def scale(fmn, fmx, prescale = (None, None, None), nsteps = 10):
"""Calculates an appropriate min, max, and step size for scaling axes on a plot.
The origin (zero) is guaranteed to be on an interval boundary.
fmn: The minimum data value
fmx: The maximum data value. Must be greater than or equal to fmn.
prescale: A 3-way tuple. A non-None min or max value (positions 0 and 1,
respectively) will be fixed to that value. A non-None interval (position 2)
be at least as big as that value. Default = (None, None, None)
nsteps: The nominal number of desired steps. Default = 10
Returns: a three-way tuple. First value is the lowest scale value, second the highest.
The third value is the step (increment) between them.
Examples:
>>> print "(%.1f, %.1f, %.1f)" % scale(1.1, 12.3, (0, 14, 2))
(0.0, 14.0, 2.0)
>>> print "(%.1f, %.1f, %.1f)" % scale(1.1, 12.3)
(0.0, 14.0, 2.0)
>>> print "(%.1f, %.1f, %.1f)" % scale(-1.1, 12.3)
(-2.0, 14.0, 2.0)
>>> print "(%.1f, %.1f, %.1f)" % scale(-12.1, -5.3)
(-13.0, -5.0, 1.0)
>>> print "(%.2f, %.2f, %.2f)" % scale(10.0, 10.0)
(10.00, 10.10, 0.01)
>>> print "(%.2f, %.4f, %.4f)" % scale(10.0, 10.001)
(10.00, 10.0010, 0.0001)
>>> print "(%.2f, %.2f, %.2f)" % scale(10.0, 10.0+1e-8)
(10.00, 10.10, 0.01)
>>> print "(%.2f, %.2f, %.2f)" % scale(0.0, 0.05, (None, None, .1), 10)
(0.00, 1.00, 0.10)
>>> print "(%.2f, %.2f, %.2f)" % scale(16.8, 21.5, (None, None, 2), 10)
(16.00, 36.00, 2.00)
>>> print "(%.2f, %.2f, %.2f)" % scale(16.8, 21.5, (None, None, 2), 4)
(16.00, 22.00, 2.00)
>>> print "(%.2f, %.2f, %.2f)" % scale(0.0, 0.21, (None, None, .02))
(0.00, 0.22, 0.02)
>>> print "(%.2f, %.2f, %.2f)" % scale(100.0, 100.0, (None, 100, None))
(99.00, 100.00, 0.20)
>>> print "(%.2f, %.2f, %.2f)" % scale(100.0, 100.0, (100, None, None))
(100.00, 101.00, 0.20)
"""
# If all the values are hard-wired in, then there's nothing to do:
if None not in prescale:
return prescale
(minscale, maxscale, min_interval) = prescale
# Make sure fmn and fmx are float values, in case a user passed
# in integers:
fmn = float(fmn)
fmx = float(fmx)
if fmx < fmn :
raise weeplot.ViolatedPrecondition("scale() called with max value less than min value")
# In case minscale and/or maxscale was specified, clip fmn and fmx to make sure they stay within bounds
if maxscale is not None:
fmx = min(fmx, maxscale)
if minscale is not None:
fmn = max(fmn, minscale)
# Check the special case where the min and max values are equal.
if _rel_approx_equal(fmn, fmx) :
# They are equal. We need to move one or the other to create a range, while
# being careful that the resultant min/max stay within the interval [minscale, maxscale]
# Pick a step out value based on min_interval if the user has supplied one. Otherwise,
# arbitrarily pick 0.1
if min_interval is not None:
step_out = min_interval * nsteps
else:
step_out = 0.01 * abs(fmx) if fmx else 0.1
if maxscale is not None:
# maxscale if fixed. Move fmn.
fmn = fmx - step_out
elif minscale is not None:
# minscale if fixed. Move fmx.
fmx = fmn + step_out
else:
# Both can float. Check special case where fmn and fmx are zero
if fmn == 0.0 :
fmx = 1.0
else :
# Just arbitrarily move one. Say, fmx.
fmx = fmn + step_out
if minscale is not None and maxscale is not None:
if maxscale < minscale:
raise weeplot.ViolatedPrecondition("scale() called with prescale max less than min")
frange = maxscale - minscale
else:
frange = fmx - fmn
steps = frange / nsteps
mag = math.floor(math.log10(steps))
magPow = math.pow(10.0, mag)
magMsd = math.floor(steps/magPow + 0.5)
if magMsd > 5.0:
magMsd = 10.0
elif magMsd > 2.0:
magMsd = 5.0
else : # magMsd > 1.0
magMsd = 2
# This will be the nominal interval size
interval = magMsd * magPow
# Test it against the desired minimum, if any
if min_interval is None or interval >= min_interval:
# Either no min interval was specified, or its safely
# less than the chosen interval.
if minscale is None:
minscale = interval * math.floor(fmn / interval)
if maxscale is None:
maxscale = interval * math.ceil(fmx / interval)
else:
