Spectral analysis on HRV data with LombScargle in Python - python
I'm working with RR peaks and want to derive the frequency domain measures for HRV to recreate the results from the native C package by Physionet (WFDB tools). Both signal processing and spectral analysis are new fields for me, but after a long week with trial an error I've hacked together some code based on the Astropy module after trying several other solutions.
from astropy.stats import LombScargle
import random
dy = 0.1 * random.randint(1,100)
t = drive01["time"].values
y = drive01["intervals"].values
frequency, power = LombScargle(t, y,dy).autopower(minimum_frequency=0.0,maximum_frequency=4)
plt.plot(frequency, power)
This creates a plot that looks quite similar to the plot from Physionets package.
Physionets HRV tools with the code get_hrv makes this plot
Then by calculating common frequency domain measures I get quite different results.
Pxx = np.nan_to_num(power)
Fxx = np.nan_to_num(frequency)
ulf = 0.003
vlf = 0.04
lf = 0.15
hf = 0.4
Fs = 15.5 # the sampling rate of the drive file
# find the indexes corresponding to the VLF, LF, and HF bands
vlf_freq_band = (Fxx >= ulf) & (Fxx <= vlf)
lf_freq_band = (Fxx >= vlf) & (Fxx <= lf)
hf_freq_band = (Fxx >= lf) & (Fxx <= hf)
tp_freq_band = (Fxx >= 0) & (Fxx <= hf)
# Calculate the area under the given frequency band
dy = 1.0 / Fs
VLF = np.trapz(y=abs(Pxx[vlf_freq_band]), x=None, dx=dy)
LF = np.trapz(y=abs(Pxx[lf_freq_band]), x=None, dx=dy)
HF = np.trapz(y=abs(Pxx[hf_freq_band]), x=None, dx=dy)
TP = np.trapz(y=abs(Pxx[tp_freq_band]), x=None, dx=dy)
LF_HF = float(LF) / HF
Python
'HF': 0.10918703853414605,
'LF': 0.050074418080717789,
'LF/HF': 0.45861137689028925,
'TP': 0.20150514290250854,
'VLF': 0.025953350304821571
From the Physionet package:
TOT PWR = 0.0185973
VLF PWR = 0.00372733
LF PWR = 0.00472635
HF PWR = 0.0101436
LF/HF = 0.465944
When comparing the results it looks like this:
Python Physionet
TP 0.201505143 0.0185973 Quite similar + decimal dif
HF 0.109187039 0.0101436 Quite similar + decimal dif
LF 0.050074418 0.00472635 Quite similar + decimal dif
VLF 0.02595335 0.00372733 Not similar
LF/HF 0.458611377 0.465944 Quite similar
The calculations in Python are based on the code from another Stackoverflow post but the fix he got from the respondent is based on a python module I'm not able to get working and he is not using the Lomb Periodgram. I'm very open for trying something else as well, as long as its working with uneven samples.
the data I'm working with is the drivedb from Physionet and I've used the Physionet packages to make a text file with RR peaks and time which is read into a Pandas DataFrame. The textfile can be found here
LombScargle based on the Astropy caculate power different with C package by Physionet (WFDB tools). I write lombscargle again in python and result the same with C package by Physionet (WFDB tools).
import numpy as np
import os
import math
import csv
from itertools import zip_longest
import time
DATA_PATH = '/home/quangpc/Desktop/Data/PhysionetData/mitdb/'
class FreqDomainClass:
#staticmethod
def power(freq, mag):
lo = [0, 0.0033, 0.04, 0.15]
hi = [0.0033, 0.04, 0.15, 0.4]
pr = np.zeros(4)
nbands = 4
for index in range(0, len(freq)):
pwr = np.power(mag[index], 2)
for n in range(0, nbands):
if (freq[index] >= lo[n]) and freq[index] <= hi[n]:
