So, I found a solution. For future reference this code should give those with the same problem what they need. I added an 'interpolation' argument to the plot.imshow() function like:
import matplotlib.pyplot as plt import numpy as np from scipy.interpolate import interp2d # fmt: off X_COORDINATE = [1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 0.0, 0.5, 1.0, 1.1, 1.5, 2.0, 3.0, 4.0, 5.0, 0.0, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0] Z_COORDINATE = [0, 0, 0, 0, 0, 0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 1, 1, 1, 1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5] C_I = [1.02414267447743, 0.210700871073941, 0.156586042435711, 0.109151033138569, 0.2279728779957, 0.204768257586954, 1.09037445301743, 0.287155868433615, 0.211257395413685, 0.132554129593619, 0.0900680495011601, 0.194608837248807, 1.34397119257655, 0.1201882143371, 0.17555070608144, 0.127220190160657, 0.204384526301353, 0.197414938747342, 0.195583977408476, 0.148150828086297, 0.183751866814816, 0.134858902076203, 0.183027629350907, 0.180267135381046, 0.0876356087026242, 0.183285092770786, 0.165502978081942, 0.0487725567447014, 0.172053559692846, 0.142204671797215, 0.166163224221791, 0.249334486033046, 0.150888488422605, 0.259452257883415] # fmt: on x_list = np.array(X_COORDINATE) z_list = np.array(Z_COORDINATE) C_I_list = np.array(C_I) # f will be a function with two arguments (x and z coordinates), # but those can be array_like structures too, in which case the # result will be a matrix representing the values in the grid # specified by those arguments f = interp2d(x_list, z_list, C_I_list, kind="linear") x_coords = np.arange(min(x_list), max(x_list) + 1) z_coords = np.arange(min(z_list), max(z_list) + 1) c_i = f(x_coords, z_coords) fig = plt.imshow( c_i, extent=[min(x_list), max(x_list), min(z_list), max(z_list)], origin="lower", interpolation="bicubic", ) # Show the positions of the sample points, just to have some reference fig.axes.set_autoscale_on(False) plt.scatter(x_list, z_list, 400, facecolors="none") plt.colorbar() plt.show()Does anybody know how I can change the resolution of the colours on the map so that I can better see the variation between values of 0 and 1 throughout the map?
The map now looks like the following:
Linear Interpolation is the technique of determining the values of the functions of any intermediate points when the values of two adjacent points are known. Linear interpolation is basically the estimation of an unknown value that falls within two known values. Linear Interpolation is used in various disciplines like statistical, economics, price determination, etc. It is used to fill the gaps in the statistical data for the sake of continuity of information.
By using the following formula we can Linearly interpolate the given data point
Here (x1, y1) are the coordinates of the first data point. And (x2,y2) are coordinates of the second data point, where x is the point on which we perform interpolation and y is the interpolated value.
Example Problem:
Let’s take an example for better understanding. We have the following data values where x denotes the number and y is the function of the square root of x. Our task is to find the square root of 5.5 (x).
x
1
2
3
4
5
6
y ( f(x) = √x )
1
1.4142
1.7320
2
2.2360
2.4494
We can use the Linear Interpolation method here.
1. Find the two adjacent (x1, y1) ,(x2,y2) from the x. i.e. (5,2.2360) and (6,2.4494).
Where x1 = 5, x2= 6, y1 = 2.2360, y2 = 2.4494, and we interpolate at point x = 5.5.
2. Using the formula y(x) = y1 + (x – x1) \frac{(y2 – y1) }{ (x2 – x1)}
3. After putting the values in the above equation.
At x = 5.5 the value of Y will be 2.3427. So by using linear interpolation we can easily determine the value of a function between two intervals.
Approach 1:
Using the formula
Example: Suppose we have a dataset of the population of a city and the year.
X(Year)
2016
2017
2018
2019
2021
Y(Population)
10001
12345
74851
12124
5700
Here, X is the year and Y is the population in any city. Our task to find the population of the city in the year 2020.
We choose our (x1, y1) ,(x2,y2) as x1=2019 , y1=12124, x2=2021, y2=5700, x = 2020, y = ?
