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On Fri, Aug 28, 2009 at 1:59 PM, DEMOLISHOR! the
Demolishor<des...@gm...> wrote:
> This is the result from a call to pyplot.pcolor() -- why do the axes
> automatically expand beyond the range of the data? And how can I set them
> back? I am not seeing an obvious keyword argument in the pcolor docs to do
> this...
>

could you post a complete example that replicates the problem?

JDH

Finetuning with axis(xmin=, xmax= , ymin= , ymax=) should yield a better
looking result.

You might use figure(frameon=False) for a transparent background.

On Fri, Aug 28, 2009 at 1:59 PM, DEMOLISHOR! the Demolishor <
des...@gm...> wrote:

> This is the result from a call to pyplot.pcolor() -- why do the axes
> automatically expand beyond the range of the data? And how can I set them
> back? I am not seeing an obvious keyword argument in the pcolor docs to do
> this...
>
> Thanks in advance
>
> - Craig
>
>
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>


-- 
Gökhan

Recently, I had a need for a monotonic piece-wise cubic Hermite  
interpolator.   Matlab provides the function "pchip" (Piecewise Cubic  
Hermite Interpolator), but when I Googled I didn't find any Python  
equivalent.   I tried "interp1d()" from scipy.interpolate but this was  
a standard cubic spline using all of the data - not a piece-wise cubic  
spline.

I had access to Matlab documentation, so I spent a some time tracing  
through the code to figure out how I might write a Python duplicate.   
This was an massive exercise in frustration and a potent reminder on  
why I love Python and use Matlab only under duress.  I find typical  
Matlab code is poorly documented (if at all) and that apparently  
includes the code included in their official releases.  I also find  
Matlab syntax “dated” and the code very difficult to “read”.

Wikipedia to the rescue.

Not to be deterred, I found a couple of very well written Wikipedia  
entries, which explained in simple language how to compute the  
interpolant.  Hats off to whoever wrote these entries – they are  
excellent.  The result was a surprising small amount of code  
considering the Matlab code was approaching 10 pages of  
incomprehensible code. Again - strong evidence that things are just  
better in Python...

Offered for those who might have the same need – a Python pchip()  
equivalent ==> pypchip().  Since I'm not sure how attachments work (or  
if they work at all...), I copied the code I used below, followed by a  
PNG showing "success":

#
#    pychip.py
#    Michalski
#    20090818
#
#    Piecewise cubic Hermite interpolation (monotonic...) in Python
#
#    References:
#
#        Wikipedia:  Monotone cubic interpolation
#                    Cubic Hermite spline
#
#    A cubic Hermte spline is a third degree spline with each  
polynomial of the spline
#    in Hermite form.  The Hermite form consists of two control points  
and two control
#    tangents for each polynomial.  Each interpolation is performed on  
one sub-interval
#    at a time (piece-wise).  A monotone cubic interpolation is a  
variant of cubic
#    interpolation that preserves monotonicity of the data to be  
interpolated (in other
#    words, it controls overshoot).  Monotonicity is preserved by  
linear interpolation
#    but not by cubic interpolation.
#
#    Use:
#
#    There are two separate calls, the first call, pchip_init(),  
computes the slopes that
#    the interpolator needs.  If there are a large number of points to  
compute,
#    it is more efficient to compute the slopes once, rather than for  
every point
#    being evaluated.  The second call, pchip_eval(), takes the slopes  
computed by
#    pchip_init() along with X, Y, and a vector of desired "xnew"s and  
computes a vector
#    of "ynew"s.  If only a handful of points is needed, pchip() is a  
third function
#    which combines a call to pchip_init() followed by pchip_eval().
#

import pylab as P

#=========================================================
def pchip(x, y, xnew):

     # Compute the slopes used by the piecewise cubic Hermite  
interpolator
     m    = pchip_init(x, y)

     # Use these slopes (along with the Hermite basis function) to  
interpolate
     ynew = pchip_eval(x, y, xnew)

     return ynew

#=========================================================
def x_is_okay(x,xvec):

     # Make sure "x" and "xvec" satisfy the conditions for
     # running the pchip interpolator

     n = len(x)
     m = len(xvec)

