# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Classes that deal with stretching, i.e. mapping a range of [0:1] values onto
another set of [0:1] values with a transformation.
"""
import numpy as np
from .transform import BaseTransform, CompositeTransform
__all__ = [
"BaseStretch",
"LinearStretch",
"SqrtStretch",
"PowerStretch",
"PowerDistStretch",
"SquaredStretch",
"LogStretch",
"AsinhStretch",
"SinhStretch",
"HistEqStretch",
"ContrastBiasStretch",
"CompositeStretch",
]
def _logn(n, x, out=None):
"""Calculate the log base n of x."""
# We define this because numpy.emath.logn doesn't support the out
# keyword.
if out is None:
return np.log(x) / np.log(n)
else:
np.log(x, out=out)
np.true_divide(out, np.log(n), out=out)
return out
def _prepare(values, clip=True, out=None):
"""
Prepare the data by optionally clipping and copying, and return the
array that should be subsequently used for in-place calculations.
"""
if clip:
return np.clip(values, 0.0, 1.0, out=out)
else:
if out is None:
return np.array(values, copy=True)
else:
out[:] = np.asarray(values)
return out
[docs]
class BaseStretch(BaseTransform):
"""
Base class for the stretch classes, which when called with an array
of values in the range [0:1], returns an transformed array of values
also in the range [0:1].
"""
@property
def _supports_invalid_kw(self):
return False
def __add__(self, other):
return CompositeStretch(other, self)
[docs]
def __call__(self, values, clip=True, out=None):
"""
Transform values using this stretch.
Parameters
----------
values : array-like
The input values, which should already be normalized to the
[0:1] range.
clip : bool, optional
If `True` (default), values outside the [0:1] range are
clipped to the [0:1] range.
out : ndarray, optional
If specified, the output values will be placed in this array
(typically used for in-place calculations).
Returns
-------
result : ndarray
The transformed values.
"""
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
[docs]
class LinearStretch(BaseStretch):
"""
A linear stretch with a slope and offset.
The stretch is given by:
.. math::
y = slope * x + intercept
Parameters
----------
slope : float, optional
The ``slope`` parameter used in the above formula. Default is 1.
intercept : float, optional
The ``intercept`` parameter used in the above formula. Default is 0.
"""
def __init__(self, slope=1, intercept=0):
super().__init__()
self.slope = slope
self.intercept = intercept
[docs]
def __call__(self, values, clip=True, out=None):
values = _prepare(values, clip=clip, out=out)
if self.slope != 1:
np.multiply(values, self.slope, out=values)
if self.intercept != 0:
np.add(values, self.intercept, out=values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return LinearStretch(1.0 / self.slope, -self.intercept / self.slope)
[docs]
class SqrtStretch(BaseStretch):
r"""
A square root stretch.
The stretch is given by:
.. math::
y = \sqrt{x}
"""
@property
def _supports_invalid_kw(self):
return True
[docs]
def __call__(self, values, clip=True, out=None, invalid=None):
"""
Transform values using this stretch.
Parameters
----------
values : array-like
The input values, which should already be normalized to the
[0:1] range.
clip : bool, optional
If `True` (default), values outside the [0:1] range are
clipped to the [0:1] range.
out : ndarray, optional
If specified, the output values will be placed in this array
(typically used for in-place calculations).
invalid : None or float, optional
Value to assign NaN values generated by this class. NaNs in
the input ``values`` array are not changed. This option is
generally used with matplotlib normalization classes, where
the ``invalid`` value should map to the matplotlib colormap
"under" value (i.e., any finite value < 0). If `None`, then
NaN values are not replaced. This keyword has no effect if
``clip=True``.
Returns
-------
result : ndarray
The transformed values.
"""
values = _prepare(values, clip=clip, out=out)
replace_invalid = not clip and invalid is not None
with np.errstate(invalid="ignore"):
if replace_invalid:
idx = values < 0
np.sqrt(values, out=values)
if replace_invalid:
# Assign new NaN (i.e., NaN not in the original input
# values, but generated by this class) to the invalid value.
values[idx] = invalid
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return PowerStretch(2)
[docs]
class PowerStretch(BaseStretch):
r"""
A power stretch.