# The request for a minimum interval has kicked in.
# Sometimes this can make for a plot with just one or
# two intervals in it. Adjust the min and max values
# to get a nice plot
interval = float(min_interval)
if minscale is None:
if maxscale is None:
# Both can float. Pick values so the range is near the bottom
# of the scale:
minscale = interval * math.floor(fmn / interval)
maxscale = minscale + interval * nsteps
else:
# Only minscale can float
minscale = maxscale - interval * nsteps
else:
if maxscale is None:
# Only maxscale can float
maxscale = minscale + interval * nsteps
else:
# Both are fixed --- nothing to be done
pass
return (minscale, maxscale, interval)
def scaletime(tmin_ts, tmax_ts) :
"""Picks a time scaling suitable for a time plot.
tmin_ts, tmax_ts: The time stamps in epoch time around which the times will be picked.
Returns a scaling 3-tuple. First element is the start time, second the stop
time, third the increment. All are in seconds (epoch time in the case of the
first two).
Example 1: 24 hours on an hour boundary
>>> from weeutil.weeutil import timestamp_to_string as to_string
>>> time_ts = time.mktime(time.strptime("2013-05-17 08:00", "%Y-%m-%d %H:%M"))
>>> xmin, xmax, xinc = scaletime(time_ts - 24*3600, time_ts)
>>> print to_string(xmin), to_string(xmax), xinc
2013-05-16 09:00:00 PDT (1368720000) 2013-05-17 09:00:00 PDT (1368806400) 10800
Example 2: 24 hours on a 3-hour boundary
>>> time_ts = time.mktime(time.strptime("2013-05-17 09:00", "%Y-%m-%d %H:%M"))
>>> xmin, xmax, xinc = scaletime(time_ts - 24*3600, time_ts)
>>> print to_string(xmin), to_string(xmax), xinc
2013-05-16 09:00:00 PDT (1368720000) 2013-05-17 09:00:00 PDT (1368806400) 10800
Example 3: 24 hours on a non-hour boundary
>>> time_ts = time.mktime(time.strptime("2013-05-17 09:01", "%Y-%m-%d %H:%M"))
>>> xmin, xmax, xinc = scaletime(time_ts - 24*3600, time_ts)
>>> print to_string(xmin), to_string(xmax), xinc
2013-05-16 12:00:00 PDT (1368730800) 2013-05-17 12:00:00 PDT (1368817200) 10800
Example 4: 27 hours
>>> time_ts = time.mktime(time.strptime("2013-05-17 07:45", "%Y-%m-%d %H:%M"))
>>> xmin, xmax, xinc = scaletime(time_ts - 27*3600, time_ts)
>>> print to_string(xmin), to_string(xmax), xinc
2013-05-16 06:00:00 PDT (1368709200) 2013-05-17 09:00:00 PDT (1368806400) 10800
Example 5: 3 hours on a 15 minute boundary
>>> time_ts = time.mktime(time.strptime("2013-05-17 07:45", "%Y-%m-%d %H:%M"))
>>> xmin, xmax, xinc = scaletime(time_ts - 3*3600, time_ts)
>>> print to_string(xmin), to_string(xmax), xinc
2013-05-17 05:00:00 PDT (1368792000) 2013-05-17 08:00:00 PDT (1368802800) 900
Example 6: 3 hours on a non-15 minute boundary
>>> time_ts = time.mktime(time.strptime("2013-05-17 07:46", "%Y-%m-%d %H:%M"))
>>> xmin, xmax, xinc = scaletime(time_ts - 3*3600, time_ts)
>>> print to_string(xmin), to_string(xmax), xinc
2013-05-17 05:00:00 PDT (1368792000) 2013-05-17 08:00:00 PDT (1368802800) 900
Example 7: 12 hours
>>> time_ts = time.mktime(time.strptime("2013-05-17 07:46", "%Y-%m-%d %H:%M"))
>>> xmin, xmax, xinc = scaletime(time_ts - 12*3600, time_ts)
>>> print to_string(xmin), to_string(xmax), xinc
2013-05-16 20:00:00 PDT (1368759600) 2013-05-17 08:00:00 PDT (1368802800) 3600
Example 8: 15 hours
