def test_adding_some_values(self):
columns = 2
rows = 3
matrix = Matrix(rows, columns)
matrix.setValue(2, 1, 2)
matrix.setValue(3, 2, 6)
self.assertEqual(2, matrix.getValue(2, 1))
self.assertEqual(6, matrix.getValue(3, 2))
class Spline():
def __init__(self, xValues, yValues, firstDerivate, lastDerivate):
assert len(xValues) == len(yValues)
self.xValues = [float(value) for value in xValues]
self.yValues = yValues
self.firstDerivate = firstDerivate
self.lastDerivate = lastDerivate
self.length = len(xValues)
self.calculate_lambdas_and_mys()
self.calculate_ds()
self.create_matrix()
#self.cancel_out_bottom_row()
self.calculate_new_lambdas()
self.calculate_new_ds()
self.calculate_Mis()
self.calculate_coefficients()
def calculate_lambdas_and_mys(self):
self.calculate_lambdas()
self.mys = [False]
for l in [1 - l for l in self.lambdas[1:]]:
self.mys.append(l)
self.mys.append(1) # myn is always 1 (capter 3 page 33)
def calculate_lambdas(self):
self.lambdas = [1] # lambda0 is always 1 (capter 3 page 33)
for i in range(1, self.length - 1):
self.lambdas.append((self.xValues[i + 1] - self.xValues[i]) /
(self.xValues[i + 1] - self.xValues[i - 1])
)
def calculate_ds(self):
xValues = self.xValues
yValues = self.yValues
self.ds = []
self.ds.append(self.calculate_d0())
for i in range(1, self.length -1):
firstFraction = 6 / (xValues[i + 1] - xValues[i - 1])
secondFraction = ((yValues[i + 1] - yValues[i]) /
(xValues[i + 1] - xValues[i])
)
thirdFraction = ((yValues[i] - yValues[i - 1]) /
(xValues[i] - xValues[i - 1])
)
self.ds.append(firstFraction * (secondFraction - thirdFraction))
self.ds.append(self.calculate_dn())
def calculate_d0(self):
xValues = self.xValues
yValues = self.yValues
return 6 / (xValues[1] - xValues[0]) * ((yValues[1] - yValues[0]) /
(xValues[1] - xValues[0])
-self.firstDerivate)
def calculate_dn(self):
xValues = self.xValues
yValues = self.yValues
return 6 / (xValues[-1] - xValues[-2]) * (self.lastDerivate -
(yValues[-1] - yValues[-2]) /
(xValues[-1] - xValues[-2])
)
def create_matrix(self):
self.matrix = Matrix(self.length, self.length)
#2s
for i in range(1, self.matrix.rowCount + 1):
self.matrix.setValue(i, i, 2)
#lambdas
for i in range(1, self.matrix.rowCount):
self.matrix.setValue(i, i + 1, self.lambdas[i - 1])
#µs
for i in range(2, self.matrix.rowCount + 1):
self.matrix.setValue(i, i - 1, self.mys[i -1])
def calculate_new_lambdas(self):
self.new_lambdas = []
self.new_lambdas.append(self.lambdas[0] / 2.0)
for i in range(1, len(self.lambdas)):
self.new_lambdas.append(self.lambdas[i] /
(2 - self.new_lambdas[i -1] * self.mys[i])
)
def calculate_new_ds(self):
self.new_ds = []
self.new_ds.append(self.ds[0] / 2.0)
for i in range(1, len(self.ds)):
self.new_ds.append((self.ds[i] - self.new_ds[i -1] * self.mys[i])/
(2 - self.new_lambdas[i -1] * self.mys[i])
)
def calculate_Mis(self):
self.Mis = [0] * self.length
self.Mis[-1] = self.new_ds[-1]
for i in range(self.length - 2, -1, -1):
self.Mis[i] = (self.new_ds[i]
- self.new_lambdas[i] * self.Mis[i + 1]
)
def calculate_coefficients(self):
self.coefficients = []
for i in range(0, self.length - 1):
self.coefficients.append([])
self.coefficients[i].append(self.yValues[i])
self.coefficients[i].append(-self.Mis[i] * ((self.xValues[i+1] - self.xValues[i])/2) + ((self.yValues[i+1] - self.yValues[i])/(self.xValues[i+1] - self.xValues[i])) - ((self.Mis[i+1] - self.Mis[i]) / 6) * (self.xValues[i+1] - self.xValues[i]))
self.coefficients[i].append(self.Mis[i]/2)
self.coefficients[i].append((self.Mis[i+1]-self.Mis[i])/(6*(self.xValues[i+1] - self.xValues[i])))