custom colormap

Apologies, but as usual, I'm under a bit of pressure to display a pcolor
using a custom colormap and it's not intuitively obvious how to do it (but
I'll keep looking). If there's a kind soul out there who can quickly point
me/show me how, I'd appreciate it. In my simple example, I want to have
just 4 bands of color: 2 shades of blue for all negative scalar values and
2 shades of red for all positive values.

thanks, Randy

I responded to this off list (through a separate request). I did want to
point out that the data structure used to create linear segmented colormaps
does provide the capability for easily defining constant color bands. There
is a simple, but not very general, means of just restricting the number of
points in the color map. By making this a small number, one will just have
that many distinct colors available (by default it is set to 256, which
generally makes it hard to distinguish the distinct levels). This is only
useful if you wish the thresholds for the constant levels to be uniformly
spaced between 0 and 1 after normalizing the data values to that interval.
In this particular case choosing N to be small (7) didn't align 0 with one
of these thresholds and thus wasn't useful for this purpose.

The more general means of setting arbitrary constant color bands is to take
advantage of the fact that the definition of the linear segments allows for
discontinuities at each threshold. Two examples are shown below. The first
is a continuous colormap and the second illustrates use of constant color
bands.

The data structure is simply dictionary that has entries for each of the 3
colors. Each of these is set a tuple of tuples. Each of the interior tuples
represents the color value(s) at a normalized data value (i.e., values ranging
from 0 to 1). The first value is the normalized data value for which the
color intensities apply. Two color intensities are required to allow for
discontinuities. So the second value of the tuple is the color intensity
just below the data value, and the third the value is the value just above.
If the color map is to be continuous at that point, these two values should
be the same. The tuples should be monotonic in data values and should start
with 0. and end with 1. The color intensities are linearly interpolated
between the specified data points. (Actually, color lookup tables are generated
instead and simple value lookup is used. As mentioned, the default number of
entries in the lookup tables is 256. This can be overridden by specifying
how many levels are desired) The following examples illustrate two simple cases.

mycmdata1 = {
     'red' : ((0., 0., 0.), (0.5, 0.9, 0.9), (1., 1., 1.)),
     'green': ((0., 0., 0.), (1., 0., 0.)),
     'blue' : ((0., 0., 0.), (1., 0., 0.))
   }
mycm1 = LinearSegmentedColormap('mycm', mycmdata1)

This color map is intended to show only red with values between 0 and 0.5 using
90% of the red color range, values running from 0.5 to 1.0 only result in a
minor increase of the red intensity from 0.9 to 1.0.

mycmdata2 = {
     'red' : ((0., 1., 1.), (0.1, 1., 0.), (1., 0., 0.)),
     'green': ((0., 0., 0.), (0.1, 0., 1.), (0.9, 1., 0.), (1., 0., 0.)),
     'blue' : ((0., 0., 0.), (0.9, 0., 1.), (1., 1., 1.))
   }
mycm2 = LinearSegmentedColormap('mycm', mycmdata2)

For this color map, value between 0. and 0.1 will be full red, values between
0.1 and 0.9 will be full green, and values between 0.9 and 1. will be full blue.
Note that in this case the difference in the 2nd and 3rd values in the tuples
at the changes in color. Color values are interpolated between the normalized
data values and since they are the same over the interval, they are constant.

Randy's case is a bit unusual in that one needs to figure out where 0 in the
original data maps to the normalized data, and then construct a colormap that
used that "normalized" 0 value as a threshold. So one must construct a colormap
for each such image (admittedly a bit clumsy).

Perry

···

On Jan 5, 2005, at 7:41 AM, Randy Heiland wrote:

Apologies, but as usual, I'm under a bit of pressure to display a pcolor
using a custom colormap and it's not intuitively obvious how to do it (but
I'll keep looking). If there's a kind soul out there who can quickly point
me/show me how, I'd appreciate it. In my simple example, I want to have
just 4 bands of color: 2 shades of blue for all negative scalar values and
2 shades of red for all positive values.

thanks, Randy