numpy_matplot_ejemplos

numpy matplot ejemplos

April 17, 2015

0.1 Numpy

0.1.1 Biblioteca(modulo) numerico de Python

Arrays multimensionales (ndarray) Mas cercano al hardware(numericamente mas eficiente) Designado para aplicaciones cientficas Utiliza memoria de manera mas eficiente Todos los modulos cientificos lo utilizan como tipo de dato basico(Opencv a partir de Opencv2)

0.2 Under the hood: la dispocision de memoria en un numpy array es :

bloque de memoria + esquema de indexado + descriptor del tipo de dato

datos planos como alocar elementos como interpretar elementos

In [58]: #Importamos el modulo numpy con el alias np

import numpy as np

In [59]: #Creo un array

a = np.array([1,0,0])

a

Out[59]: array([1, 0, 0])

In [60]: type(a)

Out[60]: numpy.ndarray

0.2.1 Python posee por defecto un tipo de datos que se asemeja(listas), pero esnumericamente ineficiente

In [61]: #Ejemplo creo una lista de Python de 0 a 1000 y calculo el cuadrado de cada elemento

L = range(1000)

In [62]: %%timeit

[i**2 for i in L]

10000 loops, best of 3: 101 s per loop

In [63]: #Ahora hago lo mismo con Numpy

a = np.arange(1000)

In [64]: %%timeit

a**2

1

The slowest run took 16.56 times longer than the fastest. This could mean that an intermediate result is being cached

100000 loops, best of 3: 2.31 s per loop

In [65]: print Numpy es

print 111/5.4

print veces mas rapido

Numpy es

20.5555555556

veces mas rapido

0.3 Caracteristicas y utilidades principales:

In [66]: #Creando arrays

a = np.array([1,1,1]) # 1D

b = np.array([[1,1,1],[1,1,1]]) #2d (Matrix)

c = np.array([[[1,1,1],[1,1,1],[1,1,1]]]) #3D (Tensor...)

In [67]: print a.shape

print b.shape

print c.shape

(3,)

(2, 3)

(1, 3, 3)

In [68]: #Podemos crear arrays predeterminados con funciones muy utiles

a = np.arange(10) # un array de enteros 0 a 10(no lo incluye)

a

Out[68]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

In [69]: # Array de 1 a 9 con paso 2

b = np.arange(1, 9, 2)

b

Out[69]: array([1, 3, 5, 7])

In [70]: #Como en Matlab

a = np.ones((3,3))

a

Out[70]: array([[ 1., 1., 1.],

[ 1., 1., 1.],

[ 1., 1., 1.]])

In [71]: b = np.zeros((5,5))

b

Out[71]: array([[ 0., 0., 0., 0., 0.],

[ 0., 0., 0., 0., 0.],

[ 0., 0., 0., 0., 0.],

[ 0., 0., 0., 0., 0.],

[ 0., 0., 0., 0., 0.]])

2

In [72]: c = np.eye(10)

c

Out[72]: array([[ 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],

[ 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],

[ 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],

[ 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.],

[ 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],

[ 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.],

[ 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],

[ 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],

[ 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.],

[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 1.]])

In [73]: d = np.diag(np.array([1, 2, 3, 4]))

d

Out[73]: array([[1, 0, 0, 0],

[0, 2, 0, 0],

[0, 0, 3, 0],

[0, 0, 0, 4]])

In [74]: #Complex numbers

e = np.array([1+2j, 3+4j, 5+6*1j])

e

Out[74]: array([ 1.+2.j, 3.+4.j, 5.+6.j])

In [75]: #boolean

e = np.array([True, False, False, True])

e

Out[75]: array([ True, False, False, True], dtype=bool)

In [76]: #String

f = np.array([Bonjour, Hello, Hallo,])

f

Out[76]: array([Bonjour, Hello, Hallo],

dtype=|S7)

