From fb540f6436d1116a00b01c62b77b2a21a439cfbc Mon Sep 17 00:00:00 2001
From: Anton Khirnov <anton@khirnov.net>
Date: Tue, 21 Oct 2014 16:41:42 +0200
Subject: Initial commit.

---
 __init__.py         |  0
 basis.py            | 55 +++++++++++++++++++++++++++++++++++++++++++++
 series_expansion.py | 65 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 120 insertions(+)
 create mode 100644 __init__.py
 create mode 100644 basis.py
 create mode 100644 series_expansion.py

diff --git a/__init__.py b/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/basis.py b/basis.py
new file mode 100644
index 0000000..759ebfe
--- /dev/null
+++ b/basis.py
@@ -0,0 +1,55 @@
+import abc
+import math
+import numpy as np
+
+class ExpansionBasis1D(object):
+    """
+    A family of one-dimensional functions that make up a basis.
+    """
+
+    __metaclass__ = abc.ABCMeta
+
+    @abc.abstractmethod
+    def eval(self, idx, coord, diff_order = 0):
+        """
+        Evaluate the diff_order-th derivative of the idx-th basis function at
+        the specified coordinates (where zeroth derivative means evaluating the
+        function itself).
+        """
+        pass
+
+    @abc.abstractmethod
+    def colloc_grid(self, order):
+        """
+        Get the coordinates of the optimal collocation grid of the specified
+        order (i.e. exactly order coordinates will be returned).
+        """
+        pass
+
+class CosBasis(ExpansionBasis1D):
+    PARITY_NONE = 0
+    PARITY_EVEN = 1
+    PARITY_ODD  = 2
+
+    _diff_fact = [(1, np.cos), (-1, np.sin), (-1, np.cos), (1, np.sin)]
+    _parity = None
+
+    def __init__(self, parity = PARITY_NONE):
+        self._parity = parity
+
+    def eval(self, idx, coord, diff_order = 0):
+        fact, f = self._diff_fact[diff_order % 4]
+
+        if self._parity == self.PARITY_EVEN:
+            idx *= 2
+        elif self._parity == self.PARITY_ODD:
+            idx = 2 * idx + 1
+
+        fact *= idx ** diff_order
+        return fact * f(idx * coord)
+
+    def colloc_grid(self, order):
+        if self._parity == self.PARITY_NONE:
+            return (np.array(range(0, order)) + 1) * 2 * np.pi / (order + 1)
+        else:
+            return (np.array(range(0, order)) + 1) * np.pi / (2 * (order + 1))
diff --git a/series_expansion.py b/series_expansion.py
new file mode 100644
index 0000000..9cd7671
--- /dev/null
+++ b/series_expansion.py
@@ -0,0 +1,65 @@
+import numpy as np
+
+class SeriesExpansion(object):
+    """
+    An N-dimensional function approximated as a series expansion in some chosen
+    basis
+    """
+
+    _dim    = None
+    _coeffs = None
+    _basis  = None
+
+    def __init__(self, coeffs, basis):
+        self._dim    = coeffs.ndim
+        self._coeffs = coeffs
+
+        # for 1D, allow passing just the basis object itself
+        # without being wrapped in an iterable
+        if self._dim == 1:
+            try:
+                basis[0]
+            except TypeError:
+                basis = [basis]
+
+        if len(basis) != coeffs.ndim:
+            raise ValueError('Mismatching number of coefficient and basis functions')
+
+        self._basis  = basis
+
+    @property
+    def coeffs(self):
+        return self._coeffs
+
+    @property
+    def basis(self):
+        return self._basis
+
+    def eval(self, coords, diff_order = None):
+        # for 1D, allow passing just the plain array of coords
+        # without being wrapped in an iterable
+        if self._dim == 1:
+            try:
+                coords[0][0]
+            except TypeError:
+                coords = [coords]
+
+        if diff_order is None:
+            diff_order = [0] * len(coords)
+
+        shape = [len(c) for c in coords]
+        ret = np.zeros(shape)
+
+        basis_vals = []
+        for i, (b, c, d) in enumerate(zip(self._basis, coords, diff_order)):
+            val = []
+            for idx in xrange(self._coeffs.shape[i]):
+                val.append(b.eval(idx, c, d))
+            basis_vals.append(val)
+
+        if self._dim == 1:
+            for c, val in zip(self._coeffs, basis_vals[0]):
+                ret += val * c
+            return ret
+        else:
+            raise NotImplementedError('Unsupported number of dimensions')
-- 
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