Bases: Kernel
Ramp kernel class for Gaussian Processes (GPs).
The Ramp class defines a kernel that produces a covariance structure resembling a "ramp" function.
It is characterized by a sill (variance) and a range (length scale) and can optionally use a metric for scaling.
Parameters:
-
range
(float or Variable)
–
The length scale parameter that controls how quickly the covariance decreases with distance.
-
sill
(float or Variable)
–
The variance (sill) of the kernel, representing the maximum covariance value.
-
scale
(optional, default:
None
)
–
An optional scale parameter that can be used to modify the metric. Default is None.
-
metric
(optional, default:
None
)
–
An optional metric used for distance calculation. Default is None.
Examples:
Creating and using a Ramp kernel:
from geostat.kernel import Ramp
# Create a Ramp kernel with sill=1.0 and range=2.0
ramp_kernel = Ramp(range=2.0, sill=1.0)
locs1 = np.array([[0.0], [1.0], [2.0]])
locs2 = np.array([[0.0], [1.0], [2.0]])
covariance_matrix = ramp_kernel({'locs1': locs1, 'locs2': locs2, 'sill': 1.0, 'range': 2.0})
Notes:
- The
call method computes the covariance matrix using the ramp function:
\( C(x, x') = \text{sill} \cdot \text{ramp}\left(\frac{\sqrt{d^2}}{\text{range}}\right) \),
where \(d^2\) is the squared distance between locs1 and locs2.
- The
vars method returns the parameter dictionary for both sill and range using the ppp function.
- The
Ramp kernel can be used in cases where the covariance structure exhibits a linear decay with increasing distance.
Source code in src/geostat/kernel.py
| class Ramp(Kernel):
"""
Ramp kernel class for Gaussian Processes (GPs).
The `Ramp` class defines a kernel that produces a covariance structure resembling a "ramp" function.
It is characterized by a sill (variance) and a range (length scale) and can optionally use a metric for scaling.
Parameters:
range (float or tf.Variable):
The length scale parameter that controls how quickly the covariance decreases with distance.
sill (float or tf.Variable):
The variance (sill) of the kernel, representing the maximum covariance value.
scale (optional):
An optional scale parameter that can be used to modify the metric. Default is None.
metric (optional):
An optional metric used for distance calculation. Default is None.
Examples:
Creating and using a `Ramp` kernel:
```python
from geostat.kernel import Ramp
# Create a Ramp kernel with sill=1.0 and range=2.0
ramp_kernel = Ramp(range=2.0, sill=1.0)
locs1 = np.array([[0.0], [1.0], [2.0]])
locs2 = np.array([[0.0], [1.0], [2.0]])
covariance_matrix = ramp_kernel({'locs1': locs1, 'locs2': locs2, 'sill': 1.0, 'range': 2.0})
```
Examples: Notes:
- The `call` method computes the covariance matrix using the ramp function:
\\( C(x, x') = \\text{sill} \cdot \\text{ramp}\left(\\frac{\sqrt{d^2}}{\\text{range}}\\right) \\),
where \\(d^2\\) is the squared distance between `locs1` and `locs2`.
- The `vars` method returns the parameter dictionary for both `sill` and `range` using the `ppp` function.
- The `Ramp` kernel can be used in cases where the covariance structure exhibits a linear decay with increasing distance.
"""
def __init__(self, range, sill, scale=None, metric=None):
fa = dict(sill=sill, range=range, scale=scale)
autoinputs = scale_to_metric(scale, metric)
super().__init__(fa, dict(d2=autoinputs))
def vars(self):
return ppp(self.fa['sill']) | ppp(self.fa['range'])
def call(self, e):
return e['sill'] * ramp(tf.sqrt(e['d2']) / e['range'])
|