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INTUITION PHASE in solving Lagrange interpolation problem:
STEP 0:
a[1:]-a[:-1]
a[::2][1:]-a[::2][:-1]
a[1::2][1:]-a[1::2][:-1]
c[::3][:-1]=a[::3][1:]-a[::3][:-1]
c[1::3][:-1]=a[1::3][1:]-a[1::3][:-1]
c[2::3][:-1]=a[2::3][1:]-a[2::3][:-1]
c[3::3][:-1]=a[3::3][1:]-a[3::3][:-1]
c[4::3][:-1]=a[4::3][1:]-a[4::3][:-1]
c[5::3][:-1]=a[5::3][1:]-a[5::3][:-1]
c[6::3][:-1]=a[6::3][1:]-a[6::3][:-1]
6=9-3
for i in range(len(a)-1-3):
c[i::3]=a[i::3][1:]-a[i::3][:-1]
STEP 1:
c[::9]
c=d=ones((n+1,n))
c[0]=a
c[1]=f
QUESTIONs:
+c=ones((n+1),n)#i.e lines below
+c=ones((n+1),n)
+j from 1 or 2 ?
+if from 1 what menans i
STEP 5:
c[0]=a[1:]-a[:-1]
for j in range(len(a)-1+1)[2:]:
for i in range(len(a)-1-j+1):
c[j-1][i::j][:-1]=a[i::j][1:]-a[i::j][:-1]
d[j+2]=(d[j+1][1:]-d[j+1][:-1])/float(c[j+2])
SOME USEFUL REMARKs:
f = implemented_function(Function('f'), lambda x: x+1)
func = lambdify(x, f(x))
func(4)
expr=sp.parsing.sympy_parser.parse_expr("sin(x)+x**2")
sp.diff(expr)
ff=sp.lambdify(x,sp.diff(expr),"numpy")
TESTS:
import src.lagrange as lg
lg.lagrangeInterp(listX=[pi,2*pi,3*pi,2*pi])
lg.lagrangeInterp(listX=[0,-2,0.5,2/3.],func='x*sin(pi*x)')
lg.lagrangeInterp(listX=[-1,-1,1,1],func="sin(pi*x)")
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DECRCIPTION:
find len(points)-1 derivation of function func
step1 (find b):
b[n]=a[n]
for k=n-1,...,1 do
b[k]=a[k]+(x0-x[k])b[k+1]
b[1] is f'(x0)
step2:
a=b
and try agen step1
after k+1 steps
b[1]=f'(x0),...,b[k]=f^{k}(x0)
INPUT:
func-whom derivations we want to find
x0 is point to find derivations in
points will be generated in small area near x0 as Chebyshev points
questions:
+x0 from left in points?
+check array.copy's
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