>>> time_ts = time.mktime(time.strptime("2013-05-17 07:46", "%Y-%m-%d %H:%M"))
>>> xmin, xmax, xinc = scaletime(time_ts - 15*3600, time_ts)
>>> print to_string(xmin), to_string(xmax), xinc
2013-05-16 17:00:00 PDT (1368748800) 2013-05-17 08:00:00 PDT (1368802800) 7200
"""
if tmax_ts <= tmin_ts :
raise weeplot.ViolatedPrecondition("scaletime called with tmax <= tmin")
tdelta = tmax_ts - tmin_ts
tmin_dt = datetime.datetime.fromtimestamp(tmin_ts)
tmax_dt = datetime.datetime.fromtimestamp(tmax_ts)
if tdelta <= 16 * 3600:
if tdelta <= 3*3600:
# For time intervals less than 3 hours, use an increment of 15 minutes
interval = 900
elif tdelta <= 12 * 3600:
# For intervals from 3 hours up through 12 hours, use one hour
interval = 3600
else:
# For intervals from 12 through 16 hours, use two hours.
interval = 7200
# Get to the one hour boundary below tmax:
stop_dt = tmax_dt.replace(minute=0, second=0, microsecond=0)
# if tmax happens to be on a one hour boundary we're done. Otherwise, round
# up to the next one hour boundary:
if tmax_dt > stop_dt:
stop_dt += datetime.timedelta(hours=1)
n_hours = int((tdelta + 3599) / 3600)
start_dt = stop_dt - datetime.timedelta(hours=n_hours)
elif tdelta <= 27 * 3600:
# A day plot is wanted. A time increment of 3 hours is appropriate
interval = 3 * 3600
# h is the hour of tmax_dt
h = tmax_dt.timetuple()[3]
# Subtract off enough to get to the lower 3-hour boundary from tmax:
stop_dt = tmax_dt.replace(minute=0, second=0, microsecond=0) - datetime.timedelta(hours = h % 3)
# If tmax happens to lie on a 3 hour boundary we don't need to do anything. If not, we need
# to round up to the next 3 hour boundary:
if tmax_dt > stop_dt:
stop_dt += datetime.timedelta(hours=3)
# The stop time is one day earlier
start_dt = stop_dt - datetime.timedelta(days=1)
if tdelta == 27 * 3600 :
# A "slightly more than a day plot" is wanted. Start 3 hours earlier:
start_dt -= datetime.timedelta(hours=3)
elif 27 * 3600 < tdelta <= 31 * 24 * 3600 :
# The time scale is between a day and a month. A time increment of one day is appropriate
start_dt = tmin_dt.replace(hour=0, minute=0, second=0, microsecond=0)
stop_dt = tmax_dt.replace(hour=0, minute=0, second=0, microsecond=0)
tmax_tt = tmax_dt.timetuple()
if tmax_tt[3]!=0 or tmax_tt[4]!=0 :
stop_dt += datetime.timedelta(days=1)
interval = 24 * 3600
elif tdelta < 2 * 365.25 * 24 * 3600 :
# The time scale is between a month and 2 years. A time increment of a month is appropriate
start_dt = tmin_dt.replace(day=1, hour=0, minute=0, second=0, microsecond=0)
(year , mon, day) = tmax_dt.timetuple()[0:3]
if day != 1 :
mon += 1
if mon==13 :
mon = 1
year += 1
stop_dt = datetime.datetime(year, mon, 1)
# Average month length:
interval = 365.25/12 * 24 * 3600
else :
# The time scale is between a month and 2 years. A time increment of a year is appropriate
start_dt = tmin_dt.replace(day=1, hour=0, minute=0, second=0, microsecond=0)
(year , mon, day) = tmax_dt.timetuple()[0:3]
if day != 1 or mon !=1 :
day = 1
mon = 1
year += 1
stop_dt = datetime.datetime(year, mon, 1)
# Average year length
interval = 365.25 * 24 * 3600
# Convert to epoch time stamps
start_ts = int(time.mktime(start_dt.timetuple()))
stop_ts = int(time.mktime(stop_dt.timetuple()))
return (start_ts, stop_ts, interval)