diff --git a/vkoga_2L/kernels.py b/vkoga_2L/kernels.py
index ab6d209f7de7425654f81ec4f3d90f09633c2386..ca47965c6e1db06e4211f13c7faf6450e72eb6eb 100644
--- a/vkoga_2L/kernels.py
+++ b/vkoga_2L/kernels.py
@@ -76,42 +76,58 @@ class IMQ(RBF):
self.rbf = lambda ep, r: 1. / np.sqrt(1 + (ep * r) ** 2)
class Matern(RBF):
- def __init__(self, ep=1, k=0):
- self.ep = ep
+ def __init__(self, ep=1, k=0, flag_normalize_y=False, flag_normalize_x=False):
+
+ # flag_normalize_x: Adjusts the shape parameter such that we "converge" to the Gaussian kernel as k -> inf
+ # flag_normalize_y: Adjusts the kernel such that the diagonal is 1
+
+
+ self.ep = ep * np.sqrt(2 * k + 1) if flag_normalize_x else ep
+
if k == 0:
self.name = 'mat0'
- self.rbf = lambda ep, r : np.exp(-ep * r)
+ self.rbf_ = lambda ep, r : np.exp(-ep * r)
elif k == -1:
self.name = 'derivative kernel ob quadratic matern'
- self.rbf = lambda ep, r: np.exp(-r) * (r**2 - (2 * 1 + 3) * r + 1 ** 2 + 2 * 1)
+ self.rbf_ = lambda ep, r: np.exp(-r) * (r**2 - (2 * 1 + 3) * r + 1 ** 2 + 2 * 1)
elif k == 1:
self.name = 'mat1'
- self.rbf = lambda ep, r: np.exp(-ep * r) * (1 + ep * r)
+ self.rbf_ = lambda ep, r: np.exp(-ep * r) * (1 + ep * r)
elif k == 2:
self.name = 'mat2'
- self.rbf = lambda ep, r: np.exp(-ep * r) * (3 + 3 * ep * r + 1 * (ep * r) ** 2)
+ self.rbf_ = lambda ep, r: np.exp(-ep * r) * (3 + 3 * ep * r + 1 * (ep * r) ** 2)
elif k == 3:
self.name = 'mat3'
- self.rbf = lambda ep, r: np.exp(-ep * r) * (15 + 15 * ep * r + 6 * (ep * r) ** 2 + 1 * (ep * r) ** 3)
+ self.rbf_ = lambda ep, r: np.exp(-ep * r) * (15 + 15 * ep * r + 6 * (ep * r) ** 2 + 1 * (ep * r) ** 3)
elif k == 4:
self.name = 'mat4'
- self.rbf = lambda ep, r: np.exp(-ep * r) * (105 + 105 * ep * r + 45 * (ep * r) ** 2 + 10 * (ep * r) ** 3 + 1 * (ep * r) ** 4)
+ self.rbf_ = lambda ep, r: np.exp(-ep * r) * (105 + 105 * ep * r + 45 * (ep * r) ** 2 + 10 * (ep * r) ** 3 + 1 * (ep * r) ** 4)
elif k == 5:
self.name = 'mat5'
- self.rbf = lambda ep, r: np.exp(-ep * r) * (945 + 945 * ep * r + 420 * (ep * r) ** 2 + 105 * (ep * r) ** 3 + 15 * (ep * r) ** 4 + 1 * (ep * r) ** 5)
+ self.rbf_ = lambda ep, r: np.exp(-ep * r) * (945 + 945 * ep * r + 420 * (ep * r) ** 2 + 105 * (ep * r) ** 3 + 15 * (ep * r) ** 4 + 1 * (ep * r) ** 5)
elif k == 6:
self.name = 'mat6'
- self.rbf = lambda ep, r: np.exp(-ep * r) * (10395 + 10395 * ep * r + 4725 * (ep * r) ** 2 + 1260 * (ep * r) ** 3 + 210 * (ep * r) ** 4 + 21 * (ep * r) ** 5 + 1 * (ep * r) ** 6)
+ self.rbf_ = lambda ep, r: np.exp(-ep * r) * (10395 + 10395 * ep * r + 4725 * (ep * r) ** 2 + 1260 * (ep * r) ** 3 + 210 * (ep * r) ** 4 + 21 * (ep * r) ** 5 + 1 * (ep * r) ** 6)
