def cholesky(A,b):
answer = {}
answer["error"] = False
dict_A = {}
dict_L = {}
dict_U = {}
dict_X = {}
try:
A,b = parser_input_helper.parse_input(A,b)
dict_A[0] = parser_input_helper.rebuild_matrix(copy.deepcopy(A))
if np.linalg.det(A) == 0:
raise Exception("Derterminant can not be 0")
n = len(A)
L = [[0.0 for x in range(n)]
for y in range(n)]
U = [[0.0 for x in range(n)]
for y in range(n)]
L = np.array(L)
U = np.array(U)
step = 1
for k in range(n):
sum1 = 0.0
for i in range(n):
sum1 += L[k][i] * U[i][k]
L[k][k] = math.sqrt(A[k][k] - sum1)
U[k][k] = L[k][k]
for i in range(k + 1, n):
sum2 = 0.0
for p in range(k):
sum2 += L[i][p] * U[p][k]
L[i][k] = (A[i][k] - sum2) / U[k][k]
for j in range(k + 1, n):
sum3 = 0.0
for p in range(k):
sum3 += L[k][p] * U [p][j]
U[k][j] = (A[k][j] - sum3) / L[k][k]
# print("Step 0")
# npA = np.array(A)
# dict_A[0] = rebuild_matrix(copy.deepcopy(npA))
# print(dict_A[0])
dict_L[step] = parser_input_helper.rebuild_matrix(copy.deepcopy(L))
dict_U[step] = parser_input_helper.rebuild_matrix(copy.deepcopy(U))
step += 1
z = np.array(matrix_function.soltion(L,b),float)
x = matrix_function.soltion(U,z)
except ValueError as valueError:
answer["error"] = "A complex operation was encounter while running the method"
except BaseException as e:
answer["error"] = str(e)
print(json.dumps(answer))
print(json.dumps(dict_A))
print(json.dumps(dict_L))
print(json.dumps(dict_U))
try:
dict_X["solution"] = list(x)
print(json.dumps(dict_X))
except BaseException:
pass
def crout(A, b):
try:
A, b, matrix = mf.mix_matrix(A, b)
A = np.array(A)
b = np.array(b)
n = len(A)
L = np.eye(n)
U = np.eye(n)
dic_a = {}
dic_l = {}
dic_u = {}
dic_a[0] = np.array(A)
dic_l[0] = np.array(L)
dic_u[0] = np.array(U)
for i in range(n):
for k in range(i, n):
suma = 0
for j in range(i):
suma += (L[k][j] * U[j][i])
L[k][i] = A[k][i] - suma
for k in range(i, n):
if (i == k):
U[i][i] = 1
else:
suma = 0
for j in range(i):
suma += (L[i][j] * U[j][k])
U[i][k] = ((A[i][k] - suma) / L[i][i])
dic_a[i + 1] = np.array(A)
dic_l[i + 1] = np.array(L)
dic_u[i + 1] = np.array(U)
z = np.array(mf.soltion(L, b), float)
x = mf.soltion(U, z)
sol = []
for i in range(0, len(x)):
sol.append(float(x[i]))
solution = {}
solution[0] = sol
except BaseException as e:
print("Error" + str(e))
exit(1)
dic_a = mf.rebuild_matrix(dic_a)
dic_l = mf.rebuild_matrix(dic_l)
dic_u = mf.rebuild_matrix(dic_u)
print(json.dumps(solution))
print(json.dumps(dic_a))
print(json.dumps(dic_l))
print(json.dumps(dic_u))
def doolittle(A, b, size):
size = int(size)
A, b, matrix = matrix_function.mix_matrix(A, b)
A = np.array(A)
if matrix_function.determinant(A):
try:
b = np.array(b)
L = np.eye(size)
U = np.eye(size)
dictL = {}
dictU = {}
count = 0
dictL[count] = copy.deepcopy(L)
dictU[count] = copy.deepcopy(U)
for i in range(size):
for k in range(i, size):
suma = 0
for j in range(i):
suma += (L[i][j] * U[j][k])
U[i][k] = A[i][k] - suma
for k in range(i, size):
if (i == k):
L[i][i] = 1
else:
suma = 0
for j in range(i):
suma += (L[k][j] * U[j][i])
L[k][i] = ((A[k][i] - suma) / U[i][i])
count = count + 1
dictL[count] = copy.deepcopy(L)
dictU[count] = copy.deepcopy(U)
z = np.array(matrix_function.soltion(L, b), float)
x = matrix_function.soltion(U, z)
sol = []
for i in range(0, len(x)):