The stretch is given by:
.. math::
y = x^a
Parameters
----------
a : float
The power index (see the above formula). ``a`` must be greater
than 0.
"""
@property
def _supports_invalid_kw(self):
return True
def __init__(self, a):
super().__init__()
if a <= 0:
raise ValueError("a must be > 0")
self.a = a
[docs]
def __call__(self, values, clip=True, out=None, invalid=None):
"""
Transform values using this stretch.
Parameters
----------
values : array-like
The input values, which should already be normalized to the
[0:1] range.
clip : bool, optional
If `True` (default), values outside the [0:1] range are
clipped to the [0:1] range.
out : ndarray, optional
If specified, the output values will be placed in this array
(typically used for in-place calculations).
invalid : None or float, optional
Value to assign NaN values generated by this class. NaNs in
the input ``values`` array are not changed. This option is
generally used with matplotlib normalization classes, where
the ``invalid`` value should map to the matplotlib colormap
"under" value (i.e., any finite value < 0). If `None`, then
NaN values are not replaced. This keyword has no effect if
``clip=True``.
Returns
-------
result : ndarray
The transformed values.
"""
values = _prepare(values, clip=clip, out=out)
replace_invalid = (
not clip and invalid is not None and ((-1 < self.a < 0) or (0 < self.a < 1))
)
with np.errstate(invalid="ignore"):
if replace_invalid:
idx = values < 0
np.power(values, self.a, out=values)
if replace_invalid:
# Assign new NaN (i.e., NaN not in the original input
# values, but generated by this class) to the invalid value.
values[idx] = invalid
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return PowerStretch(1.0 / self.a)
[docs]
class PowerDistStretch(BaseStretch):
r"""
An alternative power stretch.
The stretch is given by:
.. math::
y = \frac{a^x - 1}{a - 1}
Parameters
----------
a : float, optional
The ``a`` parameter used in the above formula. ``a`` must be
greater than or equal to 0, but cannot be set to 1. Default is
1000.
"""
def __init__(self, a=1000.0):
if a < 0 or a == 1: # singularity
raise ValueError("a must be >= 0, but cannot be set to 1")
super().__init__()
self.a = a
[docs]
def __call__(self, values, clip=True, out=None):
values = _prepare(values, clip=clip, out=out)
np.power(self.a, values, out=values)
np.subtract(values, 1, out=values)
np.true_divide(values, self.a - 1.0, out=values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return InvertedPowerDistStretch(a=self.a)
class InvertedPowerDistStretch(BaseStretch):
r"""
Inverse transformation for
`~astropy.image.scaling.PowerDistStretch`.
The stretch is given by:
.. math::
y = \frac{\log(y (a-1) + 1)}{\log a}
Parameters
----------
a : float, optional
The ``a`` parameter used in the above formula. ``a`` must be
greater than or equal to 0, but cannot be set to 1. Default is
1000.
"""
def __init__(self, a=1000.0):
if a < 0 or a == 1: # singularity
raise ValueError("a must be >= 0, but cannot be set to 1")
super().__init__()
self.a = a
def __call__(self, values, clip=True, out=None):
values = _prepare(values, clip=clip, out=out)
np.multiply(values, self.a - 1.0, out=values)
np.add(values, 1, out=values)
_logn(self.a, values, out=values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return PowerDistStretch(a=self.a)
[docs]
class SquaredStretch(PowerStretch):
r"""
A convenience class for a power stretch of 2.
The stretch is given by:
.. math::
y = x^2
"""
def __init__(self):
super().__init__(2)
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return SqrtStretch()
[docs]
class LogStretch(BaseStretch):
r"""
A log stretch.
The stretch is given by:
.. math::
y = \frac{\log{(a x + 1)}}{\log{(a + 1)}}
Parameters
----------
a : float
The ``a`` parameter used in the above formula. ``a`` must be
greater than 0. Default is 1000.
