Revision: 7482
http://matplotlib.svn.sourceforge.net/matplotlib/?rev=7482&view=rev
Author: efiring
Date: 2009-08-14 00:24:40 +0000 (Fri, 14 Aug 2009)
Log Message:
-----------
Remove older versions of some functions in mlab.py; closes bug 2806535
Modified Paths:
--------------
branches/v0_99_maint/lib/matplotlib/mlab.py
Modified: branches/v0_99_maint/lib/matplotlib/mlab.py
===================================================================
--- branches/v0_99_maint/lib/matplotlib/mlab.py 2009-08-13 22:55:24 UTC (rev
7481)
+++ branches/v0_99_maint/lib/matplotlib/mlab.py 2009-08-14 00:24:40 UTC (rev
7482)
@@ -1304,181 +1304,6 @@
else: return X
-def slopes(x,y):
- """
- SLOPES calculate the slope y'(x) Given data vectors X and Y SLOPES
- calculates Y'(X), i.e the slope of a curve Y(X). The slope is
- estimated using the slope obtained from that of a parabola through
- any three consecutive points.
-
- This method should be superior to that described in the appendix
- of A CONSISTENTLY WELL BEHAVED METHOD OF INTERPOLATION by Russel
- W. Stineman (Creative Computing July 1980) in at least one aspect:
-
- Circles for interpolation demand a known aspect ratio between x-
- and y-values. For many functions, however, the abscissa are given
- in different dimensions, so an aspect ratio is completely
- arbitrary.
-
- The parabola method gives very similar results to the circle
- method for most regular cases but behaves much better in special
- cases
-
- Norbert Nemec, Institute of Theoretical Physics, University or
- Regensburg, April 2006 Norbert.Nemec at physik.uni-regensburg.de
-
- (inspired by a original implementation by Halldor Bjornsson,
- Icelandic Meteorological Office, March 2006 halldor at vedur.is)
- """
- # Cast key variables as float.
- x=np.asarray(x, np.float_)
- y=np.asarray(y, np.float_)
-
- yp=np.zeros(y.shape, np.float_)
-
- dx=x[1:] - x[:-1]
- dy=y[1:] - y[:-1]
- dydx = dy/dx
- yp[1:-1] = (dydx[:-1] * dx[1:] + dydx[1:] * dx[:-1])/(dx[1:] + dx[:-1])
- yp[0] = 2.0 * dy[0]/dx[0] - yp[1]
- yp[-1] = 2.0 * dy[-1]/dx[-1] - yp[-2]
- return yp
-
-
-def stineman_interp(xi,x,y,yp=None):
- """
- STINEMAN_INTERP Well behaved data interpolation. Given data
- vectors X and Y, the slope vector YP and a new abscissa vector XI
- the function stineman_interp(xi,x,y,yp) uses Stineman
- interpolation to calculate a vector YI corresponding to XI.
-
- Here's an example that generates a coarse sine curve, then
- interpolates over a finer abscissa:
-
- x = linspace(0,2*pi,20); y = sin(x); yp = cos(x)
- xi = linspace(0,2*pi,40);
- yi = stineman_interp(xi,x,y,yp);
- plot(x,y,'o',xi,yi)
-
- The interpolation method is described in the article A
- CONSISTENTLY WELL BEHAVED METHOD OF INTERPOLATION by Russell
- W. Stineman. The article appeared in the July 1980 issue of
- Creative Computing with a note from the editor stating that while
- they were
-
- not an academic journal but once in a while something serious
- and original comes in adding that this was
- "apparently a real solution" to a well known problem.
-
- For yp=None, the routine automatically determines the slopes using
- the "slopes" routine.
-
- X is assumed to be sorted in increasing order
-
- For values xi[j] < x[0] or xi[j] > x[-1], the routine tries a
- extrapolation. The relevance of the data obtained from this, of
- course, questionable...
-
- original implementation by Halldor Bjornsson, Icelandic
- Meteorolocial Office, March 2006 halldor at vedur.is
-
- completely reworked and optimized for Python by Norbert Nemec,
- Institute of Theoretical Physics, University or Regensburg, April
- 2006 Norbert.Nemec at physik.uni-regensburg.de
-
- """
-
- # Cast key variables as float.
- x=np.asarray(x, np.float_)
- y=np.asarray(y, np.float_)
- assert x.shape == y.shape
- N=len(y)
-
- if yp is None:
- yp = slopes(x,y)
- else:
- yp=np.asarray(yp, np.float_)
-
- xi=np.asarray(xi, np.float_)
- yi=np.zeros(xi.shape, np.float_)
-
- # calculate linear slopes
- dx = x[1:] - x[:-1]
- dy = y[1:] - y[:-1]
- s = dy/dx #note length of s is N-1 so last element is #N-2
-
- # find the segment each xi is in
- # this line actually is the key to the efficiency of this implementation
- idx = np.searchsorted(x[1:-1], xi)
-
- # now we have generally: x[idx[j]] <= xi[j] <= x[idx[j]+1]
- # except at the boundaries, where it may be that xi[j] < x[0] or xi[j] >
x[-1]
-
- # the y-values that would come out from a linear interpolation:
- sidx = s.take(idx)
- xidx = x.take(idx)
- yidx = y.take(idx)
- xidxp1 = x.take(idx+1)
- yo = yidx + sidx * (xi - xidx)
-
- # the difference that comes when using the slopes given in yp
- dy1 = (yp.take(idx)- sidx) * (xi - xidx) # using the yp slope of the
left point
- dy2 = (yp.take(idx+1)-sidx) * (xi - xidxp1) # using the yp slope of the
right point
-
- dy1dy2 = dy1*dy2
- # The following is optimized for Python. The solution actually
- # does more calculations than necessary but exploiting the power
- # of numpy, this is far more efficient than coding a loop by hand
- # in Python
- yi = yo + dy1dy2 * np.choose(np.array(np.sign(dy1dy2), np.int32)+1,
- ((2*xi-xidx-xidxp1)/((dy1-dy2)*(xidxp1-xidx)),
- 0.0,
- 1/(dy1+dy2),))
- return yi
-
-def inside_poly(points, verts):
- """
- points is a sequence of x,y points
- verts is a sequence of x,y vertices of a poygon
-
- return value is a sequence of indices into points for the points
- that are inside the polygon
- """
- res, = np.nonzero(nxutils.points_inside_poly(points, verts))
- return res
-
-def poly_below(ymin, xs, ys):
- """
- given a arrays *xs* and *ys*, return the vertices of a polygon
- that has a scalar lower bound *ymin* and an upper bound at the *ys*.
-
- intended for use with Axes.fill, eg::
-
- xv, yv = poly_below(0, x, y)
- ax.fill(xv, yv)
- """
- return poly_between(xs, ys, xmin)
-
-
-def poly_between(x, ylower, yupper):
- """
- given a sequence of x, ylower and yupper, return the polygon that
- fills the regions between them. ylower or yupper can be scalar or
- iterable. If they are iterable, they must be equal in length to x
-
- return value is x, y arrays for use with Axes.fill
- """
- Nx = len(x)
- if not cbook.iterable(ylower):
- ylower = ylower*np.ones(Nx)
-
- if not cbook.iterable(yupper):
- yupper = yupper*np.ones(Nx)
-
- x = np.concatenate( (x, x[::-1]) )
- y = np.concatenate( (yupper, ylower[::-1]) )
- return x,y
-
### the following code was written and submitted by Fernando Perez
### from the ipython numutils package under a BSD license
# begin fperez functions
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