0.4 Indexing and slicing

0.4.1 Los items de un array pueden accederse de una manera natural como en Matlab(hayque tener en cuenta que los indices comienzan en 0)

In [77]: a = np.arange(10)

a

Out[77]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

In [78]: #creo una tupla

a[0],a[2],a[-1]

Out[78]: (0, 2, 9)

3

In [79]: # Slicing [comienzo:final:paso]

# Los tres no son necesarios explicitamente ya que por default comienzo=0, final=[-1] y el paso=1

a[2:8:2]

Out[79]: array([2, 4, 6])

In [80]: a[::4] # solo cambiamos el paso

Out[80]: array([0, 4, 8])

0.5 Fancy indexing

0.5.1 Hay mas maneras de indexar y asignar

In [81]: np.random.seed(3)

a = np.random.random_integers(0, 20, 15)

a

Out[81]: array([10, 3, 8, 0, 19, 10, 11, 9, 10, 6, 0, 20, 12, 7, 14])

In [82]: (a % 3 == 0)

Out[82]: array([False, True, False, True, False, False, False, True, False,

True, True, False, True, False, False], dtype=bool)

In [83]: mask = (a % 3 == 0)

a_multiplos_3 = a[mask]

a_multiplos_3

Out[83]: array([ 3, 0, 9, 6, 0, 12])

In [84]: #Puedo indexar y asignar al mismo tiempo

a[a % 3 == 0] = -1

a

Out[84]: array([10, -1, 8, -1, 19, 10, 11, -1, 10, -1, -1, 20, -1, 7, 14])

0.6 Elementwise operations

0.6.1 Operar con funciones en cada elemento de un array(NO USE FOR)

In [85]: a = np.array([1, 2, 3, 4])

a

Out[85]: array([1, 2, 3, 4])

In [86]: #todas las operaciones aritmeticas funcionan

a+1

Out[86]: array([2, 3, 4, 5])

In [87]: j = np.arange(5)

2**(j + 1) - j

Out[87]: array([ 2, 3, 6, 13, 28])

In [88]: #Multiplicacion ES ELEMENTO A ELEMENTO

a * a

4

Out[88]: array([ 1, 4, 9, 16])

In [89]: #Para hacer multiplicaciones matriciales usamos dot

b = np.random.rand(3,3)

c = np.random.rand(3,3)

In [90]: np.dot(b,c)

Out[90]: array([[ 0.75172429, 0.76559311, 0.82038214],

[ 0.5466532 , 0.49578046, 0.62333632],

[ 0.46871279, 0.54809788, 0.43332846]])

In [91]: #cado objeto ndarray tiene muuchos metodos eje

c.sum()

Out[91]: 4.4680994807263517

1 Optimizaciones con Fortran y C

In [92]: %%file hellofortran.f

C File hellofortran.f

subroutine hellofortran (n)

integer n

do 100 i=0, n

print *, "Hola Soy Fortran tengo muuchos a~nos"

100 continue

end

Overwriting hellofortran.f

1.0.2 Generamos un modulo de Python con f2py

In [93]: !f2py -c -m hellofortran hellofortran.f

running build

running config cc

unifing config cc, config, build clib, build ext, build commands --compiler options

running config fc

unifing config fc, config, build clib, build ext, build commands --fcompiler options

running build src

build src

building extension "hellofortran" sources

f2py options: []

f2py:> /tmp/tmpYoWbrk/src.linux-x86 64-2.7/hellofortranmodule.c

creating /tmp/tmpYoWbrk/src.linux-x86 64-2.7

Reading fortran codes...

Reading file hellofortran.f (format:fix,strict)

Post-processing...

Block: hellofortran

Block: hellofortran

Post-processing (stage 2)...

Building modules...

Building module "hellofortran"...