"""
@property
def _supports_invalid_kw(self):
return True
def __init__(self, a=1000.0):
super().__init__()
if a <= 0: # singularity
raise ValueError("a must be > 0")
self.a = a
[docs]
def __call__(self, values, clip=True, out=None, invalid=None):
"""
Transform values using this stretch.
Parameters
----------
values : array-like
The input values, which should already be normalized to the
[0:1] range.
clip : bool, optional
If `True` (default), values outside the [0:1] range are
clipped to the [0:1] range.
out : ndarray, optional
If specified, the output values will be placed in this array
(typically used for in-place calculations).
invalid : None or float, optional
Value to assign NaN values generated by this class. NaNs in
the input ``values`` array are not changed. This option is
generally used with matplotlib normalization classes, where
the ``invalid`` value should map to the matplotlib colormap
"under" value (i.e., any finite value < 0). If `None`, then
NaN values are not replaced. This keyword has no effect if
``clip=True``.
Returns
-------
result : ndarray
The transformed values.
"""
values = _prepare(values, clip=clip, out=out)
replace_invalid = not clip and invalid is not None
with np.errstate(invalid="ignore"):
if replace_invalid:
idx = values < 0
np.multiply(values, self.a, out=values)
np.add(values, 1.0, out=values)
np.log(values, out=values)
np.true_divide(values, np.log(self.a + 1.0), out=values)
if replace_invalid:
# Assign new NaN (i.e., NaN not in the original input
# values, but generated by this class) to the invalid value.
values[idx] = invalid
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return InvertedLogStretch(self.a)
class InvertedLogStretch(BaseStretch):
r"""
Inverse transformation for `~astropy.image.scaling.LogStretch`.
The stretch is given by:
.. math::
y = \frac{e^{y \log{a + 1}} - 1}{a} \\
y = \frac{e^{y} (a + 1) - 1}{a}
Parameters
----------
a : float, optional
The ``a`` parameter used in the above formula. ``a`` must be
greater than 0. Default is 1000.
"""
def __init__(self, a):
super().__init__()
if a <= 0: # singularity
raise ValueError("a must be > 0")
self.a = a
def __call__(self, values, clip=True, out=None):
values = _prepare(values, clip=clip, out=out)
np.multiply(values, np.log(self.a + 1.0), out=values)
np.exp(values, out=values)
np.subtract(values, 1.0, out=values)
np.true_divide(values, self.a, out=values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return LogStretch(self.a)
[docs]
class AsinhStretch(BaseStretch):
r"""
An asinh stretch.
The stretch is given by:
.. math::
y = \frac{{\rm asinh}(x / a)}{{\rm asinh}(1 / a)}.
Parameters
----------
a : float, optional
The ``a`` parameter used in the above formula. The value of this
parameter is where the asinh curve transitions from linear to
logarithmic behavior, expressed as a fraction of the normalized
image. The stretch becomes more linear as the ``a`` value is
increased. ``a`` must be greater than 0. Default is 0.1.
"""
def __init__(self, a=0.1):
super().__init__()
if a <= 0:
raise ValueError("a must be > 0")
self.a = a
[docs]
def __call__(self, values, clip=True, out=None):
values = _prepare(values, clip=clip, out=out)
np.true_divide(values, self.a, out=values)
np.arcsinh(values, out=values)
np.true_divide(values, np.arcsinh(1.0 / self.a), out=values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return SinhStretch(a=1.0 / np.arcsinh(1.0 / self.a))
[docs]
class SinhStretch(BaseStretch):
r"""
A sinh stretch.
The stretch is given by:
.. math::
y = \frac{{\rm sinh}(x / a)}{{\rm sinh}(1 / a)}
Parameters
----------
a : float, optional
The ``a`` parameter used in the above formula. The stretch
becomes more linear as the ``a`` value is increased. ``a`` must
be greater than 0. Default is 1/3.
"""
def __init__(self, a=1.0 / 3.0):
super().__init__()
if a <= 0:
raise ValueError("a must be > 0")
self.a = a
[docs]
def __call__(self, values, clip=True, out=None):
values = _prepare(values, clip=clip, out=out)
np.true_divide(values, self.a, out=values)
np.sinh(values, out=values)
np.true_divide(values, np.sinh(1.0 / self.a), out=values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return AsinhStretch(a=1.0 / np.sinh(1.0 / self.a))
[docs]
class HistEqStretch(BaseStretch):
"""
A histogram equalization stretch.
