) print "sum=", a.sum() print "max=", a.max() print "min=", a.min() a = array( random.random(10) * 100, dtype="int" ) print "sum=", a.sum() print "max=", a.max() print "min=", a.min() Very few methods... sum()return sum of all elements max() return largest element min()return smallest element
12
Copyright ©2000-9 CRS Enterprises Ltd 12 06 basic functions # perform operations along specified axis result = average(a, axis=0) # create new arrays b = msort(a) b = insert(a, (1,5,9), (-1,-2,-3) ).reshape(3,5) b = append(a, (-1,-2,-3,-4) ).reshape(4,4) b = round_(a ** 1.1, 2) # perform operations along specified axis result = average(a, axis=0) # create new arrays b = msort(a) b = insert(a, (1,5,9), (-1,-2,-3) ).reshape(3,5) b = append(a, (-1,-2,-3,-4) ).reshape(4,4) b = round_(a ** 1.1, 2) Although arrays are mutable... these methods return new arrays
13
Copyright ©2000-9 CRS Enterprises Ltd 13 07 slicing and iterating Slicing similar to regular Python Iteration only works on first dimension but you can use flat to convert to a 1D array # one dimensional arrays a = arange(20); print a[7:14] # multi-dimensional arrays a = arange(24).reshape(4,3,2) print a[0:2,0:2,0:2] # iterate (works on first dimension) for row in a: print row # flatten array (not a function) to iterate over every element for element in a.flat: print element, # one dimensional arrays a = arange(20); print a[7:14] # multi-dimensional arrays a = arange(24).reshape(4,3,2) print a[0:2,0:2,0:2] # iterate (works on first dimension) for row in a: print row # flatten array (not a function) to iterate over every element for element in a.flat: print element,
![Copyright © CRS Enterprises Ltd slicing and iterating Slicing similar to regular Python Iteration only works on first dimension but you can use flat to convert to a 1D array # one dimensional arrays a = arange(20); print a[7:14] # multi-dimensional arrays a = arange(24).reshape(4,3,2) print a[0:2,0:2,0:2] # iterate (works on first dimension) for row in a: print row # flatten array (not a function) to iterate over every element for element in a.flat: print element, # one dimensional arrays a = arange(20); print a[7:14] # multi-dimensional arrays a = arange(24).reshape(4,3,2) print a[0:2,0:2,0:2] # iterate (works on first dimension) for row in a: print row # flatten array (not a function) to iterate over every element for element in a.flat: print element,](http://images.slideplayer.com./42/11421439/slides/slide_13.jpg "Copyright © CRS Enterprises Ltd slicing and iterating Slicing similar to regular Python Iteration only works on first dimension but you can use flat to convert to a 1D array # one dimensional arrays a = arange(20); print a[7:14] # multi-dimensional arrays a = arange(24).reshape(4,3,2) print a[0:2,0:2,0:2] # iterate (works on first dimension) for row in a: print row # flatten array (not a function) to iterate over every element for element in a.flat: print element, # one dimensional arrays a = arange(20); print a[7:14] # multi-dimensional arrays a = arange(24).reshape(4,3,2) print a[0:2,0:2,0:2] # iterate (works on first dimension) for row in a: print row # flatten array (not a function) to iterate over every element for element in a.flat: print element,")
14
Copyright ©2000-9 CRS Enterprises Ltd 14 08 stacking arrays a = ones( (3,5) ) b = zeros( (3,5) ) # stacking h = hstack( (a,b) ) v = vstack( (a,b) ) # create a 1D array a = r_[10:20, 55, 66, 80:90] a = ones( (3,5) ) b = zeros( (3,5) ) # stacking h = hstack( (a,b) ) v = vstack( (a,b) ) # create a 1D array a = r_[10:20, 55, 66, 80:90] Arrays can be stacked... horizontally or vertically
![Copyright © CRS Enterprises Ltd stacking arrays a = ones( (3,5) ) b = zeros( (3,5) ) # stacking h = hstack( (a,b) ) v = vstack( (a,b) ) # create a 1D array a = r_[10:20, 55, 66, 80:90] a = ones( (3,5) ) b = zeros( (3,5) ) # stacking h = hstack( (a,b) ) v = vstack( (a,b) ) # create a 1D array a = r_[10:20, 55, 66, 80:90] Arrays can be stacked...](http://images.slideplayer.com./42/11421439/slides/slide_14.jpg "horizontally or vertically.")
15
Copyright ©2000-9 CRS Enterprises Ltd 15 09 splitting arrays a = array( random.random((3,5)) * 100 ); # split horizontally a0,a1,a2,a3,a4 = hsplit(a,5) # split vertically a0,a1,a2 = vsplit(a,3) # split unequally horizontally" a0,a1,a2 = hsplit(a,(1,2)) # 2 splits a = array( random.random((3,5)) * 100 ); # split horizontally a0,a1,a2,a3,a4 = hsplit(a,5) # split vertically a0,a1,a2 = vsplit(a,3) # split unequally horizontally" a0,a1,a2 = hsplit(a,(1,2)) # 2 splits Splitting arrays... by each row (1st dimension) by each column (lat dimension) by unequal amounts (as specified by a tuple)
16
Copyright ©2000-9 CRS Enterprises Ltd 16 10 shallow copies a = arange(12) c = a.view()# a and c point to different arrays that share data # reshape one array - data unchanged c.shape = 3,4 # slice creates a view - data unchanged d = a[2:5] # d sees the change made by a a[3] = 88 a = arange(12) c = a.view()# a and c point to different arrays that share data # reshape one array - data unchanged c.shape = 3,4 # slice creates a view - data unchanged d = a[2:5] # d sees the change made by a a[3] = 88 Views are shallow copies the new array is a different from the old array, but the underlying data is shared
![Copyright © CRS Enterprises Ltd shallow copies a = arange(12) c = a.view()# a and c point to different arrays that share data # reshape one array - data unchanged c.shape = 3,4 # slice creates a view - data unchanged d = a[2:5] # d sees the change made by a a[3] = 88 a = arange(12) c = a.view()# a and c point to different arrays that share data # reshape one array - data unchanged c.shape = 3,4 # slice creates a view - data unchanged d = a[2:5] # d sees the change made by a a[3] = 88 Views are shallow copies the new array is a different from the old array, but the underlying data is shared](http://images.slideplayer.com./42/11421439/slides/slide_16.jpg "Copyright © CRS Enterprises Ltd shallow copies a = arange(12) c = a.view()# a and c point to different arrays that share data # reshape one array - data unchanged c.shape = 3,4 # slice creates a view - data unchanged d = a[2:5] # d sees the change made by a a[3] = 88 a = arange(12) c = a.view()# a and c point to different arrays that share data # reshape one array - data unchanged c.shape = 3,4 # slice creates a view - data unchanged d = a[2:5] # d sees the change made by a a[3] = 88 Views are shallow copies the new array is a different from the old array, but the underlying data is shared")
17
Copyright ©2000-9 CRS Enterprises Ltd 17 11 deep copies a = arange(12) b = a.copy() # changes to a do not affect b a[3] = 99 a = arange(12) b = a.copy() # changes to a do not affect b a[3] = 99 Use copy() to... create a new array and copy the underlying data
![Copyright © CRS Enterprises Ltd deep copies a = arange(12) b = a.copy() # changes to a do not affect b a[3] = 99 a = arange(12) b = a.copy() # changes to a do not affect b a[3] = 99 Use copy() to...](http://images.slideplayer.com./42/11421439/slides/slide_17.jpg "create a new array and copy the underlying data.")