pr[n] += pwr
break
return pr
#staticmethod
def avevar(y):
var = 0.0
ep = 0.0
ave = np.mean(y)
for i in range(len(y)):
s = y[i] - ave
ep += s
var += s * s
var = (var - ep * ep / len(y)) / (len(y) - 1)
return var
def lomb(self, t, h, ofac, hifac):
period = max(t) - min(t)
z = h - np.mean(h)
f = np.arange(1 / (period * ofac), hifac * len(h) / (2 * period), 1 / (period * ofac))
f = f[:int(len(f) / 2) + 1]
f = np.reshape(f, (len(f), -1))
w = 2 * np.pi * f
lenght_t = len(t)
t = np.reshape(t, (lenght_t, -1))
t = np.transpose(t)
tau = np.arctan2(np.sum(np.sin(2 * w * t), axis=1), np.sum(np.cos(2 * w * t), axis=1)) / (2 * w)
tau = np.diag(tau)
tau = np.reshape(tau, (len(tau), -1))
tau = np.tile(tau, (1, lenght_t))
cos = np.cos(w * (t - tau))
sin = np.sin(w * (t - tau))
pc = np.power(np.sum(z * cos, axis=1), 2)
ps = np.power(np.sum(z * sin, axis=1), 2)
cs = pc / np.sum(np.power(cos, 2), axis=1)
ss = ps / np.sum(np.power(sin, 2), axis=1)
p = cs + ss
pwr = self.avevar(h)
nout = len(h)
p = p / (2 * pwr)
p = p / (nout / (2.0 * pwr))
return f, np.sqrt(p)
def lomb_for(self, t, h, ofac, hifac):
period = max(t) - min(t)
f = np.arange(1 / (period * ofac), hifac * len(h) / (2 * period), 1 / (period * ofac))
f = f[:int(len(f) / 2) + 1]
z = h - np.mean(h)
p = np.zeros(len(f))
for i in range(len(f)):
w = 2 * np.pi * f[i]
if w > 0:
twt = 2 * w * t
y = sum(np.sin(twt))
x = sum(np.cos(twt))
tau = math.atan2(y, x) / (2 * w)
wtmt = w * (t - tau)
cs = np.power(sum(np.multiply(z, np.cos(wtmt))), 2) / sum(np.power((np.cos(wtmt)), 2))
ss = np.power(sum(np.multiply(z, np.sin(wtmt))), 2) / sum(np.power((np.sin(wtmt)), 2))
p[i] = cs + ss
else:
p[i] = np.power(sum(np.multiply(z, t)), 1) / sum(np.power(t), 1)
pwr = self.avevar(h)
nout = len(h)
p = p / (2 * pwr)
p = p / (nout / (2.0 * pwr))
return f, np.sqrt(p)
def freq_domain(self, time, rr_intervals):
frequency, mag0 = self.lomb(time, rr_intervals, 4.0, 2.0)
frequency = np.round(frequency, 8)
mag0 = mag0 / 2.0
mag0 = np.round(mag0, 8)
result = self.power(frequency, mag0)
return result[0], result[1], result[2], result[3], result[0] + result[1] + result[2] + result[3], \
result[2] / result[3]
def time_domain(time, rr_intervals, ann):
sum_rr = 0.0
sum_rr2 = 0.0
rmssd = 0.0
totnn = 0
totnnn = 0
nrr = 1
totrr = 1
nnx = 0
nnn = 0
lastann = ann[0]
lastrr = int(rr_intervals[0])
lenght = 300
t = float(time[0])
end = t + lenght
i = 0
ratbuf = np.zeros(2400)
avbuf = np.zeros(2400)
sdbuf = np.zeros(2400)
for x in range(1, len(ann)):
t = float(time[x])
while t > (end+lenght):
i += 1
end += lenght
if t >= end:
if nnn > 1:
ratbuf[i] = nnn/nrr
sdbuf[i] = np.sqrt(((sdbuf[i] - avbuf[i]*avbuf[i]/nnn) / (nnn-1)))
avbuf[i] /= nnn
i += 1
nnn = nrr = 0
end += lenght
nrr += 1
totrr += 1
if ann[x] == 'N' and ann[x-1] == 'N':
rr_intervals[x] = int(rr_intervals[x])
nnn += 1
avbuf[i] += rr_intervals[x]
sdbuf[i] += (rr_intervals[x] * rr_intervals[x])
sum_rr += rr_intervals[x]
sum_rr2 += (rr_intervals[x] * rr_intervals[x])
totnn += 1
if lastann == 'N':
totnnn += 1
rmssd += (rr_intervals[x] - lastrr) * (rr_intervals[x] - lastrr)
# nndif[0] = NNDIF
if abs(rr_intervals[x] - lastrr) - 0.05 > (10 ** -10):
nnx += 1
lastann = ann[x-1]
lastrr = rr_intervals[x]
if totnn == 0:
return 0, 0, 0, 0
sdnn = np.sqrt((sum_rr2 - sum_rr * sum_rr / totnn) / (totnn - 1))
rmssd = np.sqrt(rmssd/totnnn)
pnn50 = nnx / totnnn