     # Make sure "x" is in sorted order (brute force, but works...)
     xx = x.copy()
     xx.sort()
     total_matches = (xx == x).sum()
     if total_matches != n:
         print "*" * 50
         print "x_is_okay()"
         print "x values weren't in sorted order --- aborting"
         return False

     # Make sure 'x' doesn't have any repeated values
     delta = x[1:] - x[:-1]
     if (delta == 0.0).any():
         print "*" * 50
         print "x_is_okay()"
         print "x values weren't monotonic--- aborting"
         return False

     # Check for in-range xvec values (beyond upper edge)
     check = xvec > x[-1]
     if check.any():
         print "*" * 50
         print "x_is_okay()"
         print "Certain 'xvec' values are beyond the upper end of 'x'"
         print "x_max = ", x[-1]
         indices = P.compress(check, range(m))
         print "out-of-range xvec's = ", xvec[indices]
         print "out-of-range xvec indices = ", indices
         return False

     # Second - check for in-range xvec values (beyond lower edge)
     check = xvec< x[0]
     if check.any():
         print "*" * 50
         print "x_is_okay()"
         print "Certain 'xvec' values are beyond the lower end of 'x'"
         print "x_min = ", x[0]
         indices = P.compress(check, range(m))
         print "out-of-range xvec's = ", xvec[indices]
         print "out-of-range xvec indices = ", indices
         return False

     return True

#=========================================================
def pchip_eval(x, y, m, xvec):

     # Evaluate the piecewise cubic Hermite interpolant with  
monoticity preserved
     #
     #    x = array containing the x-data
     #    y = array containing the y-data
     #    m = slopes at each (x,y) point [computed to preserve  
monotonicity]
     #    xnew = new "x" value where the interpolation is desired
     #
     #    x must be sorted low to high... (no repeats)
     #    y can have repeated values
     #
     # This works with either a scalar or vector of "xvec"

     n = len(x)
     mm = len(xvec)

     ############################
     # Make sure there aren't problems with the input data
     ############################
     if not x_is_okay(x, xvec):
         print "pchip_eval2() - ill formed 'x' vector!!!!!!!!!!!!!"

         # Cause a hard crash...
         STOP_pchip_eval2

    # Find the indices "k" such that x[k] < xvec < x[k+1]

     # Create "copies" of "x" as rows in a mxn 2-dimensional vector
     xx = P.resize(x,(mm,n)).transpose()
     xxx = xx > xvec

     # Compute column by column differences
     z = xxx[:-1,:] - xxx[1:,:]

     # Collapse over rows...
     k = z.argmax(axis=0)

     # Create the Hermite coefficients
     h = x[k+1] - x[k]
     t = (xvec - x[k]) / h[k]

     # Hermite basis functions
     h00 = (2 * t**3) - (3 * t**2) + 1
     h10 =      t**3  - (2 * t**2) + t
     h01 = (-2* t**3) + (3 * t**2)
     h11 =      t**3  -      t**2

     # Compute the interpolated value of "y"
     ynew = h00*y[k] + h10*h*m[k] + h01*y[k+1] + h11*h*m[k+1]

     return ynew

#=========================================================
def pchip_init(x,y):

     # Evaluate the piecewise cubic Hermite interpolant with  
monoticity preserved
     #
     #    x = array containing the x-data
     #    y = array containing the y-data
     #
     #    x must be sorted low to high... (no repeats)
     #    y can have repeated values
     #
     #    x input conditioning is assumed but not checked

     n = len(x)

     # Compute the slopes of the secant lines between successive points
     delta = (y[1:] - y[:-1]) / (x[1:] - x[:-1])

     # Initialize the tangents at every points as the average of the  
secants
     m = P.zeros(n, dtype='d')

     # At the endpoints - use one-sided differences
     m[0] = delta[0]
     m[n-1] = delta[-1]

     # In the middle - use the average of the secants
     m[1:-1] = (delta[:-1] + delta[1:]) / 2.0

     # Special case: intervals where y[k] == y[k+1]

     # Setting these slopes to zero guarantees the spline connecting
     # these points will be flat which preserves monotonicity
     indices_to_fix = P.compress((delta == 0.0), range(n))

#    print "zero slope indices to fix = ", indices_to_fix

     for ii in indices_to_fix:
         m[ii]   = 0.0
         m[ii+1] = 0.0

     alpha = m[:-1]/delta
     beta  = m[1:]/delta
     dist  = alpha**2 + beta**2
     tau   = 3.0 / P.sqrt(dist)

     # To prevent overshoot or undershoot, restrict the position vector
     # (alpha, beta) to a circle of radius 3.  If (alpha**2 +  
beta**2)>9,
     # then set m[k] = tau[k]alpha[k]delta[k] and m[k+1] =  
tau[k]beta[b]delta[k]
     # where tau = 3/sqrt(alpha**2 + beta**2).

