colour.continuous.Signal¶

class colour.continuous.Signal(data: Optional[Union[ArrayLike, dict, Series, Signal]] = None, domain: Optional[ArrayLike] = None, **kwargs: Any)[source]

Define the base class for continuous signal.

The class implements the Signal.function() method so that evaluating the function for any independent domain variable $$x \in\mathbb{R}$$ returns a corresponding range variable $$y \in\mathbb{R}$$. It adopts an interpolating function encapsulated inside an extrapolating function. The resulting function independent domain, stored as discrete values in the colour.continuous.Signal.domain property corresponds with the function dependent and already known range stored in the colour.continuous.Signal.range property.

Important

Specific documentation about getting, setting, indexing and slicing the continuous signal values is available in the Spectral Representation and Continuous Signal section.

Parameters
• data (Optional[Union[ArrayLike, dict, Series, Signal]]) – Data to be stored in the continuous signal.

• domain (Optional[ArrayLike]) – Values to initialise the colour.continuous.Signal.domain attribute with. If both data and domain arguments are defined, the latter with be used to initialise the colour.continuous.Signal.domain property.

• dtype – Floating point data type.

• extrapolator – Extrapolator class type to use as extrapolating function.

• extrapolator_kwargs – Arguments to use when instantiating the extrapolating function.

• interpolator – Interpolator class type to use as interpolating function.

• interpolator_kwargs – Arguments to use when instantiating the interpolating function.

• name – Continuous signal name.

• kwargs (Any) –

Attributes

Methods

Examples

Instantiation with implicit domain:

>>> range_ = np.linspace(10, 100, 10)
>>> print(Signal(range_))
[[   0.   10.]
[   1.   20.]
[   2.   30.]
[   3.   40.]
[   4.   50.]
[   5.   60.]
[   6.   70.]
[   7.   80.]
[   8.   90.]
[   9.  100.]]


Instantiation with explicit domain:

>>> domain = np.arange(100, 1100, 100)
>>> print(Signal(range_, domain))
[[  100.    10.]
[  200.    20.]
[  300.    30.]
[  400.    40.]
[  500.    50.]
[  600.    60.]
[  700.    70.]
[  800.    80.]
[  900.    90.]
[ 1000.   100.]]


Instantiation with a dict:

>>> print(Signal(dict(zip(domain, range_))))
[[  100.    10.]
[  200.    20.]
[  300.    30.]
[  400.    40.]
[  500.    50.]
[  600.    60.]
[  700.    70.]
[  800.    80.]
[  900.    90.]
[ 1000.   100.]]


Instantiation with a Pandas pandas.Series:

>>> if is_pandas_installed():
...     from pandas import Series
...     print(Signal(
...         Series(dict(zip(domain, range_)))))
[[  100.    10.]
[  200.    20.]
[  300.    30.]
[  400.    40.]
[  500.    50.]
[  600.    60.]
[  700.    70.]
[  800.    80.]
[  900.    90.]
[ 1000.   100.]]


Retrieving domain y variable for arbitrary range x variable:

>>> x = 150
>>> range_ = np.sin(np.linspace(0, 1, 10))
>>> Signal(range_, domain)[x]
0.0359701...
>>> x = np.linspace(100, 1000, 3)
>>> Signal(range_, domain)[x]
array([  ...,   4.7669395...e-01,   8.4147098...e-01])


Using an alternative interpolating function:

>>> x = 150
>>> from colour.algebra import CubicSplineInterpolator
>>> Signal(
...     range_,
...     domain,
...     interpolator=CubicSplineInterpolator)[x]
0.0555274...
>>> x = np.linspace(100, 1000, 3)
>>> Signal(
...     range_,
...     domain,
...     interpolator=CubicSplineInterpolator)[x]
array([ 0.        ,  0.4794253...,  0.8414709...])

__init__(data: Optional[Union[ArrayLike, dict, Series, Signal]] = None, domain: Optional[ArrayLike] = None, **kwargs: Any)[source]
Parameters
• data (Optional[Union[ArrayLike, dict, Series, Signal]]) –

• domain (Optional[ArrayLike]) –

• kwargs (Any) –

property dtype

Getter and setter property for the continuous signal dtype.

Parameters

value – Value to set the continuous signal dtype with.

Returns

Continuous signal dtype.

Return type

DTypeFloating

property domain: numpy.ndarray

Getter and setter property for the continuous signal independent domain variable $$x$$.

Parameters

value – Value to set the continuous signal independent domain variable $$x$$ with.