18
Copyright ©2000-9 CRS Enterprises Ltd 18 12 broadcasting a = array([100,200,300,400]) b = arange(16).reshape(4,4) # a has shape = 4 # converted to 1,4 # then broadcasted to 4,4 c = a + b; a = array([100,200,300,400]) b = arange(16).reshape(4,4) # a has shape = 4 # converted to 1,4 # then broadcasted to 4,4 c = a + b; Allows operations to be performed on different sized arrays Extra dimensions are added to smaller arrays each dimension has size 1 The new dimensions are then adjusted to the size of the larger array by broadcasting values duplicated across new columns
![Copyright © CRS Enterprises Ltd broadcasting a = array([100,200,300,400]) b = arange(16).reshape(4,4) # a has shape = 4 # converted to 1,4 # then broadcasted to 4,4 c = a + b; a = array([100,200,300,400]) b = arange(16).reshape(4,4) # a has shape = 4 # converted to 1,4 # then broadcasted to 4,4 c = a + b; Allows operations to be performed on different sized arrays Extra dimensions are added to smaller arrays each dimension has size 1 The new dimensions are then adjusted to the size of the larger array by broadcasting values duplicated across new columns](http://images.slideplayer.com./42/11421439/slides/slide_18.jpg "Copyright © CRS Enterprises Ltd broadcasting a = array([100,200,300,400]) b = arange(16).reshape(4,4) # a has shape = 4 # converted to 1,4 # then broadcasted to 4,4 c = a + b; a = array([100,200,300,400]) b = arange(16).reshape(4,4) # a has shape = 4 # converted to 1,4 # then broadcasted to 4,4 c = a + b; Allows operations to be performed on different sized arrays Extra dimensions are added to smaller arrays each dimension has size 1 The new dimensions are then adjusted to the size of the larger array by broadcasting values duplicated across new columns")
19
Copyright ©2000-9 CRS Enterprises Ltd 19 13 indexing # set up an array to be used in indexing a = arange(10)**2 # setup index array index = array( [2,3,5,9] ) # apply index to a (to extract items 2,3,5 and 9 b = a[index] # set up a boolean filter for a a = arange(24).reshape(6,4) filter = a % 3 == 0 a[filter] = 99 # only change every 3rd element # set up an array to be used in indexing a = arange(10)**2 # setup index array index = array( [2,3,5,9] ) # apply index to a (to extract items 2,3,5 and 9 b = a[index] # set up a boolean filter for a a = arange(24).reshape(6,4) filter = a % 3 == 0 a[filter] = 99 # only change every 3rd element Indexing is an advanced form of slicing used to select items from an array by index or by expressions
![Copyright © CRS Enterprises Ltd indexing # set up an array to be used in indexing a = arange(10)**2 # setup index array index = array( [2,3,5,9] ) # apply index to a (to extract items 2,3,5 and 9 b = a[index] # set up a boolean filter for a a = arange(24).reshape(6,4) filter = a % 3 == 0 a[filter] = 99 # only change every 3rd element # set up an array to be used in indexing a = arange(10)**2 # setup index array index = array( [2,3,5,9] ) # apply index to a (to extract items 2,3,5 and 9 b = a[index] # set up a boolean filter for a a = arange(24).reshape(6,4) filter = a % 3 == 0 a[filter] = 99 # only change every 3rd element Indexing is an advanced form of slicing used to select items from an array by index or by expressions](http://images.slideplayer.com./42/11421439/slides/slide_19.jpg "Copyright © CRS Enterprises Ltd indexing # set up an array to be used in indexing a = arange(10)**2 # setup index array index = array( [2,3,5,9] ) # apply index to a (to extract items 2,3,5 and 9 b = a[index] # set up a boolean filter for a a = arange(24).reshape(6,4) filter = a % 3 == 0 a[filter] = 99 # only change every 3rd element # set up an array to be used in indexing a = arange(10)**2 # setup index array index = array( [2,3,5,9] ) # apply index to a (to extract items 2,3,5 and 9 b = a[index] # set up a boolean filter for a a = arange(24).reshape(6,4) filter = a % 3 == 0 a[filter] = 99 # only change every 3rd element Indexing is an advanced form of slicing used to select items from an array by index or by expressions")
20
Copyright ©2000-9 CRS Enterprises Ltd 20 14 ix function # set up arrays to be used for 3D grid a = array([2,5,7]) b = array([4,8,1]) c = array([3,5,2]) ax,bx,cx = ix_(a,b,c) result = ax * (bx + cx) # these are equivalent print result[1,2,1] print a[1] * (b[2] + c[1]) # set up arrays to be used for 3D grid a = array([2,5,7]) b = array([4,8,1]) c = array([3,5,2]) ax,bx,cx = ix_(a,b,c) result = ax * (bx + cx) # these are equivalent print result[1,2,1] print a[1] * (b[2] + c[1]) ix function... used to create multi-dimensional grids useful in 3D plotting
![Copyright © CRS Enterprises Ltd ix function # set up arrays to be used for 3D grid a = array([2,5,7]) b = array([4,8,1]) c = array([3,5,2]) ax,bx,cx = ix_(a,b,c) result = ax * (bx + cx) # these are equivalent print result[1,2,1] print a[1] * (b[2] + c[1]) # set up arrays to be used for 3D grid a = array([2,5,7]) b = array([4,8,1]) c = array([3,5,2]) ax,bx,cx = ix_(a,b,c) result = ax * (bx + cx) # these are equivalent print result[1,2,1] print a[1] * (b[2] + c[1]) ix function...](http://images.slideplayer.com./42/11421439/slides/slide_20.jpg "used to create multi-dimensional grids useful in 3D plotting.")
