* Simplified spline interpolation tools for 2-D curves (single curve or

piecewise curve).

math/spline_2d.py

@@ -0,0 +1,91 @@
+# $Id: spline_2d.py,v 1.1 2010-01-22 18:48:19 wirawan Exp $
+#
+# wpylib.math.spline_2d module
+# Created: 20091204
+# Wirawan Purwanto
+#
+
+import numpy
+import scipy.interpolate
+
+class spline_2d:
+  """Simple interpolation for two-dimensional curve.
+  Created to handle the quirks of current SciPy interpolation
+  routines."""
+  # Important notes on spline CAVEATS:
+  # - for some reason we HAVE to make a copy of the 'x' array
+  #   (to make it contiguous, probably?)
+  # - also, the x values better be sorted in ascending order, or else
+  #   the routine would return nonsense (i.e. NaN's).
+  def __init__(self, x, y):
+    self.init(x,y)
+
+  def init(self, x, y):
+    # First, the x must be sorted, so we make a private copy of
+    # the data:
+    self.data = numpy.array(zip(x, y), dtype=[('x', float), ('y', float)])
+    # Quirk 1: The x axis data must be sorted ascending
+    self.data.sort(order=['x'])
+    self.x = self.data['x']
+    self.y = self.data['y']
+    # Quirk 2: the x data for spline function must be contiguous
+    # See below in init_spline_params()
+    #self.x_copy = self.x.copy()
+
+    try:
+      del self.spline_params
+    except:
+      pass
+
+  def init_spline_params(self):
+    """Initialize spline params with default params.
+    You can call something to initialize the spline params before
+    calling the first spline function if you want different, non-default
+    parameters."""
+    self.spline_params \
+      = scipy.interpolate.splmake(self.x.copy(), self.y)
+
+  def spline(self, xnew):
+    try:
+      params = self.spline_params
+    except:
+      self.init_spline_params()
+    return scipy.interpolate.spleval(self.spline_params, xnew)
+
+
+
+class spline_2d_piecewise:
+  """Simple spline_2d interpolator with piecewise datasets.
+  Interpolation is possible only in the ranges defined by the piecewise
+  datasets.
+  No checking is done whether the pieces are overlapping, discontinuous, etc.
+  The first piece found enclosing the coordinate will be taken for
+  interpolation."""
+  def __init__(self, *datasets):
+    self.init(*datasets)
+
+  def init(self, *datasets):
+    #if len(dsets) % 2:
+    #  raise ValueError, "The input datasets must be given in x, y pairs
+    self.pieces = []
+    for dset in datasets:
+      x = dset[0]
+      y = dset[1]
+      xmin = numpy.min(x)
+      xmax = numpy.max(x)
+      piece = spline_2d(x, y)
+      piece.xmin = xmin
+      piece.xmax = xmax
+      self.pieces.append(piece)
+
+  def in_range(self, piece, x):
+    return piece.xmin <= x and x <= piece.xmax
+
+  def get_piece(self, x):
+    for p in self.pieces:
+      if self.in_range(p, x):
+        return p
+    raise ValueError, "Out-of-range x value = %g" % x
+
+  def spline(self, x):
+    return self.get_piece(x).spline(x)