Returns

Continuous signal independent domain variable $$x$$.

Return type

numpy.ndarray

property range: numpy.ndarray

Getter and setter property for the continuous signal corresponding range variable $$y$$.

Parameters

value – Value to set the continuous signal corresponding range $$y$$ variable with.

Returns

Continuous signal corresponding range variable $$y$$.

Return type

numpy.ndarray

property interpolator: Type[colour.hints.TypeInterpolator]

Getter and setter property for the continuous signal interpolator type.

Parameters

value – Value to set the continuous signal interpolator type with.

Returns

Continuous signal interpolator type.

Return type

Type[TypeInterpolator]

property interpolator_kwargs: Dict

Getter and setter property for the continuous signal interpolator instantiation time arguments.

Parameters

value – Value to set the continuous signal interpolator instantiation time arguments to.

Returns

Continuous signal interpolator instantiation time arguments.

Return type

dict

property extrapolator: Type[colour.hints.TypeExtrapolator]

Getter and setter property for the continuous signal extrapolator type.

Parameters

value – Value to set the continuous signal extrapolator type with.

Returns

Continuous signal extrapolator type.

Return type

Type[TypeExtrapolator]

property extrapolator_kwargs: Dict

Getter and setter property for the continuous signal extrapolator instantiation time arguments.

Parameters

value – Value to set the continuous signal extrapolator instantiation time arguments to.

Returns

Continuous signal extrapolator instantiation time arguments.

Return type

dict

property function: Callable

Getter property for the continuous signal callable.

Returns

Continuous signal callable.

Return type

Callable

__str__() str[source]

Return a formatted string representation of the continuous signal.

Returns

Formatted string representation.

Return type

str

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> print(Signal(range_))
[[   0.   10.]
[   1.   20.]
[   2.   30.]
[   3.   40.]
[   4.   50.]
[   5.   60.]
[   6.   70.]
[   7.   80.]
[   8.   90.]
[   9.  100.]]

__repr__() str[source]

Return an evaluable string representation of the continuous signal.

Returns

Evaluable string representation.

Return type

str

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> Signal(range_)
Signal([[   0.,   10.],
[   1.,   20.],
[   2.,   30.],
[   3.,   40.],
[   4.,   50.],
[   5.,   60.],
[   6.,   70.],
[   7.,   80.],
[   8.,   90.],
[   9.,  100.]],
interpolator=KernelInterpolator,
interpolator_kwargs={},
extrapolator=Extrapolator,
extrapolator_kwargs={...})

__hash__() int[source]

Return the abstract continuous function hash.

Returns

Object hash.

Return type

numpy.integer

__getitem__(x: Union[FloatingOrArrayLike, slice]) FloatingOrNDArray[source]

Return the corresponding range variable $$y$$ for independent domain variable $$x$$.

Parameters

x (Union[FloatingOrArrayLike, slice]) – Independent domain variable $$x$$.

Returns

Variable $$y$$ range value.

Return type

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> signal = Signal(range_)
>>> print(signal)
[[   0.   10.]
[   1.   20.]
[   2.   30.]
[   3.   40.]
[   4.   50.]
[   5.   60.]
[   6.   70.]
[   7.   80.]
[   8.   90.]
[   9.  100.]]
>>> signal[0]
10.0
>>> signal[np.array([0, 1, 2])]
array([ 10.,  20.,  30.])
>>> signal[0:3]
array([ 10.,  20.,  30.])
>>> signal[np.linspace(0, 5, 5)]
array([ 10.        ,  22.8348902...,  34.8004492...,  47.5535392...,  60.        ])

__setitem__(x: Union[FloatingOrArrayLike, slice], y: FloatingOrArrayLike)[source]

Set the corresponding range variable $$y$$ for independent domain variable $$x$$.

Parameters
• x (Union[FloatingOrArrayLike, slice]) – Independent domain variable $$x$$.

• y (FloatingOrArrayLike) – Corresponding range variable $$y$$.