if nnn > 1:
ratbuf[i] = nnn / nrr
sdbuf[i] = np.sqrt((sdbuf[i] - avbuf[i] * avbuf[i] / nnn) / (nnn - 1))
avbuf[i] /= nnn
nb = i + 1
sum_rr = 0.0
sum_rr2 = 0.0
k = 0
h = 0
while k < nb:
if ratbuf[k] != 0:
h += 1
sum_rr += avbuf[k]
sum_rr2 += (avbuf[k] * avbuf[k])
k += 1
sdann = np.sqrt((sum_rr2 - sum_rr * sum_rr / h) / (h - 1))
return sdnn, sdann, rmssd, pnn50
def get_result_from_get_hrv(filename):
with open(filename, 'r') as f:
csv_reader = csv.reader(f, delimiter=',')
index = 0
for row in csv_reader:
if index > 0:
output = [s.strip() for s in row[0].split('=') if s]
# print('output = ', output)
if output[0] == 'SDNN':
sdnn = output[1]
if output[0] == 'SDANN':
sdann = output[1]
if output[0] == 'rMSSD':
rmssd = output[1]
if output[0] == 'pNN50':
pnn50 = output[1]
if output[0] == 'ULF PWR':
ulf = output[1]
if output[0] == 'VLF PWR':
vlf = output[1]
if output[0] == 'LF PWR':
lf = output[1]
if output[0] == 'HF PWR':
hf = output[1]
if output[0] == 'TOT PWR':
tp = output[1]
if output[0] == 'LF/HF':
ratio_lf_hf = output[1]
index += 1
return float(sdnn), float(sdann), float(rmssd), float(pnn50), float(ulf), float(vlf), \
float(lf), float(hf), float(tp), float(ratio_lf_hf)
def save_file():
extension = "atr"
result_all = []
file_process = ['File']
sdnn_l = ['sdnn']
sdann_l = ['sdann']
rmssd_l = ['rmssd']
pnn50_l = ['pnn50']
ulf_l = ['ulf']
vlf_l = ['vlf']
lf_l = ['lf']
hf_l = ['hf']
tp_l = ['tp']
ratio_lf_hf_l = ['ratio_lf_hf']
sdnn_l_p = ['sdnn']
sdann_l_p = ['sdann']
rmssd_l_p = ['rmssd']
pnn50_l_p = ['pnn50']
ulf_l_p = ['ulf']
vlf_l_p = ['vlf']
lf_l_p = ['lf']
hf_l_p = ['hf']
tp_l_p = ['tp']
ratio_lf_hf_l_p = ['ratio_lf_hf']
test_file = ['103', '113', '117', '121', '123', '200', '202', '210', '212', '213',
'219', '221', '213', '228', '231', '233', '234',
'101', '106', '108', '112', '114', '115', '116', '119', '122', '201', '203',
'205', '208', '209', '215', '220', '223', '230',
'105', '100']
file_dis = ['109', '111', '118', '124', '207', '214', '232']
for root, dirs, files in os.walk(DATA_PATH):
files = np.sort(files)
for name in files:
if extension in name:
if os.path.basename(name[:-4]) not in test_file:
continue
print('Processing file...', os.path.basename(name))
cur_dir = os.getcwd()
os.chdir(DATA_PATH)
os.system('rrlist {} {} -M -s >{}.rr'.format(extension, name.split('.')[0], name.split('.')[0]))
time_m = []
rr_intervals = []
ann = []
with open(name.split('.')[0] + '.rr', 'r') as rr_file:
for line in rr_file:
time_m.append(line.split(' ')[0])
rr_intervals.append(line.split(' ')[1])
ann.append(line.split(' ')[2].split('\n')[0])
time_m = np.asarray(time_m, dtype=float)
rr_intervals = np.asarray(rr_intervals, dtype=float)
sdnn, sdann, rmssd, pnn50 = time_domain(time_m, rr_intervals, ann)
if sdnn == 0 and sdann == 0 and rmssd == 0 and pnn50 == 0:
print('No result hrv')
file_dis.append(os.path.basename(name[:-4]))
continue
print('sdnn', sdnn)
print('rmssd', rmssd)
print('pnn50', pnn50)
print('sdann', sdann)
time_m = time_m - time_m[0]
time_m = np.round(time_m, 3)
time_nn = []
nn_intervals = []
for i in range(1, len(ann)):
if ann[i] == 'N' and ann[i - 1] == 'N':
nn_intervals.append(rr_intervals[i])
time_nn.append(time_m[i])
time_nn = np.asarray(time_nn, dtype=float)
nn_intervals = np.asarray(nn_intervals, dtype=float)
fc = FreqDomainClass()
ulf, vlf, lf, hf, tp, ratio_lf_hf = fc.freq_domain(time_nn, nn_intervals)
