def PolyDivModOverZn(a: poly, b: poly, n: int) -> (poly, poly):
if n < 1:
raise ValueError
if n==1:
raise ZeroDivisionError
a = poly(np.mod(a.coef, n))
b = poly(np.mod(b.coef, n))
a = a.trim()
b = b.trim()
deg_a, deg_b = len(a.coef), len(b.coef)
if deg_a < deg_b:
return poly([0]), a
else:
f = poly(b.coef[::-1]).trim()
g = PolyInverseModOverZn(f, deg_a - deg_b + 1, n)
if g is None:
raise ZeroDivisionError
q = (poly(a.coef[::-1]).trim() * g).truncate(deg_a - deg_b + 1) # q:=rev_n(a)g mod x^(n-m+1)
q = poly(np.mod(q.coef, n))
q = poly(q.coef[::-1]).trim() # q:=rev_(n-m)(q)
if len(q.coef) < deg_a - deg_b + 1:
q.coef = np.concatenate([np.zeros(deg_a - deg_b + 1 - len(q)), q.coef])
bq = poly(np.mod((b * q).coef, n))
r = a - bq
r = poly(np.mod(r.coef, n))
q = poly(np.mod(q.coef, n))
r = r.trim()
q = q.trim()
return q, r
def test_1dfit(self):
p = [100, -20, 1, -0.2]
h = Histogram(100, [0, 10])
x = h.axes[0].bincenters
h.data = poly(p)(x) + rand.normal(0, np.sqrt(p[0]), len(x))
p0 = [1, 1, 1, 1]
popt, pcov, ptest = h.fit(lambda x, *p: poly(p)(x), p0)
assert np.allclose(popt, p, rtol=0.03, atol=0.5)
assert pcov.shape == (len(p), len(p))
def test_1dfit(self):
p = [100, -20, 1, -0.2]
h = Histogram(100, [0, 10])
x = h.axes[0].bincenters
h.data = poly(p)(x) + rand.normal(0, np.sqrt(p[0]), len(x))
p0 = [1, 1, 1, 1]
popt, pcov, ptest = h.fit(lambda x, *p: poly(p)(x), p0)
assert np.allclose(popt, p, rtol=0.03, atol=0.5)
assert pcov.shape == (len(p), len(p))
def test_2dfit(self):
fn = lambda xy, *p: poly(p[:4])(xy[0]) + poly([0] + list(p[4:]))(xy[1])
p = [100, -20, 1, -0.2, 80, -5, 0.8]
h = Histogram(100, [0, 10], 100, [0, 10])
xy = h.grid
h.data = fn(xy, *p)
h.data += rand.normal(0, np.sqrt(p[0]), h.data.shape)
p0 = [1, 1, 1, 1, 1, 1, 1]
popt, pcov, ptest = h.fit(fn, p0)
assert np.allclose(popt, p, rtol=0.01, atol=0.01)
assert pcov.shape == (len(p), len(p))
def test_2dfit(self):
fn = lambda xy, *p: poly(p[:4])(xy[0]) + poly([0] + list(p[4:]))(xy[1])
p = [100, -20, 1, -0.2, 80, -5, 0.8]
h = Histogram(100, [0, 10], 100, [0, 10])
xy = h.grid
h.data = fn(xy, *p)
h.data += rand.normal(0, np.sqrt(p[0]), h.data.shape)
p0 = [1, 1, 1, 1, 1, 1, 1]
popt, pcov, ptest = h.fit(fn, p0)
assert np.allclose(popt, p, rtol=0.01, atol=0.01)
assert pcov.shape == (len(p), len(p))
def test_1dfit_zeros(self):
p = [100, -20, 1, -0.2]
h = Histogram(100, [0, 10])
x = h.axes[0].bincenters
h.data = poly(p)(x) + rand.normal(0, np.sqrt(p[0]), len(x))
ii = rand.randint(0, h.axes[0].nbins, 5)
h.data[ii] = 0
p0 = [1, 1, 1, 1]
popt, pcov, ptest = h.fit(lambda x, *p: poly(p)(x), p0)
assert np.allclose(popt, p, rtol=0.1, atol=1.0)
assert pcov.shape == (len(p), len(p))
def test_1dfit_zeros(self):
p = [100, -20, 1, -0.2]
h = Histogram(100, [0, 10])
x = h.axes[0].bincenters
h.data = poly(p)(x) + rand.normal(0, np.sqrt(p[0]), len(x))
ii = rand.randint(0, h.axes[0].nbins, 5)
h.data[ii] = 0
p0 = [1, 1, 1, 1]
popt, pcov, ptest = h.fit(lambda x, *p: poly(p)(x), p0)
assert np.allclose(popt, p, rtol=0.1, atol=1.)
assert pcov.shape == (len(p), len(p))
def PolyDivModOverQ(a: poly, b: poly) -> (poly, poly):
if not b.coef.any(): #если полином нулевой
raise ZeroDivisionError
a = a.trim()
b = b.trim()
n, m = len(a.coef), len(b.coef) # степени полиномов
if n < m:
return poly([0]), a
else:
f = poly(b.coef[::-1]).trim() #f:=rev_m(b)
g = PolyInverseModOverQ(f, n - m + 1) #q inverse of f modulo x^(n-m+1)
q = (poly(a.coef[::-1]).trim() * g).truncate(n - m + 1)#q:=rev_n(a)g mod x^(n-m+1)
q = poly(q.coef[::-1]).trim() #q:=rev_(n-m)(q)
if len(q.coef) < n - m + 1:
q.coef = np.concatenate([np.zeros(n - len(q)), q.coef])
r = a - b * q #r:=a-bq
r = r.trim()
q = q.trim()
return q, r
def PolyInverseModOverZn(f: poly, r: int, n: int) :
if r < 1 or n < 1:
raise ValueError
if f.coef[0] == 0 or n == 1:
return None
f = poly(np.mod(f.coef, n))
c = func(f.coef[0], n)
if c is None:
return None
g = poly([c])
r = int(np.ceil(np.log2(r)))
x = 2
for i in range(r):
g = (2 * g - f * g ** 2).truncate(x)
g.coef = np.mod(g.coef, n)
x <<= 1
return g
def PolyInverseModOverQ(f: poly, r): # f*g=1modx^r
if r < 1:
raise ValueError
l = int(np.ceil(np.log2(r)))
if f.coef[0] != 0:
g=poly([1 / f.coef[0]])
else:
return None
x = 2
if g==None:
return None
for number in range(l):
g = (2 * g - f * g ** 2).truncate(x)
x <<= 1
return g
