/usr/lib/python2.7/dist-packages/chaco/scales/scales.py is in python-chaco 4.4.1-1.2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 | """
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]
|