Parameters
----------
data : array-like
The data defining the equalization.
values : array-like, optional
The input image values, which should already be normalized to
the [0:1] range.
"""
def __init__(self, data, values=None):
# Assume data is not necessarily normalized at this point
self.data = np.sort(data.ravel())
self.data = self.data[np.isfinite(self.data)]
vmin = self.data.min()
vmax = self.data.max()
self.data = (self.data - vmin) / (vmax - vmin)
# Compute relative position of each pixel
if values is None:
self.values = np.linspace(0.0, 1.0, len(self.data))
else:
self.values = values
[docs]
def __call__(self, values, clip=True, out=None):
values = _prepare(values, clip=clip, out=out)
values[:] = np.interp(values, self.data, self.values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return InvertedHistEqStretch(self.data, values=self.values)
class InvertedHistEqStretch(BaseStretch):
"""
Inverse transformation for `~astropy.image.scaling.HistEqStretch`.
Parameters
----------
data : array-like
The data defining the equalization.
values : array-like, optional
The input image values, which should already be normalized to
the [0:1] range.
"""
def __init__(self, data, values=None):
self.data = data[np.isfinite(data)]
if values is None:
self.values = np.linspace(0.0, 1.0, len(self.data))
else:
self.values = values
def __call__(self, values, clip=True, out=None):
values = _prepare(values, clip=clip, out=out)
values[:] = np.interp(values, self.values, self.data)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return HistEqStretch(self.data, values=self.values)
[docs]
class ContrastBiasStretch(BaseStretch):
r"""
A stretch that takes into account contrast and bias.
The stretch is given by:
.. math::
y = (x - {\rm bias}) * {\rm contrast} + 0.5
and the output values are clipped to the [0:1] range.
Parameters
----------
contrast : float
The contrast parameter (see the above formula).
bias : float
The bias parameter (see the above formula).
"""
def __init__(self, contrast, bias):
super().__init__()
self.contrast = contrast
self.bias = bias
[docs]
def __call__(self, values, clip=True, out=None):
# As a special case here, we only clip *after* the
# transformation since it does not map [0:1] to [0:1]
values = _prepare(values, clip=False, out=out)
np.subtract(values, self.bias, out=values)
np.multiply(values, self.contrast, out=values)
np.add(values, 0.5, out=values)
if clip:
np.clip(values, 0, 1, out=values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return InvertedContrastBiasStretch(self.contrast, self.bias)
class InvertedContrastBiasStretch(BaseStretch):
"""
Inverse transformation for ContrastBiasStretch.
Parameters
----------
contrast : float
The contrast parameter (see
`~astropy.visualization.ConstrastBiasStretch).
bias : float
The bias parameter (see
`~astropy.visualization.ConstrastBiasStretch).
"""
def __init__(self, contrast, bias):
super().__init__()
self.contrast = contrast
self.bias = bias
def __call__(self, values, clip=True, out=None):
# As a special case here, we only clip *after* the
# transformation since it does not map [0:1] to [0:1]
values = _prepare(values, clip=False, out=out)
np.subtract(values, 0.5, out=values)
np.true_divide(values, self.contrast, out=values)
np.add(values, self.bias, out=values)
if clip:
np.clip(values, 0, 1, out=values)
return values
@property
def inverse(self):
"""A stretch object that performs the inverse operation."""
return ContrastBiasStretch(self.contrast, self.bias)
[docs]
class CompositeStretch(CompositeTransform, BaseStretch):
"""
A combination of two stretches.
Parameters
----------
stretch_1 : :class:`astropy.visualization.BaseStretch`
The first stretch to apply.
stretch_2 : :class:`astropy.visualization.BaseStretch`
The second stretch to apply.
"""
[docs]
def __call__(self, values, clip=True, out=None):
return self.transform_2(
self.transform_1(values, clip=clip, out=out), clip=clip, out=out
)
