/usr/share/pyshared/chaco/scales/scales.py is in python-chaco 4.1.0-1.
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Functions and classes that compute ticks and labels for graph axes, with
special handling of time and calendar axes.
"""
from bisect import bisect
from math import ceil, floor, log10
from numpy import abs, argmin, array, isnan, linspace
# Local imports
from formatters import BasicFormatter
__all__ = ["AbstractScale", "DefaultScale", "FixedScale", "Pow10Scale",
"LogScale", "ScaleSystem", "heckbert_interval", "frange"]
def frange(min, max, delta):
""" Floating point range. """
count = int(round((max - min) / delta)) + 1
return [min + i*delta for i in range(count)]
class AbstractScale(object):
""" Defines the general interface for scales. """
DEFAULT_NUM_TICKS = 8
def ticks(self, start, end, desired_ticks=None):
""" Returns the set of "nice" positions on this scale that enclose and
fall inside the interval (*start*,*end*).
Parameters
----------
start : number
The beginning of the scale interval.
end : number
The end of the scale interval.
desired_ticks : integer
Number of ticks that the caller would like to get
"""
raise NotImplementedError
def num_ticks(self, start, end, desired_ticks=None):
""" Returns an approximate number of ticks that this scale
produces for the given interval.
This method is used by the scale system to determine whether this is
the appropriate scale to use for an interval; the returned number of
ticks does not have to be exactly the same as what ticks() returns.
Parameters
----------
start : number
The beginning of the scale interval.
end : number
The end of the scale interval.
desired_ticks : integer
Number of ticks that the caller would like to get
Returns
-------
A float or an integer.
"""
raise NotImplementedError
def labels(self, start, end, numlabels=None, char_width=None):
""" Returns a series of ticks and corresponding strings for labels
that fall inside the interval (*start*,*end*).
Parameters
----------
start : number
The beginning of the scale interval.
end : number
The end of the scale interval.
numlabels : number
The ideal number of labels to generate on the interval.
char_width : number
The total character width available for labelling the interval.
One of *numlabels* or *char_width* must be provided. If both are
provided, then both are considered when picking label density and format.
"""
ticks = self.ticks(start, end, numlabels)
labels = self.formatter.format(ticks, numlabels, char_width)
return zip(ticks, labels)
def label_width(self, start, end, numlabels=None, char_width=None):
""" Returns an estimate of the total number of characters used by the
the labels that this scale produces for the given set of
inputs, as well as the number of labels.
Parameters
----------
start : number
The beginning of the scale interval.
end : number
The end of the scale interval.
numlabels : number
The ideal number of labels to generate on the interval.
char_width : number
The total character width available for labelling the interval.
Returns
-------
(numlabels, total label width)
"""
return self.formatter.estimate_width(start, end, numlabels, char_width,
ticker=self)
class FixedScale(AbstractScale):
""" A scale with fixed resolution, and "nice" points that line up at
multiples of the resolution. An optional zero value can be defined
that offsets the "nice" points to (N*resolution+zero).
"""
def __init__(self, resolution, zero=0.0, formatter=None):
self.resolution = resolution
self.zero = zero
if formatter is None:
formatter = BasicFormatter()
self.formatter = formatter
def ticks(self, start, end, desired_ticks=None):
""" For FixedScale, *desired_ticks* is ignored.
Overrides AbstractScale.
"""
if start == end or isnan(start) or isnan(end):
return []
res = self.resolution
start -= self.zero
end -= self.zero
start_tick = int(ceil(start / res))
end_tick = int(floor(end / res))
ticks = [i*res for i in range(start_tick, end_tick+1)]
return ticks
def num_ticks(self, start, end, desired_ticks=None):
""" For FixedScale, *desired_ticks* is ignored.
Overrides AbstractScale.
