A1: Asmt#1: Integration using trapezoids

You are given the following data as a list. All values are floating point approximations.

A width of each sample (first data value, a positive value).
A collection of height data points (rest of the data values, all non-negative).

You are to compute and output the following.

A number and area of each trapezoid.
At the end, display the area under the curve of using the trapezoid method.

Do not use modules, classes, functions, or any other external libraries (other than those in the example). This will be a future extension.

Domain knowledge is the background knowledge that is useful in solving a problem, designing a solution, implementing the solution, etc.

You are provided with the following starter program in file integrate.py.

Do not remove any comment that starts with two hash signs.

Here is the Python code.

## File: integrate.py
## Purpose: Integration using trapezoids
## Author: (your name)
## Help received:
# (add here)
## pseudo-code:
# (add here)

import sys
import json

##:BEGIN ToDo

##:END ToDo

You are to fill in the missing parts of the program according to the work requirements (see above).

In the comments at the top, you are to fill in the author (your name), help received (person and type of help), and pseudo-code parts which are not in the solution (usually provided, but you need to add them). Remove the parentheses too.

Begin solution

Here is a possible solution to the above problem. Note: Once a solution is provided, or the day before the next class, further submissions for this work receive no credit.

## File: integrate.py
## Purpose: Integration using trapezoids
## Author: (your name)
## Help received:
# (add here)
## pseudo-code:
# (add here)

import sys
import json

##:BEGIN ToDo
print("Enter data in required JSON format.")
text1 = sys.stdin.read()
list1 = json.loads(text1)
dx1 = list1[0]
print("")
print("The width of each trapezoid is dx={0:0.2f}".format(dx1))
print("")
print("Trapezoids: y1 y2 area")
y1 = list1[1]
areaAll1 = 0.0
len1 = len(list1)
for i1 in range(2,len1):
	y2 = list1[i1]
	areaOne1 = dx1 * 0.5*(y1+y2)
	areaAll1 += areaOne1
	print("\t{0:d}: {1:0.2f} {2:0.2f} {3:0.2f}".format(i1-1,y1,y2,areaOne1))
	y1 = y2
print("Area under curve: {0:0.2f}".format(areaAll1))
##:END ToDo

End solution

Here are some examples of input and output for the above program code.

Here is an example input from file input1.txt.

[
 1.00, 
 0.20, 0.16, 0.13, 0.11, 0.09, 
 0.07, 0.06, 0.05, 0.04, 0.03, 
 0.03, 0.02, 0.02, 0.01, 0.01, 
 0.01, 0.01, 0.01, 0.01, 0.00, 
 0.00, 0.00, 0.00, 0.00, 0.00
]

For the above example input, here is the expected output.

Enter data in required JSON format.

The width of each trapezoid is dx=1.00

Trapezoids: y1 y2 area
	1: 0.20 0.16 0.18
	2: 0.16 0.13 0.15
	3: 0.13 0.11 0.12
	4: 0.11 0.09 0.10
	5: 0.09 0.07 0.08
	6: 0.07 0.06 0.07
	7: 0.06 0.05 0.06
	8: 0.05 0.04 0.04
	9: 0.04 0.03 0.04
	10: 0.03 0.03 0.03
	11: 0.03 0.02 0.03
	12: 0.02 0.02 0.02
	13: 0.02 0.01 0.01
	14: 0.01 0.01 0.01
	15: 0.01 0.01 0.01
	16: 0.01 0.01 0.01
	17: 0.01 0.01 0.01
	18: 0.01 0.01 0.01
	19: 0.01 0.00 0.01
	20: 0.00 0.00 0.00
	21: 0.00 0.00 0.00
	22: 0.00 0.00 0.00
	23: 0.00 0.00 0.00
	24: 0.00 0.00 0.00
Area under curve: 0.97

Here is an example input from file input2.txt.

[
 0.20, 
 0.02, 0.04, 0.05, 0.08, 0.11, 
 0.15, 0.19, 0.24, 0.29, 0.33, 
 0.37, 0.39, 0.40, 0.39, 0.37, 
 0.33, 0.29, 0.24, 0.19, 0.15, 
 0.11, 0.08, 0.05, 0.04, 0.02
]

For the above example input, here is the expected output.

Enter data in required JSON format.

The width of each trapezoid is dx=0.20

Trapezoids: y1 y2 area
	1: 0.02 0.04 0.01
	2: 0.04 0.05 0.01
	3: 0.05 0.08 0.01
	4: 0.08 0.11 0.02
	5: 0.11 0.15 0.03
	6: 0.15 0.19 0.03
	7: 0.19 0.24 0.04
	8: 0.24 0.29 0.05
	9: 0.29 0.33 0.06
	10: 0.33 0.37 0.07
	11: 0.37 0.39 0.08
	12: 0.39 0.40 0.08
	13: 0.40 0.39 0.08
	14: 0.39 0.37 0.08
	15: 0.37 0.33 0.07
	16: 0.33 0.29 0.06
	17: 0.29 0.24 0.05
	18: 0.24 0.19 0.04
	19: 0.19 0.15 0.03
	20: 0.15 0.11 0.03
	21: 0.11 0.08 0.02
	22: 0.08 0.05 0.01
	23: 0.05 0.04 0.01
	24: 0.04 0.02 0.01
Area under curve: 0.98

A pseudo-code is a false-code that concisely conveys what a much larger piece of physical code is doing. A pseudo-code for this problem might be as follows.

Get the width of each trapezoid and the adjacent y value pairs of data. Set the cumulative area to zero. For each pair of adjacent y value pairs Do Determine the area of that trapezoid. Add that area to the cumulative area. End For Output the area under the curve.

Note: Echoing input and computations along the way are not part of the pseudo-code (unless important to the method).

Note: An order of the y value pairs is not specified. In the code, an order needs to be used - usually the easiest order to use. But the pseudo-code does not specify that order (unless important to the method).

Note: A pseudo-code is required in the program comment header. You can copy-paste this pseudo-code or modify it as might be appropriate.

CS 496 - A1 : Asmt#1: Integration using trapezoids Your grade: _ / 30 [LATE] Late or redo penalty: _ / -30 [SUBMIT] Not submitted properly: _ / -30 [RUN] Does not compile, run-time crash, etc.: _ / -30 [ETHICS] Ethical issues: _ / -30 [HEADER] Header comments not done as required: _ / -15 [STYLE] Inconsistant style or indentation: _ / -15 [CODE] Code guidelines ignored: _ / -30 [XCODE] Code used not yet covered: _ / -15 [REMOVED] Triple slash comments removed: _ / -15 [ADDED] Code added outside of marked areas: _ / -15 [OUTPUT] Functional requirements met: _ / 30 [CREDIT] Extra credit: _ / +6 Comments: