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![suppose we know the function value at a set of points yi-fx), for i = 1 n. To approximate the function at a new point x we find the closest known points below and above, say xbelowxand xabove > x, draw a straight line between (xbelow, ybelow) and (xabove, yabove), and take the value ywhere this line is at x. The general form of the straight line is a *x + b, where a = 0above-ybelow)/(xabove-xbelow) and b = ybelow - a xbelow. Using this, we can calculate y a *x+ b lask. Your task is to implement a function interpolate(x·y, x-test) that computes the linear interpolation of the unknown function f at a new point x_test. The sample is given in the form of two sequences x and y. Both sequences have the same length, and their elements are numbers. The x sequence contains the points where the function has been sampled, and the y sequence contains the function value at the corresponding point. In other words, y[i] f(x(i]) Assumptions and restrictions: You can assume that the arguments are as described: that is, x and y are sequences, both have the same length, and their elements are numbers You should NOT make any assumption about what type of sequence the x and y arguments are You can assume that the values in x are ordered in increasing order, and that they are unique (that is, there are no repeated x-values) You can assume that x_test is a number, and it is between two values in the x sequence, or possibly equal to a value in the sequence. If x_test is equal to a sample value (a value in the input xsequence), your function should simply return the corresponding function value fromy Your function must return a number. The scipy library has a whole module, scipy.interpolate which performs various kinds of interpolation, including linear interpolation as described above. Obviously, you may not use this module, or any other module that provides a ready-made solution to the problem, since the goal of the assignment is for you to demonstrate that you can implement the function yourself. You can of course use the scipy interpolation function as a reference to test your implementation NOTE: must be done on python 3, using only function definitions](https://d2vlcm61l7u1fs.cloudfront.net/media%2Fe3c%2Fe3c3eba1-6b55-43f3-98c0-c8ff886a260b%2Fphp6clwQ8.png "Question & Answer: Python code with explanation will be so helfup. Greatest appreciation!..... 1")
Python code with explanation will be so helfup. Greatest appreciation!
Suppose we know the function value at a set of points yi = f(xi), for i = l … n. To approximate the function at a new point x’, we find the closest known points below and above, say xbelow x’ draw a straight line between (xbelow: ybelow) and (xabove, yabove), and take the value y’ where this line is at x’. The general form of the straight line is a *x + b, where a = (yabove – ybelow)/(xabove – xbelow) and b = ybelow – a * xbelow. Using this, we can calculate y’ = a * x + b Task: Your task is to implement a function interpolate (x, y, x_ test) that computes the linear interpolation of the unknown function f at a new point x_test. The sample is given in the form of two sequences x and y. Both sequences have the same length, and their elements are numbers. The x sequence contains the points where the function has been sampled, and the y sequence contains the function value at the corresponding point. In other words, y[i] = f(x[i]). Assumptions and restrictions: You can assume that the arguments are as described: that is, x and y are sequences, both have the same length, and their elements are numbers. You should NOT make any assumption about what type of sequence the x and y arguments are. You can assume that the values in x are ordered in increasing order, and that they are unique (that is, there are no repeated x-values). You can assume that x_test is a number, and it is between two values in the x sequence, or possibly equal to a value in the sequence. If x_test is equal to a sample value (a value in the input xsequence), your function should simply return the corresponding function value from y. Your function must return a number. The scipy library has a whole module, scipy. interpolate which performs various kinds of interpolation, including linear interpolation as described above. Obviously, you may not use this module, or any other module that provides a ready-made solution to the problem, since the goal of the assignment is for you to demonstrate that you can implement the function yourself. You can of course use the scipy interpolation function as a reference to test your implementation.
Expert Answer
Please find the code below :
def interpolate(x, y, x_test):
l = len(x)
for i in range(l) : #looping through the series x
if (x[i] == x_test) : #checking if x_test is equal to a value of series x
return y[i]
elif (i<l-1 and x[i] < x_test and x[i+1] > x_test): #checking if x_test in between two values of series x
a = (y[i] – y[i+1])/(x[i] – x[i+1]) #calculating a
b = y[i] – (a*x[i]) #calculating b
y_test = a*x_test + b #calculating y_test
return y_test
x = [1,2,3,4,5] #defining series x
y = [2,4,6,8,10] #defining series y
print(“xityi”)
for i in range(len(x)):
print(x[i],”t”,y[i])
x_test = .5
y_test = interpolate(x,y,x_test)
print(“x_test :”,x_test)
print(“y_test :”,y_test)
x_test = 5.5
y_test = interpolate(x,y,x_test)
print(“x_test :”,x_test)
print(“y_test :”,y_test)
x_test = 2.5
y_test = interpolate(x,y,x_test)
print(“x_test :”,x_test)
print(“y_test :”,y_test)
Output :
P
