def is_linear_flow_rate(flow_rate):
""" Test whether a flow rate (UnitScalar) has a unit of a volume per time.
"""
try:
convert(flow_rate, from_unit=flow_rate.units, to_unit=m / second)
return True
except InvalidConversion:
return False
def volume_to_depth(volume, column, to_unit="meters"):
""" Translate a volume of fluid into a depth in infinitely long column.
"""
if volume.units != chr_units.column_volumes:
volume = convert(volume,
from_unit=volume.units,
to_unit=column.volume.units)
volume *= column.volume
volume = float(volume)
depth = volume * column.bed_height_actual
if to_unit:
depth = convert(depth,
from_unit=depth.units,
to_unit=parse_unit(to_unit))
return float(depth)
def unit_scalar_almost_equal(x1, x2, eps=1e-9):
""" Returns whether 2 UnitScalars are almost equal.
Parameters
----------
x1 : UnitScalar
First unit scalar to compare.
x2 : UnitScalar
Second unit scalar to compare.
eps : float
Absolute precision of the comparison.
"""
if not isinstance(x1, UnitScalar):
msg = "x1 is supposed to be a UnitScalar but a {} was passed."
msg = msg.format(type(x1))
logger.exception(msg)
raise ValueError(msg)
if not isinstance(x2, UnitScalar):
msg = "x2 is supposed to be a UnitScalar but a {} was passed."
msg = msg.format(type(x2))
logger.exception(msg)
raise ValueError(msg)
a1 = float(x1)
try:
a2 = convert(float(x2), from_unit=x2.units, to_unit=x1.units)
except InvalidConversion:
return False
return np.abs(a1 - a2) < eps
def convertUnit(self, value, unit_from, unit_to):
if (self.delete == True):
return
exec('from scimath.units.SI import *')
exec('from scimath.units.pressure import *')
exec('from scimath.units.acceleration import *')
exec('from scimath.units.angle import *')
exec('from scimath.units.area import *')
exec('from scimath.units.density import *')
exec('from scimath.units.electromagnetism import *')
exec('from scimath.units.energy import *')
exec('from scimath.units.force import *')
exec('from scimath.units.frequency import *')
exec('from scimath.units.length import *')
exec('from scimath.units.mass import *')
exec('from scimath.units.power import *')
exec('from scimath.units.pressure import *')
exec('from scimath.units.speed import *')
exec('from scimath.units.substance import *')
exec('from scimath.units.temperature import *')
exec('from scimath.units.time import *')
exec('from scimath.units.volume import *')
from scimath.units.api import convert
try:
value = convert(value, eval(unit_from), eval(unit_to))
except:
print(
'Einheit "' + unit_from + '" oder "' + unit_to +
'" wird nicht unterstuetzt von scimath. Funktion wird beendet...'
)
return (False)
return (value)
def get_step_velocity(step, column=None):
""" Extract the step linear superficial velocity (flow_rate), in m/s.
"""
if is_volumetric_flow_rate(step.flow_rate):
step_velocity = volumetric_flow_rate_to_linear(
step.flow_rate, column.column_type.diameter, to_unit="m/s")
else:
step_velocity = convert(step.flow_rate,
from_unit=step.flow_rate.units,
to_unit=meter / second)
return float(step_velocity)
def linear_flow_rate_to_volumetric(linear_flow_rate, diam, to_unit=""):
""" Convert a linear flow rate in a column of diameter diam to a volumetric
flow rate.
"""
vol_flow_rate = (np.pi * diam**2 / 4.) * linear_flow_rate
if to_unit:
parse_unit = unit_parser.parse_unit
from_unit = vol_flow_rate.units
to_unit = parse_unit(to_unit)
vol_flow_rate_val = convert(float(vol_flow_rate),
from_unit=from_unit,
to_unit=to_unit)
vol_flow_rate = UnitScalar(vol_flow_rate_val, units=to_unit)
return vol_flow_rate
def time_to_volume(time, flow_rate, column=None, to_unit="CV"):
""" Convert a flow time to a volume, assuming a specified flow rate.
Parameters
----------
time : UnitScalar
Time of flow.
flow_rate : UnitScalar
Flow rate.
column : Column [OPTIONAL]
Column in which the flow occur. Only needed if providing linear flow
rate, or if the output unit must be CV.
to_unit : str
String representation of the output unit.