5

Constructing wrapper function "hellofortran"...

hellofortran(n)

Wrote C/API module "hellofortran" to file "/tmp/tmpYoWbrk/src.linux-x86 64-2.7/hellofortranmodule.c"

adding /tmp/tmpYoWbrk/src.linux-x86 64-2.7/fortranobject.c to sources.

adding /tmp/tmpYoWbrk/src.linux-x86 64-2.7 to include dirs.

copying /home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/f2py/src/fortranobject.c -> /tmp/tmpYoWbrk/src.linux-x86 64-2.7

copying /home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/f2py/src/fortranobject.h -> /tmp/tmpYoWbrk/src.linux-x86 64-2.7

build src: building npy-pkg config files

running build ext

customize UnixCCompiler

customize UnixCCompiler using build ext

customize Gnu95FCompiler

Found executable /usr/bin/gfortran


customize Gnu95FCompiler using build ext

building hellofortran extension

compiling C sources

C compiler: gcc -pthread -fno-strict-aliasing -g -O2 -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC

creating /tmp/tmpYoWbrk/tmp

creating /tmp/tmpYoWbrk/tmp/tmpYoWbrk

creating /tmp/tmpYoWbrk/tmp/tmpYoWbrk/src.linux-x86 64-2.7

compile options: -I/tmp/tmpYoWbrk/src.linux-x86 64-2.7 -I/home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/core/include -I/home/elsuizo/anaconda/include/python2.7 -c

gcc: /tmp/tmpYoWbrk/src.linux-x86 64-2.7/hellofortranmodule.c

In file included from /home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1804:0,

from /home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17,

from /home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:4,

from /tmp/tmpYoWbrk/src.linux-x86 64-2.7/fortranobject.h:13,

from /tmp/tmpYoWbrk/src.linux-x86 64-2.7/hellofortranmodule.c:17:

/home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/core/include/numpy/npy 1 7 deprecated api.h:15:2: warning: #warning "Using deprecated NumPy API, disable it by " "#defining NPY NO DEPRECATED API NPY 1 7 API VERSION" [-Wcpp]

#warning "Using deprecated NumPy API, disable it by " \^

gcc: /tmp/tmpYoWbrk/src.linux-x86 64-2.7/fortranobject.c




from /tmp/tmpYoWbrk/src.linux-x86 64-2.7/fortranobject.h:13,

from /tmp/tmpYoWbrk/src.linux-x86 64-2.7/fortranobject.c:2:



compiling Fortran sources

Fortran f77 compiler: /usr/bin/gfortran -Wall -g -ffixed-form -fno-second-underscore -fPIC -O3 -funroll-loops

Fortran f90 compiler: /usr/bin/gfortran -Wall -g -fno-second-underscore -fPIC -O3 -funroll-loops

Fortran fix compiler: /usr/bin/gfortran -Wall -g -ffixed-form -fno-second-underscore -Wall -g -fno-second-underscore -fPIC -O3 -funroll-loops

compile options: -I/tmp/tmpYoWbrk/src.linux-x86 64-2.7 -I/home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/core/include -I/home/elsuizo/anaconda/include/python2.7 -c

gfortran:f77: hellofortran.f

/usr/bin/gfortran -Wall -g -Wall -g -shared /tmp/tmpYoWbrk/tmp/tmpYoWbrk/src.linux-x86 64-2.7/hellofortranmodule.o /tmp/tmpYoWbrk/tmp/tmpYoWbrk/src.linux-x86 64-2.7/fortranobject.o /tmp/tmpYoWbrk/hellofortran.o -L/home/elsuizo/anaconda/lib -lpython2.7 -lgfortran -o ./hellofortran.so

Removing build directory /tmp/tmpYoWbrk

1.0.3 Importamos el modulo que generamos y lo utilizamos

In [94]: %%file hello.py

import hellofortran

6

hellofortran.hellofortran(5)

Overwriting hello.py

In [95]: # corremos el script

!python hello.py

Hola Soy Fortran tengo muuchos a~nos






1.0.4 Ejemplo 2: suma acumulativa, entrada vector, salida vector

Primero hacemos la implementacion en Python puro, este tipo de suma es particularmente costoso ya quese necesitan loops for

