def processTrajectories(fileName):
"""
处理弹道数据，输出图形。
:param fileName:
:return: None，显示图形，用一次和二次多项式拟合弹道轨迹。
"""
distances, heights = getTrajectoryData(fileName)
numTrials = len(heights)
distances = pylab.array(distances)
#生成一个数组，用于存储每个距离的高度，并计算平均值
totHeights = pylab.array([0] * len(distances))
for h in heights:
totHeights = totHeights + pylab.array(h)
meanHeights = totHeights / len(heights)
# 绘图
title = 'Trajectory of Projectile (Mean of ' + str(numTrials) + ' Trials)'
pylab.figure(title)
pylab.title(title)
pylab.xlabel('Inches from Launch Point')
pylab.ylabel('Inches Above Launch Point')
pylab.plot(distances, meanHeights, 'ko')
fit = pylab.polyfit(distances, meanHeights, 1)
altitudes = pylab.polyval(fit, distances)
pylab.plot(distances, altitudes, 'b', label='Linear Fit')
print('RSquare of linear fit =', rSquared(meanHeights, altitudes))
fit = pylab.polyfit(distances, meanHeights, 2)
# 用实验数据对应的点位distances来绘图，导致点少的区域上，曲线不够平滑。
altitudes = pylab.polyval(fit, distances)
pylab.plot(distances, altitudes, 'k:', label='Quadratic Fit')
print('RSquare of quadratic fit =', rSquared(meanHeights, altitudes))
pylab.legend()
# 计算落地时的水平速度，打印输出。
getHorizontalSpeed(fit, distances[-1], distances[0])
def plotPopulations(numSteps):
""" Plots populations of Foxes & Rabbits for given timesteps. """
rab_pop, fox_pop = runSimulation(numSteps)
# for i in range(len(rab_pop)):
# print(rab_pop[i], fox_pop[i])
r_style = 'bo' # blue - continuous line
f_style = 'ro' # red - continuous line
pylab.figure('Fox / Rabit Populations')
pylab.plot(rab_pop, r_style, label='Rabbit Pop')
pylab.plot(fox_pop, f_style, label='Fox Pop')
pylab.title('Fox / Rabit Populations: {} timesteps'.format(numSteps))
pylab.xlabel('Time Steps')
pylab.ylabel('Population')
pylab.legend(loc='best')
degree = 2
rab_coeff = pylab.polyfit(range(len(rab_pop)), rab_pop, degree)
pylab.plot(pylab.polyval(rab_coeff, range(len(rab_pop))), 'b-')
fox_coeff = pylab.polyfit(range(len(fox_pop)), fox_pop, degree)
pylab.plot(pylab.polyval(fox_coeff, range(len(fox_pop))), 'r-')
pylab.show()
def evaluate_models_on_training(x, y, models):
"""
For each regression model, compute the R-square for this model with the
standard error over slope of a linear regression line (only if the model is
linear), and plot the data along with the best fit curve.
For the plots, you should plot data points (x,y) as blue dots and your best
fit curve (aka model) as a red solid line. You should also label the axes
of this figure appropriately and have a title reporting the following
information:
degree of your regression model,
R-square of your model evaluated on the given data points
Args:
x: a list of length N, representing the x-coords of N sample points
y: a list of length N, representing the y-coords of N sample points
models: a list containing the regression models you want to apply to
your data. Each model is a numpy array storing the coefficients of
a polynomial.
Returns:
None
"""
r_sqr=0
for model in models:
if r_squared(y,pylab.polyval(model,x)) > r_sqr :
r_sqr=r_squared(y,pylab.polyval(model,x))
best=model
EST_values= pylab.polyval(best,x)
pylab.plot(x,y,'bo',label='points')
pylab.plot(x,EST_values,'r',label='linear fit , R^2 = '+str(round(r_squared(y,EST_values),5)))
pylab.legend(loc='best')
pylab.show()
def getApices(y):
"""
returns the time (in frames) and position of initial and final apex
height from a given trajectory y, which are obtained by fitting a cubic
spline
==========
parameter:
==========
y : *array* (1D)
the trajectory. Should ideally start ~1 frame before an apex and end ~1
frame behind an apex
========
returns:
========
[x0, xF], [y0, yF] : location (in frames) and value of the first and final
apices
"""
# the math behind here is: fitting a 2nd order polynomial and finding
# the root of its derivative. Here, only the results are applied, that's
# why it appears like "magic" numbers
c = dot(array([[.5, -1, .5], [-1.5, 2., -.5], [1., 0., 0.]]), y[:3])
x0 = -1. * c[1] / (2. * c[0])
y0 = polyval(c, x0)
c = dot(array([[.5, -1, .5], [-1.5, 2., -.5], [1., 0., 0.]]), y[-3:])
xF = -1. * c[1] / (2. * c[0])
yF = polyval(c, xF)
xF += len(y) - 3
return [x0, xF], [y0, yF]
def plotPopulations(numSteps):
""" Plots populations of Foxes & Rabbits for given timesteps. """
rab_pop, fox_pop = runSimulation(numSteps)
# for i in range(len(rab_pop)):
# print(rab_pop[i], fox_pop[i])
r_style = 'bo' # blue - continuous line
f_style = 'ro' # red - continuous line
pylab.figure('Fox / Rabit Populations')
pylab.plot(rab_pop, r_style, label='Rabbit Pop')
pylab.plot(fox_pop, f_style, label='Fox Pop')
pylab.title('Fox / Rabit Populations: {} timesteps'.format(numSteps))
pylab.xlabel('Time Steps')
pylab.ylabel('Population')
pylab.legend(loc='best')
degree = 2
rab_coeff = pylab.polyfit(range(len(rab_pop)), rab_pop, degree)
pylab.plot(pylab.polyval(rab_coeff, range(len(rab_pop))), 'b-')
fox_coeff = pylab.polyfit(range(len(fox_pop)), fox_pop, degree)
pylab.plot(pylab.polyval(fox_coeff, range(len(fox_pop))), 'r-')
pylab.show()
def fitData(fileName):
xVals, yVals = getData(fileName)
xVals = pylab.array(xVals)
yVals = pylab.array(yVals)
xVals = xVals * 9.81 #get force
pylab.plot(xVals, yVals, 'bo', label='Measured points')
model = pylab.polyfit(xVals, yVals, 1)
xVals = xVals + [2]
yVals = yVals + []
estYVals = pylab.polyval(model, xVals)
pylab.plot(xVals,
estYVals,
'r',
label='Linear fit, r**2 = ' +
str(round(rSquared(yVals, estYVals), 5)))
model = pylab.polyfit(xVals, yVals, 2)
estYVals = pylab.polyval(model, xVals)
pylab.plot(xVals,
estYVals,
'g--',
label='Quadratic fit, r**2 = ' +
str(round(rSquared(yVals, estYVals), 5)))
pylab.title('A Linear Spring')
labelPlot()
pylab.legend(loc='best')
def fitData(inputFile):
masses, distances = getData(inputFile)
distances = pylab.array(distances)
forces = pylab.array(masses) * 9.81
pylab.plot(forces, distances, 'ko', label='Measured displacements')
pylab.title('Measured displacement of spring')
pylab.xlabel('|Force| (Newtons)')
pylab.ylabel('Distances (meters)')
a, b = pylab.polyfit(forces, distances, 1)
k = 1 / a
predVals = pylab.polyval((a, b), forces)
pylab.plot(forces,
predVals,
label='Displacements predicted by \nlinear fit, k = ' +
str(round(k, 5)))
forces2 = numpy.append(forces, [1.5 * 9.81])
fitAll = pylab.polyfit(forces, distances, 3)
k2 = 1 / fitAll[0]
cubePredVals = pylab.polyval(fitAll, forces2)
pylab.plot(forces2,
cubePredVals,
'k:',
label='Displacements predicted by \nlinear fit, k = ' +
str(round(k2, 5)))
pylab.legend(loc='best')
def runSimulation(numSteps):
"""
Runs the simulation for `numSteps` time steps.