Here (x1, y1) and (x2, y2) are two adjacent points and x is the year for which we want to predict the value of the y population.
Python3
# Python3 code
# Implementing Linear interpolation
# Creating Function to calculate the
# linear interpolation
def interpolation(d, x):
Population on year 2020 is 8912.00Population on year 2020 is 8912.01 Population on year 2020 is 8912.02Population on year 2020 is 8912.03Population on year 2020 is 8912.04Population on year 2020 is 8912.05Population on year 2020 is 8912.06Population on year 2020 is 8912.07 Population on year 2020 is 8912.08Population on year 2020 is 8912.09 Population on year 2020 is 8912.02Population on year 2020 is 8912.03Population on year 2020 is 8912.04Population on year 2020 is 8912.03Value of y at x = 2.5 is 2.854Value of y at x = 2.5 is 2.855 Value of y at x = 2.5 is 2.856Population on year 2020 is 8912.05Population on year 2020 is 8912.04Population on year 2020 is 8912.05Population on year 2020 is 8912.06Population on year 2020 is 8912.09 Population on year 2020 is 8912.02Population on year 2020 is 8912.03Population on year 2020 is 8912.04Population on year 2020 is 8912.05Value of y at x = 2.5 is 2.854# Python3 code7# Python3 code8Population on year 2020 is 8912.05Population on year 2020 is 8912.04Population on year 2020 is 8912.03Population on year 2020 is 8912.06Population on year 2020 is 8912.09 Population on year 2020 is 8912.02Population on year 2020 is 8912.03Population on year 2020 is 8912.04Population on year 2020 is 8912.03# Implementing Linear interpolation8
# Creating Function to calculate the0 Population on year 2020 is 8912.00
# Creating Function to calculate the2
# Creating Function to calculate the3Population on year 2020 is 8912.01# Creating Function to calculate the5# Creating Function to calculate the6# Creating Function to calculate the7# Creating Function to calculate the8# Creating Function to calculate the9# linear interpolation0# Creating Function to calculate the7# linear interpolation2# linear interpolation3
# linear interpolation4Population on year 2020 is 8912.01# linear interpolation6
# linear interpolation7
# linear interpolation8# linear interpolation9def0def1def2def3
def4def5
OutputPopulation on year 2020 is 8912.0
Approach 2:
Using scipy.interpolate.interp1d
Similarly, we can achieve linear interpolation using a scipy library function called interpolate.interp1d.
Syntax : scipy.interpolate.interp1d(x, y, kind=’linear’, axis=- 1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False)
Sr. no.
Parameters
Description
1.
x
A 1-D array of real values.
2.
y
A N-D array of real values.
3.
kind
i.e. kind of interpolation do you want it can be ‘linear’, ‘nearest’, ‘nearest-up’, ‘zero’, ‘slinear’, ‘quadratic’, ‘cubic’, ‘previous’, or ‘next’. ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’, by defaults it is linear.
4.
axis
Specifies the axis of y along which we interpolate.
5.
copy
It holds boolean values if True, the class makes internal copies of x and y .
6.
bounds_error
It holds boolean values If True, a ValueError is raised when interpolation is attempted on a value outside the range of x.
Example:
Let’s have a random dataset :
X = [1,2,3,4,5], Y = [11,2.2,3.5,-88,1], and we want to find the value of Y at point 2.5.
Python3
def6
def7
def8 def9interpolation(d, x):0 interpolation(d, x):1
interpolation(d, x):2Population on year 2020 is 8912.01 interpolation(d, x):4Population on year 2020 is 8912.05# Creating Function to calculate the7interpolation(d, x):7# Creating Function to calculate the7interpolation(d, x):9# Creating Function to calculate the7 1# Creating Function to calculate the7 3Population on year 2020 is 8912.06 5
6Population on year 2020 is 8912.01 interpolation(d, x):4 9# Creating Function to calculate the7Population on year 2020 is 8912.001# Creating Function to calculate the7Population on year 2020 is 8912.003# Creating Function to calculate the7Population on year 2020 is 8912.09Population on year 2020 is 8912.006# Creating Function to calculate the7Population on year 2020 is 8912.05Population on year 2020 is 8912.06Population on year 2020 is 8912.010