I've got strange (from my point of view) result from numpy polyfit. My code:
import numpy as np
data=np.array([2482.9, 2483.0, 2485.9, 2486.0, 2486.4, 2485.1, 2485.4, 2484.9, 2484.8, 2484.8, 2484.8, 2484.0, 2484.1, 2484.1, 2484.1])
wr = range(len(data))
poly = np.polyfit(wr , data, deg = 2)
wp = np.poly1d(poly)
el = 2484.1
res = wp(el)
print(res)
#result -225256.888955
Is this a bug?
As #DSM has already said - it doesn't look like a quadratic polynom.
We can try to fit it with a higher degree though:
import numpy.polynomial.polynomial as poly
x = wr; y = data
coefs = poly.polyfit(x, y, 4)
ffit = poly.Polynomial(coefs)
plt.plot(x, y)
plt.plot(x, ffit(x))
plt.legend(['y(x)','ffit(x)'])
Result:
Related
I am relatively new to coding in Python. I have mainly used MatLab in the past and am used to having vectors that can be referenced explicitly rather than appended lists. I have a script where I generate a list of x- and y- (z-, v-, etc) values. Later, I want to interpolate and then print a table of the values at specified points. Here is a MWE. The problem is at line 48:
yq = interp1d(x_list, y_list, xq(nn))#interp1(output1(:,1),output1(:,2),xq(nn))
I'm not sure I have the correct syntax for the last two lines either:
table[nn] = ('%.2f' %xq, '%.2f' %yq)
print(table)
Here is the full script for the MWE:
#This script was written to test how to interpolate after data was created in a loop and stored as a list. Can a list be accessed explicitly like a vector in matlab?
#
from scipy.interpolate import interp1d
from math import * #for ceil
from astropy.table import Table #for Table
import numpy as np
# define the initial conditions
x = 0 # initial x position
y = 0 # initial y position
Rmax = 10 # maxium range
""" initializing variables for plots"""
x_list = [x]
y_list = [y]
""" define functions"""
# not necessary for this MWE
"""create sample data for MWE"""
# x and y data are calculated using functions and appended to their respective lists
h = 1
t = 0
tf = 10
N=ceil(tf/h)
# Example of interpolation without a loop: https://docs.scipy.org/doc/scipy/tutorial/interpolate.html#d-interpolation-interp1d
#x = np.linspace(0, 10, num=11, endpoint=True)
#y = np.cos(-x**2/9.0)
#f = interp1d(x, y)
for i in range(N):
x = h*i
y = cos(-x**2/9.0)
""" appends selected data for ability to plot"""
x_list.append(x)
y_list.append(y)
## Interpolation after x- and y-lists are already created
intervals = 0.5
nfinal = ceil(Rmax/intervals)
NN = nfinal+1 # length of table
dtype = [('Range (units?)', 'f8'), ('Drop? (units)', 'f8')]
table = Table(data=np.zeros(N, dtype=dtype))
for nn in range(NN):#for nn = 1:NN
xq = 0.0 + (nn-1)*intervals #0.0 + (nn-1)*intervals
yq = interp1d(x_list, y_list, xq(nn))#interp1(output1(:,1),output1(:,2),xq(nn))
table[nn] = ('%.2f' %xq, '%.2f' %yq)
print(table)
Your help and patience will be greatly appreciated!
Best regards,
Alex
Your code has some glaring issues that made it really difficult to understand. Let's first take a look at some things I needed to fix:
for i in range(N):
x = h*1
y = cos(-x**2/9.0)
""" appends selected data for ability to plot"""
x_list.append(x)
y_list.append(y)
You are appending a single value without modifying it. What I presume you wanted is down below.
intervals = 0.5
nfinal = ceil(Rmax/intervals)
NN = nfinal+1 # length of table
dtype = [('Range (units?)', 'f8'), ('Drop? (units)', 'f8')]
table = Table(data=np.zeros(N, dtype=dtype))
for nn in range(NN):#for nn = 1:NN
xq = 0.0 + (nn-1)*intervals #0.0 + (nn-1)*intervals
yq = interp1d(x_list, y_list, xq(nn))#interp1(output1(:,1),output1(:,2),xq(nn))
table[nn] = ('%.2f' %xq, '%.2f' %yq)
This is where things get strange. First: use pandas tables, this is the more popular choice. Second: I have no idea what you are trying to loop over. What I presume you wanted was to vary the number of points for the interpolation, which I have done so below. Third: you are trying to interpolate a point, when you probably want to interpolate over a range of points (...interpolation). Lastly, you are using the interp1d function incorrectly. Please take a look at the code below or run it here; let me know what you exactly wanted (specifically: what should xq / xq(nn) be?), because the MRE you provided is quite confusing.