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> signal = Signal(range_)
>>> print(signal)
[[   0.   10.]
[   1.   20.]
[   2.   30.]
[   3.   40.]
[   4.   50.]
[   5.   60.]
[   6.   70.]
[   7.   80.]
[   8.   90.]
[   9.  100.]]
>>> signal[0] = 20
>>> signal[0]
20.0
>>> signal[np.array([0, 1, 2])] = 30
>>> signal[np.array([0, 1, 2])]
array([ 30.,  30.,  30.])
>>> signal[0:3] = 40
>>> signal[0:3]
array([ 40.,  40.,  40.])
>>> signal[np.linspace(0, 5, 5)] = 50
>>> print(signal)
[[   0.     50.  ]
[   1.     40.  ]
[   1.25   50.  ]
[   2.     40.  ]
[   2.5    50.  ]
[   3.     40.  ]
[   3.75   50.  ]
[   4.     50.  ]
[   5.     50.  ]
[   6.     70.  ]
[   7.     80.  ]
[   8.     90.  ]
[   9.    100.  ]]
>>> signal[np.array([0, 1, 2])] = np.array([10, 20, 30])
>>> print(signal)
[[   0.     10.  ]
[   1.     20.  ]
[   1.25   50.  ]
[   2.     30.  ]
[   2.5    50.  ]
[   3.     40.  ]
[   3.75   50.  ]
[   4.     50.  ]
[   5.     50.  ]
[   6.     70.  ]
[   7.     80.  ]
[   8.     90.  ]
[   9.    100.  ]]

__contains__(x: Union[FloatingOrArrayLike, slice]) bool[source]

Return whether the continuous signal contains given independent domain variable $$x$$.

Parameters

x (Union[FloatingOrArrayLike, slice]) – Independent domain variable $$x$$.

Returns

Whether $$x$$ domain value is contained.

Return type

bool

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> signal = Signal(range_)
>>> 0 in signal
True
>>> 0.5 in signal
True
>>> 1000 in signal
False

__eq__(other: Any) bool[source]

Return whether the continuous signal is equal to given other object.

Parameters

other (Any) – Object to test whether it is equal to the continuous signal.

Returns

Whether given object is equal to the continuous signal.

Return type

bool

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> signal_1 = Signal(range_)
>>> signal_2 = Signal(range_)
>>> signal_1 == signal_2
True
>>> signal_2[0] = 20
>>> signal_1 == signal_2
False
>>> signal_2[0] = 10
>>> signal_1 == signal_2
True
>>> from colour.algebra import CubicSplineInterpolator
>>> signal_2.interpolator = CubicSplineInterpolator
>>> signal_1 == signal_2
False

__ne__(other: Any) bool[source]

Return whether the continuous signal is not equal to given other object.

Parameters

other (Any) – Object to test whether it is not equal to the continuous signal.

Returns

Whether given object is not equal to the continuous signal.

Return type

bool

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> signal_1 = Signal(range_)
>>> signal_2 = Signal(range_)
>>> signal_1 != signal_2
False
>>> signal_2[0] = 20
>>> signal_1 != signal_2
True
>>> signal_2[0] = 10
>>> signal_1 != signal_2
False
>>> from colour.algebra import CubicSplineInterpolator
>>> signal_2.interpolator = CubicSplineInterpolator
>>> signal_1 != signal_2
True

arithmetical_operation(a: Union[FloatingOrArrayLike, AbstractContinuousFunction], operation: Literal['+', '-', '*', '/', '**'], in_place: Boolean = False) [source]

Perform given arithmetical operation with operand $$a$$, the operation can be either performed on a copy or in-place.

Parameters
• a (Union[FloatingOrArrayLike, AbstractContinuousFunction]) – Operand $$a$$.

• operation (Literal[('+', '-', '*', '/', '**')]) – Operation to perform.

• in_place (Boolean) – Operation happens in place.

Returns

Continuous signal.

Return type

colour.continuous.Signal

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> signal_1 = Signal(range_)
>>> print(signal_1)
[[   0.   10.]
[   1.   20.]
[   2.   30.]
[   3.   40.]
[   4.   50.]
[   5.   60.]
[   6.   70.]
[   7.   80.]
[   8.   90.]
[   9.  100.]]
>>> print(signal_1.arithmetical_operation(10, '+', True))
[[   0.   20.]
[   1.   30.]
[   2.   40.]
[   3.   50.]
[   4.   60.]
[   5.   70.]
[   6.   80.]
[   7.   90.]
[   8.  100.]
[   9.  110.]]


>>> a = np.linspace(10, 100, 10)
>>> print(signal_1.arithmetical_operation(a, '+', True))
[[   0.   30.]
[   1.   50.]
[   2.   70.]
[   3.   90.]
[   4.  110.]
[   5.  130.]
[   6.  150.]
[   7.  170.]
[   8.  190.]
[   9.  210.]]