Returns a tuple of two lists: (rabbit_populations, fox_populations)
where rabbit_populations is a record of the rabbit population at the
END of each time step, and fox_populations is a record of the fox population
at the END of each time step.
Both lists should be `numSteps` items long.
"""
rabbits = []
foxes = []
for i in range(numSteps):
rabbitGrowth()
foxGrowth()
rabbits.append(CURRENTRABBITPOP)
foxes.append(CURRENTFOXPOP)
pylab.plot(rabbits, label='rabbits')
pylab.plot(foxes, label='foxes')
pylab.legend(loc='upper center')
coeff1 = pylab.polyfit(range(len(rabbits)), rabbits, 2)
pylab.plot(pylab.polyval(coeff1, range(len(rabbits))))
coeff2 = pylab.polyfit(range(len(foxes)), foxes, 2)
pylab.plot(pylab.polyval(coeff2, range(len(foxes))))
pylab.show
return rabbits, foxes
def equil():
eq_m = -0.0001
rise_rate = 0.0125
mag = 20
ts = linspace(0, 400, 500)
f = F(ts, mag=mag)
# g = eq_m * f
g = G(ts, f, rate=eq_m)
b = rise_rate * ts
fg = f + g + b
plot(ts, f, label='F Equilibration')
plot(ts, g, label='G Consumption')
plot(ts, fg, label='F-G (Sniff Evo)')
rf, rollover_F, vi_F = calc_optimal_eqtime(ts, f)
rfg, rollover_FG, vi_FG = calc_optimal_eqtime(ts, fg)
m = 2 * eq_m * mag
axvline(x=rollover_F, ls='--', color='blue')
axvline(x=rollover_FG, ls='--', color='red')
idx = list(ts).index(rollover_F)
b = fg[idx] - m * rollover_F
evo = polyval((m, b), ts)
plot(ts, evo, ls='-.', color='blue', label='Static Evo. A')
# ee = where(evo > mag)[0]
# to_F = ts[max(ee)]
# print 'F', rollover_F, b, to_F
b = vi_FG - m * rollover_FG
evo = polyval((m, b), ts)
plot(ts, evo, ls='-.', color='red', label='Static Evo. B')
print polyval((m, b), 200)
ee = where(evo > mag)[0]
# to_FG = ts[max(ee)]
# print 'FG', rollover_FG, b, to_FG
# axvline(x=to_FG, ls='-', color='red')
# axvline(x=to_F, ls='-', color='blue')
axhline(y=mag, ls='-', color='black')
# plot([ti], [mag], 'bo')
legend(loc=0)
# ylim(2980, 3020)
ylim(18, 21)
xlim(0, 20)
ylabel('Intensity')
xlabel('t (s)')
# fig = gcf()
# fig.text(0.1, 0.01, 'asdfasfasfsadfsdaf')
show()
def plotFittingCurve(rabbits, foxes):
r_coeff = pylab.polyfit(range(len(rabbits)), rabbits, 2)
f_coeff = pylab.polyfit(range(len(foxes)), foxes, 2)
pylab.plot(pylab.polyval(r_coeff, range(len(rabbits))), label = "Rabbits Curve")
pylab.plot(pylab.polyval(f_coeff, range(len(foxes))), label = "Foxes Curve")
pylab.legend()
pylab.show()
def runSimulation(numSteps):
"""
Runs the simulation for `numSteps` time steps.
Returns a tuple of two lists: (rabbit_populations, fox_populations)
where rabbit_populations is a record of the rabbit population at the
END of each time step, and fox_populations is a record of the fox population
at the END of each time step.
Both lists should be `numSteps` items long.
"""
rabbitPop = []
foxPop = []
for i in range(numSteps):
rabbitGrowth()
foxGrowth()
rabbitPop.append(CURRENTRABBITPOP)
foxPop.append(CURRENTFOXPOP)
#return (rabbitPop,foxPop)
pylab.plot(rabbitPop)
pylab.plot(foxPop)
pylab.show()
rabbitPopulationOverTime = rabbitPop[:]
coeff = pylab.polyfit(range(len(rabbitPopulationOverTime)), rabbitPopulationOverTime, 2)
pylab.plot(pylab.polyval(coeff, range(len(rabbitPopulationOverTime))))
pylab.show()
rabbitPopulationOverTime = foxPop[:]
coeff = pylab.polyfit(range(len(rabbitPopulationOverTime)), rabbitPopulationOverTime, 2)
pylab.plot(pylab.polyval(coeff, range(len(rabbitPopulationOverTime))))
pylab.show()
def evaluate_models_on_training(x, y, models):
"""
For each regression model, compute the R-square for this model with the
standard error over slope of a linear regression line (only if the model is
linear), and plot the data along with the best fit curve.
For the plots, you should plot data points (x,y) as blue dots and your best
fit curve (aka model) as a red solid line. You should also label the axes
of this figure appropriately and have a title reporting the following
information:
degree of your regression model,
R-square of your model evaluated on the given data points
Args:
x: a list of length N, representing the x-coords of N sample points
y: a list of length N, representing the y-coords of N sample points
models: a list containing the regression models you want to apply to
your data. Each model is a numpy array storing the coefficients of
a polynomial.
