def find_idx_with_nonzero(self, coeficient_idx, start_idx=0):
"""Find the first equation index where coeficient "coeficient_idx" is not zero.
Args:
coeficient_idx(int): The index of the coefficient to check.
start_idx(int): Start the search in this row of the system.
Returns:
bool: Returns False if there is not an equation in this system
with coefficient "coeficient_idx" different than zero.
int: Returns the index of the equation with the first non-zero
coefficient in variable "coeficient_idx". Default value is
zero.
Raises:
IndexError: If start_idx is out of the bounds of self.planes array.
"""
for i in range(start_idx, len(self.planes)):
row_var_value = self.planes[i].normal_vector[coeficient_idx]
row_var_value = MyDecimal(row_var_value)
if(not row_var_value.is_near_zero()):
return i
return False
def compute_triangular_form(self):
"""This function will return a different copy of this system in triangular form.
Returns:
LinearSystem: A new system equals to this one in triangular form.
"""
system = deepcopy(self)
n = system.dimension
j= 0
for i,_ in enumerate(system.planes):
while j < n:
c = MyDecimal(system.planes[i].normal_vector[j])
if c.is_near_zero():
row_with_nonzero = system.find_idx_with_nonzero(j, i)
if row_with_nonzero:
system.swap_rows(i, row_with_nonzero)
else:
j += 1
continue;
system.clear_var(i,j)
j += 1
break;
return system
def var_count(self):
"""Returns a count of the number of variables present in the equation.
Returns:
int: Count of variables in this plane's equation.
"""
var_count = 0;
for _, coefficient in enumerate(self.normal_vector):
var_coefficient = MyDecimal(coefficient)
if(not var_coefficient.is_near_zero()):
var_count += 1
return var_count
def solve(self):
"""Returns the solution of this system of equation.
Returns:
vector.Vector: If there is an unique solution, will return a vector
representing the x,y,z points of the solution.
bool: False if there is no solution and True if there are many
solutions.
"""
rref = self.compute_rref()
unique_solution = ['0','0','0']
first_nonzeros = rref.indices_of_first_nonzero_terms_in_each_row()
response = None
one_variable_alone = False
single_solution = True
for i,plane in enumerate(rref.planes):
pivot_var_idx = first_nonzeros[i]
constant_term = MyDecimal(plane.constant_term)
if(pivot_var_idx < 0 and not constant_term.is_near_zero() ):
return False
number_of_vars = rref[i].var_count()
if(number_of_vars == 1):
one_variable_alone = True
unique_solution[pivot_var_idx] = plane.constant_term/plane.normal_vector[pivot_var_idx]
elif(number_of_vars > 1):
single_solution = False
if(one_variable_alone and not single_solution):
response = False
elif(not one_variable_alone and not single_solution):
response = True
else:
response = unique_solution
return response