In [96]: # Esta no es la mejor implementacion

#Porque el loop esta implementado en Python

def py_dcumsum(a):

b = np.empty_like(a)

b[0] = a[0]

for n in range(1,len(a)):

b[n] = b[n-1]+a[n]

return b

Ahora hacemos la implementacion en Fortran

In [97]: %%file dcumsum.f

c File dcumsum.f

subroutine dcumsum(a, b, n)

double precision a(n)

double precision b(n)

integer n

cf2py intent(in) :: a

cf2py intent(out) :: b

cf2py intent(hide) :: n

b(1) = a(1)

do 100 i=2, n

b(i) = b(i-1) + a(i)

100 continue

end

Overwriting dcumsum.f

Compilamos directamente a un modulo de python

In [98]: !f2py -c dcumsum.f -m dcumsum

running build

running config cc

unifing config cc, config, build clib, build ext, build commands --compiler options

running config fc

7

unifing config fc, config, build clib, build ext, build commands --fcompiler options

running build src

build src

building extension "dcumsum" sources

f2py options: []

f2py:> /tmp/tmpztScmZ/src.linux-x86 64-2.7/dcumsummodule.c

creating /tmp/tmpztScmZ/src.linux-x86 64-2.7

Reading fortran codes...

Reading file dcumsum.f (format:fix,strict)

Post-processing...

Block: dcumsum

Block: dcumsum

Post-processing (stage 2)...

Building modules...

Building module "dcumsum"...

Constructing wrapper function "dcumsum"...

b = dcumsum(a)

Wrote C/API module "dcumsum" to file "/tmp/tmpztScmZ/src.linux-x86 64-2.7/dcumsummodule.c"

adding /tmp/tmpztScmZ/src.linux-x86 64-2.7/fortranobject.c to sources.

adding /tmp/tmpztScmZ/src.linux-x86 64-2.7 to include dirs.

copying /home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/f2py/src/fortranobject.c -> /tmp/tmpztScmZ/src.linux-x86 64-2.7

copying /home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/f2py/src/fortranobject.h -> /tmp/tmpztScmZ/src.linux-x86 64-2.7

build src: building npy-pkg config files

running build ext

customize UnixCCompiler

customize UnixCCompiler using build ext


Found executable /usr/bin/gfortran


customize Gnu95FCompiler using build ext

building dcumsum extension

compiling C sources

C compiler: gcc -pthread -fno-strict-aliasing -g -O2 -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -fPIC

creating /tmp/tmpztScmZ/tmp

creating /tmp/tmpztScmZ/tmp/tmpztScmZ

creating /tmp/tmpztScmZ/tmp/tmpztScmZ/src.linux-x86 64-2.7

compile options: -I/tmp/tmpztScmZ/src.linux-x86 64-2.7 -I/home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/core/include -I/home/elsuizo/anaconda/include/python2.7 -c

gcc: /tmp/tmpztScmZ/src.linux-x86 64-2.7/dcumsummodule.c




from /tmp/tmpztScmZ/src.linux-x86 64-2.7/fortranobject.h:13,

from /tmp/tmpztScmZ/src.linux-x86 64-2.7/dcumsummodule.c:18:



/tmp/tmpztScmZ/src.linux-x86 64-2.7/dcumsummodule.c:111:12: warning: f2py size defined but not used [-Wunused-function]

static int f2py size(PyArrayObject* var, ...)