Returns:
None
"""
pyplot.plot(x, y, 'bo')
for i in models:
pyplot.plot(x,
pylab.polyval(i, x),
label='R^2 = ' + str(r_squared(y, pylab.polyval(i, x))))
pylab.title('Year vs Temp.')
pylab.legend(loc='best')
pylab.xlabel('Year')
pylab.ylabel('Temperature')
def fitData(inputFile):
masses, distances = getData(inputFile)
distances = pylab.array(distances)
masses = pylab.array(masses)
forces = pylab.array(masses) * 9.81
pylab.plot(forces, distances, 'ko', label="Measurement Displacements")
pylab.title("Measured Displacement of Spring")
pylab.xlabel("|Force| (Newtons)")
pylab.ylabel("Distance (Meters)")
# find linear fit
a, b = pylab.polyfit(forces, distances, 1)
predictedDistances = a * pylab.array(forces) + b
k = 1.0 / a # a is dDist/dForce, k is dForce/dDist or a inverse
pylab.plot(forces,
predictedDistances,
label="Displacements Predicted by \nLinear Fit, k = " +
str(round(k, 5)))
pylab.legend(loc='best')
# find cubic fit
fit = pylab.polyfit(forces, distances, 3)
predictedDistances = pylab.polyval(fit, forces)
forces_extend = pylab.append(forces, pylab.array([15]))
predicted_distances_extend = pylab.polyval(fit, forces_extend)
pylab.plot(forces_extend,
predicted_distances_extend,
'k:',
label='cubic fit')
pylab.xlim(0, 16)
def equil():
eq_m = -0.0001
rise_rate = 0.0125
mag = 20
ts = linspace(0, 400, 500)
f = F(ts, mag=mag)
# g = eq_m * f
g = G(ts, f, rate=eq_m)
b = rise_rate * ts
fg = f + g + b
plot(ts, f, label='F Equilibration')
plot(ts, g, label='G Consumption')
plot(ts, fg, label='F-G (Sniff Evo)')
rf, rollover_F, vi_F = calc_optimal_eqtime(ts, f)
rfg, rollover_FG, vi_FG = calc_optimal_eqtime(ts, fg)
m = 2 * eq_m * mag
axvline(x=rollover_F, ls='--', color='blue')
axvline(x=rollover_FG, ls='--', color='red')
idx = list(ts).index(rollover_F)
b = fg[idx] - m * rollover_F
evo = polyval((m, b), ts)
plot(ts, evo, ls='-.', color='blue', label='Static Evo. A')
# ee = where(evo > mag)[0]
# to_F = ts[max(ee)]
# print 'F', rollover_F, b, to_F
b = vi_FG - m * rollover_FG
evo = polyval((m, b), ts)
plot(ts, evo, ls='-.', color='red', label='Static Evo. B')
print polyval((m, b), 200)
ee = where(evo > mag)[0]
# to_FG = ts[max(ee)]
# print 'FG', rollover_FG, b, to_FG
# axvline(x=to_FG, ls='-', color='red')
# axvline(x=to_F, ls='-', color='blue')
axhline(y=mag, ls='-', color='black')
# plot([ti], [mag], 'bo')
legend(loc=0)
# ylim(2980, 3020)
ylim(18, 21)
xlim(0, 20)
ylabel('Intensity')
xlabel('t (s)')
# fig = gcf()
# fig.text(0.1, 0.01, 'asdfasfasfsadfsdaf')
show()
def runSimulation2(numSteps):
"""
Runs the simulation for `numSteps` time steps.
Returns a tuple of two lists: (rabbit_populations, fox_populations)
where rabbit_populations is a record of the rabbit population at the
END of each time step, and fox_populations is a record of the fox population
at the END of each time step.
Both lists should be `numSteps` items long.
"""
rabbitPopulationOverTime = []
foxPopulationOverTime = []
for step in range(numSteps):
rabbitGrowth()
rabbitPopulationOverTime.append(CURRENTRABBITPOP)
foxGrowth()
foxPopulationOverTime.append(CURRENTFOXPOP)
print "CURRENTRABBITPOP", CURRENTRABBITPOP, rabbitPopulationOverTime
print "CURRENTFOXPOP", CURRENTFOXPOP, foxPopulationOverTime
pylab.plot(range(numSteps), rabbitPopulationOverTime, '-g', label='Rabbit population')
pylab.plot(range(numSteps), foxPopulationOverTime, '-o', label='Fox population')
rabbit_coeff = pylab.polyfit(range(len(rabbitPopulationOverTime)), rabbitPopulationOverTime, 2)
pylab.plot(pylab.polyval(rabbit_coeff, range(len(rabbitPopulationOverTime))))
fox_coeff = pylab.polyfit(range(len(foxPopulationOverTime)), foxPopulationOverTime, 2)
pylab.plot(pylab.polyval(fox_coeff, range(len(rabbitPopulationOverTime))))
pylab.title('Fox and rabbit population in the wood')
xlabel = "Plot for simulation of {} steps".format(numSteps)
pylab.xlabel(xlabel)
pylab.ylabel('Current fox and rabbit population')
pylab.legend(loc='upper right')
pylab.tight_layout()
pylab.show()
pylab.clf()
def runSimulation(numSteps):
"""
Runs the simulation for `numSteps` time steps.
Returns a tuple of two lists: (rabbit_populations, fox_populations)
where rabbit_populations is a record of the rabbit population at the
END of each time step, and fox_populations is a record of the fox population
at the END of each time step.
Both lists should be `numSteps` items long.
"""
rabbit,fox=[],[]
for i in range(numSteps):
rabbitGrowth()
foxGrowth()
rabbit.append(CURRENTRABBITPOP)
fox.append(CURRENTFOXPOP)
pylab.plot(rabbit)
pylab.plot(fox)
coeffr = pylab.polyfit(range(len(rabbit)), rabbit, 2)
pylab.plot(pylab.polyval(coeffr, range(len(rabbit))),label='rabbit')
coefff = pylab.polyfit(range(len(fox)), fox, 2)
pylab.plot(pylab.polyval(coefff, range(len(fox))),label='fox')
pylab.legend()
return rabbit,fox
def getApices(y):
"""
returns the time (in frames) and position of initial and final apex
height from a given trajectory y, which are obtained by fitting a cubic
spline
==========
parameter:
==========
y : *array* (1D)
the trajectory. Should ideally start ~1 frame before an apex and end ~1
frame behind an apex
========
returns:
========
[x0, xF], [y0, yF] : location (in frames) and value of the first and final
apices
"""
# the math behind here is: fitting a 2nd order polynomial and finding
# the root of its derivative. Here, only the results are applied, that's
# why it appears like "magic" numbers
c = dot(array([[.5, -1, .5], [-1.5, 2., -.5], [1., 0., 0.]]), y[:3])
x0 = -1. * c[1] / (2. * c[0])
y0 = polyval(c, x0)
c = dot(array([[.5, -1, .5], [-1.5, 2., -.5], [1., 0., 0.]]), y[-3:])
xF = -1. * c[1] / (2. * c[0])
yF = polyval(c, xF)
xF += len(y) - 3
return [x0, xF], [y0, yF]
def runSimulation(numSteps):
"""
Runs the simulation for `numSteps` time steps.
