funfit module

get y = f(x) based on pair of two points using given function shape.

This is the internal module to help point values calculation.

lin_fit(x, xy_0: tuple, xy_1: tuple)

Get value of point using linear function

Get \(y = f(x)\) using linear function of form \(y = ax\) on range \((x_0, x_1)\)

Parameters:

  • x (scalar) – Point for which return value of y

  • xy_0 (tuple of two floats) – Starting point (x0, y0)

  • xy_1 (tuple of two floats) – Ending point (x1, y1)

Returns:

Value of y at point x.

Return type:

float

Examples

>>> xy_0 = (10, 10)
>>> xy_1 = (20, 30)
>>> x = 11
>>> lin_fit(x, xy_0, xy_1)
12.0
exp_fit(x, xy_0: tuple, xy_1: tuple, alpha: float = 2.0)

Get value of point using exponential function

Get \(y = f(x)\) using exp function of form \(y = ax^\alpha\) on range \((0, 1)\) scaled to \((x_0, x_1)\)

Parameters:

  • x (float) – Point for which return value of y

  • xy_0 (tuple of two floats) – Starting point (x0, y0)

  • xy_1 (tuple of two floats) – Ending point (x1, y1)

  • alpha (float, optional) – Exponent factor. Default is 2.

Returns:

Value of y at point x.

Return type:

float

Examples

>>> xy_0 = (10, 10)
>>> xy_1 = (20, 30)
>>> x = 11
>>> exp_fit(x, xy_0, xy_1, alpha=2.0)
10.2
exp_xy_fit(x, xy_0: tuple, xy_1: tuple, alpha: float = 2.0)

Get value of point using exponential function mirrored over y=x

Get \(y = f(x)\) using exp function mirrored over \(x = y\) line of form \(y = a (1 - (1-x)^\alpha)\) on range \((0, 1)\) scaled to \((x_0, x_1)\)

Parameters:

  • x (float) – Point for which return value of y

  • xy_0 (tuple of two floats) – Starting point (x0, y0)

  • xy_1 (tuple of two floats) – Ending point (x1, y1)

  • alpha (float, optional) – Exponent factor. Default is 2.

Returns:

Value of y at point x.

Return type:

float

Examples

>>> xy_0 = (10, 10)
>>> xy_1 = (20, 30)
>>> x = 19
>>> exp_xy_fit(x, xy_0, xy_1, alpha=2.0)
29.8
exp_lin_fit(x, xy_0: tuple, xy_1: tuple, alpha=2)

Get value of point using combination of linear and exponential function

Get \(y = f(x)\) using linear and exp function line of form \(y = a ((1- b) \cdot x + b \cdot x^\alpha)\) on range \((0, 1)\) scaled to \((x_0, x_1)\) where \(b = (x - x_0)\)

It is a linear combination of values returned be exp_fit() and lin_fit().

Parameters:

  • x (float) – Point for which return value of y

  • xy_0 (tuple of two floats) – Starting point (x0, y0)

  • xy_1 (tuple of two floats) – Ending point (x1, y1)

  • alpha (float, optional) – Exponent factor. Default is 2.

Returns:

Value of y at point x.

Return type:

float

Examples

>>> xy_0 = (10, 10)
>>> xy_1 = (20, 30)
>>> x = 19
>>> exp_lin_fit(x, xy_0, xy_1, alpha=2.0)
27.82
lin_exp_xy_fit(x, xy_0: tuple, xy_1: tuple, alpha=2)

Get value of point using combination of linear and exponential function mirrored over xy line

Get \(y = f(x)\) using linear and exp function line mirrored over xy of form \(y = a (x + 1 - (1-x)^\alpha)\) on range \((0, 1)\) scaled to \((x_0, x_1)\)

It is a linear combination of values returned be lin_fit() and exp_xy_fit().

Parameters:

  • x (float) – Point for which return value of y

  • xy_0 (tuple of two floats) – Starting point (x0, y0)

  • xy_1 (tuple of two floats) – Ending point (x1, y1)

  • alpha (float, optional) – Exponent factor. Default is 2.

Returns:

Value of y at point x.

Return type:

float

Examples

>>> xy_0 = (10, 10)
>>> xy_1 = (20, 30)
>>> x = 19
>>> exp_xy_fit(x, xy_0, xy_1, alpha=2.0)
29.8