Source code for boxplots

"""
Elastic Functional Boxplots

moduleauthor:: J. Derek Tucker <jdtuck@sandia.gov>

"""
import numpy as np
from scipy.integrate import trapz
import fdasrsf.utility_functions as uf
import fdasrsf.geometry as geo
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import collections


[docs]class ampbox: """ This class provides amplitude boxplot for functional data using the SRVF framework Usage: obj = ampbox(warp_data) :param warp_data: fdawarp class with alignment data :type warp_data: fdawarp :param Q1: First quartile :param Q3: Second quartile :param Q1a: First quantile based on alpha :param Q3a: Second quantile based on alpha :param minn: minimum extreme function :param maxx: maximum extreme function :param outlier_index: indexes of outlier functions :param f_median: median function :param q_median: median srvf :param plt: surface plot mesh Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov> Date : 15-Mar-2018 """ def __init__(self, fdawarp): """ Construct an instance of the ampbox class :param fdawarp: fdawarp class """ if fdawarp.fn.size==0: raise Exception('Please align fdawarp class using srsf_align!') if fdawarp.type=="mean": raise Exception('Please align fdawarp class using srsf_align with method="median"!') self.warp_data = fdawarp
[docs] def construct_boxplot(self, alpha=.05, k_a=1): """ This function constructs the amplitude boxplot using the elastic square-root slope (srsf) framework. :param alpha: quantile value (e.g.,=.05, i.e., 95%) :param k_a: scalar for outlier cutoff (e.g.,=1) """ if self.warp_data.rsamps: ft = self.warp_data.fs f_median = self.warp_data.fmean qt = self.warp_data.qs q_median = self.warp_data.mqn time = self.warp_data.time else: ft = self.warp_data.fn f_median = self.warp_data.fmean qt = self.warp_data.qn q_median = self.warp_data.mqn time = self.warp_data.time N = ft.shape[1] lam = 0.5 # compute amplitude distances dy = np.zeros(N) for i in range(0,N): dy[i] = np.sqrt(trapz((q_median-qt[:,i])**2,time)) dy_ordering = dy.argsort() CR_50 = dy_ordering[0:np.ceil(N/2).astype('int')] tmp = dy[CR_50] m = tmp.max() # identify amplitude quartiles angle = np.zeros((CR_50.shape[0],CR_50.shape[0])) energy = np.zeros((CR_50.shape[0],CR_50.shape[0])) for i in range(0,CR_50.shape[0]-1): for j in range(i+1,CR_50.shape[0]): q1 = qt[:,CR_50[i]] - q_median q3 = qt[:,CR_50[j]] - q_median q1 = q1/np.sqrt(trapz(q1**2,time)) q3 = q3/np.sqrt(trapz(q3**2,time)) angle[i,j] = trapz(q1*q3,time) energy[i,j] = (1-lam) * (dy[CR_50[i]]/m+dy[CR_50[j]]/m) - lam * (angle[i,j] + 1) maxloc = energy.argmax() maxloc_row,maxloc_col = np.unravel_index(maxloc,energy.shape) Q1_index = CR_50[maxloc_row] Q3_index = CR_50[maxloc_col] Q1_q = qt[:,Q1_index] Q3_q = qt[:,Q3_index] Q1 = ft[:,Q1_index] Q3 = ft[:,Q3_index] # identify amplitude quantiles dy_ordering = dy.argsort() CR_alpha = dy_ordering[0:np.round(N*(1-alpha)).astype('int')] tmp = dy[CR_alpha] m = tmp.max() angle = np.zeros((CR_alpha.shape[0],CR_alpha.shape[0])) energy = np.zeros((CR_alpha.shape[0],CR_alpha.shape[0])) for i in range(0,CR_alpha.shape[0]-1): for j in range(i+1,CR_alpha.shape[0]): q1 = qt[:,CR_alpha[i]] - q_median q3 = qt[:,CR_alpha[j]] - q_median q1 /= np.sqrt(trapz(q1**2,time)) q3 /= np.sqrt(trapz(q3**2,time)) angle[i,j] = trapz(q1*q3,time) energy[i,j] = (1-lam) * (dy[CR_alpha[i]]/m+dy[CR_alpha[j]]/m) - lam * (angle[i,j] + 1) maxloc = energy.argmax() maxloc_row,maxloc_col = np.unravel_index(maxloc,energy.shape) Q1a_index = CR_alpha[maxloc_row] Q3a_index = CR_alpha[maxloc_col] Q1a_q = qt[:,Q1a_index] Q3a_q = qt[:,Q3a_index] Q1a = ft[:,Q1a_index] Q3a = ft[:,Q3a_index] # compute amplitude whiskers IQR = dy[Q1_index] + dy[Q3_index] v1 = Q1_q - q_median v3 = Q3_q - q_median upper_q = Q3_q + k_a * IQR * v3 / np.sqrt(trapz(v3**2,time)) lower_q = Q1_q + k_a * IQR * v1 / np.sqrt(trapz(v1**2,time)) upper_dis = np.sqrt(trapz((upper_q - q_median)**2,time)) lower_dis = np.sqrt(trapz((lower_q-q_median)**2,time)) whisker_dis = max(upper_dis,lower_dis) # identify amplitude outliers outlier_index = np.array([]) for i in range(0,N): if dy[dy_ordering[N-i-1]] > whisker_dis: outlier_index = np.append(outlier_index,dy[dy_ordering[N+1-i]]) # identify amplitude extremes distance_to_upper = np.full(N, np.inf) distance_to_lower = np.full(N, np.inf) out_50_CR = np.setdiff1d(np.arange(0,N), outlier_index) for i in range(0,out_50_CR.shape[0]): j = out_50_CR[i] distance_to_upper[j] = np.sqrt(trapz((upper_q-qt[:,j])**2,time)) distance_to_lower[j] = np.sqrt(trapz((lower_q-qt[:,j])**2,time)) max_index = distance_to_upper.argmin() min_index = distance_to_lower.argmin() min_q = qt[:,min_index] max_q = qt[:,max_index] minn = ft[:,min_index] maxx = ft[:,max_index] s = np.linspace(0,1,100) Fs2 = np.zeros((time.shape[0],595)) Fs2[:,0] = (1-s[0]) * minn + s[0] * Q1 for j in range(1,100): Fs2[:,j] = (1-s[j]) * minn + s[j] * Q1a Fs2[:,98+j] = (1-s[j]) * Q1a + s[j] * Q1 Fs2[:,197+j] = (1-s[j]) * Q1 + s[j] * f_median Fs2[:,296+j] = (1-s[j]) * f_median + s[j] * Q3 Fs2[:,395+j] = (1-s[j]) * Q3 + s[j] * Q3a Fs2[:,494+j] = (1-s[j]) * Q3a + s[j] * maxx d1 = np.sqrt(trapz((q_median-Q1_q)**2,time)) d1a = np.sqrt(trapz((Q1_q-Q1a_q)**2,time)) dl = np.sqrt(trapz((Q1a_q-min_q)**2,time)) d3 = np.sqrt(trapz((q_median-Q3_q)**2,time)) d3a = np.sqrt(trapz((Q3_q-Q3a_q)**2,time)) du = np.sqrt(trapz((Q3a_q-max_q)**2,time)) part1=np.linspace(-d1-d1a-dl,-d1-d1a,100) part2=np.linspace(-d1-d1a,-d1,100) part3=np.linspace(-d1,0,100) part4=np.linspace(0,d3,100) part5=np.linspace(d3,d3+d3a,100) part6=np.linspace(d3+d3a,d3+d3a+du,100) allparts = np.hstack((part1,part2[1:100],part3[1:100],part4[1:100],part5[1:100],part6[1:100])) U, V = np.meshgrid(time, allparts) U = np.transpose(U) V = np.transpose(V) self.Q1 = Q1 self.Q3 = Q3 self.Q1a = Q1a self.Q3a = Q3a self.minn = minn self.maxx = maxx self.outlier_index = outlier_index self.f_median = f_median self.q_median = q_median plt = collections.namedtuple('plt', ['U', 'V', 'Fs2', 'allparts', 'd1', 'd1a', 'dl', 'd3', 'd3a', 'du', 'Q1q','Q3q']) self.plt = plt(U,V,Fs2,allparts,d1,d1a,dl,d3,d3a,du,Q1a_q,Q3a_q) return