21
Copyright ©2000-9 CRS Enterprises Ltd 21 15 grids x = arange(1,11) y = arange(1,11) # Make a 2-d array containing a function of x and y. First create # xm and ym which contain the x and y values in a matrix form that # can be `broadcast' into a matrix of the appropriate shape: xm = x[ :, newaxis ] ym = y[ newaxis, : ] # generate 2D grid of values m = xm * ym x = arange(1,11) y = arange(1,11) # Make a 2-d array containing a function of x and y. First create # xm and ym which contain the x and y values in a matrix form that # can be `broadcast' into a matrix of the appropriate shape: xm = x[ :, newaxis ] ym = y[ newaxis, : ] # generate 2D grid of values m = xm * ym Alternative to ix_function
22
Copyright ©2000-9 CRS Enterprises Ltd 22 16 matrices # matrix multiplication (not element wise multiplication) a = matrix( [[3,4,5],[2,3,8],[4,1,7]] ) b = matrix( [[2,3,4],[1,2,7],[3,0,6]] ) c = a * b a = matrix( [[3,5],[4,1]] ) print "Transpose", a.T print "Inverse", a.I # linear algebra # 5x + 3y = 31 # 2x - 7y = -45 # solution x=2, y=7 a = matrix( [[ 5, 3 ],[ 2, -7 ]] ) v = matrix( [[ 31 ],[ -45 ]] ) print linalg.solve(a,v) # matrix multiplication (not element wise multiplication) a = matrix( [[3,4,5],[2,3,8],[4,1,7]] ) b = matrix( [[2,3,4],[1,2,7],[3,0,6]] ) c = a * b a = matrix( [[3,5],[4,1]] ) print "Transpose", a.T print "Inverse", a.I # linear algebra # 5x + 3y = 31 # 2x - 7y = -45 # solution x=2, y=7 a = matrix( [[ 5, 3 ],[ 2, -7 ]] ) v = matrix( [[ 31 ],[ -45 ]] ) print linalg.solve(a,v) Subclass of Array
![Copyright © CRS Enterprises Ltd matrices # matrix multiplication (not element wise multiplication) a = matrix( [[3,4,5],[2,3,8],[4,1,7]] ) b = matrix( [[2,3,4],[1,2,7],[3,0,6]] ) c = a * b a = matrix( [[3,5],[4,1]] ) print Transpose , a.T print Inverse , a.I # linear algebra # 5x + 3y = 31 # 2x - 7y = -45 # solution x=2, y=7 a = matrix( [[ 5, 3 ],[ 2, -7 ]] ) v = matrix( [[ 31 ],[ -45 ]] ) print linalg.solve(a,v) # matrix multiplication (not element wise multiplication) a = matrix( [[3,4,5],[2,3,8],[4,1,7]] ) b = matrix( [[2,3,4],[1,2,7],[3,0,6]] ) c = a * b a = matrix( [[3,5],[4,1]] ) print Transpose , a.T print Inverse , a.I # linear algebra # 5x + 3y = 31 # 2x - 7y = -45 # solution x=2, y=7 a = matrix( [[ 5, 3 ],[ 2, -7 ]] ) v = matrix( [[ 31 ],[ -45 ]] ) print linalg.solve(a,v) Subclass of Array](http://images.slideplayer.com./42/11421439/slides/slide_22.jpg "Copyright © CRS Enterprises Ltd matrices # matrix multiplication (not element wise multiplication) a = matrix( [[3,4,5],[2,3,8],[4,1,7]] ) b = matrix( [[2,3,4],[1,2,7],[3,0,6]] ) c = a * b a = matrix( [[3,5],[4,1]] ) print Transpose , a.T print Inverse , a.I # linear algebra # 5x + 3y = 31 # 2x - 7y = -45 # solution x=2, y=7 a = matrix( [[ 5, 3 ],[ 2, -7 ]] ) v = matrix( [[ 31 ],[ -45 ]] ) print linalg.solve(a,v) # matrix multiplication (not element wise multiplication) a = matrix( [[3,4,5],[2,3,8],[4,1,7]] ) b = matrix( [[2,3,4],[1,2,7],[3,0,6]] ) c = a * b a = matrix( [[3,5],[4,1]] ) print Transpose , a.T print Inverse , a.I # linear algebra # 5x + 3y = 31 # 2x - 7y = -45 # solution x=2, y=7 a = matrix( [[ 5, 3 ],[ 2, -7 ]] ) v = matrix( [[ 31 ],[ -45 ]] ) print linalg.solve(a,v) Subclass of Array")
25
Copyright ©2000-9 CRS Enterprises Ltd 25 Chapter 2 2
26
Copyright ©2000-9 CRS Enterprises Ltd 26 Plotting with gnuplot plotting data points using data files multiple plots vector fields hardcopies surface plots
27
Copyright ©2000-9 CRS Enterprises Ltd 27 01 data plot import Gnuplot gp = Gnuplot.Gnuplot() gp('set data style lines') # Pairs of x and y values data = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] gp.plot(data) # Triplets of x,y,z values data = [[0, 0, 0], [1, 1, 1], [2, 4, 8], [3, 9, 27], [4, 16, 64]] gp.splot(data) import Gnuplot gp = Gnuplot.Gnuplot() gp('set data style lines') # Pairs of x and y values data = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] gp.plot(data) # Triplets of x,y,z values data = [[0, 0, 0], [1, 1, 1], [2, 4, 8], [3, 9, 27], [4, 16, 64]] gp.splot(data) Supply list of 2D or 3D points
![Copyright © CRS Enterprises Ltd data plot import Gnuplot gp = Gnuplot.Gnuplot() gp( set data style lines ) # Pairs of x and y values data = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] gp.plot(data) # Triplets of x,y,z values data = [[0, 0, 0], [1, 1, 1], [2, 4, 8], [3, 9, 27], [4, 16, 64]] gp.splot(data) import Gnuplot gp = Gnuplot.Gnuplot() gp( set data style lines ) # Pairs of x and y values data = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] gp.plot(data) # Triplets of x,y,z values data = [[0, 0, 0], [1, 1, 1], [2, 4, 8], [3, 9, 27], [4, 16, 64]] gp.splot(data) Supply list of 2D or 3D points](http://images.slideplayer.com./42/11421439/slides/slide_27.jpg "Copyright © CRS Enterprises Ltd data plot import Gnuplot gp = Gnuplot.Gnuplot() gp( set data style lines ) # Pairs of x and y values data = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] gp.plot(data) # Triplets of x,y,z values data = [[0, 0, 0], [1, 1, 1], [2, 4, 8], [3, 9, 27], [4, 16, 64]] gp.splot(data) import Gnuplot gp = Gnuplot.Gnuplot() gp( set data style lines ) # Pairs of x and y values data = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] gp.plot(data) # Triplets of x,y,z values data = [[0, 0, 0], [1, 1, 1], [2, 4, 8], [3, 9, 27], [4, 16, 64]] gp.splot(data) Supply list of 2D or 3D points")
28
Copyright ©2000-9 CRS Enterprises Ltd 28 02 data files import Gnuplot gp = Gnuplot.Gnuplot() f = open("data/f1.dat") # read in the data points data = [] for line in f: point = line.split() data.append(point) # plot them gp.plot(data) import Gnuplot gp = Gnuplot.Gnuplot() f = open("data/f1.dat") # read in the data points data = [] for line in f: point = line.split() data.append(point) # plot them gp.plot(data) Read data from a file