"""
if self.resolution is None or self.resolution == 0.0:
return 0
else:
return (end - start) / self.resolution
def _nice(x, round=False):
""" Returns a bracketing interval around interval *x*, whose endpoints fall
on "nice" values. If *round* is False, then it uses ceil(range)
This function is adapted from the original in Graphics Gems; the boundaries
have been changed to use (1, 2.5, 5, 10) as the nice values instead of
(1, 2, 5, 10).
"""
if x <= 0:
import warnings
warnings.warn("Invalid (negative) range passed to tick interval calculation")
x = abs(x)
expv = floor(log10(x))
f = x / pow(10, expv)
if round:
if f < 1.75:
nf = 1.0
elif f < 3.75:
nf = 2.5
elif f < 7.0:
nf = 5.0
else:
nf = 10.0
else:
if f <= 1.0:
nf = 1.0
elif f <= 2.5:
nf = 2.5
elif f <= 5.0:
nf = 5.0
else:
nf = 10.0
return nf * pow(10, expv)
def heckbert_interval(data_low, data_high, numticks=8, nicefunc=_nice, enclose=False):
""" Returns a "nice" range and resolution for an interval and a preferred
number of ticks, using Paul Heckbert's algorithm in Graphics Gems.
If *enclose* is True, then the function returns a min and a max that fall
inside *data_low* and *data_high*; if *enclose* is False, the nice interval
can be larger than the input interval.
"""
if data_high == data_low:
return data_high, data_low, 0
if numticks == 0:
numticks = 1
range = nicefunc(data_high - data_low)
if numticks > 1:
numticks -= 1
d = nicefunc(range / numticks, round=True)
if enclose:
graphmin = ceil(data_low / d) * d
graphmax = floor(data_high / d) * d
else:
graphmin = floor(data_low / d) * d
graphmax = ceil(data_high / d) * d
return graphmin, graphmax, d
class DefaultScale(AbstractScale):
""" A dynamic scale that tries to place ticks at nice numbers (1, 2, 5, 10)
so that ticks don't "pop" as the resolution changes.
"""
def __init__(self, formatter=None):
if formatter is None:
formatter = BasicFormatter()
self.formatter = formatter
def ticks(self, start, end, desired_ticks=8):
""" Returns the set of "nice" positions on this scale that enclose and
fall inside the interval (*start*,*end*).
Implements AbstractScale.
"""
if start == end or isnan(start) or isnan(end):
return [start]
min, max, delta = heckbert_interval(start, end, desired_ticks, enclose=True)
return frange(min, max, delta)
def num_ticks(self, start, end, desired_ticks=8):
""" Returns an approximate number of ticks that this scale
produces for the given interval.
Implements AbstractScale.
"""
return len(self.ticks(start, end, desired_ticks))
class Pow10Scale(AbstractScale):
""" A dynamic scale that shows only whole multiples of powers of 10
(including powers < 1).
"""
def __init__(self, formatter=None):
if formatter is None:
formatter = BasicFormatter()
self.formatter = formatter
def ticks(self, start, end, desired_ticks=8):
""" Returns the set of "nice" positions on this scale that enclose and
fall inside the interval (*start*,*end*).
Implements AbstractScale.
"""
if start == end or isnan(start) or isnan(end):
return [start]
min, max, delta = heckbert_interval(start, end, desired_ticks,
nicefunc=self._nice_pow10,
enclose = True)
return frange(min, max, delta)
def num_ticks(self, start, end, desired_ticks=8):
""" Returns an approximate number of ticks that this scale
produces for the given interval.
Implements AbstractScale.
"""
return len(self.ticks(start, end, desired_ticks))
def _nice_pow10(self, x, round=False):
return pow(10, floor(log10(x)))
class LogScale(AbstractScale):
""" A dynamic scale that only produces ticks and labels that work well when
plotting data on a logarithmic scale.