sol.append(float(x[i]))
solution = {}
solution[0] = sol
dictL = matrix_function.rebuild_matrix(dictL)
dictU = matrix_function.rebuild_matrix(dictU)
print(json.dumps(solution))
print(json.dumps(dictL))
print(json.dumps(dictU))
except:
results = {}
results[0] = "Error Divide by 0"
print(json.dumps(results))
else:
results = {}
results[0] = "Error The matrix determinant is 0"
print(json.dumps(results))
def initialData(A,b):
results = {}
try:
A,b,matrix2 = matrix_function.mix_matrix(A,b)
if (matrix_function.determinant(A) == True):
matrix2 = np.array(matrix2)
A,B,dic = SteppedPartialPivot(matrix2)
dic = matrix_function.rebuild_matrix(dic)
print(json.dumps(dic))
x = matrix_function.soltion(A,B)
x = x.tolist()
xSolution = {}
xSolution[0] = x
print(json.dumps(xSolution))
else:
results[0] = "Error the matrix determinant is 0"
print(json.dumps(results))
except BaseException as e:
results[0] = "Error" + str(e)
print(json.dumps(results))
def vandermonde(X, Y):
dic = {}
X = X.replace('[', '').replace(']', '').split(',')
Y = Y.replace('[', '').replace(']', '').split(',')
X = np.array(X, dtype=float)
Y = np.array(Y, dtype=float)
validate = False
unique_elements, counts_elements = np.unique(X, return_counts=True)
for i in counts_elements:
if(i>1):
validate=True
break
if (validate):
dic[0]="Error: there are equal points in the vector X"
else:
n = len(X)
A = np.zeros((n,n))
for i in range(n):
for j in range(n):
A[j][i] = X[j]**(n-(i+1))
coef = np.array(mf.soltion(A, Y.T))
dic["v_matrix"] = np.array(A)
dic = mf.rebuild_matrix(dic)
dic["coef"] = str(coef)
polynomial = ""
for i in range(len(coef)):
if coef[i][0] != '-' and i != 0:
polynomial += "+"
polynomial += coef[i]
if(i != len(coef)-1):
polynomial += "x^"+str((len(coef)-(i+1)))
dic["polynomial"] = polynomial
print(json.dumps(dic))
def gaussianTridiagonalMatrixMethod(a, b, c, d):
dic = {}
a = a.replace('[', '').replace(']', '').split(',')
b = b.replace('[', '').replace(']', '').split(',')
c = c.replace('[', '').replace(']', '').split(',')
d = d.replace('[', '').replace(']', '').split(',')
a = np.array(a, dtype=float)
b = np.array(b, dtype=float)
c = np.array(c, dtype=float)
d = np.array(d, dtype=float)
validate = False
for i in b:
if (i==0):
validate = True
break
if (validate):
dic[0]="Error: There are points equals to zero in vector b"
else:
n = len(d) # número de filas
matrix = np.zeros((n,n))
matrix[0][0] = b[0]
for i in range(n-1):
m = a[i]/b[i]
matrix[i+1][i+1] = b[i+1] = b[i+1] - (m*c[i])
matrix[i][i+1] = c[i]
d[i+1] = d[i+1] - (m*d[i])
dic[i]=np.array(matrix)
d = np.array(d)
dic[n-1] = np.array(matrix)
dic = matrix_function.rebuild_matrix(dic)
x = matrix_function.soltion(matrix, d)
dic["x"]=x.tolist()
print(json.dumps(dic))
def solve_matrix(a, b, matrix_type):
try:
solution_dic = {}
a, b, matrix = matrix_function.mix_matrix(a, b)
if (matrix_function.determinant(a)):
if (matrix_type == 'S'):
a, b, dic = simple_gaussian_method.simpleGaussianMethod(matrix)
elif (matrix_type == 'P'):
a, b, dic = partial_gaussian_method.partialGaussianMethod(
matrix)
elif (matrix_type == 'T'):
a, b, dic, movement = total_gaussian_method.totalGaussianMethod(
matrix)
elif (matrix_type == 'LUS'): #LU_simple
l, u, dic, dic_l, dic_u = lu_simple_method.luSimpleMethod(a)
elif (matrix_type == 'LUP'): #partial_lu
