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find aproximation use least squares method
func must be set while initialisation
basis and points added directly or
use pointsSet for point
and createBasisH or createBasisJ for Head or Jacoby basis
see tests for examples
used as
l=LeastSquares(func='cos(x)')
l.points=list of points or
l.points=lg.choosingPoints(x0=0,n=10)
l.createBasisH()
l.leastSquares(weightFunction=1)
l.plot()
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find interplated function iF for function sin(x) (if you create LeastSquares object
as default)
in Chebyshev points
used Head function basis
r r r r r' r$ N)r r r � createBasisHr* r7 )r r! r! r" �test1HG s
zLeastSquares.test1Hc
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find interplated function iF for function sin(x) (if you create LeastSquares object
as default)
in points from interval 0,\pi
used Head function basis
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find interplated function iF for function sin(x) (if you create LeastSquares object
as default)
in Chebyshev points
used Jacoby basis
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DESCRIPTION:
create basis from Jacobi polynomials
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� | j t | � � q� W| | _ | S) a�
DESCRIPTION:
create Head functions for points:
(x-p_{i-1})/(p_{i}-p_{i-1}) ,x \in [p_{i-1},p_{i}]
H_{i}(x)=(p_{i+1}-x)/(p_{i+1}-p_{i}) ,x \in [p_{i},p_{i+1}]
0,otherwise
it use sympy.Piecewise for conditions
every conditions must be rigorus (<,>), otherwise uninfinite integrals
will be wrong
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DECRIPTIONS:
find a_{i} that satisfy
\integral(g(x)-\sum a_{j}*H_{j}(x))^2)->min
i.e:
find best aproximation of function func in form
L_{2} g= \sum a_{j}*H_{j}(x)
INPUT:
weight function:
for Head functions =1
for Jacobi functions=(1-x)**alpha*(1+x)**beta
self.points:
for Head functions same as for createBasisH
for Jacobi functions points=[-1,1]
self.func:
is function (as string) whom will be aproximated
when you useing Jacoby func mast be from -1 to 1
(for that use subset: f(x)=F((a+b)/2+(b-a)*x/2))
EXAMPLES:
forHead:
see self.test1H and test2H methods
l=LeastSquares(func='cos(x)')
l.points=lg.choocingPoints(x0=0,n=10)
l.createBasisH()
l.leastSquares()
l.plot()
for Jacoby:
see self.test1J methods
x=symbols('x')
W=(1-x)*(1+x)
l.points=[-1,1]
l.createBasisJ(n=5,alpha=1,beta=1)
l.leastSquares(weightFunction=W)
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