     # Find the indices that need adjustment
     over = (dist > 9.0)
     indices_to_fix = P.compress(over, range(n))

#    print "overshoot indices to fix... = ", indices_to_fix

     for ii in indices_to_fix:
         m[ii]   = tau[ii] * alpha[ii] * delta[ii]
         m[ii+1] = tau[ii] * beta[ii]  * delta[ii]

     return m

#= 
=======================================================================
def CubicHermiteSpline(x, y, x_new):

     # Piecewise Cubic Hermite Interpolation using Catmull-Rom
     # method for computing the slopes.
     #
     # Note - this only works if delta-x is uniform?

     # Find the two points which "bracket" "x_new"
     found_it = False

     for ii in range(len(x)-1):
         if (x[ii] <= x_new) and (x[ii+1] > x_new):
             found_it = True
             break

     if not found_it:
         print
         print "requested x=<%f> outside X range[%f,%f]" % (x_new,  
x[0], x[-1])
         STOP_CubicHermiteSpline()

     # Starting and ending data points
     x0 = x[ii]
     x1 = x[ii+1]

     y0 = y[ii]
     y1 = y[ii+1]

     # Starting and ending tangents (using Catmull-Rom spline method)

     # Handle special cases (hit one of the endpoints...)
     if ii == 0:

         # Hit lower endpoint
         m0 = (y[1] - y[0])
         m1 = (y[2] - y[0]) / 2.0

     elif ii == (len(x) - 2):

         # Hit upper endpoints
         m0 = (y[ii+1] - y[ii-1]) / 2.0
         m1 = (y[ii+1] - y[ii])

     else:

         # Inside the field...
         m0 = (y[ii+1] - y[ii-1])/ 2.0
         m1 = (y[ii+2] - y[ii])  / 2.0

     # Normalize to x_new to [0,1] interval
     h = (x1 - x0)
     t = (x_new - x0) / h

     # Compute the four Hermite basis functions
     h00 = ( 2.0 * t**3) - (3.0 * t**2) + 1.0
     h10 = ( 1.0 * t**3) - (2.0 * t**2) + t
     h01 = (-2.0 * t**3) + (3.0 * t**2)
     h11 = ( 1.0 * t**3) - (1.0 * t**2)

     h = 1

     y_new = (h00 * y0) + (h10 * h * m0) + (h01 * y1) + (h11 * h * m1)

     return y_new

#==============================================================
def main():

     ############################################################
     # Sine wave test
     ############################################################

     # Create a example vector containing a sine wave.
     x = P.arange(30.0)/10.
     y = P.sin(x)

     # Interpolate the data above to the grid defined by "xvec"
     xvec = P.arange(250.)/100.

     # Initialize the interpolator slopes
     m = pchip_init(x,y)

     # Call the monotonic piece-wise Hermite cubic interpolator
     yvec2 = pchip_eval(x, y, m, xvec)

     P.figure(1)
     P.plot(x,y, 'ro')
     P.title("pchip() Sin test code")

     # Plot the interpolated points
     P.plot(xvec, yvec2, 'b')

      
#########################################################################
     # Step function test...
      