Returns a tuple of two lists: (rabbit_populations, fox_populations)
where rabbit_populations is a record of the rabbit population at the
END of each time step, and fox_populations is a record of the fox population
at the END of each time step.
Both lists should be `numSteps` items long.
"""
foxpop = []
rabbitpop = []
for i in range(numSteps):
rabbitGrowth()
foxGrowth()
rabbitpop.append(CURRENTRABBITPOP)
foxpop.append(CURRENTFOXPOP)
pylab.plot(rabbitpop, 'b')
pylab.plot(foxpop, 'r')
rabbit_coeff = pylab.polyfit(range(len(rabbitpop)), rabbitpop, 2)
pylab.plot(pylab.polyval(rabbit_coeff, range(len(rabbitpop))))
fox_coeff = pylab.polyfit(range(len(foxpop)), foxpop, 2)
pylab.plot(pylab.polyval(fox_coeff, range(len(foxpop))))
pylab.show()
return rabbitpop, foxpop
def evaluate_models_on_testing(x, y, models):
"""
For each regression model, compute the RMSE for this model and plot the
test data along with the model’s estimation.
For the plots, you should plot data points (x,y) as blue dots and your best
fit curve (aka model) as a red solid line. You should also label the axes
of this figure appropriately and have a title reporting the following
information:
degree of your regression model,
RMSE of your model evaluated on the given data points.
Args:
x: an 1-d pylab array with length N, representing the x-coordinates of
the N sample points
y: an 1-d pylab array with length N, representing the y-coordinates of
the N sample points
models: a list containing the regression models you want to apply to
your data. Each model is a pylab array storing the coefficients of
a polynomial.
Returns:
None
"""
for model in models:
estimates=pylab.polyval(model,x)
pylab.plot(x,y,'o',markersize=6)
#xmin=1961
#xmax=2010
pylab.plot(x, estimates,'r-')
pylab.title('Model with RMSE = ' + str(rmse(y,pylab.polyval(model,x))) + '\n' + ' degrees = ' + str(len(model)-1) )
pylab.xlabel('year')
pylab.ylabel('degrees Celsius')
pylab.show()
def processTrajectories(fileName):
distances, heights = getTrajectoryData(fileName)
numTrials = len(heights)
distances = pylab.array(distances)
# Get array containing mean height at each distance
totHeights = pylab.array([0] * len(distances))
for h in heights:
totHeights = totHeights + pylab.array(h)
meanHeights = totHeights / len(heights)
pylab.title("Trajectory of Projectile (Mean of " + str(numTrials) +
'Trials)')
pylab.xlabel("Inches from Launch Point")
pylab.ylabel("Inches Above Launch Point")
pylab.plot(distances, meanHeights, 'ko')
fit = pylab.polyfit(distances, meanHeights, 1)
altitudes = pylab.polyval(fit, distances)
pylab.plot(distances, altitudes, 'b', label="Linear Fit")
print('RSquare of Linear Fit = ', rSquared(meanHeights, altitudes))
fit = pylab.polyfit(distances, meanHeights, 2)
altitudes = pylab.polyval(fit, distances)
pylab.plot(distances, altitudes, 'k:', label="Quadratic Fit")
print('Rsquare of Quadratic Fit = ', rSquared(meanHeights, altitudes))
pylab.legend()
getHorizontalSpeed(fit, distances[-1], distances[0])
def plotFittingCurve(rabbits, foxes):
r_coeff = pylab.polyfit(range(len(rabbits)), rabbits, 2)
f_coeff = pylab.polyfit(range(len(foxes)), foxes, 2)
pylab.plot(pylab.polyval(r_coeff, range(len(rabbits))),
label="Rabbits Curve")
pylab.plot(pylab.polyval(f_coeff, range(len(foxes))), label="Foxes Curve")
pylab.legend()
pylab.show()
def make_joining_whisker(px,py,dist,lthick,lscore,rthick,rscore): w = Whisker_Seg() tt = linspace(0,1,round(dist)) w.x = polyval(px,tt).astype(float32) w.y = polyval(py,tt).astype(float32) w.thick = polyval( [rthick-lthick,lthick], tt ).astype(float32) w.scores = polyval( [rscore-lscore,lscore], tt ).astype(float32) return w
def plotFitSimulation(numSteps):
ans = runSimulation(numSteps)
rabbitCoeff = pylab.polyfit(range(numSteps), ans[0], 2)
foxCoeff = pylab.polyfit(range(numSteps), ans[1], 2)
print rabbitCoeff, foxCoeff
pylab.plot(pylab.polyval(rabbitCoeff, range(numSteps)), 'r')
pylab.plot(pylab.polyval(foxCoeff, range(numSteps)), 'g')
pylab.title("polyfit result")
pylab.show()
def evaluate_models_on_training(x, y, models):
"""
For each regression model, compute the R-squared value for this model with the
standard error over slope of a linear regression line (only if the model is
linear), and plot the data along with the best fit curve.
For the plots, you should plot data points (x,y) as blue dots and your best
fit curve (aka model) as a red solid line. You should also label the axes
of this figure appropriately and have a title reporting the following
information:
degree of your regression model,
R-square of your model evaluated on the given data points,
and SE/slope (if degree of this model is 1 -- see se_over_slope).
Args:
x: an 1-d pylab array with length N, representing the x-coordinates of
the N sample points
y: an 1-d pylab array with length N, representing the y-coordinates of
the N sample points
models: a list containing the regression models you want to apply to
your data. Each model is a pylab array storing the coefficients of
a polynomial.