from scipy.interpolate import interp1d
from math import *
import numpy as np
Rmax = 10
h = 1
t = 0
tf = 10
N = ceil(tf/h)
x = np.arange(0,N+1)
y = np.cos(-x**2/9.0)
interval = 0.5
NN = ceil(Rmax/interval) + 1
ip_list = np.arange(1,interval*NN,interval)
xtable = []
ytable = []
for i,nn in enumerate(ip_list):
f = interp1d(x,y)
x_i = np.arange(0,nn+interval,interval)
xtable += [x_i]
ytable += [f(x_i)]
[print(i) for i in xtable]
[print(i) for i in ytable]
I have this input image and I wan to find pixel maxima and it should look like image2.
I tried contouring but its not working.I also tried scipy pixel_maxima it doesn't gives me result as image2.
here is the code, I have refered this answer (Get coordinates of local maxima in 2D array above certain value)
import numpy as np
import scipy.misc
import scipy.ndimage as ndimage
import scipy.ndimage.filters as filters
import matplotlib.pyplot as plt
import imageio
from skimage.color import rgb2gray
fname = 'slice-0001-trim.jpg'
neighborhood_size = 10
threshold = 12
data = imageio.imread(fname,as_gray=True)
data_max = filters.maximum_filter(data, neighborhood_size)
maxima = (data == data_max)
data_min = filters.minimum_filter(data, neighborhood_size)
diff = ((data_max - data_min) > threshold)
maxima[diff == 0] = 0
labeled, num_objects = ndimage.label(maxima)
slices = ndimage.find_objects(labeled)
x, y = [], []
for dy,dx in slices:
x_center = (dx.start + dx.stop - 1)/2
x.append(x_center)
y_center = (dy.start + dy.stop - 1)/2
y.append(y_center)
plt.imshow(data)
plt.savefig('sample.jpg', bbox_inches = 'tight')
plt.autoscale(False)
plt.plot(x,y, 'ro')
plt.savefig('result.png', bbox_inches = 'tight')
I need this image as result
But, I get this image as output
I am trying to minimize the "function()" with respect to two parameters. I have done so by creating mesh arrays and used them in the above "function()" to return similar meshed array values. However, upon using "fmin()" to find the minimum, the output says that the operators could not be broadcasted.
The code is pasted below:
import numpy as np
from scipy.optimize import fmin
import matplotlib.pyplot as plt
i=0
x_values = np.arange(-10,10,2)
y_values = np.arange(-10,10,2)
x_mesh = np.empty((0,len(x_values)))
y_mesh = np.empty((0,len(y_values)))
for i in range(len(x_values)):
y_mesh = np.vstack((y_mesh, y_values))
i=0
for i in range(len(y_values)):
x_mesh = np.vstack((x_mesh, x_values))
y_mesh = np.transpose(y_mesh)
def function(x_mesh, y_mesh):
return (2*x_mesh**2 + y_mesh**2)
''' Want to minimize function '''
x_start = np.zeros((len(x_values), len(y_values)))
y_start = x_start
y = fmin(lamda x_mesh: function(x_mesh, y_mesh), (x_start, y_start), full_output = True, disp = 0)
The output shown was:
File "C:/Users/User/Documents/Year2/Programming/elrter.py", line 42, in function
return (2*x_mesh**2 + y_mesh**2)
ValueError: operands could not be broadcast together with shapes (200,) (10,10)
But why does this happen? What is the solution?