![Copyright © CRS Enterprises Ltd data files import Gnuplot gp = Gnuplot.Gnuplot() f = open( data/f1.dat ) # read in the data points data = [] for line in f: point = line.split() data.append(point) # plot them gp.plot(data) import Gnuplot gp = Gnuplot.Gnuplot() f = open( data/f1.dat ) # read in the data points data = [] for line in f: point = line.split() data.append(point) # plot them gp.plot(data) Read data from a file](http://images.slideplayer.com./42/11421439/slides/slide_28.jpg "Copyright © CRS Enterprises Ltd data files import Gnuplot gp = Gnuplot.Gnuplot() f = open( data/f1.dat ) # read in the data points data = [] for line in f: point = line.split() data.append(point) # plot them gp.plot(data) import Gnuplot gp = Gnuplot.Gnuplot() f = open( data/f1.dat ) # read in the data points data = [] for line in f: point = line.split() data.append(point) # plot them gp.plot(data) Read data from a file")
29
Copyright ©2000-9 CRS Enterprises Ltd 29 03 multiple plots import Gnuplot gp = Gnuplot.Gnuplot() gp('set data style lines') data1 = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] # The first data set (a quadratic) data2 = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]] # The second data set (a straight line) # Make the plot items plot1 = Gnuplot.PlotItems.Data(data1, with_="lines", title="Quadratic") plot2 = Gnuplot.PlotItems.Data(data2, with_="points 3", title="Linear") gp.plot(plot1, plot2) import Gnuplot gp = Gnuplot.Gnuplot() gp('set data style lines') data1 = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] # The first data set (a quadratic) data2 = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]] # The second data set (a straight line) # Make the plot items plot1 = Gnuplot.PlotItems.Data(data1, with_="lines", title="Quadratic") plot2 = Gnuplot.PlotItems.Data(data2, with_="points 3", title="Linear") gp.plot(plot1, plot2) Multiple plots on same graph
![Copyright © CRS Enterprises Ltd multiple plots import Gnuplot gp = Gnuplot.Gnuplot() gp( set data style lines ) data1 = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] # The first data set (a quadratic) data2 = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]] # The second data set (a straight line) # Make the plot items plot1 = Gnuplot.PlotItems.Data(data1, with_= lines , title= Quadratic ) plot2 = Gnuplot.PlotItems.Data(data2, with_= points 3 , title= Linear ) gp.plot(plot1, plot2) import Gnuplot gp = Gnuplot.Gnuplot() gp( set data style lines ) data1 = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] # The first data set (a quadratic) data2 = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]] # The second data set (a straight line) # Make the plot items plot1 = Gnuplot.PlotItems.Data(data1, with_= lines , title= Quadratic ) plot2 = Gnuplot.PlotItems.Data(data2, with_= points 3 , title= Linear ) gp.plot(plot1, plot2) Multiple plots on same graph](http://images.slideplayer.com./42/11421439/slides/slide_29.jpg "Copyright © CRS Enterprises Ltd multiple plots import Gnuplot gp = Gnuplot.Gnuplot() gp( set data style lines ) data1 = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] # The first data set (a quadratic) data2 = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]] # The second data set (a straight line) # Make the plot items plot1 = Gnuplot.PlotItems.Data(data1, with_= lines , title= Quadratic ) plot2 = Gnuplot.PlotItems.Data(data2, with_= points 3 , title= Linear ) gp.plot(plot1, plot2) import Gnuplot gp = Gnuplot.Gnuplot() gp( set data style lines ) data1 = [[0, 0], [1, 1], [2, 4], [3, 9], [4, 16]] # The first data set (a quadratic) data2 = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]] # The second data set (a straight line) # Make the plot items plot1 = Gnuplot.PlotItems.Data(data1, with_= lines , title= Quadratic ) plot2 = Gnuplot.PlotItems.Data(data2, with_= points 3 , title= Linear ) gp.plot(plot1, plot2) Multiple plots on same graph")
30
Copyright ©2000-9 CRS Enterprises Ltd 30 04 vector fields import Gnuplot gp = Gnuplot.Gnuplot() # Generate the vector field data data = [] for i in range(-10, 11): for j in range(-10, 11): data.append([i/10., j/10., -i/100., -j/100.]) # Each data entry has the form [x, y, u, v] # Plot plot = Gnuplot.PlotItems.Data(data, with_ = 'vectors') gp.plot(plot) import Gnuplot gp = Gnuplot.Gnuplot() # Generate the vector field data data = [] for i in range(-10, 11): for j in range(-10, 11): data.append([i/10., j/10., -i/100., -j/100.]) # Each data entry has the form [x, y, u, v] # Plot plot = Gnuplot.PlotItems.Data(data, with_ = 'vectors') gp.plot(plot) Read data from a file
![Copyright © CRS Enterprises Ltd vector fields import Gnuplot gp = Gnuplot.Gnuplot() # Generate the vector field data data = [] for i in range(-10, 11): for j in range(-10, 11): data.append([i/10., j/10., -i/100., -j/100.]) # Each data entry has the form [x, y, u, v] # Plot plot = Gnuplot.PlotItems.Data(data, with_ = vectors ) gp.plot(plot) import Gnuplot gp = Gnuplot.Gnuplot() # Generate the vector field data data = [] for i in range(-10, 11): for j in range(-10, 11): data.append([i/10., j/10., -i/100., -j/100.]) # Each data entry has the form [x, y, u, v] # Plot plot = Gnuplot.PlotItems.Data(data, with_ = vectors ) gp.plot(plot) Read data from a file](http://images.slideplayer.com./42/11421439/slides/slide_30.jpg "Copyright © CRS Enterprises Ltd vector fields import Gnuplot gp = Gnuplot.Gnuplot() # Generate the vector field data data = [] for i in range(-10, 11): for j in range(-10, 11): data.append([i/10., j/10., -i/100., -j/100.]) # Each data entry has the form [x, y, u, v] # Plot plot = Gnuplot.PlotItems.Data(data, with_ = vectors ) gp.plot(plot) import Gnuplot gp = Gnuplot.Gnuplot() # Generate the vector field data data = [] for i in range(-10, 11): for j in range(-10, 11): data.append([i/10., j/10., -i/100., -j/100.]) # Each data entry has the form [x, y, u, v] # Plot plot = Gnuplot.PlotItems.Data(data, with_ = vectors ) gp.plot(plot) Read data from a file")
31