Returns
-------
UnitScalar
Volume that flowed during the specified time.
"""
if not isinstance(time, UnitScalar):
msg = "The time provided should be a UnitScalar."
logger.exception(msg)
raise ValueError(msg)
if not is_volumetric_flow_rate(flow_rate):
diam = column.column_type.diameter
flow_rate = linear_flow_rate_to_volumetric(flow_rate, diam)
volume = time * flow_rate
if to_unit:
if to_unit == "CV":
volume = UnitScalar(float(volume / column.volume), units="CV")
else:
# Convert to target unit
parse_unit = unit_parser.parse_unit
volume = convert(volume,
from_unit=volume.units,
to_unit=parse_unit(to_unit))
return volume
def build_flow_rate_array(times, experiment, to_unit="liter/minute"):
""" Build array of flow rates in liter/min at each time of 'times' array.
Parameters
----------
times : numpy.array
Array of chromatogram times at which to extract the flow rates.
experiment : Experiment
Experiment to extract the flow rates from.
to_unit : str
Unit of the output.
Returns
-------
UnitArray
Array of flow rates at the times of the times array.
"""
method_steps = experiment.method.method_steps
step_boundary_times = experiment.method_step_boundary_times
flow_rates = ones(times.shape) * nan
for i, step in enumerate(method_steps):
step_start_time = step_boundary_times[i]
step_stop_time = step_boundary_times[i+1]
mask = (times >= step_start_time) & (times < step_stop_time)
if is_linear_flow_rate(step.flow_rate):
diam = experiment.column.column_type.diameter
flow_rate = linear_flow_rate_to_volumetric(step.flow_rate, diam,
to_unit=to_unit)
elif is_volumetric_flow_rate(step.flow_rate):
flow_rate = convert(step.flow_rate, from_unit=step.flow_rate.units,
to_unit=unit_parser.parse_unit(to_unit))
else:
flow_rate = volumetric_CV_flow_rate_to_volumetric_flow_rate(
step.flow_rate, experiment.column, to_unit=to_unit
)
flow_rates[mask] = float(flow_rate)
return UnitArray(flow_rates, units=to_unit)
def create_cadet_external_and_validate(self, sim=None):
if sim is None:
sim = self.sim
cadet_ext = CADETPhExternalProfile.from_simulation(sim)
# lengths of arrays:
self.assertEqual(len(cadet_ext.ext_prof_delta),
len(cadet_ext.ext_profile))
one_col_length = float(
convert_str(self.column.bed_height_actual, "cm", "m"))
# Initial values: depths start at 0, and includes 1 column of initial
# buffer:
self.assertEqual(cadet_ext.ext_prof_delta[0], 0.0)
self.assertEqual(cadet_ext.ext_prof_delta[1], one_col_length)
init_solution = self.sim.method.initial_buffer
first_step = self.sim.method.method_steps[0]
self.assertEqual(cadet_ext.ext_profile[0], float(init_solution.pH))
self.assertEqual(cadet_ext.ext_profile[1], first_step.solutions[0].pH)
flow_rate0 = first_step.flow_rate
first_velocity = convert(float(flow_rate0),
from_unit=flow_rate0.units,
to_unit=meter / second)
self.assertEqual(cadet_ext.ext_velocity, first_velocity)
# Step lengths, in column, all add up to the profile_deltas:
col_lengths = [one_col_length]
step_velocity0 = get_step_velocity(first_step)
for step in self.method.method_steps:
step_velocity = float(get_step_velocity(step))
step_volume = float(step.volume)
# Normalize the duration based on the velocity of the step
col_length = step_volume * step_velocity0 / step_velocity
col_length *= one_col_length
col_lengths.append(float(col_length))
self.assertAlmostEqual(cadet_ext.ext_prof_delta.sum(),
sum(col_lengths))
return cadet_ext
def vol_to_time(volume, flow_rate, column=None, to_unit="minute"):
""" Convert a volume to a time, using a flow rate.
Parameters
----------
volume : UnitScalar
Volume to convert to a time.
flow_rate : UnitScalar
Flow rate used to convert a volume to a time.
column : Column [OPTIONAL]
Column the volume is flowing through. From that object are read the
diameter and colume of the column for unit conversion if needed.
to_unit : str [OPTIONAL, default: minutes]
Target time unit. Must be parsable by scimath's unit parser.