sdnn_l.append(sdnn)
sdann_l.append(sdann)
rmssd_l.append(rmssd)
pnn50_l.append(pnn50)
ulf_l.append(ulf)
vlf_l.append(vlf)
lf_l.append(lf)
hf_l.append(hf)
tp_l.append(tp)
ratio_lf_hf_l.append(ratio_lf_hf)
print('ULF PWR: ', ulf)
print('VLF PWR: ', vlf)
print('LF PWR: ', lf)
print('HF PWR: ', hf)
print('TOT PWR: ', tp)
print('LF/HF: ', ratio_lf_hf)
if os.path.exists('physionet_hrv.txt'):
os.remove('physionet_hrv.txt')
os.system('get_hrv -R ' + name.split('.')[0] + '.rr >> ' + 'physionet_hrv.txt')
sdnn, sdann, rmssd, pnn50, ulf, vlf, lf, hf, tp, ratio_lf_hf = \
get_result_from_get_hrv('physionet_hrv.txt')
file_process.append(os.path.basename(name[:-4]))
sdnn_l_p.append(sdnn)
sdann_l_p.append(sdann)
rmssd_l_p.append(rmssd)
pnn50_l_p.append(pnn50)
ulf_l_p.append(ulf)
vlf_l_p.append(vlf)
lf_l_p.append(lf)
hf_l_p.append(hf)
tp_l_p.append(tp)
ratio_lf_hf_l_p.append(ratio_lf_hf)
os.chdir(cur_dir)
result_all.append(file_process)
result_all.append(sdnn_l)
result_all.append(sdnn_l_p)
result_all.append(sdann_l)
result_all.append(sdann_l_p)
result_all.append(rmssd_l)
result_all.append(rmssd_l_p)
result_all.append(pnn50_l)
result_all.append(pnn50_l_p)
result_all.append(ulf_l)
result_all.append(ulf_l_p)
result_all.append(vlf_l)
result_all.append(vlf_l_p)
result_all.append(lf_l)
result_all.append(lf_l_p)
result_all.append(hf_l)
result_all.append(hf_l_p)
result_all.append(tp_l)
result_all.append(tp_l_p)
result_all.append(ratio_lf_hf_l)
result_all.append(ratio_lf_hf_l_p)
print(file_dis)
with open('hrv2.csv', 'w+') as f:
writer = csv.writer(f)
for values in zip_longest(*result_all):
writer.writerow(values)
def main():
extension = "atr"
for root, dirs, files in os.walk(DATA_PATH):
files = np.sort(files)
for name in files:
if extension in name:
if name not in ['101.atr']:
continue
cur_dir = os.getcwd()
os.chdir(DATA_PATH)
os.system('rrlist {} {} -M -s >{}.rr'.format(extension, name.split('.')[0], name.split('.')[0]))
time_m = []
rr_intervals = []
ann = []
with open(name.split('.')[0] + '.rr', 'r') as rr_file:
for line in rr_file:
time_m.append(line.split(' ')[0])
rr_intervals.append(line.split(' ')[1])
ann.append(line.split(' ')[2].split('\n')[0])
time_m = np.asarray(time_m, dtype=float)
rr_intervals = np.asarray(rr_intervals, dtype=float)
sdnn, sdann, rmssd, pnn50 = time_domain(time_m, rr_intervals, ann)
if sdnn == 0 and sdann == 0 and rmssd == 0 and pnn50 == 0:
print('No result hrv')
return 0
print('sdnn', sdnn)
print('rmssd', rmssd)
print('pnn50', pnn50)
print('sdann', sdann)
time_m = time_m - time_m[0]
time_m = np.round(time_m, 3)
time_nn = []
nn_intervals = []
for i in range(1, len(ann)):
if ann[i] == 'N' and ann[i - 1] == 'N':
nn_intervals.append(rr_intervals[i])
time_nn.append(time_m[i])
time_nn = np.asarray(time_nn, dtype=float)
nn_intervals = np.asarray(nn_intervals, dtype=float)
start = time.time()
fc = FreqDomainClass()
ulf, vlf, lf, hf, tp, ratio_lf_hf = fc.freq_domain(time_nn, nn_intervals)
end = time.time()
print('ULF PWR: ', ulf)
print('VLF PWR: ', vlf)
print('LF PWR: ', lf)
print('HF PWR: ', hf)
print('TOT PWR: ', tp)
print('LF/HF: ', ratio_lf_hf)
print('finish', end - start)
os.chdir(cur_dir)
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Find optimal value of model by Koshi simulated annealing
I should find optimal value of model by Koshi simulated annealing.