Copyright ©2000-9 CRS Enterprises Ltd 31 05 hardcopies import Gnuplot gp = Gnuplot.Gnuplot()... gp.plot(plot) gp.hardcopy(filename="data/mygraph.ps",terminal="postscript") import Gnuplot gp = Gnuplot.Gnuplot()... gp.plot(plot) gp.hardcopy(filename="data/mygraph.ps",terminal="postscript") gnuplot can convert plots into hardcopy but only postscript available
32
Copyright ©2000-9 CRS Enterprises Ltd 32 06 delayed plotting from numpy import * import Gnuplot, math gp = Gnuplot.Gnuplot(debug=1) x = arange(10, dtype='float_') y = x**2 # save plots for displaying later plot1 = Gnuplot.Data(x, y, title='squares', with_='points 3 3') plot2 = Gnuplot.Func('x**2', title='calculated by gnuplot') # Plot gp.title('The function x**2') gp.xlabel('x'); gp.ylabel('x**2') gp.plot(plot1, plot2) from numpy import * import Gnuplot, math gp = Gnuplot.Gnuplot(debug=1) x = arange(10, dtype='float_') y = x**2 # save plots for displaying later plot1 = Gnuplot.Data(x, y, title='squares', with_='points 3 3') plot2 = Gnuplot.Func('x**2', title='calculated by gnuplot') # Plot gp.title('The function x**2') gp.xlabel('x'); gp.ylabel('x**2') gp.plot(plot1, plot2) Plots can be cached in memory displayed later with plot()
33
Copyright ©2000-9 CRS Enterprises Ltd 33 07 plotting styles mport Gnuplot import math gp = Gnuplot.Gnuplot(debug=1) x = arange(10, dtype='float_') y = x**2 # save plots for displaying later plot1 = Gnuplot.Func('x**2/100.', title='x**2', with_='boxes') plot2 = Gnuplot.Func('cos(x)', title='cos(x)', with_='lines') plot3 = Gnuplot.Func('norm(x)', title='norm(x)', with_='errorbars') # Plot gp.title('Various functions and styles') gp.xlabel('x'); gp.ylabel('y') gp.plot(plot1, plot2, plot3) mport Gnuplot import math gp = Gnuplot.Gnuplot(debug=1) x = arange(10, dtype='float_') y = x**2 # save plots for displaying later plot1 = Gnuplot.Func('x**2/100.', title='x**2', with_='boxes') plot2 = Gnuplot.Func('cos(x)', title='cos(x)', with_='lines') plot3 = Gnuplot.Func('norm(x)', title='norm(x)', with_='errorbars') # Plot gp.title('Various functions and styles') gp.xlabel('x'); gp.ylabel('y') gp.plot(plot1, plot2, plot3) Many different plotting styles available
34
Copyright ©2000-9 CRS Enterprises Ltd 34 08 surface plots import Gnuplot, math g = Gnuplot.Gnuplot(debug=1) # Demonstrate a 3-d plot: x = arange(25) y = arange(25) # Make a 2-d array containing a function of x and y xm = x[:,newaxis] ym = y[newaxis,:] m = xm * ym**2 g('set parametric'); g('set data style lines'); g('set hidden') g('set contour base'); g.title('An example of a surface plot') g.xlabel('x'); g.ylabel('y') g.splot(Gnuplot.GridData(m,x,y)) import Gnuplot, math g = Gnuplot.Gnuplot(debug=1) # Demonstrate a 3-d plot: x = arange(25) y = arange(25) # Make a 2-d array containing a function of x and y xm = x[:,newaxis] ym = y[newaxis,:] m = xm * ym**2 g('set parametric'); g('set data style lines'); g('set hidden') g('set contour base'); g.title('An example of a surface plot') g.xlabel('x'); g.ylabel('y') g.splot(Gnuplot.GridData(m,x,y)) 3D surface plots available can rotate views with mouse
![Copyright © CRS Enterprises Ltd surface plots import Gnuplot, math g = Gnuplot.Gnuplot(debug=1) # Demonstrate a 3-d plot: x = arange(25) y = arange(25) # Make a 2-d array containing a function of x and y xm = x[:,newaxis] ym = y[newaxis,:] m = xm * ym**2 g( set parametric ); g( set data style lines ); g( set hidden ) g( set contour base ); g.title( An example of a surface plot ) g.xlabel( x ); g.ylabel( y ) g.splot(Gnuplot.GridData(m,x,y)) import Gnuplot, math g = Gnuplot.Gnuplot(debug=1) # Demonstrate a 3-d plot: x = arange(25) y = arange(25) # Make a 2-d array containing a function of x and y xm = x[:,newaxis] ym = y[newaxis,:] m = xm * ym**2 g( set parametric ); g( set data style lines ); g( set hidden ) g( set contour base ); g.title( An example of a surface plot ) g.xlabel( x ); g.ylabel( y ) g.splot(Gnuplot.GridData(m,x,y)) 3D surface plots available can rotate views with mouse](http://images.slideplayer.com./42/11421439/slides/slide_34.jpg "Copyright © CRS Enterprises Ltd surface plots import Gnuplot, math g = Gnuplot.Gnuplot(debug=1) # Demonstrate a 3-d plot: x = arange(25) y = arange(25) # Make a 2-d array containing a function of x and y xm = x[:,newaxis] ym = y[newaxis,:] m = xm * ym**2 g( set parametric ); g( set data style lines ); g( set hidden ) g( set contour base ); g.title( An example of a surface plot ) g.xlabel( x ); g.ylabel( y ) g.splot(Gnuplot.GridData(m,x,y)) import Gnuplot, math g = Gnuplot.Gnuplot(debug=1) # Demonstrate a 3-d plot: x = arange(25) y = arange(25) # Make a 2-d array containing a function of x and y xm = x[:,newaxis] ym = y[newaxis,:] m = xm * ym**2 g( set parametric ); g( set data style lines ); g( set hidden ) g( set contour base ); g.title( An example of a surface plot ) g.xlabel( x ); g.ylabel( y ) g.splot(Gnuplot.GridData(m,x,y)) 3D surface plots available can rotate views with mouse")
37
Copyright ©2000-9 CRS Enterprises Ltd 37 Chapter 3 3
38
Copyright ©2000-9 CRS Enterprises Ltd 38 Plotting with matplotlib 2D plots only data points polynomials multiple plots subplots polar plots histograms
39
Copyright ©2000-9 CRS Enterprises Ltd 39 01 simple plot import matplotlib.pyplot as plt redCircles = "ro" plt.plot([1,2,3,4], [1,4,9,16], redCircles) plt.ylabel("squares") plt.show() import matplotlib.pyplot as plt redCircles = "ro" plt.plot([1,2,3,4], [1,4,9,16], redCircles) plt.ylabel("squares") plt.show() Supply x and y data... as separate lists
![Copyright © CRS Enterprises Ltd simple plot import matplotlib.pyplot as plt redCircles = ro plt.plot([1,2,3,4], [1,4,9,16], redCircles) plt.ylabel( squares ) plt.show() import matplotlib.pyplot as plt redCircles = ro plt.plot([1,2,3,4], [1,4,9,16], redCircles) plt.ylabel( squares ) plt.show() Supply x and y data...](http://images.slideplayer.com./42/11421439/slides/slide_39.jpg "as separate lists.")
