def calc_linear_least_squares(
points: list[Point]) -> Optional[ApproximationResult]:
sx = sxx = sy = sxy = 0
number_of_points = len(points)
for point in points:
sx += point.x
sxx += point.x**2
sy += point.y
sxy += point.x * point.y
determinant = sxx * number_of_points - sx * sx
if determinant == 0:
return None
a = (sxy * number_of_points - sx * sy) / determinant
b = (sxx * sy - sx * sxy) / determinant
def func(x):
return a * x + b
func_text = '{:.3f} * x + {:.3f}'.format(a, b)
measure = calc_deviation_measure(func, points)
standard_deviation = calc_standard_deviation(func, points)
return ApproximationResult(func, [a, b],
points,
measure,
standard_deviation,
func_text=func_text,
description='Линейная аппроксимация')
def calc_logarithmic_least_squares(
points: list[Point]) -> Optional[ApproximationResult]:
sx = sxx = sy = sxy = 0
number_of_points = len(points)
for point in points:
if point.x <= 0 or point.y <= 0:
return None
sx += log(point.x)
sxx += log(point.x)**2
sy += point.y
sxy += log(point.x) * point.y
determinant = sxx * number_of_points - sx * sx
if determinant == 0:
return None
a = (sxy * number_of_points - sx * sy) / determinant
b = (sxx * sy - sx * sxy) / determinant
def func(x):
return a * log(x) + b
func_text = '{:.3f} * log(x) + {:.3f}'.format(a, b)
measure = calc_deviation_measure(func, points)
standard_deviation = calc_standard_deviation(func, points)
return ApproximationResult(func, [a, b],
points,
measure,
standard_deviation,
func_text=func_text,
description='Логарифмическая аппроксимация')
def calc_power_least_squares(
points: list[Point]) -> Optional[ApproximationResult]:
sx = sxx = sy = sxy = 0
number_of_points = len(points)
# X = ln(x)
# Y = ln(y)
for point in points:
if point.x <= 0:
return None
sx += log(point.x)
sxx += log(point.x)**2
sy += log(point.y)
sxy += log(point.x) * log(point.y)
determinant = sxx * number_of_points - sx * sx
if determinant == 0:
return None
b = (sxy * number_of_points - sx * sy) / determinant
a = (sxx * sy - sx * sxy) / determinant
a1 = exp(a) # a = ln(a1)
b1 = b
def func(x):
return a1 * x**b1
func_text = '{:.3f} * x^{:.3f}'.format(a1, b1)
measure = calc_deviation_measure(func, points)
standard_deviation = calc_standard_deviation(func, points)
return ApproximationResult(func, [a1, b1],
points,
measure,
standard_deviation,
func_text=func_text,
description='Степенная аппроксимация')
def calc_exponential_least_squares(
points: list[Point]) -> Optional[ApproximationResult]:
sx = sxx = sy = sxy = 0
number_of_points = len(points)
for point in points:
sx += point.x
sxx += point.x**2
if point.y <= 0:
return None
sy += log(point.y)
sxy += point.x * log(point.y)
determinant = sxx * number_of_points - sx * sx
if determinant == 0:
return None
b = (sxy * number_of_points - sx * sy) / determinant
a = (sxx * sy - sx * sxy) / determinant
a1 = exp(a) # a = ln(a1)
b1 = b
def func(x):
return a1 * exp(b1 * x)
func_text = '{:.3f} * e^({:.3f} * x)'.format(a1, b1)
measure = calc_deviation_measure(func, points)
standard_deviation = calc_standard_deviation(func, points)
return ApproximationResult(func, [a1, b1],
points,
measure,
standard_deviation,
func_text=func_text,
description='Экспоненциальная аппроксимация')
def calc_quadratic_least_squares(
points: list[Point]) -> Optional[ApproximationResult]:
sx = sy = sx2 = sx3 = sx4 = sxy = sx2y = 0
number_of_points = len(points)
for x, y in points:
sx += x
sx2 += x**2
sx3 += x**3
sx4 += x**4
sy += y
sxy += x * y
sx2y += x**2 * y
matrix = [[number_of_points, sx, sx2, sy], [sx, sx2, sx3, sxy],
[sx2, sx3, sx4, sx2y]]
decision_count, decisions, _ = solve_sle(matrix)
if decision_count != Decision.SINGLE:
return None
a0, a1, a2 = decisions
def func(arg):
return a0 + a1 * arg + a2 * arg**2
func_text = '{:3f} + {:.3f} * x + {:.3f} * x^2'.format(a0, a1, a2)
measure = calc_deviation_measure(func, points)
standard_deviation = calc_standard_deviation(func, points)
return ApproximationResult(func, [a0, a1, a2],
points,
measure,
standard_deviation,
func_text=func_text,
description='Квадратичная аппроксимация')