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 $y=a{x}^{\alpha }$ 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 = 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