Returns:
None
"""
# TODO
for m in models:
if len(m) == 2:
estimated = pylab.array(pylab.polyval(m, x))
pylab.scatter(x, y, c="b")
pylab.plot(x, estimated, c="r")
pylab.xlabel("years")
pylab.ylabel("Celsius")
r = r_squared(y, estimated)
se_over_slope2 = se_over_slope(x, y, estimated, m)
pylab.title("For model with degree: " + str(len(m) - 1) + " and " +
"with R-square: " + str(r) + "\n" +
"The data is linear so ratio of se_over_slope is " +
"\n" + str(se_over_slope2))
pylab.show()
pylab.pause(15)
pylab.close()
else:
estimated = pylab.array(pylab.polyval(m, x))
pylab.scatter(x, y, c="b")
pylab.plot(x, estimated, c="r")
pylab.xlabel("years")
pylab.ylabel("Celsius")
r = r_squared(y, estimated)
pylab.title("For model with degree: " + str(len(m) - 1) + " and " +
"with R-square: " + str(r))
pylab.show()
pylab.pause(15)
pylab.close()
return None
def plotSimulation(numSteps):
rabbits, foxes = runSimulation(numSteps)
pylab.plot(range(numSteps), rabbits, label='Rabbits')
rabbit_coefficients = pylab.polyfix(range(len(rabbits)), rabbits, 2)
pylab.plot(pylab.polyval(rabbit_coefficients, range(numSteps)))
pylab.plot(range(numSteps), foxes, label='Foxes')
fox_coefficients = pylab.polyfix(range(len(foxes)), foxes, 2)
pylab.plot(pylab.polyval(fox_coefficients, range(numSteps)))
pylab.show()
def compute_join_curvature( px, py ): from scipy.integrate import quad xp = polyder( px, 1 ) xpp = polyder( px, 2 ) yp = polyder( py, 1 ) ypp = polyder( py, 2 ) pn = polyadd( polymul( xp, ypp ), polymul( yp, xpp )) #numerator pd = polyadd( polymul( xp, xp ) , polymul( yp, yp ) ) #denominator integrand = lambda t: fabs(polyval( pn, t )/( polyval( pd, t )**(1.5)) ) return quad(integrand, 0, 1) [0]
def plotSimulation():
rabbits, foxes = runSimulation(200)
pylab.plot(rabbits, label='Rabbits')
pylab.plot(foxes, label='Foxes')
a, b, c = pylab.polyfit(range(len(rabbits)), rabbits, 2)
pylab.plot(pylab.polyval([a, b, c], range(len(rabbits))), label='Rabbits')
d, e, f = pylab.polyfit(range(len(foxes)), foxes, 2)
pylab.plot(pylab.polyval([d, e, f], range(len(foxes))), label='Foxes')
pylab.grid()
pylab.legend()
pylab.show()
def plot(steps):
z = runSimulation(steps)
pylab.plot(range(steps), z[0], label='Rabbits')
pylab.plot(range(steps), z[1], label='Foxes')
pylab.xlabel('Time Steps')
pylab.ylabel('Population')
Rcoef = pylab.polyfit(range(steps), z[0], 2)
pylab.plot(range(steps), pylab.polyval(Rcoef, range(steps)), label='Rabz')
Fcoef = pylab.polyfit(range(steps), z[1], 2)
pylab.plot(range(steps), pylab.polyval(Fcoef, range(steps)), label='Foxez')
pylab.legend()
def createPlots(data):
x = data[0]
y = data[1]
a, b, c = polyFit(x, y, 2)
x = pylab.arange(201)
y = a * x**2 + b * x + c
print pylab.polyval((a, b, c), 200)
pylab.plot(x, y)
pylab.show()
def createPlots(data):
x = data[0]
y = data[1]
a,b,c = polyFit(x, y, 2)
x = pylab.arange(201)
y = a*x**2 + b*x + c
print pylab.polyval((a,b,c), 200)
pylab.plot(x, y)
pylab.show()
def plotLineFit():
rabbitPops, foxPops = runSimulation(200)
steps = [n for n in range(1, 201)]
coeff = pylab.polyfit(range(len(rabbitPops)), rabbitPops, 2)
pylab.plot(pylab.polyval(coeff, range(len(rabbitPops))))
coeff = pylab.polyfit(range(len(foxPops)), foxPops, 2)
pylab.plot(pylab.polyval(coeff, range(len(foxPops))))
pylab.title('Fox vs. Rabbit')
pylab.legend(('Rabbit Pop', 'Fox Pop'))
pylab.xlabel('Step')
pylab.ylabel('Population')
pylab.show()
def simPlot(numSteps):
rabbit_populations, fox_populations = runSimulation(numSteps)
pylab.plot(np.arange(numSteps), rabbit_populations, '-r')
pylab.plot(np.arange(numSteps), fox_populations, '-b')
coeff = pylab.polyfit(np.arange(numSteps), rabbit_populations, 2)
pylab.plot(pylab.polyval(coeff, np.arange(numSteps)))
coeff = pylab.polyfit(np.arange(numSteps), fox_populations, 2)
pylab.plot(pylab.polyval(coeff, np.arange(numSteps)))
pylab.show()
def plot():
rp, fp = runSimulation(200)
rabbitCoeff = pylab.polyfit(range(len(rp)), rp, 2)
foxCoeff = pylab.polyfit(range(len(fp)), fp, 2)
pylab.plot(rp, label="rabbit")
pylab.plot(fp, label="fox")
pylab.plot(pylab.polyval(rabbitCoeff, range(len(rp))), label="rabbitEst")
pylab.plot(pylab.polyval(foxCoeff, range(len(fp))), label="foxEst")
pylab.xlabel("time step")
pylab.ylabel("population")
pylab.legend(loc="best")
pylab.show()
def plotLineFit():
rabbitPops, foxPops = runSimulation(200)
steps = [n for n in range(1, 201)]
coeff = pylab.polyfit(range(len(rabbitPops)), rabbitPops, 2)
pylab.plot(pylab.polyval(coeff, range(len(rabbitPops))))
coeff = pylab.polyfit(range(len(foxPops)), foxPops, 2)
pylab.plot(pylab.polyval(coeff, range(len(foxPops))))
pylab.title('Fox vs. Rabbit')
pylab.legend(('Rabbit Pop', 'Fox Pop'))
pylab.xlabel('Step')
pylab.ylabel('Population')
pylab.show()
def plot(rabbits, foxes):
N = len(rabbits)
pylab.plot(range(N), rabbits, 'go', label = "rabbit pop")
pylab.plot(range(N), foxes, 'ro', label = "foxes pop")
rab_coeff = pylab.polyfit(range(N), rabbits, 2)
fox_coeff = pylab.polyfit(range(N), foxes, 2)
pylab.plot(pylab.polyval(rab_coeff, range(N)), 'g-', label = "rabbit polyfit")
pylab.plot(pylab.polyval(fox_coeff, range(N)), 'r-', label = "fox polyfit")
pylab.xlabel("Time")
pylab.ylabel("Population")
pylab.title("Dynamics of Rabbit and Fox Population")
pylab.legend()
pylab.show()
def ddPsi(a,s):
'''
# second derivative of polynomial
# a = polynomical constants (needs to be in list/array form so len() command works)
# s = position along polynomial (needs to be in list/array form so len() command works)
'''
n = len(a) # number of variables in polynimal
a1 = a[:-1]*(pl.arange(n-1,0,-1)+1)*pl.arange(n-1,0,-1)
a2 = a*(pl.arange(n-1,-1,-1)+2)*(pl.arange(n-1,-1,-1)+1)
psi = pl.polyval(a1,s) - pl.polyval(a2,s)
return psi
def fitDataWithBreakFlat(fileName):