^

gcc: /tmp/tmpztScmZ/src.linux-x86 64-2.7/fortranobject.c




8

from /tmp/tmpztScmZ/src.linux-x86 64-2.7/fortranobject.h:13,

from /tmp/tmpztScmZ/src.linux-x86 64-2.7/fortranobject.c:2:



compiling Fortran sources

Fortran f77 compiler: /usr/bin/gfortran -Wall -g -ffixed-form -fno-second-underscore -fPIC -O3 -funroll-loops

Fortran f90 compiler: /usr/bin/gfortran -Wall -g -fno-second-underscore -fPIC -O3 -funroll-loops

Fortran fix compiler: /usr/bin/gfortran -Wall -g -ffixed-form -fno-second-underscore -Wall -g -fno-second-underscore -fPIC -O3 -funroll-loops

compile options: -I/tmp/tmpztScmZ/src.linux-x86 64-2.7 -I/home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/core/include -I/home/elsuizo/anaconda/include/python2.7 -c

gfortran:f77: dcumsum.f

/usr/bin/gfortran -Wall -g -Wall -g -shared /tmp/tmpztScmZ/tmp/tmpztScmZ/src.linux-x86 64-2.7/dcumsummodule.o /tmp/tmpztScmZ/tmp/tmpztScmZ/src.linux-x86 64-2.7/fortranobject.o /tmp/tmpztScmZ/dcumsum.o -L/home/elsuizo/anaconda/lib -lpython2.7 -lgfortran -o ./dcumsum.so

Removing build directory /tmp/tmpztScmZ

In [99]: #importamos el modulo recien creado

import dcumsum

In [100]: a = np.array([1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0])

In [101]: py_dcumsum(a)

Out[101]: array([ 1., 3., 6., 10., 15., 21., 28., 36.])

In [102]: dcumsum.dcumsum(a)

Out[102]: array([ 1., 3., 6., 10., 15., 21., 28., 36.])

1.0.5 Ahora los ponemos a prueba

In [103]: a = np.random.rand(10000)

In [104]: %%timeit

py_dcumsum(a)

100 loops, best of 3: 4.38 ms per loop

In [105]: %%timeit

dcumsum.dcumsum(a)

The slowest run took 16.02 times longer than the fastest. This could mean that an intermediate result is being cached


In [106]: %%timeit

a.cumsum()


1.1 Guauuuu

2 Ejemplo de vectorizacion

In [107]: %run srinivasan_pruebas.py

srinivasan pruebas.py:58: RuntimeWarning: overflow encountered in square

a 2 2 = np.sum((imagen5 - imagen4) ** 2 * mask)

srinivasan pruebas.py:58: RuntimeWarning: invalid value encountered in multiply

a 2 2 = np.sum((imagen5 - imagen4) ** 2 * mask)

9

---------------------------------------------------------------------------

LinAlgError Traceback (most recent call last)

/home/elsuizo/Charlas presentaciones/Python scientific/srinivasan pruebas.py in ()

71

72 #Resolvemos el sistema

---> 73 x = np.linalg.solve(A,B)

74

75 #tiempo de procesamiento

/home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/linalg/linalg.pyc in solve(a, b)

379 signature = DD->D if isComplexType(t) else dd->d

380 extobj = get linalg error extobj( raise linalgerror singular)

--> 381 r = gufunc(a, b, signature=signature, extobj=extobj)

382

383 return wrap(r.astype(result t))

/home/elsuizo/anaconda/lib/python2.7/site-packages/numpy/linalg/linalg.pyc in raise linalgerror singular(err, flag)

88

89 def raise linalgerror singular(err, flag):

---> 90 raise LinAlgError("Singular matrix")

91

92 def raise linalgerror nonposdef(err, flag):

LinAlgError: Singular matrix

In [108]: %run srinivasan_pruebas_vec.py

Tiempo de procesamiento: 0.068244934082

[-0.5 -0.5]

10

3 Matplotlib

3.1 Es el modulo para realizar y visualizar graficos

Pagina oficial

In [109]: #para que los graficos queden empotrados

%pylab inline

Populating the interactive namespace from numpy and matplotlib

WARNING: pylab import has clobbered these variables: [f, arrow, e]

%matplotlib prevents importing * from pylab and numpy

In [110]: X = np.linspace(-np.pi, np.pi, 256, endpoint=True)

C, S = np.cos(X), np.sin(X)