"""
def __init__(self, formatter=None):
if formatter is None:
formatter = BasicFormatter()
self.formatter = formatter
# In the following utility functions, "irep" stands for "integer representation".
# For a given base interval size i (i.e. "magic number"), there is a one-to-one
# mapping between the nice tick values and the integers.
def _irep_to_value(self,n,i):
""" For a given "magic number" i (i.e. spacing of the evenly spaced ticks
in the decade [1,10]), compute the tick value of the given integer
representation."""
if i == 1:
j,k = divmod(n,9)
v = (k+1)*10**j
return v
else:
j,k = divmod(n,int(10.0/i))
if k == 0:
v = 10**j
else:
v = i*k*10**j
return v
def _power_and_interval(self,x,i):
# j is the power of 10 of the decade in which x lies
j = int(ceil(log10(x))) - 1
# b is the interval size of the evenly spaced ticks in the decade
b = i*10**j
return (j,b)
def _power_and_index_to_irep(self,j,k,i):
if i == 1:
n = j*9+(k-1)
else:
n = j*int(10.0/i)+k
return n
def _logtickceil_as_irep(self,x,i):
""" For a given "magic number" i (i.e. spacing of the evenly spaced ticks
in the decade [1,10]), compute the integer representation of the smallest
tick not less than x."""
j,b = self._power_and_interval(x,i)
k = int(ceil(float(x)/b))
n = self._power_and_index_to_irep(j,k,i)
return n
def _logtickfloor_as_irep(self,x,i):
""" For a given "magic number" i (i.e. spacing of the evenly spaced ticks
in the decade [1,10]), compute the integer representation of the largest
tick not greater than x."""
j,b = self._power_and_interval(x,i)
k = int(floor(float(x)/b))
n = self._power_and_index_to_irep(j,k,i)
return n
def ticks(self, start, end, desired_ticks=8):
""" Compute a "nice" set of ticks for a log scale."""
if start > end:
start, end = end, start
if start == 0.0:
# Whoever calls us with a value of 0.0 puts themselves at our mercy
log_start = 1e-9
else:
log_start = log10(start)
if end == 0.0:
log_end = 1e-9
else:
log_end = log10(end)
log_interval = log_end - log_start
if log_interval < 1.0:
# If the data is spaced by less than a factor of 10, then use
# regular/linear ticking
min, max, delta = heckbert_interval(start, end, desired_ticks,
enclose=True)
return frange(min, max, delta)
elif log_interval < desired_ticks:
magic_numbers = [1, 2, 5]
for interval in magic_numbers:
n1 = self._logtickceil_as_irep(start,interval)
n2 = self._logtickfloor_as_irep(end,interval)
ticks = [self._irep_to_value(n,interval) for n in range(n1,n2+1)]
if len(ticks) < desired_ticks * 1.5:
return ticks
return ticks
else:
# Put lines at every power of ten
startlog = ceil(log_start)
endlog = floor(log_end)
expticks = linspace(startlog, endlog, endlog - startlog + 1)
return 10**expticks
def num_ticks(self, start, end, desired_ticks=8):
""" Returns an approximate number of ticks that this scale
produces for the given interval.
Implements AbstractScale.
"""
return len(self.ticks(start, end, desired_ticks))
##############################################################################
#
# ScaleSystem
#
##############################################################################
class ScaleSystem(object):
""" Represents a collection of scales over some range of resolutions.
This class has settings for a default scale that is used when ticking an
interval that is smaller than the finest resolution scale or larger than
the coarsest resolution scale.
"""
def __init__(self, *scales, **kw):
""" Creates a ScaleSystem
Usage::
ScaleSystem(scale1, .., scaleN, default_scale = DefaultScale())
If *default_scale* is not specified, then an instance of DefaultScale()
is created. If no *default_scale* is needed, then set it to None.
"""
self.scales = scales
self.default_scale = kw.get("default_scale", DefaultScale())
# Heuristics for picking labels
# The ratio of total label character count to the available character width
self.fill_ratio = 0.3
self.default_numticks = 8
def ticks(self, start, end, numticks=None):
""" Computes nice locations for tick marks.