40
Copyright ©2000-9 CRS Enterprises Ltd 40 02 polynomials from matplotlib.mlab import normpdf import matplotlib.numerix as nx import pylab as p """ calculate polynomial: y = -2x^2 + 1 """ def poly(input): output = [(-2 * a * a + 1) for a in input] return output x = nx.arange(-4, 4, 0.01) y = poly(x) p.plot(x,y, color='red', lw=2) p.show() from matplotlib.mlab import normpdf import matplotlib.numerix as nx import pylab as p """ calculate polynomial: y = -2x^2 + 1 """ def poly(input): output = [(-2 * a * a + 1) for a in input] return output x = nx.arange(-4, 4, 0.01) y = poly(x) p.plot(x,y, color='red', lw=2) p.show() Plotting functiond is easy!
![Copyright © CRS Enterprises Ltd polynomials from matplotlib.mlab import normpdf import matplotlib.numerix as nx import pylab as p calculate polynomial: y = -2x^2 + 1 def poly(input): output = [(-2 * a * a + 1) for a in input] return output x = nx.arange(-4, 4, 0.01) y = poly(x) p.plot(x,y, color= red , lw=2) p.show() from matplotlib.mlab import normpdf import matplotlib.numerix as nx import pylab as p calculate polynomial: y = -2x^2 + 1 def poly(input): output = [(-2 * a * a + 1) for a in input] return output x = nx.arange(-4, 4, 0.01) y = poly(x) p.plot(x,y, color= red , lw=2) p.show() Plotting functiond is easy!](http://images.slideplayer.com./42/11421439/slides/slide_40.jpg "Copyright © CRS Enterprises Ltd polynomials from matplotlib.mlab import normpdf import matplotlib.numerix as nx import pylab as p calculate polynomial: y = -2x^2 + 1 def poly(input): output = [(-2 * a * a + 1) for a in input] return output x = nx.arange(-4, 4, 0.01) y = poly(x) p.plot(x,y, color= red , lw=2) p.show() from matplotlib.mlab import normpdf import matplotlib.numerix as nx import pylab as p calculate polynomial: y = -2x^2 + 1 def poly(input): output = [(-2 * a * a + 1) for a in input] return output x = nx.arange(-4, 4, 0.01) y = poly(x) p.plot(x,y, color= red , lw=2) p.show() Plotting functiond is easy!")
41
Copyright ©2000-9 CRS Enterprises Ltd 41 03 multiple plots import numpy as np import matplotlib.pyplot as plt # evenly sampled time at 200ms intervals t = np.arange(0.0, 5.0, 0.200) redDashes = "r--" blueSquares = "bs" greenTriangles = "g^" plt.plot(t, t, redDashes, t, t**2, blueSquares, t, t**3, greenTriangles) plt.show() import numpy as np import matplotlib.pyplot as plt # evenly sampled time at 200ms intervals t = np.arange(0.0, 5.0, 0.200) redDashes = "r--" blueSquares = "bs" greenTriangles = "g^" plt.plot(t, t, redDashes, t, t**2, blueSquares, t, t**3, greenTriangles) plt.show() Put several plot on one graph with different formats
42
Copyright ©2000-9 CRS Enterprises Ltd 42 04 subplots import numpy as np import matplotlib.pyplot as plt def f(t): return np.exp(-t) * np.cos(2*np.pi*t) t1 = np.arange(0.0, 5.0, 0.1) t2 = np.arange(0.0, 5.0, 0.02) plt.figure(1) plt.subplot(211) # 2 rows, 1 column, fig.1 plt.plot(t1, f(t1), 'bo', t2, f(t2), 'k') plt.subplot(212) # 2 rows, 1 column, fig.2 plt.plot(t2, np.cos(2*np.pi*t2), 'r--') plt.show() import numpy as np import matplotlib.pyplot as plt def f(t): return np.exp(-t) * np.cos(2*np.pi*t) t1 = np.arange(0.0, 5.0, 0.1) t2 = np.arange(0.0, 5.0, 0.02) plt.figure(1) plt.subplot(211) # 2 rows, 1 column, fig.1 plt.plot(t1, f(t1), 'bo', t2, f(t2), 'k') plt.subplot(212) # 2 rows, 1 column, fig.2 plt.plot(t2, np.cos(2*np.pi*t2), 'r--') plt.show() Combine different graphs on same figure
43
Copyright ©2000-9 CRS Enterprises Ltd 43 import numpy as np import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(111, polar=True) r = np.arange(0,1,0.001) theta = 2*2*np.pi*r line, = ax.plot(theta, r, color="#ee8d18", lw=3) ind = 800 thisr, thistheta = r[ind], theta[ind] ax.plot([thistheta], [thisr], "o")... import numpy as np import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(111, polar=True) r = np.arange(0,1,0.001) theta = 2*2*np.pi*r line, = ax.plot(theta, r, color="#ee8d18", lw=3) ind = 800 thisr, thistheta = r[ind], theta[ind] ax.plot([thistheta], [thisr], "o")... ax.annotate( "a polar annotation", xy=(thistheta, thisr), # theta, radius xytext=(0.05, 0.05), # fraction, fraction textcoords="figure fraction", arrowprops=dict(facecolor="black", shrink=0.05), horizontalalignment="left", verticalalignment="bottom",) plt.show()... ax.annotate( "a polar annotation", xy=(thistheta, thisr), # theta, radius xytext=(0.05, 0.05), # fraction, fraction textcoords="figure fraction", arrowprops=dict(facecolor="black", shrink=0.05), horizontalalignment="left", verticalalignment="bottom",) plt.show() 05 polar plots
![Copyright © CRS Enterprises Ltd 43 import numpy as np import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(111, polar=True) r = np.arange(0,1,0.001) theta = 2*2*np.pi*r line, = ax.plot(theta, r, color= #ee8d18 , lw=3) ind = 800 thisr, thistheta = r[ind], theta[ind] ax.plot([thistheta], [thisr], o )...](http://images.slideplayer.com./42/11421439/slides/slide_43.jpg "import numpy as np import matplotlib.pyplot as plt fig = plt.figure() ax = fig.add_subplot(111, polar=True) r = np.arange(0,1,0.001) theta = 2*2*np.pi*r line, = ax.plot(theta, r, color= #ee8d18 , lw=3) ind = 800 thisr, thistheta = r[ind], theta[ind] ax.plot([thistheta], [thisr], o )... ax.annotate( a polar annotation , xy=(thistheta, thisr), # theta, radius xytext=(0.05, 0.05), # fraction, fraction textcoords= figure fraction , arrowprops=dict(facecolor= black , shrink=0.05), horizontalalignment= left , verticalalignment= bottom ,) plt.show()... ax.annotate( a polar annotation , xy=(thistheta, thisr), # theta, radius xytext=(0.05, 0.05), # fraction, fraction textcoords= figure fraction , arrowprops=dict(facecolor= black , shrink=0.05), horizontalalignment= left , verticalalignment= bottom ,) plt.show() 05 polar plots.")