elif k == 7:
self.name = 'mat7'
- self.rbf = lambda ep, r: np.exp(-ep * r) * (135135 + 135135 * ep * r + 62370 * (ep * r) ** 2 + 17325 * (ep * r) ** 3 + 3150 * (ep * r) ** 4 + 378 * (ep * r) ** 5 + 28 * (ep * r) ** 6 + 1 * (ep * r) ** 7)
+ self.rbf_ = lambda ep, r: np.exp(-ep * r) * (135135 + 135135 * ep * r + 62370 * (ep * r) ** 2 + 17325 * (ep * r) ** 3 + 3150 * (ep * r) ** 4 + 378 * (ep * r) ** 5 + 28 * (ep * r) ** 6 + 1 * (ep * r) ** 7)
else:
self.name = None
- self.rbf = None
+ self.rbf_ = None
raise Exception('This Matern kernel is not implemented')
+
+ if flag_normalize_y:
+ c_norm = 1 / self.rbf_(ep, 0)
+ else:
+ c_norm = 1
+
+ self.rbf = lambda ep, r: c_norm * self.rbf_(ep, r)
class Wendland(RBF):
- def __init__(self, ep=1, k=0, d=1):
+ def __init__(self, ep=1, k=0, d=1, flag_normalize_y=False):
+
+ # flag_normalize_y: Adjusts the kernel such that the diagonal is 1
+
self.ep = ep
self.name = 'wen_' + str(d) + '_' + str(k)
l = np.floor(d / 2) + k + 1
@@ -129,7 +145,13 @@ class Wendland(RBF):
raise Exception('This Wendland kernel is not implemented')
c = np.math.factorial(l + 2 * k) / np.math.factorial(l)
e = l + k
- self.rbf = lambda ep, r: np.maximum(1 - ep * r, 0) ** e * p(ep * r) / c
+
+ if flag_normalize_y:
+ c_norm = c / p(0)
+ else:
+ c_norm = 1
+
+ self.rbf = lambda ep, r: c_norm * np.maximum(1 - ep * r, 0) ** e * p(ep * r) / c
# Polynomial kernels
diff --git a/vkoga_2L/tkernels.py b/vkoga_2L/tkernels.py
index 26e26602f18e4819b4ba4ff29f0345e83b26bf95..40a032d4e9a90f5a4679a2ee0d6eae7590a75730 100644
--- a/vkoga_2L/tkernels.py
+++ b/vkoga_2L/tkernels.py
@@ -75,43 +75,56 @@ class IMQ(RBF):
class Matern(RBF):
- def __init__(self, ep=1, k=0):
- self.ep = ep
+ def __init__(self, ep=1, k=0, flag_normalize_y=False, flag_normalize_x=False):
+
+ # flag_normalize_x: Adjusts the shape parameter such that we "converge" to the Gaussian kernel as k -> inf
+ # flag_normalize_y: Adjusts the kernel such that the diagonal is 1
+
+
+ self.ep = ep * np.sqrt(2 * k + 1) if flag_normalize_x else ep
+
if k == 0:
self.name = 'mat0'
- self.rbf = lambda ep, r: torch.exp(-ep * r)
+ self.rbf_ = lambda ep, r: torch.exp(-ep * r)
elif k == 1:
self.name = 'mat1'
- self.rbf = lambda ep, r: torch.exp(-ep * r) * (1 + ep * r)
+ self.rbf_ = lambda ep, r: torch.exp(-ep * r) * (1 + ep * r)
elif k == 2:
self.name = 'mat2'
- self.rbf = lambda ep, r: torch.exp(-ep * r) * (3 + 3 * ep * r + (ep * r) ** 2)
+ self.rbf_ = lambda ep, r: torch.exp(-ep * r) * (3 + 3 * ep * r + (ep * r) ** 2)