xValsBase, yValsBase = getData(fileName)
bestFitSoFar = None
bestFitBreak = None
for br in range(3, len(xValsBase) - 3):
xValsLow = pylab.array(xValsBase[:br])
xValsHigh = pylab.array(xValsBase[br:])
yValsLow = pylab.array(yValsBase[:br])
yValsHigh = pylab.array(yValsBase[br:])
xValsLow = xValsLow * 9.81
xValsHigh = xValsHigh * 9.81
modelLow = pylab.polyfit(xValsLow, yValsLow, 1)
modelHigh = pylab.polyfit(xValsHigh, yValsHigh, 0)
estYValsLow = pylab.polyval(modelLow, xValsLow)
estYValsHigh = pylab.polyval(modelHigh, xValsHigh)
fit = aveMeanSquareError(yValsLow, estYValsLow) + \
aveMeanSquareError(yValsHigh, estYValsHigh)
if bestFitSoFar == None or bestFitSoFar > fit:
bestFitSoFar = fit
bestFitBreak = br
pylab.figure()
pylab.plot(xValsLow, yValsLow, 'bo', label='Measured points')
pylab.plot(xValsHigh, yValsHigh, 'bo', label='Measured points')
labelPlot()
br = bestFitBreak
xValsLow = pylab.array(xValsBase[:br])
xValsHigh = pylab.array(xValsBase[br:])
yValsLow = pylab.array(yValsBase[:br])
yValsHigh = pylab.array(yValsBase[br:])
xValsLow = xValsLow * 9.81
xValsHigh = xValsHigh * 9.81
modelLow = pylab.polyfit(xValsLow, yValsLow, 1)
modelHigh = pylab.polyfit(xValsHigh, yValsHigh, 0)
estYValsLow = pylab.polyval(modelLow, xValsLow)
estYValsHigh = pylab.polyval(modelHigh, xValsHigh)
pylab.plot(xValsLow,
estYValsLow,
'g',
label='Linear fit, k = ' + str(round(1 / modelLow[0], 5)))
pylab.plot(xValsHigh,
estYValsHigh,
'g',
label='Linear fit,, k = ' + str(round(1 / modelHigh[0], 5)))
pylab.legend(loc='best')
print('rSquared value, low = ', rSquared(yValsLow, estYValsLow))
print('rSquared value, high = ', rSquared(yValsHigh, estYValsHigh))
## for slide 57
#fitDataWithBreakFlat('springData.txt')
def plotSimulation(numSteps):
rabbits, foxes = [], []
for _ in range(numSteps):
rabbitGrowth()
foxGrowth()
rabbits.append(CURRENTRABBITPOP)
foxes.append(CURRENTFOXPOP)
pylab.plot(range(numSteps), rabbits, label='Rabbits')
rabbit_coeff = pylab.polyfit(range(numSteps), rabbits, 2)
pylab.plot(pylab.polyval(rabbit_coeff, range(numSteps)))
pylab.plot(range(numSteps), foxes, label='Foxes')
fox_coeff = pylab.polyfit(range(numSteps), foxes, 2)
pylab.plot(pylab.polyval(fox_coeff, range(numSteps)))
pylab.show()
def plotSim():
numSim = 400
rabbit_populations, fox_populations = runSimulation(numSim)
pylab.figure(1)
pylab.plot(range(numSim), rabbit_populations, label = "rabit")
pylab.plot(range(numSim), fox_populations, label = "fox")
# pylab.figure(2)
coeff = pylab.polyfit(range(numSim), rabbit_populations, 2)
pylab.plot(pylab.polyval(coeff, range(numSim)), label = "rabit fitting")
coeff = pylab.polyfit(range(numSim), fox_populations, 2)
pylab.plot(pylab.polyval(coeff, range(numSim)), label = "fox fitting")
pylab.legend()
pylab.show()
def animate_line(i, x, y, order=1, mu=1E-4):
global anim_coeffs
N = len(x)
plt.title('Iteration %d\n%s' % (i, Eqn_Str3(anim_coeffs)))
for i in range(N):
Err = y[i] - polyval(anim_coeffs, x[i])
# anim_coeffs = anim_coeffs + mu*Err*np.array([x[i]**2, x[i], 1])
X_Vect = np.fliplr(np.polynomial.polynomial.polyvander(x[i], order))[0]
anim_coeffs = anim_coeffs + mu * Err * X_Vect\
#/(np.linalg.norm(X_Vect)**2)
# print(anim_coeffs, np.fliplr(np.polynomial.polynomial.polyvander(x[i], 2)))
line.set_xdata(x)
line.set_ydata(polyval(anim_coeffs, x))
return line,
def get_minmax(data, deg=2):
"""
returns the interpolated extremum and position (in fractions of frames)
:args:
data (iterable): data to be fitted with a <deg> degree polynomial
deg (int): degree of polynomial to fit
:returns:
val, pos: a tuple of floats indicating the position
"""
x = arange(len(data))
p = polyfit(x, data, deg)
d = (arange(len(p))[::-1] * p)[:-1]
r = roots(d)
cnt = 0
idx = None
for nr, rx in enumerate(r):
if isreal(r):
idx = nr
cnt +=1
if cnt > 1:
raise ValueError("Too many real roots found." +
"Reduce order of polynomial!")
x0 = r[nr].real
return x0, polyval(p, x0)
def evaluate_models_on_training(x, y, models):
"""
For each regression model, compute the R-square for this model with the
standard error over slope of a linear regression line (only if the model is
linear), and plot the data along with the best fit curve.
For the plots, you should plot data points (x,y) as blue dots and your best
fit curve (aka model) as a red solid line. You should also label the axes
of this figure appropriately and have a title reporting the following
information:
degree of your regression model,
R-square of your model evaluated on the given data points
Args:
x: a list of length N, representing the x-coords of N sample points
y: a list of length N, representing the y-coords of N sample points
models: a list containing the regression models you want to apply to
your data. Each model is a numpy array storing the coefficients of
a polynomial.
Returns:
None
"""
for model in models:
print(model)
estimated = pylab.polyval(model, x)
pylab.clf()
pylab.plot(x, y, 'bo', label='Observed Data')
pylab.plot(x, estimated, 'r', label='Estimated Model')
pylab.title(
str(len(model - 1)) + ' Degree Model' + '\n' + "R Squared: " +
str(r_squared(y, estimated)))
pylab.xlabel('Years')
pylab.ylabel('Temperature')
pylab.legend()
pylab.show()
def get_minmax(data, deg=2):
"""
returns the interpolated extremum and position (in fractions of frames)
:args:
data (iterable): data to be fitted with a <deg> degree polynomial
deg (int): degree of polynomial to fit
:returns:
val, pos: a tuple of floats indicating the position
"""
x = arange(len(data))
p = polyfit(x, data, deg)
d = (arange(len(p))[::-1] * p)[:-1]
r = roots(d)
cnt = 0
idx = None
for nr, rx in enumerate(r):
if isreal(r):
idx = nr
cnt += 1
if cnt > 1:
raise ValueError("Too many real roots found." +
"Reduce order of polynomial!")