Adding a colour.continuous.Signal class:

>>> signal_2 = Signal(range_)
>>> print(signal_1.arithmetical_operation(signal_2, '+', True))
[[   0.   40.]
[   1.   70.]
[   2.  100.]
[   3.  130.]
[   4.  160.]
[   5.  190.]
[   6.  220.]
[   7.  250.]
[   8.  280.]
[   9.  310.]]

static signal_unpack_data(data=Optional[Union[ArrayLike, dict, Series, 'Signal']], domain: Optional[ArrayLike] = None, dtype: Optional[Type[DTypeFloating]] = None) Tuple[source]

Unpack given data for continuous signal instantiation.

Parameters
Returns

Independent domain variable $$x$$ and corresponding range variable $$y$$ unpacked for continuous signal instantiation.

Return type

tuple

Examples

Unpacking using implicit domain:

>>> range_ = np.linspace(10, 100, 10)
>>> domain, range_ = Signal.signal_unpack_data(range_)
>>> print(domain)
[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9.]
>>> print(range_)
[  10.   20.   30.   40.   50.   60.   70.   80.   90.  100.]


Unpacking using explicit domain:

>>> domain = np.arange(100, 1100, 100)
>>> domain, range = Signal.signal_unpack_data(range_, domain)
>>> print(domain)
[  100.   200.   300.   400.   500.   600.   700.   800.   900.  1000.]
>>> print(range_)
[  10.   20.   30.   40.   50.   60.   70.   80.   90.  100.]


Unpacking using a dict:

>>> domain, range_ = Signal.signal_unpack_data(
...     dict(zip(domain, range_)))
>>> print(domain)
[  100.   200.   300.   400.   500.   600.   700.   800.   900.  1000.]
>>> print(range_)
[  10.   20.   30.   40.   50.   60.   70.   80.   90.  100.]


Unpacking using a Pandas pandas.Series:

>>> if is_pandas_installed():
...     from pandas import Series
...     domain, range = Signal.signal_unpack_data(
...         Series(dict(zip(domain, range_))))
...
>>> print(domain)
[  100.   200.   300.   400.   500.   600.   700.   800.   900.  1000.]
>>> print(range_)
[  10.   20.   30.   40.   50.   60.   70.   80.   90.  100.]


Unpacking using a colour.continuous.Signal class:

>>> domain, range_ = Signal.signal_unpack_data(
...     Signal(range_, domain))
>>> print(domain)
[  100.   200.   300.   400.   500.   600.   700.   800.   900.  1000.]
>>> print(range_)
[  10.   20.   30.   40.   50.   60.   70.   80.   90.  100.]

fill_nan(method: Union[Literal['Constant', 'Interpolation'], str] = 'Interpolation', default: Number = 0) [source]

Fill NaNs in independent domain variable $$x$$ and corresponding range variable $$y$$ using given method.

Parameters
• method (Union[Literal['Constant', 'Interpolation'], str]) – Interpolation method linearly interpolates through the NaNs, Constant method replaces NaNs with default.

• default (Number) – Value to use with the Constant method.

Returns

NaNs filled continuous signal.

Return type

colour.continuous.Signal

Examples

>>> range_ = np.linspace(10, 100, 10)
>>> signal = Signal(range_)
>>> signal[3:7] = np.nan
>>> print(signal)
[[   0.   10.]
[   1.   20.]
[   2.   30.]
[   3.   nan]
[   4.   nan]
[   5.   nan]
[   6.   nan]
[   7.   80.]
[   8.   90.]
[   9.  100.]]
>>> print(signal.fill_nan())
[[   0.   10.]
[   1.   20.]
[   2.   30.]
[   3.   40.]
[   4.   50.]
[   5.   60.]
[   6.   70.]
[   7.   80.]
[   8.   90.]
[   9.  100.]]
>>> signal[3:7] = np.nan
>>> print(signal.fill_nan(method='Constant'))
[[   0.   10.]
[   1.   20.]
[   2.   30.]
[   3.    0.]
[   4.    0.]
[   5.    0.]
[   6.    0.]
[   7.   80.]
[   8.   90.]
[   9.  100.]]

to_series() <MagicMock id='139819393691456'>[source]

Convert the continuous signal to a Pandas pandas.Series class instance.

Returns

Continuous signal as a Pandaspandas.Series class instance.

Return type

pandas.Series

Examples

>>> if is_pandas_installed():
...     range_ = np.linspace(10, 100, 10)
...     signal = Signal(range_)
...     print(signal.to_series())
0.0     10.0
1.0     20.0
2.0     30.0
3.0     40.0
4.0     50.0
5.0     60.0
6.0     70.0
7.0     80.0
8.0     90.0
9.0    100.0
Name: Signal (...), dtype: float64