Returns
-------
float
Value of the time needed for the provided volume to flow through the
column.
"""
if not isinstance(volume, UnitScalar):
raise ValueError("The volume provided should be a UnitScalar.")
elif volume.units == chr_units.column_volumes:
volume = float(volume) * column.volume
# Convert a linear flow rate into a volumetric flow rate
if not is_volumetric_flow_rate(flow_rate):
diam = column.column_type.diameter
flow_rate = linear_flow_rate_to_volumetric(flow_rate, diam)
# Compute the time
time = volume / flow_rate
if to_unit:
# Convert to target unit
time = convert(time, from_unit=time.units, to_unit=parse_unit(to_unit))
return float(time)
def _set_volume(self, value):
""" Back-calculate the column's bed height H to have requested volume.
To make sure that the volume follows::
vol = pi * D^2 * H / 4
the bed height is set to::
H = 4 * vol / (pi * D^2)
Note that this may raise an exception if the resulting bed height
doesn't fall in the range set by the column type.
"""
#: Do nothing if value requested is already the value of the volume:
if unit_scalar_almost_equal(value, self.volume):
return
if not isinstance(value, UnitScalar):
msg = "Setting the column volume must be done providing a " \
"UnitScalar to specify the unit."
logger.exception(msg)
raise ValueError(msg)
if not has_volume_units(value):
msg = "Setting the column volume must be done providing a " \
"UnitScalar to specify the unit."
logger.exception(msg)
raise ValueError(msg)
diam = self.column_type.diameter
bed_height_actual = 4. * value / (diam**2 * pi)
val = convert(
float(bed_height_actual), from_unit=bed_height_actual.units,
to_unit=centimeter
)
self.bed_height_actual = UnitScalar(val, units=centimeter)
def from_simulation(cls, sim):
""" Compute the profiles and instantiate a CADETExternal.
"""
column = sim.column
# Initial array values
step0 = sim.method.method_steps[0]
step0_ph = float(step0.solutions[0].pH)
step0_velocity = get_step_velocity(step0, column)
# Initialization of the profiles to build
init_ph = sim.method.initial_buffer.pH
column_length = convert(column.bed_height_actual,
to_unit=meter,
from_unit=column.bed_height_actual.units)
ph_values = [init_ph, step0_ph]
depth_deltas = [0., float(column_length)]
for step in sim.method.method_steps:
step_depth = volume_to_depth(step.volume,
column=column,
to_unit="meter")
step_velocity = get_step_velocity(step, column)
# If a step flows N times faster, we model this by making its
# duration N times smaller.
step_depth *= step0_velocity / step_velocity
if len(step.solutions) == 0:
msg = "Step with no solution not supported"
raise NotImplementedError(msg)
# Deal with the transition from the previous step
start_step_ph = float(step.solutions[0].pH)
transition_needed = ph_values[-1] != start_step_ph
if transition_needed:
# Create a fake gradient of pH since CADET requires pH profile
# to be differentiable
depth_deltas.append(EPS)
ph_values.append(start_step_ph)
step_depth -= EPS
# Deal with the contributions from this step:
num_solutions = len(step.solutions)
if num_solutions == 1:
end_step_ph = start_step_ph
elif num_solutions == 2:
# 2 solutions during gradient elution when the buffer
# composition goes from 1 solution to the other:
end_step_ph = float(step.solutions[1].pH)
else:
msg = "Found a step with more than 2 solutions. Don't know " \
"how to compute the pH profile in that case."
logger.exception(msg)
raise NotImplementedError(msg)
ph_values.append(end_step_ph)
depth_deltas.append(step_depth)
ext_profile = np.array(ph_values, dtype="float64")
ext_prof_delta = np.array(depth_deltas, dtype="float64")
return cls(ext_profile=ext_profile,
ext_prof_delta=ext_prof_delta,
ext_velocity=step0_velocity)
def compute_mass_from_abs_data(absorb_data, ext_coeff, experim, t_start=None,
t_stop=None, t_start_idx=None, t_stop_idx=None):
""" Compute total mass of a product component between start and stop times.
The total mass is computed by integrating the specified chromatogram,
between t_start and t_stop and using the specified extinction coefficient
and flow rate at each time.