x0 = r[nr].real
return x0, polyval(p, x0)
def part1():
# I (amps)
x = [3.12, 6.18, 9.28, 12.36, 15.52, 18.62, 21.8, 24.9, 28.0, 31.4]
# V (Volts)
y = [float(v) for v in range(1, 11)]
# This gives m,b from (y = mx + b)
m, b = pylab.polyfit(x, y, 1)
# This calculates the slope for us
slope = pylab.polyval([m, b], x)
# Acordding to the lab R = m, but it's * 10 ^-3
R_slope = m * 10**-3
R_dmm = .000325
print("Part 1")
print("R_slope = %f" % (R_slope))
percent_diff = (abs(R_dmm - R_slope) / R_dmm + R_slope / 2) * 100
print("percent difference %f" % (percent_diff))
plt.plot(x, slope, "-r", label="slope")
plt.scatter(x, y)
plt.title("Carbon Resistor ")
plt.ylabel("V (Volts)")
plt.xlabel("I (amps) * 10^-3")
plt.show()
def evaluate_models_on_training(x, y, models):
"""
For each regression model, compute the R-square for this model with the
standard error over slope of a linear regression line (only if the model is
linear), and plot the data along with the best fit curve.
For the plots, you should plot data points (x,y) as blue dots and your best
fit curve (aka model) as a red solid line. You should also label the axes
of this figure appropriately and have a title reporting the following
information:
degree of your regression model,
R-square of your model evaluated on the given data points
Args:
x: a list of length N, representing the x-coords of N sample points
y: a list of length N, representing the y-coords of N sample points
models: a list containing the regression models you want to apply to
your data. Each model is a numpy array storing the coefficients of
a polynomial.
Returns:
None
"""
pylab.plot(x, y, 'o', label='Data')
for i in range(len(models)):
y_estimated = pylab.polyval(models[i], x)
error = r_squared(y, y_estimated)
pylab.plot(x, y_estimated,
label = 'Fit of degree '\
+ '2'\
+ ', R2 = ' + str(round(error, 5)))
pylab.legend(loc='best')
pylab.title("Problem 3")
pylab.show()
def part2():
# I (amps)
x = [67.3, 93.0, 114.7, 133.6, 150.4, 166.4, 180.9, 194.6]
# V (Volts)
y = [(v * .50) for v in range(0, 8)]
# This gives m,b from (y = mx + b)
m, b = pylab.polyfit(x, y, 1)
# This calculates the slope for us
slope = pylab.polyval([m, b], x)
# Acordding to the lab R_min and R_max are the lowest and highest values of the slope
# removing the first value becaue it's negative
slope1 = list(filter(lambda x: x > 0, slope))
print(slope1)
R_min = min(slope1) * 10**-3
R_max = max(slope1) * 10**-3
print("Part 2")
print("R_min = %f" % (R_min))
print("R_max = %f" % (R_max))
percent_diff = (abs(R_max - R_min) / R_max + R_min / 2) * 100
print("percent difference %f" % (percent_diff))
plt.plot(x, slope, "-r", label="slope")
plt.scatter(x, y)
plt.title("Light Bulb")
plt.ylabel("V (Volts)")
plt.xlabel("I (amps) * 10^-3")
plt.show()
def PolinomialRegression(self,Data,FileOutPath,hasHeader,polinoimalDegree):
NVars = len(Data[0])
# Plot column name if both are the same variables (diagonal).
# For different variables, a scatter plot with both variables and their regression.
Header = []
if (hasHeader):
Header = Data[0]
Data = Data[1:]
else:
for i in range(NVars):
Header.append("column "+str(i+1))
Data = Data
loc = 1
for i in range(NVars):
for j in range(NVars):
P.subplot(NVars, NVars, loc)
if (i==j):
P.text(0.2, 0.5, Header[i], size=12)
else:
fit = P.polyfit(Data[:,i],Data[:,j],polinoimalDegree)
yp = P.polyval(fit,np.sort(Data[:,i]))
P.plot(np.sort(Data[:,i]),yp,'g-',Data[:,i],Data[:,j],'b.')
P.grid(True)
loc = loc + 1
# Store as SVG
P.savefig(FileOutPath)
def visualize(numStep):
foxPop, rabbitPop = runSimulation(numStep)
print foxPop
print rabbitPop
x = range(numStep)
# coeff = [a, b, c] where ax^2 + bx + c
coeff = pylab.polyfit(x, rabbitPop, 2)
rabbitPred = pylab.polyval(coeff, x)
coeff = pylab.polyfit(x, foxPop, 2)
foxPred = pylab.polyval(coeff, x)
pylab.figure()
pylab.plot(x, foxPop, "r")
pylab.plot(x, foxPred, "y")
pylab.plot(x, rabbitPop, "b")
pylab.plot(x, rabbitPred, "g")
pylab.show()
def parse():
# Split the input up
rows = [x.strip().split(':') for x in fileinput.input()]
# Automatically turn numbers into the base type
rows = [[to_float(y) for y in x] for x in rows]
# Scan once to calculate the overhead
r = [Record(*(x + [0, 0, 0])) for x in rows]
bounces = pylab.array([(x.loops, x.rawtime) for x in r if x.test == 'bounce'])
fit = pylab.polyfit(bounces[:,0], bounces[:,1], 1)
records = []
for row in rows:
# Make a dummy record so we can use the names
r1 = Record(*(row + [0, 0, 0]))
bytes = r1.size * r1.loops
# Calculate the bounce time
delta = pylab.polyval(fit, [r1.loops])
time = r1.rawtime - delta
rate = bytes / time
records.append(Record(*(row + [time, bytes, rate])))
return records
def evaluate_models_on_training(x, y, models):
"""
For each regression model, compute the R-square for this model with the
standard error over slope of a linear regression line (only if the model is
linear), and plot the data along with the best fit curve.
For the plots, you should plot data points (x,y) as blue dots and your best
fit curve (aka model) as a red solid line. You should also label the axes
of this figure appropriately and have a title reporting the following
information:
degree of your regression model,
R-square of your model evaluated on the given data points
Args:
x: a list of length N, representing the x-coords of N sample points
y: a list of length N, representing the y-coords of N sample points
models: a list containing the regression models you want to apply to
your data. Each model is a numpy array storing the coefficients of
a polynomial.