#########################################################################

     P.figure(2)
     P.title("pchip() step function test")

     # Create a step function (will demonstrate monotonicity)
     x = P.arange(7.0) - 3.0
     y = P.array([-1.0, -1,-1,0,1,1,1])

     # Interpolate using monotonic piecewise Hermite cubic spline
     xvec = P.arange(599.)/100. - 3.0

     # Create the pchip slopes slopes
     m    = pchip_init(x,y)

     # Interpolate...
     yvec = pchip_eval(x, y, m, xvec)

     # Call the Scipy cubic spline interpolator
     from scipy.interpolate import interpolate
     function = interpolate.interp1d(x, y, kind='cubic')
     yvec2 = function(xvec)

     # Non-montonic cubic Hermite spline interpolator using
     # Catmul-Rom method for computing slopes...
     yvec3 = []
     for xx in xvec:
         yvec3.append(CubicHermiteSpline(x,y,xx))
     yvec3 = P.array(yvec3)

     # Plot the results
     P.plot(x,    y,     'ro')
     P.plot(xvec, yvec,  'b')
     P.plot(xvec, yvec2, 'k')
     P.plot(xvec, yvec3, 'g')
     P.xlabel("X")
     P.ylabel("Y")
     P.title("Comparing pypchip() vs. Scipy interp1d() vs. non- 
monotonic CHS")
     legends = ["Data", "pypchip()", "interp1d","CHS"]
     P.legend(legends, loc="upper left")

     P.show()

###################################################################
main()

Michael Droettboom wrote:
> It's important to note that we're not, as far as I'm aware, 
> considering anything lighting or ray-tracing-like yet.  I'm not sure 
> that Phong shading actually makes sense without doing that.  The 
> Gouraud shading we're in the process of implementing uses only 
> explicit colors specified in the plot, not any sort of 
> light-source-calculated values.
>
> Add perhaps more importantly, Gouraud is implemented in a number of 
> vector formats, including PDF and PS (though matplotlib doesn't have 
> support for that yet, that's coming...)
>
> Mike

Mike:  I did add some support for crude light-source shading a while 
back.  It works directly on rgb values - see 
pylab_examples/shading_example.py.

-Jeff
>
> On 08/26/2009 07:06 PM, Nicolas Bigaouette wrote:
>> Its great news that the 3D is receiving more polish :)
>>
>> After reading on wikipedia, wouldn't it be nicier to have Phong 
>> reflection[1] instead of Gouraud?
>>
>> Maybe it would be too hard, as the Gouraud seems to be implemented 
>> directly in Agg (from what others just said...)
>>
>> Anyway, just a suggestion ;)
>>
>>
>> [1] http://en.wikipedia.org/wiki/Phong_reflection_model
>>
>>
>> 2009/8/26 Eric Firing <ef...@ha... <mailto:ef...@ha...>>
>>
>>     Reinier Heeres wrote:
>>     > Hi JJ,
>>     >
>>     > Thanks for the examples! I indeed suspected the anti-aliasing
>>     as well.
>>     > I'll include an option for linecolors = facecolors soon
>>     (probably this
>>     > weekend); it seems to be a good solution.
>>
>>     No, not in general.  There are two problems: it distorts the
>>     sizes and
>>     positions of the patches, very slightly, but enough that it might
>>     be a
>>     problem in some applications; and it does not work with alpha != 1.
>>
>>     Eric
>>
>>     ------------------------------------------------------------------------------
>>     Let Crystal Reports handle the reporting - Free Crystal Reports
>>     2008 30-Day
>>     trial. Simplify your report design, integration and deployment -
>>     and focus on
>>     what you do best, core application coding. Discover what's new with
>>     Crystal Reports now.  http://p.sf.net/sfu/bobj-july
>>     _______________________________________________
>>     Matplotlib-users mailing list
>>     Mat...@li...
>>     <mailto:Mat...@li...>
>>     https://lists.sourceforge.net/lists/listinfo/matplotlib-users
>>
>>
>>  
>> ------------------------------------------------------------------------------
>> Let Crystal Reports handle the reporting - Free Crystal Reports 2008 30-Day 
>> trial. Simplify your report design, integration and deployment - and focus on 
>> what you do best, core application coding. Discover what's new with 
>> Crystal Reports now.  http://p.sf.net/sfu/bobj-july
>>  
>> _______________________________________________
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>>   
>
> ------------------------------------------------------------------------
>
> ------------------------------------------------------------------------------
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> trial. Simplify your report design, integration and deployment - and focus on 
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>   

Maybe with the new spines support in 0.99 this could be an 
attribute/method on the spine?