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Index Height Weight
0 1 65.78331 112.9925
1 2 71.51521 136.4873
2 3 69.39874 153.0269
3 4 68.21660 142.3354
4 5 67.78781 144.2971
def mse(w):
height = dataset['Height']
weight = dataset['Weight']
predicts = list(map(lambda x: w[0] + w[1] * x, weight))
mse = mean_squared_error(height, predicts)
return mse
Initial values:
Tmax = 13
Tmin = -9.5
T = Tmax
wop0 = 1
wop1 = 100
Eglob = random.random()
w0_ = random.uniform(0, 100)
w1_ = random.uniform(0, 5)
w0 = w0_
w1 = w1_
E = mse([w0, w1])
Main function:
iteration = 0
while T > Tmin:
i = 1
for i in range(1,6000):
w0 = w0 + T * np.random.standard_cauchy()
w1 = w1 + T * np.random.standard_cauchy()
E = mse([w0, w1])
dE = E - mse([wop0, wop1])
if dE < 0:
wop0 = w0
wop1 = w1
Eglob = E
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a = random.random()
#h = 1 / (1 + np.exp(dE / T))
h = np.exp(-dE / T)
if a < h:
wop0 = w0
wop1 = w1
Eglob = E
T= Tmax / math.log(1+i);
iteration += 1
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Result:
iteration: 5999
wop0: -706.4779870159789
wop1: 3.716864959467018
mse: 93084.16405699923
But if I use basinhopping function:
from scipy.optimize import basinhopping
ret = basinhopping(mse, [0, 1], niter = 50)
print("global min: w = [%.4f, %.4f], mse(w0, w1) = %.4f" % (ret.x[0], ret.x[1], ret.fun))
Result:
global min: w = [57.5718, 0.0820], mse(w0, w1) = 2.7018
What I'm doing wrong?
Thanks
Mpi4py: printing and plotting during execution
I recently start working with mpi in order to use it to accelerate some code (a sph/gravity simulation).
So far it seem to be working. The position of my particle have change between the beginning and the end of the program, task manager show that several python thread are working...
But i have two problem:
1/ i can't print text during the execution of the program. The text is only print once it's finished
2/ I'm unable to create a graph using matplotlib.
In both case, neither python nor mpi return any error. My guess, for the text at least, is that its print when the execution end with mpiexec.
thanks for any insight !
here the code i run it with !mpiexec -n 8 python mpi4py_test.py
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
from mpi4py import MPI
class particule:
def __init__(self, h, pos, vel = [0, 0], m = 1, P = 0, density = 0, acc = [0, 0]):
self.x, self.y = pos
self.u, self.v = vel
self.acc_x, self.acc_y = acc
self.m = m
self.h = h # kernel lenght
self.P = P # Pressure
self.density = density
def kernel(part_a, part_b ):
" monaghan cubic spline "
cst = 1 / (np.pi * part_a.h**3)
dist = np.sqrt((part_b.x-part_a.x)**2 + (part_b.y-part_a.y)**2 )
r = dist / h
tmp = 0
if r < 1:
tmp = cst * (1 - 3/2* r**2 + 3/4*r**3)
elif r < 2:
tmp = cst * (1/4*(2-r)**3)
return tmp
def grad_kernel(part_a, part_b):
cst = 1 / (np.pi * part_a.h**3)
dist = np.sqrt((part_b.x-part_a.x)**2 + (part_b.y-part_a.y)**2 )
r = dist / part_a.h
tmp = 0
if r < 1:
tmp = cst * (9/4 * r**2 - 3*r)
elif r < 2:
tmp = cst * (-3/4*(2-r)**2)
return tmp
class hash_grid:
def __init__(self, cell_size):
self.cell_size = cell_size
self.cell = {}
self.part_list = []
def key(self, part):
return (part.x//self.cell_size,
part.y//self.cell_size)
def add(self, part):
tmp = self.key(part)
self.cell.setdefault(tmp, []).append(part)
self.part_list.append(part)
def neighbours(self, part):
idx = self.key(part)
cell_N = None
cell_S = None
cell_E = None
cell_W = None
cell_NE = None
cell_NW = None
cell_SE = None
cell_SW = None
if (idx[0], idx[1]+1) in self.cell: cell_N = (idx[0], idx[1]+1)
if (idx[0], idx[1]-1) in self.cell: cell_S = (idx[0], idx[1]-1)
if (idx[0]+1, idx[1]) in self.cell: cell_E = (idx[0]+1, idx[1])
if (idx[0]-1, idx[1]) in self.cell: cell_W = (idx[0]-1, idx[1])
if (idx[0]+1, idx[1]+1) in self.cell: cell_NE = (idx[0]+1, idx[1]+1)
if (idx[0]-1, idx[1]+1) in self.cell: cell_NW = (idx[0]-1, idx[1]+1)
if (idx[0]+1, idx[1]-1) in self.cell: cell_SE = (idx[0]+1, idx[1]-1)
if (idx[0]-1, idx[1]-1) in self.cell: cell_SW = (idx[0]-1, idx[1]-1)
return [value for cel in (idx, cell_N, cell_S, cell_E, cell_W, cell_NE, cell_NW, cell_SE, cell_SW) if cel!=None for value in self.cell.get(cel) ]
def split(to_split, nb_chunk):
"take a list and split it most evenly possible"
result = []
q, r = divmod(len(to_split), nb_chunk)
curr = 0
last = 0
for i in range(nb_chunk):
if r>0:
last = curr + q + 1
result.append(to_split[curr: last])
