[SciPy-user] mapminmax function?

[Scott MacDonald]

Thank you, much appreciated.

Scott

On Sun, Jan 4, 2009 at 4:11 PM, Robert Kern <robert.kern at gmail.com> wrote:

> On Sun, Jan 4, 2009 at 17:54, Scott MacDonald
> <scott.p.macdonald at gmail.com> wrote:
> > Oops, I guess that information would have been helpful.  The description:
> >
> > %   MAPMINMAX processes matrices by normalizing the minimum and maximum
> > values
> > %   of each row to [YMIN, YMAX].
> >
> > %   MAPMINMAX(X,YMIN,YMAX) takes X and optional parameters,
> > %     X - NxQ matrix or a 1xTS row cell array of NxQ matrices.
> > %     YMIN - Minimum value for each row of Y. (Default is -1)
> > %     YMAX - Maximum value for each row of Y. (Default is +1)
> > %   and returns,
> > %     Y - Each MxQ matrix (where M == N) (optional).
> > %     PS - Process settings, to allow consistent processing of values.
> >
> > %    Examples
> > %
> > %   Here is how to format a matrix so that the minimum and maximum
> > %   values of each row are mapped to default interval [-1,+1].
> > %
> > %     x1 = [1 2 4; 1 1 1; 3 2 2; 0 0 0]
> > %     [y1,ps] = mapminmax(x1)
> > %
> > %   Next, we apply the same processing settings to new values.
> > %
> > %     x2 = [5 2 3; 1 1 1; 6 7 3; 0 0 0]
> > %     y2 = mapminmax('apply',x2,ps)
>
> <sigh> Every time I manage to forget why I hate Matlab, they make a
> function with a schizoid argument spec like this.
>
> No, there's nothing floating around that does this. Here's a quick
> implementation. It needs robustifying (it doesn't handle the
> all-values-equal case), but it doesn't overload the function's
> arguments. Sometimes objects really are the solution.
>
> In [1]: import numpy as np
>
> In [3]: class MapMinMaxApplier(object):
>    def __init__(self, slope, intercept):
>        self.slope = slope
>        self.intercept = intercept
>    def __call__(self, x):
>        return x * self.slope + self.intercept
>    def reverse(self, y):
>        return (y-self.intercept) / self.slope
>   ....:
>   ....:
>
> In [11]: def mapminmax(x, ymin=-1, ymax=+1):
>   ....:     x = np.asanyarray(x)
>   ....:     xmax = x.max(axis=-1)
>   ....:     xmin = x.min(axis=-1)
>   ....:     if (xmax==xmin).any():
>   ....:         raise ValueError("some rows have no variation")
>   ....:     slope = ((ymax-ymin) / (xmax - xmin))[:,np.newaxis]
>   ....:     intercept = (-xmin*(ymax-ymin)/(xmax-xmin))[:,np.newaxis] +
> ymin
>   ....:     ps = MapMinMaxApplier(slope, intercept)
>   ....:     return ps(x), ps
>   ....:
>
> In [12]: x1 = np.array([[1.,2,4], [1,1,2], [3,2,2],[0,0,1]])
>
> In [14]: y1, ps = mapminmax(x1)
>
> In [15]: y1
> Out[15]:
> array([[-1.        , -0.33333333,  1.        ],
>       [-1.        , -1.        ,  1.        ],
>       [ 1.        , -1.        , -1.        ],
>       [-1.        , -1.        ,  1.        ]])
>
> In [16]: ps(x1)
> Out[16]:
> array([[-1.        , -0.33333333,  1.        ],
>       [-1.        , -1.        ,  1.        ],
>       [ 1.        , -1.        , -1.        ],
>       [-1.        , -1.        ,  1.        ]])
>
> In [17]: ps.reverse(y1)
> Out[17]:
> array([[ 1.,  2.,  4.],
>       [ 1.,  1.,  2.],
>       [ 3.,  2.,  2.],
>       [ 0.,  0.,  1.]])
>
> --
> Robert Kern
>
> "I have come to believe that the whole world is an enigma, a harmless
> enigma that is made terrible by our own mad attempt to interpret it as
> though it had an underlying truth."
>  -- Umberto Eco
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