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### convolve()

```>>> 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])
```

### fft()

```>>> 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()
```

### UnivariateSpline()

```>>> 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])
```

### splrep() and splev()

```>>> 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
```

```>>> 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
```

### optimize.fmin()

```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()
```

### optimize.leastsq()

```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()
```

SciPy: scipy_Example_List (last edited 2015-10-24 17:48:27 by anonymous)