[docs] def plot(self): """ plot box plot and surface plot Usage: obj.plot() """ M = self.warp_data.time.shape[0] fig1, ax1 = plt.subplots() ax1.plot(self.warp_data.time,self.f_median,'k') ax1.plot(self.warp_data.time,self.Q1,'b') ax1.plot(self.warp_data.time,self.Q3,'b') ax1.plot(self.warp_data.time,self.Q1a,'g') ax1.plot(self.warp_data.time,self.Q3a,'g') ax1.plot(self.warp_data.time,self.minn,'r') ax1.plot(self.warp_data.time,self.maxx,'r') fig2 = plt.figure() ax = fig2.gca(projection='3d') ax.plot_surface(self.plt.U,self.plt.V,self.plt.Fs2,cmap=cm.viridis,rcount=200,ccount=200) ax.plot(self.warp_data.time, np.zeros(M), self.f_median,'k') ax.plot(self.warp_data.time, np.repeat(-self.plt.d1,M), self.Q1,'b') ax.plot(self.warp_data.time, np.repeat(-self.plt.d1-self.plt.d1a,M),self.Q1a,'g') ax.plot(self.warp_data.time, np.repeat(-self.plt.d1-self.plt.d1a-self.plt.dl,M),self.minn,'r') ax.plot(self.warp_data.time, np.repeat(self.plt.d3,M),self.Q3,'b') ax.plot(self.warp_data.time, np.repeat(self.plt.d3+self.plt.d3a,M),self.Q3a,'g') ax.plot(self.warp_data.time, np.repeat(self.plt.d3+self.plt.d3a+self.plt.du,M),self.maxx,'r') plt.show()
[docs]class phbox: """ This class provides phase boxplot for functional data using the SRVF framework Usage: obj = phbox(warp_data) :param warp_data: fdawarp class with alignment data :type warp_data: fdawarp :param Q1: First quartile :param Q3: Second quartile :param Q1a: First quantile based on alpha :param Q3a: Second quantile based on alpha :param minn: minimum extreme function :param maxx: maximum extreme function :param outlier_index: indexes of outlier functions :param median_x: median warping function :param psi_median: median srvf of warping function :param plt: surface plot mesh Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov> Date : 15-Mar-2018 """ def __init__(self, fdawarp): """ Construct an instance of the phbox class :param fdawarp: fdawarp class """ if fdawarp.fn.size==0: raise Exception('Please align fdawarp class using srsf_align!') if fdawarp.type=="mean": raise Exception('Please align fdawarp class using srsf_align with method="median"!') self.warp_data = fdawarp