44
Copyright ©2000-9 CRS Enterprises Ltd 44 06 histograms import numpy as np import matplotlib.pyplot as plt mu, sigma = 100, 15 x = mu + sigma * np.random.randn(10000) # the histogram of the data n, bins, patches = plt.hist(x, 50, normed=1, facecolor='g', alpha=0.75) plt.xlabel('Smarts') plt.ylabel('Probability') plt.title('Histogram of IQ') plt.text(60,.025, r'$\mu=100,\ \sigma=15$') plt.axis([40, 160, 0, 0.03]) plt.grid(True) plt.show() import numpy as np import matplotlib.pyplot as plt mu, sigma = 100, 15 x = mu + sigma * np.random.randn(10000) # the histogram of the data n, bins, patches = plt.hist(x, 50, normed=1, facecolor='g', alpha=0.75) plt.xlabel('Smarts') plt.ylabel('Probability') plt.title('Histogram of IQ') plt.text(60,.025, r'$\mu=100,\ \sigma=15$') plt.axis([40, 160, 0, 0.03]) plt.grid(True) plt.show() Use the hist() function
![Copyright © CRS Enterprises Ltd histograms import numpy as np import matplotlib.pyplot as plt mu, sigma = 100, 15 x = mu + sigma * np.random.randn(10000) # the histogram of the data n, bins, patches = plt.hist(x, 50, normed=1, facecolor= g , alpha=0.75) plt.xlabel( Smarts ) plt.ylabel( Probability ) plt.title( Histogram of IQ ) plt.text(60,.025, r $\mu=100,\ \sigma=15$ ) plt.axis([40, 160, 0, 0.03]) plt.grid(True) plt.show() import numpy as np import matplotlib.pyplot as plt mu, sigma = 100, 15 x = mu + sigma * np.random.randn(10000) # the histogram of the data n, bins, patches = plt.hist(x, 50, normed=1, facecolor= g , alpha=0.75) plt.xlabel( Smarts ) plt.ylabel( Probability ) plt.title( Histogram of IQ ) plt.text(60,.025, r $\mu=100,\ \sigma=15$ ) plt.axis([40, 160, 0, 0.03]) plt.grid(True) plt.show() Use the hist() function](http://images.slideplayer.com./42/11421439/slides/slide_44.jpg "Copyright © CRS Enterprises Ltd histograms import numpy as np import matplotlib.pyplot as plt mu, sigma = 100, 15 x = mu + sigma * np.random.randn(10000) # the histogram of the data n, bins, patches = plt.hist(x, 50, normed=1, facecolor= g , alpha=0.75) plt.xlabel( Smarts ) plt.ylabel( Probability ) plt.title( Histogram of IQ ) plt.text(60,.025, r $\mu=100,\ \sigma=15$ ) plt.axis([40, 160, 0, 0.03]) plt.grid(True) plt.show() import numpy as np import matplotlib.pyplot as plt mu, sigma = 100, 15 x = mu + sigma * np.random.randn(10000) # the histogram of the data n, bins, patches = plt.hist(x, 50, normed=1, facecolor= g , alpha=0.75) plt.xlabel( Smarts ) plt.ylabel( Probability ) plt.title( Histogram of IQ ) plt.text(60,.025, r $\mu=100,\ \sigma=15$ ) plt.axis([40, 160, 0, 0.03]) plt.grid(True) plt.show() Use the hist() function")
47
Copyright ©2000-9 CRS Enterprises Ltd 47 Chapter 4 4
48
Copyright ©2000-9 CRS Enterprises Ltd 48 SciPy science constants integration linear equations special functions solving non-linear equations ordinary differential equations
49
Copyright ©2000-9 CRS Enterprises Ltd 49 SciPy Packages Clustering packagescipy.cluster Constantsscipy.constants Fourier transformsscipy.fftpack Integration and ODEsscipy.integrate Interpolationscipy.interpolate Input and outputscipy.io Linear algebrascipy.linalg Miscellaneous routinesscipy.misc Multi-dimensional image processingscipy.ndimage Optimization and root findingscipy.optimize Signal processingscipy.signal Sparse matricesscipy.sparse Sparse linear algebrascipy.sparse.linalg Special functionsscipy.special Statistical functionsscipy.stats
50
Copyright ©2000-9 CRS Enterprises Ltd 50 01 constants #SI prefixes print c.giga, c.mega, c.kilo # physical constants print "speed of light", c.c print "Plank's constant", c.h print "Boltzmann constant", c.k #weight in kg print "gram", c.gram print "lb", c.lb print "electron mass", c.m_e #length in meter print "inch", c.inch print "yard", c.yard print "mile", c.mile #SI prefixes print c.giga, c.mega, c.kilo # physical constants print "speed of light", c.c print "Plank's constant", c.h print "Boltzmann constant", c.k #weight in kg print "gram", c.gram print "lb", c.lb print "electron mass", c.m_e #length in meter print "inch", c.inch print "yard", c.yard print "mile", c.mile Many mathematical and physical constants defined
51
Copyright ©2000-9 CRS Enterprises Ltd 51 02 miscellaneous from numpy import * from scipy import misc # factorial print "factorial(23) =", misc.factorial(23) # differentiation print "derivative of x**5 at x=5", print misc.derivative(lambda x:x**5, 5, dx=0.0001) # combinations print "2 from 5 = ", misc.comb(5,2) print "13 from 52 = ", misc.comb(52,13) from numpy import * from scipy import misc # factorial print "factorial(23) =", misc.factorial(23) # differentiation print "derivative of x**5 at x=5", print misc.derivative(lambda x:x**5, 5, dx=0.0001) # combinations print "2 from 5 = ", misc.comb(5,2) print "13 from 52 = ", misc.comb(52,13) Miscellaneous functions group in misc module
52
Copyright ©2000-9 CRS Enterprises Ltd 52 03 integration from scipy import * from scipy.integrate import quad def f(x): return exp(-x) # integrate exp(-x) between 0 and 5 result = quad(f, 0, 5) print "result", result[0] print "error estimate", result[1] # more tests print quad(lambda x: x, 0, 10) print quad(lambda x: x**2, 0, 1) from scipy import * from scipy.integrate import quad def f(x): return exp(-x) # integrate exp(-x) between 0 and 5 result = quad(f, 0, 5) print "result", result[0] print "error estimate", result[1] # more tests print quad(lambda x: x, 0, 10) print quad(lambda x: x**2, 0, 1) Integration using quadrature
