#format wiki
#language en

[[TableOfContents]]


[[Anchor(convolve)]]
=== convolve() ===

{{{#!python numbers=disable
>>> from scipy import *
>>> x=r_[1:4]
>>> h1=zeros(15); h1[0]=1
>>> h2=zeros(15); h2[6]=1
>>> h3=zeros(15); h3[12]=1
>>> convolve(h1+h2+h3,x)
 array([1, 2, 3, 0, 0, 0, 1, 2, 3, 0, 0, 0, 1, 2, 3, 0, 0])

}}}

[[Anchor(fft)]]
=== fft() ===

{{{#!python numbers=disable
>>> from scipy import *
>>> from pylab import *
>>>
>>> sample_rate=1000.00
>>> t=r_[0:0.6:1/sample_rate]
>>> N=len(t)
>>> s=sin(2*pi*50*t)+sin(2*pi*70*t+pi/4)
>>> S=fft(s)
>>> f=sample_rate*r_[0:(N/2)]/N
>>> n=len(f)
>>> plot(f,abs(S[0:n])/N)
>>> show()

}}}

[[Anchor(spline)]]
=== UnivariateSpline() ===

{{{#!python numbers=disable

>>> import numpy
>>> import scipy
>>> import scipy.interpolate
>>> 
>>> x = numpy.arange(10,dtype='float32') * 0.3
>>> y = numpy.cos(x)
>>> 
>>> sp = scipy.interpolate.UnivariateSpline(x,y)
>>> sp(0.5) # should be a good approximation of cos(0.5)=0.8775
 array([ 0.88198072])
}}}

[[Anchor(spline)]]
=== splrep() and splev() ===

{{{#!python numbers=disable

>>> import numpy
>>> import scipy
>>> import scipy.interpolate
>>> 
>>> x = numpy.arange(10,dtype='float32') * 0.3
>>> y = numpy.cos(x)
>>> 
>>> rep = scipy.interpolate.splrep(x,y)
>>> scipy.interpolate.splev(0.5,rep) # should be a good approximation of cos(0.5)=0.8775
 0.881980721213
}}}

[[Anchor(integrate)]]
=== integrate.quad() ===

{{{#!python numbers=disable

>>> from scipy import *
>>> value, err = integrate.quad(func=pow, a=0., b=1., args=(5,))
>>> value  # integral of x^5 over [0,1]
 0.16666666666666669
}}}


[[Anchor(fmin)]]
=== optimize.fmin() ===

{{{#!python numbers=disable
from pylab import *
from numpy import *
from scipy.optimize import fmin

## Parametric function: 'v' is the parameter vector, 'x' the independent variable
fp = lambda v, x: v[0]/(x**v[1])*sin(v[2]*x)

## Noisy function (used to generate data to fit)
v_real = [1.5, 0.1, 2.]
fn = lambda x: fp(v_real, x)

## Error function
e = lambda v, x, y: ((fp(v,x)-y)**2).sum()

## Generating noisy data to fit
n = 30
xmin = 0.1
xmax = 5
x = linspace(xmin,xmax,n)
y = fn(x) + rand(len(x))*0.2*(fn(x).max()-fn(x).min())

## Initial parameter value
v0 = [3., 1, 4.]

## Fitting
v = fmin(e, v0, args=(x,y),maxiter=10000, maxfun=10000)

## Plot
def plot_fit():
    print 'Estimater parameters: ', v
    print 'Real parameters: ', v_real
    X = linspace(xmin,xmax,n*5)
    plot(x,y,'ro', X, fp(v,X))

plot_fit()
show()
}}}

[[Anchor(leastsq)]]
=== optimize.leastsq() ===

{{{#!python numbers=disable
from pylab import *
from numpy import *
from scipy.optimize import leastsq

## Parametric function: 'v' is the parameter vector, 'x' the independent varible
fp = lambda v, x: v[0]/(x**v[1])*sin(v[2]*x)

## Noisy function (used to generate data to fit)
v_real = [1.5, 0.1, 2.]
fn = lambda x: fp(v_real, x)

## Error function
e = lambda v, x, y: (fp(v,x)-y)

## Generating noisy data to fit
n = 30
xmin = 0.1
xmax = 5
x = linspace(xmin,xmax,n)
y = fn(x) + rand(len(x))*0.2*(fn(x).max()-fn(x).min())

## Initial parameter value
v0 = [3., 1, 4.]

## Fitting
v, success = leastsq(e, v0, args=(x,y), maxfev=10000)

## Plot
def plot_fit():
    print 'Estimater parameters: ', v
    print 'Real parameters: ', v_real
    X = linspace(xmin,xmax,n*5)
    plot(x,y,'ro', X, fp(v,X))

plot_fit()
show()
}}}