Returns:
None
"""
for m in models:
estYVals = pylab.polyval(m, x)
R_v_2 = r_squared(y, estYVals)
pylab.figure()
pylab.plot(x, y, 'o', label = 'Actual data')
pylab.plot(x, estYVals, 'r--', label = 'Predictive values')
print('R-squared = ', rSquared(y, estYVals))
pylab.legend(loc = 'best')
pylab.title('evaluate_models_on_training')
pylab.show()
def plot_test(px,py,thick=2): from pylab import plot tt = linspace(0,1,50) dpx = polyder(px) dpy = polyder(py) dL2 = polymul(dpx,dpx) + polymul(dpy,dpy) ux = polyval( px,tt ) uy = polyval( py,tt ) dx = diff(ux) #polyval( px,tt ) dy = diff(uy) #polyval( py,tt ) dx = r_[dx[0],dx] dy = r_[dy[0],dy] dL = sqrt( dx**2 + dy**2 ) plot( ux, uy , '.-') plot( ux + thick*dy/dL , uy - thick*dx/dL ,'-') plot( ux - thick*dy/dL , uy + thick*dx/dL ,'-' )
def fit_data(xval,yval,n):
# fit poly of order n to x,y and return poly values
ave_x = npy.average(xval)
ave_y = npy.average(yval)
cof = pl.polyfit(xval-ave_x,yval-ave_y,n)
ynew = pl.polyval(cof,xval-ave_x)
return xval,ynew+ave_y
def dPsi(a,s,psi1,psi2):
'''
First derivative of polynomial
# a = polynomical constants (needs to be in list/array form so len() command works)
# s = position along polynomial
# psi1,psi2: start and end orientation
'''
n = len(a) # number of variables in polynimal
ns = len(s) # number of parts to use for the contour
a1 = a*(pl.arange(n-1,-1,-1)+1)
a2 = pl.zeros(n+1)
a2[:-1] = a*(pl.arange(n-1,-1,-1)+2)
psi = -psi1 + psi2 + pl.polyval(a1,s) -pl.polyval(a2,s)
return psi
def compute_join_score( im, px, py, thick = 2 ): tt = linspace(0,1,50) dpx = polyder(px) dpy = polyder(py) dL2 = polymul(dpx,dpx) + polymul(dpy,dpy) ux = polyval( px,tt ) uy = polyval( py,tt ) dx = diff(ux) #polyval( px,tt ) dy = diff(uy) #polyval( py,tt ) dx = r_[dx[0],dx] dy = r_[dy[0],dy] dL = sqrt( dx**2 + dy**2 ) a = _compute_intensity(im, ux, uy ) b = _compute_intensity(im, ux + thick*dy/dL , uy - thick*dx/dL ) c = _compute_intensity(im, ux - thick*dy/dL , uy + thick*dx/dL ) return (2*a - b - c)/4.0
def compute_join_length( px, py, tlow = 0.0, thigh = 1.0 ): from scipy.integrate import quad xp = polyder( px, 1 ) yp = polyder( py, 1 ) xp2 = polymul( xp, xp ) yp2 = polymul( yp, yp ) p = polyadd( xp2, yp2 ) integrand = lambda t: sqrt( polyval( p, t ) ) return quad(integrand, tlow, thigh) [0]
def test1():
n = 200
r,f = runSimulation(n)
coeff_r = pylab.polyfit(range(len(r)), r, 2)
coeff_f = pylab.polyfit(range(len(f)), f, 2)
pylab.plot(range(n), r, label="Rabbit Count")
pylab.plot(range(n), f, label="Fox Count")
pylab.plot(pylab.polyval(coeff_r, range(len(r))), label="Rabbit Fit")
pylab.plot(pylab.polyval(coeff_f, range(len(f))), label="Fox Fit")
pylab.title('Number of critters at time t')
pylab.xlabel('Time')
pylab.ylabel('Count')
pylab.legend(title="Legend")
pylab.show()
def Psi(a,s,psi1,psi2):
'''
Basic function for the polynomial for the curve
# a = polynomical constants (needs to be in list/array form so len() command works)
# s = position along polynomial
# psi1,psi2: start and end orientation
'''
psi = (1-s)*psi1 + s*psi2 + s*(1-s)*pl.polyval(a,s)
# note: the function polyval takes its arguments backwards, so that output is e.g. a1*x**3 + a2*x**2 + a1*x etc.
return psi
def testFits(models, degrees, xVals, yVals, title):
pylab.plot(xVals, yVals, 'o', label = 'Data')
for i in range(len(models)):
estYVals = pylab.polyval(models[i], xVals)
error = rSquared(yVals, estYVals)
pylab.plot(xVals, estYVals,
label = 'Fit of degree '\
+ str(degrees[i])\
+ ', R2 = ' + str(round(error, 5)))
pylab.legend(loc = 'best')
pylab.title(title)
def demo():
import pylab
x,y,dy = data['x'],data['y'],data['dy']
A,B,C = coeff['A'],coeff['B'],coeff['C']
Io,Eo,Gamma = coeff['Io'],coeff['Eo'],coeff['Gamma']
pylab.errorbar(x, y, yerr=dy, label="data")
pylab.plot(x, pylab.polyval([C,B,A], x), label="background")
pylab.plot(x, lorentzian(x,Eo=Eo,Io=Io,Gamma=Gamma), label="peak")
pylab.plot(x, lorentzian(x,**coeff), label="peak+bkg")
pylab.legend()
pylab.show()
def DFA(data, npoints=None, degree=1, use_median=False):
"""
computes the detrended fluctuation analysis
returns the fluctuation F and the corresponding window length L
:args:
data (n-by-1 array): the data from which to compute the DFA
npoints (int): the number of points to evaluate; if omitted the log(n)
will be used
degree (int): degree of the polynomial to use for detrending
use_median (bool): use median instead of mean fluctuation
:returns:
F, L: the fluctuation F as function of the window length L
"""
# max window length: n/4
#0th: compute integral
integral = cumsum(data - mean(data))
#1st: compute different window lengths
n_samples = npoints if npoints is not None else int(log(len(data)))
lengths = sort(array(list(set(
logspace(2,log(len(data)/4.),n_samples,base=exp(1)).astype(int)
))))
#print lengths
all_flucs = []
used_lengths = []
for wlen in lengths:
# compute the fluctuation of residuals from a linear fit
# according to Kantz&Schreiber, ddof must be the degree of polynomial,
# i.e. 1 (or 2, if mean also counts? -> see in book)
curr_fluc = []
# rrt = 0
for startIdx in arange(0,len(integral),wlen):
pt = integral[startIdx:startIdx+wlen]
if len(pt) > 3*(degree+1):
resids = pt - polyval(polyfit(arange(len(pt)),pt,degree),
arange(len(pt)))
# if abs(wlen - lengths[0]) < -1:
# print resids[:20]
# elif rrt == 0:
# print "wlen", wlen, "l0", lengths[0]
# rrt += 1
curr_fluc.append(std(resids, ddof=degree+1))
if len(curr_fluc) > 0:
if use_median:
all_flucs.append(median(curr_fluc))
else:
all_flucs.append(mean(curr_fluc))
used_lengths.append(wlen)
return array(all_flucs), array(used_lengths)