colour.continuous.Signal

class colour.continuous.Signal(data=None, domain=None, **kwargs)[source]

Bases: colour.continuous.abstract.AbstractContinuousFunction

Defines the base class for continuous signal.

The class implements the Signal.function() method so that evaluating the function for any independent domain \(x \in\mathbb{R}\) variable returns a corresponding range \(y \in\mathbb{R}\) variable. 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 attribute corresponds with the function dependent and already known range stored in the colour.continuous.Signal.range attribute.

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 (Series or Signal or array_like or dict_like, optional) – Data to be stored in the continuous signal.

  • domain (array_like, optional) – 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 attribute.

Other Parameters
  • name (unicode, optional) – Continuous signal name.

  • dtype (type, optional) – {np.float16, np.float32, np.float64, np.float128}, Floating point data type.

  • interpolator (object, optional) – Interpolator class type to use as interpolating function.

  • interpolator_kwargs (dict_like, optional) – Arguments to use when instantiating the interpolating function.

  • extrapolator (object, optional) – Extrapolator class type to use as extrapolating function.

  • extrapolator_kwargs (dict_like, optional) – Arguments to use when instantiating the extrapolating function.

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 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=None, domain=None, **kwargs)[source]

Initialize self. See help(type(self)) for accurate signature.

property dtype

Getter and setter property for the continuous signal dtype.

Parameters

value (type) – Value to set the continuous signal dtype with.

Returns

Continuous signal dtype.

Return type

type

property domain

Getter and setter property for the continuous signal independent domain \(x\) variable.

Parameters

value (array_like) – Value to set the continuous signal independent domain \(x\) variable with.

Returns

Continuous signal independent domain \(x\) variable.

Return type

ndarray

property range

Getter and setter property for the continuous signal corresponding range \(y\) variable.

Parameters

value (array_like) – Value to set the continuous signal corresponding range \(y\) variable with.

Returns

Continuous signal corresponding range \(y\) variable.

Return type

ndarray

property interpolator

Getter and setter property for the continuous signal interpolator type.

Parameters

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

Returns

Continuous signal interpolator type.

Return type

type

property interpolator_kwargs

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

Parameters

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

Returns

Continuous signal interpolator instantiation time arguments.

Return type

dict

property extrapolator

Getter and setter property for the continuous signal extrapolator type.

Parameters

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

Returns

Continuous signal extrapolator type.

Return type

type

property extrapolator_kwargs

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

Parameters

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

Returns

Continuous signal extrapolator instantiation time arguments.

Return type

dict

property function

Getter property for the continuous signal callable.

Returns

Continuous signal callable.

Return type

callable

__str__()[source]

Returns a formatted string representation of the continuous signal.

Returns

Formatted string representation.

Return type

unicode

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__()[source]

Returns an evaluable string representation of the continuous signal.

Returns

Evaluable string representation.

Return type

unicode

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__()[source]

Returns the abstract continuous function hash.

Returns

Object hash.

Return type

int

__getitem__(x)[source]

Returns the corresponding range \(y\) variable for independent domain \(x\) variable.

Parameters

x (numeric, array_like or slice) – Independent domain \(x\) variable.

Returns

math:y range value.

Return type

numeric or 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, y)[source]

Sets the corresponding range \(y\) variable for independent domain \(x\) variable.

Parameters
  • x (numeric, array_like or slice) – Independent domain \(x\) variable.

  • y (numeric or ndarray) – Corresponding range \(y\) variable.

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)[source]

Returns whether the continuous signal contains given independent domain \(x\) variable.

Parameters

x (numeric, array_like or slice) – Independent domain \(x\) variable.

Returns

Is \(x\) domain value 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)[source]

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

Parameters

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

Returns

Is given object 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)[source]

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

Parameters

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

Returns

Is given object 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, operation, in_place=False)[source]

Performs given arithmetical operation with \(a\) operand, the operation can be either performed on a copy or in-place.

Parameters
  • a (numeric or ndarray or Signal) – Operand.

  • operation (object) – Operation to perform.

  • in_place (bool, optional) – Operation happens in place.

Returns

Continuous signal.

Return type

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 array_like 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=None, domain=None, dtype=None)[source]

Unpack given data for continuous signal instantiation.

Parameters
  • data (Series or Signal or array_like or dict_like, optional) – Data to unpack for continuous signal instantiation.

  • domain (array_like, optional) – 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 attribute.

  • dtype (type, optional) – {np.float16, np.float32, np.float64, np.float128}, Floating point data type.

Returns

Independent domain \(x\) variable and corresponding range \(y\) variable 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 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='Interpolation', default=0)[source]

Fill NaNs in independent domain \(x\) variable and corresponding range \(y\) variable using given method.

Parameters
  • method (unicode, optional) – {‘Interpolation’, ‘Constant’}, Interpolation method linearly interpolates through the NaNs, Constant method replaces NaNs with default.

  • default (numeric, optional) – Value to use with the Constant method.

Returns

NaNs filled continuous signal.

Return type

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()[source]

Converts the continuous signal to a Pandas Series class instance.

Returns

Continuous signal as a Pandas Series class instance.

Return type

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