r = r-1
curr = last
else:
last = curr + q
result.append(to_split[curr: last])
curr = last
return result
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
if rank == 0:
n_part = 2000
h = 2
grid = hash_grid(h)
points = np.zeros((n_part, 2))
sim_range = 20
dt = 0.005
n_iter = 2500
k = 5
for _i in range(n_part):
pos = np.random.uniform(-sim_range, sim_range, 2)
vel = np.random.uniform(-.2, .2, 2)
p = particule(h, pos, vel)
grid.add(p)
points[_i, :] = pos
for part in grid.part_list:
part.density = 0
part.P = 0
for p in grid.neighbours(part):
part.density = part.density + p.m * kernel(part, p)
part.P = k * ( part.density )**2 # - density_0)
data = split(grid.part_list,8)
for t in range(10):
if rank == 0 :
"1 - verlet 1/2 ; serial"
for i, part in enumerate(grid.part_list):
part.u, part.v = part.u + part.acc_x * dt/2, part.v + part.acc_y * dt/2
part.x, part.y = part.x + part.u * dt, part.y + part.v * dt
"2 - update grid ; serial"
jnk = grid.part_list
del grid
grid=hash_grid(h)
for p in jnk:
grid.add(p)
grid_bcast = grid
data_b = grid
chunk_of_part_list = split(grid.part_list,8)
else:
grid_bcast=None
chunk_of_part_list = None
data_b=None
grid_bcast = comm.bcast(grid_bcast, root=0)
chunk_of_part_list = comm.scatter(chunk_of_part_list, root=0)
"3 - get acc ; parallel"
for part in chunk_of_part_list:
part.acc_x = 0
part.acc_y = 0
for p in grid_bcast.neighbours(part):
if p != part:
r = np.sqrt((p.x-part.x)**2 + (p.y-part.y)**2)
if r==0: pass
else:
part.acc_x = part.acc_x - p.m * (part.P/part.density**2 + p.P/p.density**2) * grad_kernel(part, p) * (p.x - part.x)/r
part.acc_y = part.acc_y - p.m * (part.P/part.density**2 + p.P/p.density**2) * grad_kernel(part, p) * (p.y - part.y)/r
dist = np.sqrt(part.x**2+part.y**2)
part.acc_x = part.acc_x - .5 * part.x -1*part.u
part.acc_y = part.acc_y - .5 * part.y -1*part.v
chunk_of_part_list = comm.gather(chunk_of_part_list,root=0)
"4 - verlet 2/2 ; serial"
if rank == 0:
grid.part_list = list(matplotlib.cbook.flatten(chunk_of_part_list))
for i, part in enumerate(grid.part_list):
part.u, part.v = part.u + part.acc_x * dt/2, part.v + part.acc_y * dt/2
points[i,0], points[i,1] = part.x, part.y # for the figure
if rank==0:
print(t, flush=True)
if rank == 0:
print('point 0', points[0,:])
fig = plt.figure()
ax = fig.add_subplot()
sc = ax.scatter(points[:, 0], points[:, 1],s=3)
ax.set_aspect('equal', 'box')
ax.set_xlim(-sim_range,sim_range)
ax.set_ylim(-sim_range,sim_range)
offset a parallel line to a given line python
I want to draw parallel line to given X,Y coordinate below code helps to draw , import numpy as np import matplotlib.pyplot as plt x = [187, 879, 722, 322] y = [341, 344, 112, 112] newX = [] newY = [] def findIntesection(p1x, p1y, p2x, p2y, p3x,p3y, p4x, p4y): dx12 = p2x - p1x dy12 = p2y - p1y dx34 = p4x - p3x dy34 = p4y - p3y denominator = (dy12*dx34-dx12*dy34) t1 = ((p1x - p3x) * dy34 + (p3y - p1y) * dx34)/ denominator t2 = ((p3x - p1x) * dy12 + (p1y - p3y) * dx12)/ -denominator; intersectX = p1x + dx12 * t1 intersectY = p1y + dy12 * t1 if (t1 < 0): t1 = 0 elif (t1 > 1): t1 = 1 if (t2 < 0): t2 = 0 elif (t2 > 1): t2 = 1 return intersectX,intersectY def normalizeVec(x,y): distance = np.sqrt(x*x+y*y) return x/distance, y/distance def getEnlarged(oldX, oldY, offset): num_points = len(oldX) for j in range(num_points): i = j - 1 if i < 0: i += num_points k = (j + 1) % num_points vec1X = oldX[j] - oldX[i] vec1Y = oldY[j] - oldY[i] v1normX, v1normY = normalizeVec(vec1X,vec1Y) v1normX *= offset v1normY *= offset n1X = -v1normY n1Y = v1normX pij1X = oldX[i] + n1X pij1Y = oldY[i] + n1Y pij2X = oldX[j] + n1X pij2Y = oldY[j] + n1Y vec2X = oldX[k] - oldX[j] vec2Y = oldY[k] - oldY[j] v2normX, v2normY = normalizeVec(vec2X,vec2Y) v2normX *= offset v2normY *= offset n2X = -v2normY n2Y = v2normX pjk1X = oldX[j] + n2X pjk1Y = oldY[j] + n2Y pjk2X = oldX[k] + n2X pjk2Y = oldY[k] + n2Y intersectX,intersetY = findIntesection(pij1X,pij1Y,pij2X,pij2Y,pjk1X,pjk1Y,pjk2X,pjk2Y) #print(intersectX,intersetY) newX.append(intersectX) newY.append(intersetY) getEnlarged(x, y, 20) plt.plot(x, y) plt.plot(newX, newY) plt.show() This gives result as below Here it is giving good result by drawing parallel line to each line of our trapezoidal shaped , but i want it to be a closed shape in place of open shape i want to join the 1st and last coordinate so that it should form a closed shape. Any help will be appreciated .