In [111]: plot(X, C)

plot(X, S)

Out[111]: []

11

In [112]: t = 2 * np.pi / 3

plot(X, C, color="blue", linewidth=2.5, linestyle="-", label="cosine")

plot(X, S, color="red", linewidth=2.5, linestyle="-", label="sine")

plot([t, t], [0, np.cos(t)], color=blue, linewidth=2.5, linestyle="--")

scatter([t, ], [np.cos(t), ], 50, color=blue)

annotate(r$sin(\frac{2\pi}{3})=\frac{\sqrt{3}}{2}$,

xy=(t, np.sin(t)), xycoords=data,

xytext=(+10, +30), textcoords=offset points, fontsize=16,

arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

plot([t, t],[0, np.sin(t)], color=red, linewidth=2.5, linestyle="--")

scatter([t, ],[np.sin(t), ], 50, color=red)

annotate(r$cos(\frac{2\pi}{3})=-\frac{1}{2}$,

xy=(t, np.cos(t)), xycoords=data,

xytext=(-90, -50), textcoords=offset points, fontsize=16,

arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

Out[112]:

12

3.2 Ejemplos

3.3 Ejemplo 1 Ecuaciones de Navier-Stokes

3.3.1 con conveccion no-lineal en 2D

Now we solve 2D Convection, represented by the pair of coupled partial differential equations below:

u

t+ u

u

x+ v

u

y= 0

v

t+ u

v

x+ v

v

y= 0

Discretizing these equations using the methods weve applied previously yields:

un+1i,j uni,jt

+ uni,juni,j uni1,j

x+ vni,j

uni,j uni,j1y

= 0

vn+1i,j vni,jt

+ uni,jvni,j vni1,j

x+ vni,j

vni,j vni,j1y

= 0

Initial ConditionsThe initial conditions are the same that we used for 1D convection, applied in both the x and y directions.

u, v =

{2 for x, y (0.5, 1) (0.5, 1)1 everywhere else

Boundary ConditionsThe boundary conditions hold u and v equal to 1 along the boundaries of the grid .

13

u = 1, v = 1 for

{x = 0, 2

y = 0, 2

In [113]: from mpl_toolkits.mplot3d import Axes3D

import matplotlib.pyplot as plt

import numpy as np

###variable declarations

nx = 101

ny = 101

nt = 80

c = 1

dx = 2.0/(nx-1)

dy = 2.0/(ny-1)

sigma = .2

dt = sigma*dx

x = np.linspace(0,2,nx)

y = np.linspace(0,2,ny)

u = np.ones((ny,nx)) ##create a 1xn vector of 1s

v = np.ones((ny,nx))

un = np.ones((ny,nx))

vn = np.ones((ny,nx))

###Assign initial conditions

u[.5/dy:1/dy+1,.5/dx:1/dx+1]=2 ##set hat function I.C. : u(.5

Out[114]:

In [ ]:

15

NumpyBiblioteca(modulo) numrico de Python

Under the hood: la dispocisin de memoria en un numpy array es :Python posee por defecto un tipo de datos que se asemeja(listas), pero es numricamente ineficiente

Caracteristicas y utilidades principales:Indexing and slicingLos items de un array pueden accederse de una manera natural como en Matlab(hay que tener en cuenta que los indices comienzan en 0)

Fancy indexingHay ms maneras de indexar y asignar

Elementwise operationsOperar con funciones en cada elemento de un array(NO USE FOR)

Optimizaciones con Fortran y CGeneramos un modulo de Python con f2pyImportamos el modulo que generamos y lo utilizamosEjemplo 2: suma acumulativa, entrada vector, salida vectorAhora los ponemos a prueba

Guauuuu

Ejemplo de vectorizacionMatplotlibEs el modulo para realizar y visualizar graficosEjemplosEjemplo 1 Ecuaciones de Navier-Stokescon conveccin no-lineal en 2D

numpy_matplot_ejemplos

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