def fittedAlphaFunctionAlternate(self,opticalDensity):
"""using polyfit function with a cubic we get a reasonable approximation to
alpha as a function of optical density. I force alpha to 1 at optical density < 0.5.
Function uses poly1d object so is good for arrays"""
lowODLimit = 0.5
highODPolynomial = scipy.poly1d([0.2496, -0.5873, 0.3939,1.572])
lowODPolynomial = scipy.poly1d([2*(highODPolynomial(lowODLimit)-1),1.0])
return scipy.piecewise(opticalDensity, [opticalDensity<lowODLimit,opticalDensity>=lowODLimit],[lowODPolynomial,highODPolynomial])
def evaluate(t, kernel_size):
return sp.piecewise(t, [t < 0, t >= 0], [
lambda t: 0, lambda t: sp.exp(
(-t * pq.dimensionless / kernel_size).simplified)
])
def evaluate(t, kernel_size):
return sp.piecewise(
t, [t < 0, t >= 0], [
lambda t: 0,
lambda t: sp.exp(
(-t * pq.dimensionless / kernel_size).simplified)])
def get_ramp(x0, x1, vmax, a, dt, output='ramp only'):
"""
Generate a ramp trajectory from x0 to x1 with constant
acceleration, a, to maximum velocity v_max.
Note, the main purlpose of this routine is to generate a
trajectory from x0 to x1. For this reason v_max and a are adjusted
slightly to work with the given time step.
Arguments:
x0 = starting position
x1 = ending position
vmax = maximum allowed velocity
a = constant acceleration
Keywords:
output = 'ramp only' or 'full'
when ramp only is selected then only the velocity ramp is returned.
If 'full' is selected the adjusted acceleration and maximum velocity
are also returned.
Ouput:
ramp = ramp trajectory form x0 to x1
"""
# Insure we are dealing with floating point numbers
x0, x1 = float(x0), float(x1)
vmax, a = float(vmax), float(a)
dt = float(dt)
vmax, a = abs(vmax), abs(a) # Make sure that v_max and a are positive
# Check to see if there is anything to do
if x0 == x1:
return scipy.array([x0])
# Get distance and sign indicating direction
dist = abs(x1 - x0)
sign = scipy.sign(x1 - x0)
# Determine if we will reach v_max
t2vmax = vmax / a
t2halfdist = scipy.sqrt(0.5 * dist / a)
if t2vmax > t2halfdist:
# Trajectory w/o constant velocity segment
T = scipy.sqrt(dist / a)
n = int(scipy.round_((1.0 / dt) * T))
# Adjust accel and duration for rounding of n (discrete time steps)
a = dist / (n * dt)**2
T = scipy.sqrt(dist / a)
# Generate trajectory
t = scipy.linspace(0.0, 2.0 * T, 2 * n + 1)
def f1(t):
return 0.5 * sign * a * (t**2)
def f2(t):
s = t - T
return f1(T) + sign * a * T * s - 0.5 * sign * a * s**2
func_list = [f1, f2]
cond_list = [t <= T, t > T]
ramp = x0 + scipy.piecewise(t, cond_list, func_list)
else:
# Trajectory w/ constant velocity segment
# Compute acceleration time and adjust acceleration
T1 = vmax / a
n = int(scipy.round_(T1 / dt))
a = vmax / (n * dt) # Adjusted acceleration
T1 = vmax / a # Adjusted acceleration time
# Compute and adjust constant velocity time
T2 = dist / vmax - T1
m = int(scipy.round_(T2 / dt))
vmax = dist / (dt * (n + m)) # Adjusted max velocity
T2 = dist / vmax - T1 # Adjusted constant velocity time
# Generate trajectory
t = scipy.linspace(0.0, 2.0 * T1 + T2, 2 * n + m + 1)
def f1(t):
return 0.5 * sign * a * (t**2)
def f2(t):
s = t - T1
return f1(T1) + sign * vmax * s
def f3(t):
s = t - T1 - T2
return f2(T1 + T2) + sign * vmax * s - 0.5 * sign * a * s**2
func_list = [f1, f2, f3]
cond_list = [
t <= T1,
scipy.logical_and(t > T1, t <= T1 + T2), t > T1 + T2
]
ramp = x0 + scipy.piecewise(t, cond_list, func_list)
if output == 'ramp only':
return ramp
elif output == 'full':
return ramp, vmax, a
else:
raise ValueError, 'unknown keyword option output=%s' % (output, )