i am trying to use the "subs" function for differential equation
but i get the error: "can't convert expression to float"
i tryed to check the type of the arrays, but they all float
import sympy as sym
from sympy.integrals import inverse_laplace_transform
from sympy.abc import s,t,y
import numpy as np
U = 1
G =(s+1)/(s*(s+2))
Y = G*U
y = inverse_laplace_transform(Y, s, t)
tm = np.linspace(0,2,3)
y_val = np.zeros(len(tm))
for i in range(len(tm)):
y_val[i] = y.subs(t, tm[i])
print(y)
print(y_val)
line 17
y_val[i] = y.subs(t, tm[i])
TypeError: can't convert expression to float
Ths issue here is that, because tm[0] == 0, the evaluated y in the first iteration of your loop is Heaviside(0), which has no defined real value by default (see https://docs.sympy.org/latest/modules/functions/special.html#heaviside). This is because you have
from sympy.functions import exp, Heaviside
assert y == Heaviside(t) / 2 + exp(-2 * t) * Heaviside(t) / 2
The simplest workaround here is defining a linear space excluding 0, for instance
epsilon = 1e-15
tm = np.linspace(epsilon, 2, 3)
Using y_val = np.zeros(len(tm)), the default datatype of array is float. After modifying the code, you find that one of y_val elements is an object, not float. You can use a list object as a placeholder or you can specify the datatype of numpy array as object:
import sympy as sym
from sympy.integrals import inverse_laplace_transform
from sympy.abc import s,t,y
import numpy as np
U = 1
G =(s+1)/(s*(s+2))
Y = G*U
y = inverse_laplace_transform(Y, s, t)
tm = np.linspace(0,2,3)
# y_val = [0 for _ in range(len(tm))]
y_val = np.zeros(len(tm), dtype=object)
for i in range(len(tm)):
y_val[i] = y.subs(t, tm[i])
print(y_val)
result: [Heaviside(0.0) 0.567667641618306 0.509157819444367]
I have similar problem and your answers work for me, but I still need to put the data into graph.. I modified my problem for this question:
import sympy as sym
from sympy.integrals import inverse_laplace_transform
from sympy.abc import s,t,y
import numpy as np
import matplotlib.pyplot as plt
Y = (5*(1 - 5*s))/(s*(4*(s**2) + s + 1))*(1/s)
y = inverse_laplace_transform(Y, s, t)
tm = np.linspace(1e-15, 20, 100)
y_val = np.zeros(len(tm), dtype=object)
for i in range(len(tm)):
y_val[i] = y.subs(t, tm[i])
plt.plot(y_val, tm)
plt.show()
Running this code I got same error:
TypeError: can't convert expression to float
I am trying to understand how Kalman Filter for non-linear system works. While searching for an example, I cam across this good basic example.
import numpy as np
import pylab as pl
import pandas as pd
from pykalman import UnscentedKalmanFilter
# initialize parameters
def transition_function(state, noise):
a = np.sin(state[0]) + state[1] * noise[0]
b = state[1] + noise[1]
return np.array([a, b])
def observation_function(state, noise):
C = np.array([[-1, 0.5], [0.2, 0.1]])
return np.dot(C, state) + noise
transition_covariance = np.eye(2)
random_state = np.random.RandomState(0)
observation_covariance = np.eye(2) + random_state.randn(2, 2) * 0.1
initial_state_mean = [0, 0]
initial_state_covariance = [[1, 0.1], [-0.1, 1]]
# sample from model
kf = UnscentedKalmanFilter(
transition_function, observation_function,
transition_covariance, observation_covariance,
initial_state_mean, initial_state_covariance,
random_state=random_state
)
states, observations = kf.sample(50, initial_state_mean)
# estimate state with filtering and smoothing
filtered_state_estimates = kf.filter(observations)[0]
smoothed_state_estimates = kf.smooth(observations)[0]
# draw estimates
pl.figure()
lines_true = pl.plot(states, color='b')
lines_filt = pl.plot(filtered_state_estimates, color='r', ls='-')
lines_smooth = pl.plot(smoothed_state_estimates, color='g', ls='-.')
pl.legend((lines_true[0], lines_filt[0], lines_smooth[0]),
('true', 'filt', 'smooth'),
loc='lower left'
)
pl.show()
This code produces the following graph.
However,for my experiment - I have created a very small time series data ready with three columns formatted as follows. The full dataset is attached here for reproduciability.
time X Y
0.040662 1.041667 1
0.139757 1.760417 2
0.144357 1.190104 1
0.145341 1.047526 1
0.145401 1.011882 1
0.148465 1.002970 1
.... ..... .
Instead of using the random values as shown in the code, how can we input from the CSV file I attached? Here is my approach, but it doesn't seem to workout for me and I would appreciate for any help.
df = pd.read_csv('testdata.csv')
pd.set_option('use_inf_as_null', True)
df.dropna(inplace=True)
X = df.drop('Y', axis=1)
y = df['Y']
d1= np.array(X)
d2 = np.array(y)
From the link I shared, here is how you get the CSV data into Numpy Arrays.
import numpy as np
import csv
with open('testdata.csv','r') as csvfile:
r = csv.reader(csvfile, delimiter=',')
data = [i for i in r]
headings = data.pop(0)
data = np.array([[np.float(j) for j in i] for i in data])
T = data.T[0] #Time
X = data.T[1] #X
Y = data.T[2] #Y
print(T)
print(X)
print(Y)