Parameters
==========
start, end : number
The start and end values of the data.
numticks : number
The desired number of ticks to produce.
scales : a list of tuples of (min_interval, Scale)
Scales to use, in order from fine resolution to coarse.
If the end-start interval is less than a particular scale's
*min_interval*, then the previous scale is used.
Returns
=======
A list of positions where the ticks are to be placed.
"""
if numticks == 0:
return []
elif start == end or isnan(start) or isnan(end):
return []
elif numticks is None:
numticks = self.default_numticks
scale = self._get_scale(start, end, numticks)
ticks = scale.ticks(start, end, numticks)
return ticks
def labels(self, start, end, numlabels=None, char_width=None):
""" Computes position and labels for an interval
Parameters
----------
start : number
The beginning of the scale interval.
end : number
The end of the scale interval.
numlabels : number
The ideal number of labels to generate on the interval.
char_width : number
The total character width available for labelling the interval.
One of *numlabels* or *char_width* must be provided. If both are
provided, then both are considered when picking label density and format.
Returns
-------
A list of (tick position, string) tuples.
"""
# Check for insufficient arguments.
if numlabels is None and char_width is None:
raise ValueError, "Either numlabels or char_width (or both) must be given."
if numlabels == 0 or char_width == 0 or isnan(start) or isnan(end):
return []
# There are three cases:
# 1. we are given numlabels but not char_width
# 2. we are given char_width and not numlabels
# 3. we are given both
#
# Case 1: Use numlabels to find the closest scale purely on tick count.
# Case 2: Query all scales for their approximate label_width, pick the
# closest one to char_width * self.fill_ratio
# Case 3: Use numlabels to find the closest scale based on tick count.
if numlabels and not char_width:
# numlabels was given, but not char_width.
scale = self._get_scale(start, end, numlabels)
labels = scale.labels(start, end, numlabels)
else:
# char_width was given.
if numlabels:
# Both numlabels and char_width were given.
scale = self._get_scale(start, end, numlabels)
try:
ndx = list(self.scales).index(scale)
low = max(0, ndx - 1)
high = min(len(self.scales), ndx + 1)
scales = self.scales[low:high]
except ValueError:
scales = [scale]
else:
# Only char_width was given.
if len(self.scales) == 0:
scales = [self.default_scale]
else:
scales = self.scales
counts, widths = zip(*[s.label_width(start, end, char_width=char_width) \
for s in scales])
widths = array(widths)
closest = argmin(abs(widths - char_width*self.fill_ratio))
if numlabels is None:
numlabels = scales[closest].num_ticks(start, end, counts[closest])
labels = scales[closest].labels(start, end, numlabels,
char_width=char_width)
return labels
def _get_scale(self, start, end, numticks):
if len(self.scales) == 0:
closest_scale = self.default_scale
else:
closest_scale = self._get_scale_np(start, end, numticks)
if self.default_scale is not None:
# Handle the edge cases and see if there is a major discrepancy between
# what the scales offer and the desired number of ticks; if so, revert
# to using the default scale
approx_ticks = closest_scale.num_ticks(start, end, numticks)
if (approx_ticks == 0) or (numticks == 0) or \
(abs(approx_ticks - numticks) / numticks > 1.2) or \
(abs(numticks - approx_ticks) / approx_ticks > 1.2):
closest_scale = self.default_scale
return closest_scale
def _get_scale_bisect(self, start, end, numticks):
scale_intervals = [s.num_ticks(start, end, numticks) for s in self.scales]
sorted_scales = sorted(zip(scale_intervals, self.scales))
ndx = bisect(sorted_scales, numticks, lo=0, hi=len(self.scales))
if ndx == len(self.scales):
ndx -= 1
return sorted_scales[ndx][1]
def _get_scale_np(self, start, end, numticks):
# Extract the intervals from the scales we were given
scale_intervals = array([s.num_ticks(start, end, numticks) for s in self.scales])
closest = argmin(abs(scale_intervals - numticks))
return self.scales[closest]
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