From e53cc0d11fdab082a1b3548d667a6f7f0dfff0d4 Mon Sep 17 00:00:00 2001
From: Julian Valentin <julian.valentin@ipvs.uni-stuttgart.de>
Date: Sun, 1 Apr 2018 17:03:17 +0200
Subject: [PATCH] Add missing basis files

---
 py/helper/basis/hierarchical_basis.py         | 13 ++++++++
 ...hierarchical_basis_from_parent_function.py | 20 +++++++++++++
 py/helper/basis/hierarchical_bspline.py       | 30 +++++++++++++++++++
 py/helper/basis/non_uniform_bspline.py        | 28 +++++++++++++++++
 py/helper/basis/parent_function.py            | 13 ++++++++
 5 files changed, 104 insertions(+)
 create mode 100644 py/helper/basis/hierarchical_basis.py
 create mode 100644 py/helper/basis/hierarchical_basis_from_parent_function.py
 create mode 100644 py/helper/basis/hierarchical_bspline.py
 create mode 100644 py/helper/basis/non_uniform_bspline.py
 create mode 100644 py/helper/basis/parent_function.py

diff --git a/py/helper/basis/hierarchical_basis.py b/py/helper/basis/hierarchical_basis.py
new file mode 100644
index 0000000..02d34cb
--- /dev/null
+++ b/py/helper/basis/hierarchical_basis.py
@@ -0,0 +1,13 @@
+#!/usr/bin/python3
+
+import abc
+
+class HierarchicalBasis(abc.ABC):
+  def __init__(self, nu=0):
+    self.nu = nu
+  
+  @abc.abstractmethod
+  def evaluate(self, l, i, xx): pass
+
+  @abc.abstractmethod
+  def getSupport(self, l, i): pass
diff --git a/py/helper/basis/hierarchical_basis_from_parent_function.py b/py/helper/basis/hierarchical_basis_from_parent_function.py
new file mode 100644
index 0000000..f19f770
--- /dev/null
+++ b/py/helper/basis/hierarchical_basis_from_parent_function.py
@@ -0,0 +1,20 @@
+#!/usr/bin/python3
+
+from .hierarchical_basis import HierarchicalBasis
+
+class HierarchicalBasisFromParentFunction(HierarchicalBasis):
+  def __init__(self, parentFunction):
+    super().__init__(nu=parentFunction.nu)
+    self.parentFunction = parentFunction
+  
+  def evaluate(self, l, i, xx):
+    tt = 2**l * xx - i
+    yy = self.parentFunction.evaluate(tt)
+    yy *= 2**(l*self.nu)
+    return yy
+  
+  def getSupport(self, l, i):
+    lb, ub = self.parentFunction.getSupport()
+    lb = max((lb + i) / 2**l, 0)
+    ub = min((ub + i) / 2**l, 1)
+    return lb, ub
diff --git a/py/helper/basis/hierarchical_bspline.py b/py/helper/basis/hierarchical_bspline.py
new file mode 100644
index 0000000..bfeb144
--- /dev/null
+++ b/py/helper/basis/hierarchical_bspline.py
@@ -0,0 +1,30 @@
+#!/usr/bin/python3
+
+import helper.grid
+
+from .centralized_cardinal_bspline import CentralizedCardinalBSpline
+from .hierarchical_basis_from_parent_function import HierarchicalBasisFromParentFunction
+
+def restrictKnots(p, hInv, i, I):
+  offset = 0
+  
+  if i < 0:
+    I = [I[0] - j * (I[1] - I[0]) for j in range(-i, 0, -1)] + I
+    offset = -i
+  elif i > hInv:
+    I = I + [I[-1] + j * (I[-1] - I[-2]) for j in range(1, i-hInv+1)]
+  
+  I = I[i+offset:i+offset+p+2]
+  return I
+
+class HierarchicalBSpline(HierarchicalBasisFromParentFunction):
+  def __init__(self, p, nu=0):
+    super().__init__(CentralizedCardinalBSpline(p, nu=nu))
+    self.p = p
+  
+  def getKnots(self, l, i=None):
+    hInv = 2**l
+    I = list(range(-(self.p+1)//2, hInv + (self.p+1)//2 + 1))
+    if i is not None: I = restrictKnots(self.p, hInv, i, I)
+    xi = helper.grid.getCoordinates(l, I)
+    return xi
diff --git a/py/helper/basis/non_uniform_bspline.py b/py/helper/basis/non_uniform_bspline.py
new file mode 100644
index 0000000..a4235cc
--- /dev/null
+++ b/py/helper/basis/non_uniform_bspline.py
@@ -0,0 +1,28 @@
+#!/usr/bin/python3
+
+import numpy as np
+import scipy.interpolate
+
+from .parent_function import ParentFunction
+
+class NonUniformBSpline(ParentFunction):
+  def __init__(self, p, xi, k=None, nu=0):
+    if k is None:
+      super().__init__(nu)
+      fakeXi = np.hstack([p * [xi[0]], xi, p * [xi[-1]]])
+      fakeC = np.zeros((2*p+1,))
+      fakeC[p] = 1
+      self.bSpline = scipy.interpolate.BSpline(fakeXi, fakeC, p)
+      self.support = [xi[0], xi[-1]]
+    else:
+      self.__init__(p, xi[k:k+p+2], nu=nu)
+  
+  def evaluate(self, xx):
+    xx = np.array(xx).flatten().astype(float)
+    K = np.logical_and(xx >= self.support[0], xx < self.support[1])
+    yy = np.zeros_like(xx)
+    yy[K] = self.bSpline(xx[K], nu=self.nu)
+    return yy
+  
+  def getSupport(self):
+    return self.support
diff --git a/py/helper/basis/parent_function.py b/py/helper/basis/parent_function.py
new file mode 100644
index 0000000..0b6d82c
--- /dev/null
+++ b/py/helper/basis/parent_function.py
@@ -0,0 +1,13 @@
+#!/usr/bin/python3
+
+import abc
+
+class ParentFunction(abc.ABC):
+  def __init__(self, nu=0):
+    self.nu = nu
+  
+  @abc.abstractmethod
+  def evaluate(self, xx): pass
+
+  @abc.abstractmethod
+  def getSupport(self): pass