colour.continuous.Signal¶

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

Bases: colour.continuous.abstract.AbstractContinuousFunction

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

dtype
domain
range
interpolator
interpolator_kwargs
extrapolator
extrapolator_kwargs
function

Methods

__init__()
__str__()
__repr__()
__hash__()
__getitem__()
__setitem__()
__contains__()
__eq__()
__ne__()
arithmetical_operation()
signal_unpack_data()
fill_nan()
to_series()

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: numpy.floating or numpy.ndarray

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) → AbstractContinuousFunction[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

Adding a single numeric variable:

>>> 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.]]

Adding an ArrayLike variable:

>>> 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

data – Data to unpack for continuous signal instantiation.
domain (Optional[ArrayLike]) – Values to initialise the colour.continuous.Signal.domain attribute with. If both data and domain arguments are defined, the latter will be used to initialise the colour.continuous.Signal.domain property.
dtype (Optional[Type[DTypeFloating]]) – Floating point data type.

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) → colour.continuous.abstract.AbstractContinuousFunction[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

colour.continuous.AbstractContinuousFunction

colour.continuous.MultiSignals