![Copyright © CRS Enterprises Ltd integration from scipy import * from scipy.integrate import quad def f(x): return exp(-x) # integrate exp(-x) between 0 and 5 result = quad(f, 0, 5) print result , result[0] print error estimate , result[1] # more tests print quad(lambda x: x, 0, 10) print quad(lambda x: x**2, 0, 1) from scipy import * from scipy.integrate import quad def f(x): return exp(-x) # integrate exp(-x) between 0 and 5 result = quad(f, 0, 5) print result , result[0] print error estimate , result[1] # more tests print quad(lambda x: x, 0, 10) print quad(lambda x: x**2, 0, 1) Integration using quadrature](http://images.slideplayer.com./42/11421439/slides/slide_52.jpg "Copyright © CRS Enterprises Ltd integration from scipy import * from scipy.integrate import quad def f(x): return exp(-x) # integrate exp(-x) between 0 and 5 result = quad(f, 0, 5) print result , result[0] print error estimate , result[1] # more tests print quad(lambda x: x, 0, 10) print quad(lambda x: x**2, 0, 1) from scipy import * from scipy.integrate import quad def f(x): return exp(-x) # integrate exp(-x) between 0 and 5 result = quad(f, 0, 5) print result , result[0] print error estimate , result[1] # more tests print quad(lambda x: x, 0, 10) print quad(lambda x: x**2, 0, 1) Integration using quadrature")
53
Copyright ©2000-9 CRS Enterprises Ltd 53 04 linear equations from numpy import * from scipy.linalg import solve # x = 5, y = 3, z = 1 # 5x - 2y + 3z = 22 # 6x + y + z = 34 # 2x - 5y - 2z = -7 a = array( [[5,-2, 3], [6, 1, 1], [2,-5,-2] ]) b = array( [22,34,-7] ) result = solve(a, b) print result from numpy import * from scipy.linalg import solve # x = 5, y = 3, z = 1 # 5x - 2y + 3z = 22 # 6x + y + z = 34 # 2x - 5y - 2z = -7 a = array( [[5,-2, 3], [6, 1, 1], [2,-5,-2] ]) b = array( [22,34,-7] ) result = solve(a, b) print result
![Copyright © CRS Enterprises Ltd linear equations from numpy import * from scipy.linalg import solve # x = 5, y = 3, z = 1 # 5x - 2y + 3z = 22 # 6x + y + z = 34 # 2x - 5y - 2z = -7 a = array( [[5,-2, 3], [6, 1, 1], [2,-5,-2] ]) b = array( [22,34,-7] ) result = solve(a, b) print result from numpy import * from scipy.linalg import solve # x = 5, y = 3, z = 1 # 5x - 2y + 3z = 22 # 6x + y + z = 34 # 2x - 5y - 2z = -7 a = array( [[5,-2, 3], [6, 1, 1], [2,-5,-2] ]) b = array( [22,34,-7] ) result = solve(a, b) print result](http://images.slideplayer.com./42/11421439/slides/slide_53.jpg "Copyright © CRS Enterprises Ltd linear equations from numpy import * from scipy.linalg import solve # x = 5, y = 3, z = 1 # 5x - 2y + 3z = 22 # 6x + y + z = 34 # 2x - 5y - 2z = -7 a = array( [[5,-2, 3], [6, 1, 1], [2,-5,-2] ]) b = array( [22,34,-7] ) result = solve(a, b) print result from numpy import * from scipy.linalg import solve # x = 5, y = 3, z = 1 # 5x - 2y + 3z = 22 # 6x + y + z = 34 # 2x - 5y - 2z = -7 a = array( [[5,-2, 3], [6, 1, 1], [2,-5,-2] ]) b = array( [22,34,-7] ) result = solve(a, b) print result")
54
Copyright ©2000-9 CRS Enterprises Ltd 54 05 special functions from numpy import * from scipy import special # Bessel function of real order v at complex z print special.jv(6,2+3j) # Gamma function print special.gamma(5) print special.gamma(5.1) # Zeta function print special.zeta(10,2) from numpy import * from scipy import special # Bessel function of real order v at complex z print special.jv(6,2+3j) # Gamma function print special.gamma(5) print special.gamma(5.1) # Zeta function print special.zeta(10,2) Many special functions available
55
Copyright ©2000-9 CRS Enterprises Ltd 55 06 solving non linear equations from scipy import * from scipy.optimize import fsolve def f(x): return (exp(x)-1)-cos(x) # use fsolve to solve exp(x)-1 - cos(x) = 0 guess = 2.0; print fsolve(f,guess) guess = -1.0; print fsolve(f,guess) guess = -5.0; print fsolve(f,guess) guess = 0.0; print fsolve(f,guess) guess = -10.0; print fsolve(f,guess) from scipy import * from scipy.optimize import fsolve def f(x): return (exp(x)-1)-cos(x) # use fsolve to solve exp(x)-1 - cos(x) = 0 guess = 2.0; print fsolve(f,guess) guess = -1.0; print fsolve(f,guess) guess = -5.0; print fsolve(f,guess) guess = 0.0; print fsolve(f,guess) guess = -10.0; print fsolve(f,guess) Must supply an initial guess may be multiple roots finds closest root
56
Copyright ©2000-9 CRS Enterprises Ltd 56 07 ordinary differential equations scipy.integrate.odeint(func, y0, t,...) dy/dt = func(y,t0,...) func : computes the derivative of y at t0. y0 : initial condition on y (can be a vector). t : sequence of time points for which to solve for y from numpy import * from scipy.integrate import odeint from math import * # evaluate dy/dt = y for initial value of y = y0 # and a time range from t0... t1 y0 = 7; t0 = 2; t1 = 6 # solution: y = e**(t + k) # where k = log(y0) - t0 print "calculated result", odeint(lambda y,t:y, y0, [t0, t1]) k = log(y0) - t0 print "analytical result", [ y0, e**(t1 + k)] from numpy import * from scipy.integrate import odeint from math import * # evaluate dy/dt = y for initial value of y = y0 # and a time range from t0... t1 y0 = 7; t0 = 2; t1 = 6 # solution: y = e**(t + k) # where k = log(y0) - t0 print "calculated result", odeint(lambda y,t:y, y0, [t0, t1]) k = log(y0) - t0 print "analytical result", [ y0, e**(t1 + k)]
Similar presentations