elif k == 3:
self.name = 'mat3'
- self.rbf = lambda ep, r: torch.exp(-ep * r) * (15 + 15 * ep * r + 6 * (ep * r) ** 2 + 1 * (ep * r) ** 3)
+ self.rbf_ = lambda ep, r: torch.exp(-ep * r) * (15 + 15 * ep * r + 6 * (ep * r) ** 2 + 1 * (ep * r) ** 3)
elif k == 4:
self.name = 'mat4'
- self.rbf = lambda ep, r: torch.exp(-ep * r) * (
+ self.rbf_ = lambda ep, r: torch.exp(-ep * r) * (
105 + 105 * ep * r + 45 * (ep * r) ** 2 + 10 * (ep * r) ** 3 + 1 * (ep * r) ** 4)
elif k == 5:
self.name = 'mat5'
- self.rbf = lambda ep, r: torch.exp(-ep * r) * (
+ self.rbf_ = lambda ep, r: torch.exp(-ep * r) * (
945 + 945 * ep * r + 420 * (ep * r) ** 2 + 105 * (ep * r) ** 3 + 15 * (ep * r) ** 4 + 1 * (
ep * r) ** 5)
elif k == 6:
self.name = 'mat6'
- self.rbf = lambda ep, r: torch.exp(-ep * r) * (
+ self.rbf_ = lambda ep, r: torch.exp(-ep * r) * (
10395 + 10395 * ep * r + 4725 * (ep * r) ** 2 + 1260 * (ep * r) ** 3 + 210 * (
ep * r) ** 4 + 21 * (ep * r) ** 5 + 1 * (ep * r) ** 6)
elif k == 7:
self.name = 'mat7'
- self.rbf = lambda ep, r: torch.exp(-ep * r) * (
+ self.rbf_ = lambda ep, r: torch.exp(-ep * r) * (
135135 + 135135 * ep * r + 62370 * (ep * r) ** 2 + 17325 * (ep * r) ** 3 + 3150 * (
ep * r) ** 4 + 378 * (ep * r) ** 5 + 28 * (ep * r) ** 6 + 1 * (ep * r) ** 7)
else:
self.name = None
- self.rbf = None
+ self.rbf_ = None
raise Exception('This Matern kernel is not implemented')
+
+ if flag_normalize_y:
+ c_norm = 1 / self.rbf_(ep, torch.tensor(0))
+ else:
+ c_norm = 1
+
+ self.rbf = lambda ep, r: c_norm * self.rbf_(ep, r)
class HatFunction(RBF):
@@ -129,10 +142,13 @@ class PowerKernels(RBF):
class Wendland(RBF):
- def __init__(self, ep=1, k=0, d=1):
+ def __init__(self, ep=1, k=0, d=1, flag_normalize_y=False):
+
+ # flag_normalize_y: Adjusts the kernel such that the diagonal is 1
+
self.ep = ep
self.name = 'wen_' + str(d) + '_' + str(k)
- l = np.floor(d / 2) + k + 1
+ l = int(np.floor(d / 2) + k + 1)
if k == 0:
p = lambda r: 1
elif k == 1:
@@ -148,10 +164,15 @@ class Wendland(RBF):
105 * (l + 4)) * r + 105
else:
raise Exception('This Wendland kernel is not implemented')
- c = np.math.factorial(l + 2 * k) / np.math.factorial(l)
+ c = np.math.factorial(l + 2 * int(k)) / np.math.factorial(l)
e = l + k
- # self.rbf = lambda ep, r: np.maximum(1 - ep * r, 0) ** e * p(ep * r) / c
- self.rbf = lambda ep, r: torch.clamp(1 - ep * r, min=0) ** e * p(ep * r) / c
+
+ if flag_normalize_y:
+ c_norm = c / p(0)
+ else:
+ c_norm = 1
+
+ self.rbf = lambda ep, r: c_norm * torch.clamp(1 - ep * r, min=0) ** e * p(ep * r) / c
# # Polynomial kernels