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New linear algebra algorithm (#1122)

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* Added new algorithm which takes points as an input and outputs a polynom connecting them

* Rename Python-Polynom-for-points.py to python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Update python-polynom-for-points.py

* Add doctests and run thru psf/black
This commit is contained in:
Niclas Dern 2019-08-12 09:13:57 +02:00 committed by Christian Clauss
parent 55cea57ffa
commit 158b319d22
1 changed files with 130 additions and 0 deletions
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linear_algebra/src/python-polynom-for-points.py Normal file
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def points_to_polynomial(coordinates):
"""
coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
number of points you want to use
>>> print(points_to_polynomial([]))
The program cannot work out a fitting polynomial.
>>> print(points_to_polynomial([[]]))
The program cannot work out a fitting polynomial.
>>> print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*0.0
>>> print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*1.0
>>> print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
f(x)=x^2*0.0+x^1*-0.0+x^0*3.0
>>> print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
f(x)=x^2*0.0+x^1*1.0+x^0*0.0
>>> print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
f(x)=x^2*1.0+x^1*-0.0+x^0*0.0
>>> print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
f(x)=x^2*1.0+x^1*-0.0+x^0*2.0
>>> print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0
>>> print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
f(x)=x^2*5.0+x^1*-18.0+x^0*18.0
"""
try:
check = 1
more_check = 0
d = coordinates[0][0]
for j in range(len(coordinates)):
if j == 0:
continue
if d == coordinates[j][0]:
more_check += 1
solved = "x=" + str(coordinates[j][0])
if more_check == len(coordinates) - 1:
check = 2
break
elif more_check > 0 and more_check != len(coordinates) - 1:
check = 3
else:
check = 1
if len(coordinates) == 1 and coordinates[0][0] == 0:
check = 2
solved = "x=0"
except Exception:
check = 3
x = len(coordinates)
if check == 1:
count_of_line = 0
matrix = []
# put the x and x to the power values in a matrix
while count_of_line < x:
count_in_line = 0
a = coordinates[count_of_line][0]
count_line = []
while count_in_line < x:
count_line.append(a ** (x - (count_in_line + 1)))
count_in_line += 1
matrix.append(count_line)
count_of_line += 1
count_of_line = 0
# put the y values into a vector
vector = []
while count_of_line < x:
count_in_line = 0
vector.append(coordinates[count_of_line][1])
count_of_line += 1
count = 0
while count < x:
zahlen = 0
while zahlen < x:
if count == zahlen:
zahlen += 1
if zahlen == x:
break
bruch = (matrix[zahlen][count]) / (matrix[count][count])
for counting_columns, item in enumerate(matrix[count]):
# manipulating all the values in the matrix
matrix[zahlen][counting_columns] -= item * bruch
# manipulating the values in the vector
vector[zahlen] -= vector[count] * bruch
zahlen += 1
count += 1
count = 0
# make solutions
solution = []
while count < x:
solution.append(vector[count] / matrix[count][count])
count += 1
count = 0
solved = "f(x)="
while count < x:
remove_e = str(solution[count]).split("E")
if len(remove_e) > 1:
solution[count] = remove_e[0] + "*10^" + remove_e[1]
solved += "x^" + str(x - (count + 1)) + "*" + str(solution[count])
if count + 1 != x:
solved += "+"
count += 1
return solved
elif check == 2:
return solved
else:
return "The program cannot work out a fitting polynomial."
if __name__ == "__main__":
print(points_to_polynomial([]))
print(points_to_polynomial([[]]))
print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))