determinant.py

def determinant(A, output=0):
	'''
	The function return determinant of a square matrix using full recursion.
	output=0 - etablish a output at each recursion level.
	'''
	# Store indices in list for row referencing
	index=list(range(len(A)))

	# If at 2 x 2 submatrices recursive calls end
	if len(A)==2 and len(A[0])==2:
		det=A[0][0]*A[1][1] - A[0][1]*A[1][0]
		return det
	# Define submatrix for focus column and call this function
	for focuscolumn in index:
		addA=A
		addA=addA[1:]
		height=len(addA)
		for item in range(height):
			addA[item]=addA[item][0:focuscolumn]+addA[item][focuscolumn+1:]
		sign=(-1)**(focuscolumn % 2)
		subDeterminant=determinant(addA)
		# Output: all from recursion
		output=output+sign*A[0][focuscolumn]*subDeterminant
	return output

def det(A):
	'''
	Create an upper triangle matrix using row operations.
	Then product of diagonal elements is the determinant.
	'''
	# Establish n parametr size matrix A
	# additional A
	n=len(A)
	addA=A
	# Rows ops on A to get in upper triangle form
	for focusDiagonal in range(n):
		# If diagonal is zero components
		if addA[focusDiagonal][focusDiagonal]==0:
			# change to approx zero
			addA[focusDiagonal][focusDiagonal]=1.0e-16
		for i in range(focusDiagonal+1,n):
			# Current row
			numberCurrentRow=addA[i][focusDiagonal]/addA[focusDiagonal][focusDiagonal]
			for j in range(n):
				addA[i][j]=addA[i][j]-numberCurrentRow*addA[focusDiagonal][j]
	# Once additional A is in upper triangle form product of diagonals is determinant
	product=1.000
	for i in range(n):
		product=product*addA[i][i]
	return product


if __name__=="__main__":
	None