[docs] def construct_boxplot(self, alpha=.05, k_a=1): """ This function constructs phase boxplot for functional data using the elastic square-root slope (srsf) framework. :param alpha: quantile value (e.g.,=.05, i.e., 95%) :param k_a: scalar for outlier cutoff (e.g.,=1) """ if self.warp_data.rsamps: gam = self.warp_data.gams else: gam = self.warp_data.gam M,N = gam.shape t = np.linspace(0,1,M) time = t lam = 0.5 # compute phase median median_x, psi_median, psi, vec = uf.SqrtMedian(gam) # compute phase distances dx = np.zeros(N) v = np.zeros((M,N)) for k in range(0, N): v[:,k], d = geo.inv_exp_map(psi_median,psi[:,k]) dx[k] = np.sqrt(trapz(v[:,k]**2,t)) dx_ordering = dx.argsort() CR_50 = dx_ordering[0:np.ceil(N/2).astype('int')] tmp = dx[CR_50] m = tmp.max() # identify phase quartiles angle = np.zeros((CR_50.shape[0],CR_50.shape[0])) energy = np.zeros((CR_50.shape[0],CR_50.shape[0])) for i in range(0,CR_50.shape[0]-1): for j in range(i+1,CR_50.shape[0]): q1 = v[:,CR_50[i]] q3 = v[:,CR_50[j]] q1 /= np.sqrt(trapz(q1**2,time)) q3 /= np.sqrt(trapz(q3**2,time)) angle[i,j] = trapz(q1*q3,time) energy[i,j] = (1-lam) * (dx[CR_50[i]]/m+dx[CR_50[j]]/m) - lam * (angle[i,j] + 1) maxloc = energy.argmax() maxloc_row, maxloc_col = np.unravel_index(maxloc,energy.shape) Q1_index = CR_50[maxloc_row] Q3_index = CR_50[maxloc_col] Q1 = gam[:,Q1_index] Q3 = gam[:,Q3_index] Q1_psi = np.sqrt(np.gradient(Q1,1/(M-1))) Q3_psi = np.sqrt(np.gradient(Q3,1/(M-1))) # identify phase quantiles dx_ordering = dx.argsort() CR_alpha = dx_ordering[0:np.round(N*(1-alpha)).astype('int')] tmp = dx[CR_alpha] m = tmp.max() angle = np.zeros((CR_alpha.shape[0],CR_alpha.shape[0])) energy = np.zeros((CR_alpha.shape[0],CR_alpha.shape[0])) for i in range(0,CR_alpha.shape[0]-1): for j in range(i+1,CR_alpha.shape[0]): q1 = v[:,CR_alpha[i]] q3 = v[:,CR_alpha[j]] q1 /= np.sqrt(trapz(q1**2,time)) q3 /= np.sqrt(trapz(q3**2,time)) angle[i,j] = trapz(q1*q3,time) energy[i,j] = (1-lam) * (dx[CR_alpha[i]]/m+dx[CR_alpha[j]]/m) - lam * (angle[i,j] + 1) maxloc = energy.argmax() maxloc_row, maxloc_col = np.unravel_index(maxloc,energy.shape) Q1a_index = CR_alpha[maxloc_row] Q3a_index = CR_alpha[maxloc_col] Q1a = gam[:,Q1a_index] Q3a = gam[:,Q3a_index] Q1a_psi = np.sqrt(np.gradient(Q1a,1/(M-1))) Q3a_psi = np.sqrt(np.gradient(Q3a,1/(M-1))) # check quartile and quantile going in same direction tst = trapz(v[:,Q1a_index]*v[:,Q1_index]) if tst < 0: Q1a = gam[:,Q3a_index] Q3a = gam[:,Q1a_index] # compute phase whiskers IQR = dx[Q1_index] + dx[Q3_index] v1 = v[:,Q3a_index] v3 = v[:,Q3a_index] upper_v = v3 + k_a * IQR * v3 / np.sqrt(trapz(v3**2,time)) lower_v = v1 + k_a * IQR * v1 / np.sqrt(trapz(v1**2,time)) upper_dis = np.sqrt(trapz(v3**2,time)) lower_dis = np.sqrt(trapz(v1**2,time)) whisker_dis = max(upper_dis,lower_dis) # identify phase outliers outlier_index = np.array([]) for i in range(0,N): if dx[dx_ordering[N-1-i]] > whisker_dis: outlier_index = np.append(outlier_index,dx_ordering[N+1-i]) # identify phase extremes distance_to_upper = np.full(N, np.inf) distance_to_lower = np.full(N, np.inf) out_50_CR = np.setdiff1d(np.arange(0,N), outlier_index) for i in