Using approach from here outer_ccw parameters combines vertex order and desired offset direction. For CCW order and outer polygon it is 1, for inner polygon it should be -1. def makeOffsetPoly(oldX, oldY, offset, outer_ccw = 1): num_points = len(oldX) for curr in range(num_points): prev = (curr + num_points - 1) % num_points next = (curr + 1) % num_points vnX = oldX[next] - oldX[curr] vnY = oldY[next] - oldY[curr] vnnX, vnnY = normalizeVec(vnX,vnY) nnnX = vnnY nnnY = -vnnX vpX = oldX[curr] - oldX[prev] vpY = oldY[curr] - oldY[prev] vpnX, vpnY = normalizeVec(vpX,vpY) npnX = vpnY * outer_ccw npnY = -vpnX * outer_ccw bisX = (nnnX + npnX) * outer_ccw bisY = (nnnY + npnY) * outer_ccw bisnX, bisnY = normalizeVec(bisX, bisY) bislen = offset / np.sqrt((1 + nnnX*npnX + nnnY*npnY)/2) newX.append(oldX[curr] + bislen * bisnX) newY.append(oldY[curr] + bislen * bisnY) x = [0, 100, 60, 40] y = [0, 0, 50, 50] makeOffsetPoly(x, y, 20) print(newX, newY) >>>[-29.424478775259594, 129.4244787752596, 66.79706177729007, 33.202938222709925] [-14.14213562373095, -14.14213562373095, 64.14213562373095, 64.14213562373095]
Just append the first coordinates to the end of your lists. x.append(x[0]) y.append(y[0]) newX.append(newX[0]) newY.append(newY[0]) Place this right before you plot. Here's my output
Double sumption using python and the second argument depend on the first one
I have this relation to which I write the code using python to compute it , I am not sure if the code is right or not. Could you please give me any advice if it is true or how I can improve the code??, thanks import matplotlib.pyplot as plt import numpy as np from scipy.special import comb from scipy.constants import k from numpy import arange p12 = 1 # system initial state 12 w0 = 1 # system wn = 0 # wb/w0 bath U = 0.1 N = 50 n = (N/2) a =0.007 t = 1000# Time Z = 2**N * (np.cosh(U*wn/2))**N q12 = [] f11 = [] def Jrange(start, n, step): numelements = int((stop-start)/float(step)) for i in range(numelements+1): yield start + i*step def trange(tstart,tstop,tstep): tnumelements = int((tstop-tstart)/float(tstep)) for i in range(tnumelements+1): yield tstart + i*tstep for t in trange(tstart,tstop,tstep): roh2 = 0 roh12 = 0 roh1 = 0 roh11 = 0 for J in Jrange (0,stop,1) : Nj = (comb (N,(n+J))) - (comb (N,(n+J+1))) for m in arange (-J,J+1): r1 = np.sqrt (J*(J + 1) - m*(m + 1)) #r+ r2 = np.sqrt (J*(J + 1) - m*(m - 1)) #r- Omega1 = (w0 - wn) + (4 *a*(m + (1/2)))/(np.sqrt(N)) #Omeg+ gamma1 = np.sqrt( (Omega1**2 /4)+ (4*a**2 * r1**2)/N) # gamma+ Omega2 =-(w0 - wn) - (4 *a*(m - (1/2)))/(np.sqrt(N)) #Omega- gamma2 = np.sqrt( (Omega2**2 /4)+ (4*a**2 * r2**2)/N)#gamma- A1 = np.cos(gamma1*t) B1 = np.sin(gamma1*t) A2 = np.cos(gamma2*t) B2 = np.sin(gamma2*t) C = np.exp(-m*U*wn) H12 = C * (A1 - 1j*B1*Omega1/(2*gamma1)) * ((A2 +1j*B2*Omega2/(2*gamma2)) H2 = r2**2 * B2**2 * ((4*a**2)/ (gamma2**2 * N)) H1 = A1**2 + B1**2 *((Omega1**2)/ (4 * gamma1**2)) H11 = C * ((p11*H1) + (p22*H2)) roh11 = roh11+H11 roh12 = roh12 + H12 roh2= roh2 +roh12*Nj roh1 = roh1 + roh11*Nj Roh12 = roh2*D *p12*np.exp(1j*(w0-wn)*t) Roh11 = roh1 *D q12.append(Roh12) f11.append(Roh11)
Numerical issue in scipy.ode.integrate solver
I am using ode solver to solve stiff problem (since odeint function could not able to solve it). But by this way also I have some warnings and my plot get saturate at some point. Here is image What should I do? Here is the list of warnings:
DVODE-- Warning..internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). solver will continue anyway
In above, R1 = 0.3667661010318D+00 R2 = 0.1426374862242D-16
DVODE-- Warning..internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). solver will continue anyway
In above, R1 = 0.3667661010318D+00 R2 = 0.1426374862242D-16
DVODE-- Above warning has been issued I1 times.