Parameters
----------
absorb_data : XYData
Data (fraction or continuous) to integrate to compute the contained
mass.
ext_coeff : UnitScalar
Extinction coefficient to use to convert the absorbance to a product
concentration.
experim : Experiment
Experiment from which to extract the method (and therefore flow rate)
information and the system's path length.
t_start : UnitScalar
Time at which to start integrating, in minutes. Leave as None to use
the t_start_idx to specify the time range to integrate.
t_stop : UnitScalar
Time at which to stop integrating, in minutes. Leave as None to use
the t_stop_idx to specify the time range to integrate.
t_start_idx : Int or None
Index in the x_data to start integrating at (inclusive).
t_stop_idx : Int or None
Index in the x_data to stop integrating at (exclusive). Leave as None
to go all the way to the end.
Returns
-------
UnitScalar
Product mass, in grams, estimated to elute between t_start and t_stop.
"""
all_x_data = absorb_data.x_data
all_y_data = absorb_data.y_data
# Convert time inputs into minutes:
data_time_unit = unit_parser.parse_unit(absorb_data.x_metadata["units"])
all_x_data = convert(all_x_data, from_unit=data_time_unit, to_unit=minute)
if t_start is not None and t_stop is not None:
t_start = convert_units(t_start, tgt_unit=minute)
t_stop = convert_units(t_stop, tgt_unit=minute)
t_start_idx = searchsorted(all_x_data, t_start)
t_stop_idx = searchsorted(all_x_data, t_stop)
if t_start_idx == t_stop_idx:
msg = "Unable to compute the integral of the provided because" \
"t_start too close to t_stop."
logger.warning(msg)
return UnitScalar(0., units="gram")
collect_idx = slice(t_start_idx, t_stop_idx)
times = all_x_data[collect_idx]
absorbances = all_y_data[collect_idx]
#: Extract the flow rate from the experiment method:
flow_rates = build_flow_rate_array(times, experim, to_unit="liter/minute")
missing_flow_rates = where(isnan(flow_rates))[0]
if len(missing_flow_rates) > 0:
msg = "The time range requested to integrate results goes beyond the "\
"known method steps, and will need to be cropped by {} values." \
" Cropped values are {}.".format(len(missing_flow_rates),
missing_flow_rates)
logger.warning(msg)
t_stop_idx = missing_flow_rates[0]
collect_idx = slice(t_start_idx, t_stop_idx)
times = all_x_data[collect_idx]
absorbances = all_y_data[collect_idx]
flow_rates = flow_rates[collect_idx]
# Turn absorbances into AU/cm
path_length = convert_units(experim.system.abs_path_length, "cm")[()]
data_absorb_unit = unit_parser.parse_unit(absorb_data.y_metadata["units"])
absorbances_au = convert(absorbances, from_unit=data_absorb_unit,
to_unit=absorption_unit)
# Compute masses in grams
masses = (absorbances_au*array(flow_rates)) / (path_length*ext_coeff[()])
total_mass = trapz(masses, times)
return UnitScalar(total_mass, units="gram")
def has_volume_units(vol):
try:
convert(vol, from_unit=vol.units, to_unit=m**3)
return True
except InvalidConversion:
return False
#! /usr/bin/env python
from __future__ import print_function
import os
import math
from scimath.units.length import km, cm
from scimath.units.api import convert
def deflection_tangent(tangent_length, radius):
return (tangent_length**2 + radius**2)**(1.0/2.0) - radius
# cannot use math.hypot or math.sqrt:
# scimath.units.unit.InvalidConversion: dimensional quantities ('m') cannot be converted to scalars
# cannot use numpy.hypot:
# AttributeError: 'unit' object has no attribute 'hypot'
def deflection_arc(arc_length, radius):
return radius * (math.cos(arc_length/radius)**-1 - 1)
radius_earth = 6371.01 * km
length = 1.0 * km
deflection_1 = convert(deflection_tangent(length, radius_earth).value, km, cm)
deflection_2 = convert(deflection_arc(length, radius_earth).value, km, cm)
print(deflection_1, cm.label)
print(deflection_2, cm.label)
def get_step_duration(self, step):
step_duration = self.column.bed_height_actual / step.flow_rate
step_duration = convert(float(step_duration),
from_unit=step_duration.units,
to_unit=second)
return step_duration