Mike

On 08/27/2009 02:18 PM, Jae-Joon Lee wrote:
> I don't think there is a direct support for this in mpl and I guess
> only way is to adjust the parameters of each ticks.
>
> def set_ticks_both(axis):
>      ticks = list( axis.majorTicks ) # a copy
>      ticks.extend( axis.minorTicks )
>
>      for t in ticks:
>          t.tick1On = True # tick marker on left (or bottom)
>          t.tick2On = True # tick marker on right (or top)
>          t.label1On = True # tick label marker on left (or bottom)
>          t.label2On = True # tick label on right (or top)
>
> set_ticks_both(ax.yaxis)
>
> -JJ
>
>
>
> On Thu, Aug 27, 2009 at 7:22 AM, Peter Saffrey<pz...@dc...>  wrote:
>    
>> Some of my plots are very wide. I'd like Y axis labels on both sides so
>> that it's clearer to read the bars towards the right hand side.
>>
>> I can change the ticks with yaxis.set_ticks_position("both") but there
>> doesn't seem to be a similar call for labels. Any ideas?
>>
>> Thanks,
>>
>> Peter
>>
>> ------------------------------------------------------------------------------
>> Let Crystal Reports handle the reporting - Free Crystal Reports 2008 30-Day
>> trial. Simplify your report design, integration and deployment - and focus on
>> what you do best, core application coding. Discover what's new with
>> Crystal Reports now.  http://p.sf.net/sfu/bobj-july
>> _______________________________________________
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>>
>>      
> ------------------------------------------------------------------------------
> Let Crystal Reports handle the reporting - Free Crystal Reports 2008 30-Day
> trial. Simplify your report design, integration and deployment - and focus on
> what you do best, core application coding. Discover what's new with
> Crystal Reports now.  http://p.sf.net/sfu/bobj-july
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>    

It's important to note that we're not, as far as I'm aware, considering 
anything lighting or ray-tracing-like yet.  I'm not sure that Phong 
shading actually makes sense without doing that.  The Gouraud shading 
we're in the process of implementing uses only explicit colors specified 
in the plot, not any sort of light-source-calculated values.

Add perhaps more importantly, Gouraud is implemented in a number of 
vector formats, including PDF and PS (though matplotlib doesn't have 
support for that yet, that's coming...)

Mike

On 08/26/2009 07:06 PM, Nicolas Bigaouette wrote:
> Its great news that the 3D is receiving more polish :)
>
> After reading on wikipedia, wouldn't it be nicier to have Phong 
> reflection[1] instead of Gouraud?
>
> Maybe it would be too hard, as the Gouraud seems to be implemented 
> directly in Agg (from what others just said...)
>
> Anyway, just a suggestion ;)
>
>
> [1] http://en.wikipedia.org/wiki/Phong_reflection_model
>
>
> 2009/8/26 Eric Firing <ef...@ha... <mailto:ef...@ha...>>
>
>     Reinier Heeres wrote:
>     > Hi JJ,
>     >
>     > Thanks for the examples! I indeed suspected the anti-aliasing as
>     well.
>     > I'll include an option for linecolors = facecolors soon
>     (probably this
>     > weekend); it seems to be a good solution.
>
>     No, not in general.  There are two problems: it distorts the sizes and
>     positions of the patches, very slightly, but enough that it might be a
>     problem in some applications; and it does not work with alpha != 1.
>
>     Eric
>
>     ------------------------------------------------------------------------------
>     Let Crystal Reports handle the reporting - Free Crystal Reports
>     2008 30-Day
>     trial. Simplify your report design, integration and deployment -
>     and focus on
>     what you do best, core application coding. Discover what's new with
>     Crystal Reports now. http://p.sf.net/sfu/bobj-july
>     _______________________________________________
>     Matplotlib-users mailing list
>     Mat...@li...
>     <mailto:Mat...@li...>
>     https://lists.sourceforge.net/lists/listinfo/matplotlib-users
>
>
> ------------------------------------------------------------------------
>
> ------------------------------------------------------------------------------
> Let Crystal Reports handle the reporting - Free Crystal Reports 2008 30-Day
> trial. Simplify your report design, integration and deployment - and focus on
> what you do best, core application coding. Discover what's new with
> Crystal Reports now.  http://p.sf.net/sfu/bobj-july
> ------------------------------------------------------------------------
>
> _______________________________________________
> Matplotlib-users mailing list
> Mat...@li...
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>