it will not be issued again for this problem
In above message, I1 = 2
DVODE-- At current T (=R1), MXSTEP (=I1) steps
taken on this call before reaching TOUT
In above message, I1 = 500
In above message, R1 = 0.3667661010318D+00
My code:
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as si
def func():
#arguments:::
w = 1./3.
xi = 2.86
phi1 = 1.645
phi2 = 2.* 1.202
gt = 10.**(-60)
Lt = (1.202*gt)/np.pi
Lin = 10.**-5
Lf = 0.49
dt = 0.0001
gin = gt*Lt/Lin
xin = (-np.log((3. - (xi**2)*Lin)/(3. - (xi**2)*Lt)) + np.log(Lin/Lt))/4.0
uin = -(np.log(Lin/Lt))/2.
state0 = [gin,xin,uin]
print state0
def eq(L, state):
g = state[0]
x = state[1]
u = state[2]
N = (-2.*g/(6.*np.pi + 5.*g))*(18./(1. - 2.*L) + 5.*np.log(1.- 2.*L) - phi1 + 6. )
B = (-(2. - N)*L) - ((g/np.pi)* (5.*np.log(1.-2.*L) - phi2 + (5.*N/40.)))
Eqs = np.zeros((3))
gdl = Eqs[0] = ((2.+N)*g)/B
xdl = Eqs[1] = -(2./(3.*(1.+w)))* (1./(1.-(xi**2)*L/3.))*(1./B)
udl = Eqs[2]= 1./B
return Eqs
ode = si.ode(eq)
# BDF method suited to stiff systems of ODEs
ode.set_integrator('vode',nsteps=500,method='bdf')
ode.set_initial_value(state0,Lin)
L = []
G = []
while ode.successful() and ode.t < Lf:
ode.integrate(ode.t + dt)
L.append(ode.t)
G.append(ode.y)
lam = np.vstack(L)
g,x,u = np.vstack(G).T
return g,x,u,lam
r= func()
L = r[3]
g = r[0]
lng = np.log10(g)
x = r[1]
u = r[2]
w = 1./3.
xi = 2.86
O_A = np.zeros(len(L))
q = np.zeros(len(L))
for i in np.arange(len(L)):
O_A[i] = xi**2*L[i]/3.
alpha = 2./ ((3.+3.*w) * (1.- (L[i]*xi**2)/3.) )
q[i] = 1./alpha - 1.
n = np.zeros(len(L)) #eta(n)
b = np.zeros(len(L))
for j in np.arange(len(L)):
n[j] =(-2.*g[j]/(6.*np.pi + 5.*g[j]))*(18./(1. - 2.*L[j]) + 5.*np.log(1.- 2.*L[j]) - 1.645 + 6. )
b[j]= (-(2. - n[j])*L[j]) - ((g[j]/np.pi)* (5.*np.log(1.-2.*L[j]) - 2.* 1.202 + ((5.*n[j])/4.)))
P = np.zeros(len(x))
for k in np.arange(len(x)):
C = (((3. - (xi**2)*L[k])/g[k])**(3./4.)) * (((2.*L[k] + (u[k]*b[k]))*xi**2) + (n[k] * (3.- L[k]*xi**2)) )
P[k] = (np.exp(3.*x[k])) * (np.exp(4.*u[k])) * C
plt.figure()
plt.plot(L,P)
plt.xlabel('Lambda ---->')
plt.ylabel('P ----->')
plt.title('lambda Vs P')
plt.show()