range(0,out_50_CR.shape[0]): j = out_50_CR[i] distance_to_upper[j] = np.sqrt(trapz((upper_v-v[:,j])**2,time)) distance_to_lower[j] = np.sqrt(trapz((lower_v-v[:,j])**2,time)) max_index = distance_to_upper.argmin() min_index = distance_to_lower.argmin() minn = gam[:,min_index] maxx = gam[:,max_index] min_psi = psi[:,min_index] max_psi = psi[:,max_index] s = np.linspace(0,1,100) Fs2 = np.zeros((time.shape[0],595)) Fs2[:,0] = (1-s[0]) * (minn-t) + s[0] * (Q1-t) for j in range(1,100): Fs2[:,j] = (1-s[j]) * (minn-t) + s[j] * (Q1a-t) Fs2[:,98+j] = (1-s[j]) * (Q1a-t) + s[j] * (Q1-t) Fs2[:,197+j] = (1-s[j]) * (Q1-t) + s[j] * (median_x-t) Fs2[:,296+j] = (1-s[j]) * (median_x-t) + s[j] * (Q3-t) Fs2[:,395+j] = (1-s[j]) * (Q3-t) + s[j] * (Q3a-t) Fs2[:,494+j] = (1-s[j]) * (Q3a-t) + s[j] * (maxx-t) d1 = np.sqrt(trapz(psi_median*Q1_psi,time)) d1a = np.sqrt(trapz(Q1_psi*Q1a_psi,time)) dl = np.sqrt(trapz(Q1a_psi*min_psi,time)) d3 = np.sqrt(trapz((psi_median*Q3_psi),time)) d3a = np.sqrt(trapz((Q3_psi*Q3a_psi),time)) du = np.sqrt(trapz((Q3a_psi*max_psi),time)) part1=np.linspace(-d1-d1a-dl,-d1-d1a,100) part2=np.linspace(-d1-d1a,-d1,100) part3=np.linspace(-d1,0,100) part4=np.linspace(0,d3,100) part5=np.linspace(d3,d3+d3a,100) part6=np.linspace(d3+d3a,d3+d3a+du,100) allparts = np.hstack((part1,part2[1:100],part3[1:100],part4[1:100],part5[1:100],part6[1:100])) U, V = np.meshgrid(time, allparts) U = np.transpose(U) V = np.transpose(V) self.Q1 = Q1 self.Q3 = Q3 self.Q1a = Q1a self.Q3a = Q3a self.minn = minn self.maxx = maxx self.outlier_index = outlier_index self.median_x = median_x self.psi_media = psi_median plt = collections.namedtuple('plt', ['U', 'V', 'Fs2', 'allparts', 'd1', 'd1a', 'dl', 'd3', 'd3a', 'du', 'Q1_psi','Q3_psi']) self.plt = plt(U,V,Fs2,allparts,d1,d1a,dl,d3,d3a,du,Q1a_psi,Q3a_psi) return
[docs] def plot(self): """ plot box plot and surface plot Usage: obj.plot() """ M = self.warp_data.time.shape[0] time = np.linspace(0,1,M) fig1, ax1 = plt.subplots() ax1.plot(time,self.median_x,'k') ax1.plot(time,self.Q1,'b') ax1.plot(time,self.Q3,'b') ax1.plot(time,self.Q1a,'g') ax1.plot(time,self.Q3a,'g') ax1.plot(time,self.minn,'r') ax1.plot(time,self.maxx,'r') ax1.set_aspect('equal') fig2 = plt.figure() ax = fig2.gca(projection='3d') ax.plot_surface(self.plt.U,self.plt.V,self.plt.Fs2,cmap=cm.viridis,rcount=200,ccount=200) ax.plot(time, np.zeros(M), self.median_x-time,'k') ax.plot(time, np.repeat(-self.plt.d1,M), self.Q1 - time,'b') ax.plot(time, np.repeat(-self.plt.d1-self.plt.d1a,M),self.Q1a - time,'g') ax.plot(time, np.repeat(-self.plt.d1-self.plt.d1a-self.plt.dl,M),self.minn - time,'r') ax.plot(time, np.repeat(self.plt.d3,M),self.Q3 - time,'b') ax.plot(time, np.repeat(self.plt.d3+self.plt.d3a,M),self.Q3a - time,'g') ax.plot(time, np.repeat(self.plt.d3+self.plt.d3a+self.plt.du,M),self.maxx - time,'r') plt.show() return