l, u, pb, dic, dic_l, dic_u, dic_p = partial_lu.partial_lu(
a, b)
else:
print("function type doesn't exist")
if (matrix_type == 'LUP'):
z = np.array(matrix_function.soltion(l, pb), float)
x = matrix_function.soltion(u, z)
dic_l = matrix_function.rebuild_matrix(dic_l)
dic_u = matrix_function.rebuild_matrix(dic_u)
dic_p = matrix_function.rebuild_matrix(dic_p)
elif (matrix_type == 'LUS'):
z = np.array(matrix_function.soltion(l, b), float)
x = matrix_function.soltion(u, z)
dic_l = matrix_function.rebuild_matrix(dic_l)
dic_u = matrix_function.rebuild_matrix(dic_u)
#dic["dic_l"] = dic_l
#dic["dic_u"] = dic_u
else:
x = matrix_function.soltion(a, b)
dic = matrix_function.rebuild_matrix(dic)
if (matrix_type == 'T'):
x = matrix_function.sort(x, movement)
dic["x"] = x.tolist()
solution_dic["dic"] = dic
solution_dic["x"] = x
print(json.dumps(dic))
if (matrix_type == 'LUS'):
print(json.dumps(dic_l))
print(json.dumps(dic_u))
elif (matrix_type == 'LUP'):
print(json.dumps(dic_l))
print(json.dumps(dic_u))
print(json.dumps(dic_p))
else:
dic = {}
raise Exception("Error function determinant is equals to 0")
except BaseException as e:
dic = {}
dic[0] = "Error" + str(e)
print(json.dumps(dic))
exit(1)
def linealSpline(data, n):
results = {}
data = data.replace('[', '').replace(']', '').split(',')
x = []
y = []
validate = False
validate2 = False
try:
for i in range(0, len(data)):
if i < int(n):
x.append(float(data[i]))
else:
y.append(float(data[i]))
for i in range(len(x)):
if (x.count(x[i]) > 1):
validate = True
break
validate2 = True
except:
results[0] = "Error in initial data"
if validate == True:
results[0] = "Error X coordinates contain a duplicate"
elif validate2 == True:
xValor = sm.symbols('x')
sizeX = len(x)
sizeY = len(y)
if sizeX != sizeY:
results[
0] = "Error the size of the x vector is different to y vector"
else:
try:
m = 2 * (sizeX - 1)
A = np.eye(m)
for i in range(0, m):
A[i][i] = 0
counter = 0
counterRows = 0
b = []
for i in range(0, sizeX):
vec_x = x[i]
A[i][counter] = vec_x
A[i][counter + 1] = 1
counter = counter + 2
if i == 0:
counter = 0
b.append(y[i])
counterRows = counterRows + 1
counter = 0
for i in range(1, len(x) - 1):
A[counterRows][counter] = x[i]
A[counterRows][counter + 1] = 1
A[counterRows][counter + 2] = -(x[i])
A[counterRows][counter + 3] = -1
counter = counter + 2
counterRows = counterRows + 1
b.append(0)
array = []
for i in range(0, m):
array2 = []
for j in range(0, m):
array2.append(A[i][j])
array.append(array2)
A = str(array).replace(" ", "")
b = str(b)
a, b, matrix = matrix_function.mix_matrix(A, b)
a, b, dic, movement = total_gaussian_method.totalGaussianMethod(
matrix)
x = matrix_function.soltion(a, b)
x = matrix_function.sort(x, movement)
aux = []
for i in range(0, len(x)):
aux.append(x[i])
coefficient = []
counter = 0
counterAux = 0
while counter < len(aux) - 1:
i = []
i.append(aux[counter])
i.append(aux[counter + 1])
counter = counter + 2
results[counterAux] = i
counterAux = counterAux + 1
coefficient.append(i)
plotter = []
for i in range(len(coefficient)):
plotter.append(
str((float(coefficient[i][0]) * xValor) +
float(coefficient[i][1])))
results["plotter"] = plotter
except:
results[0] = "Error to found a solution to x array"
data = json.dumps(results)
print(data)