def test_02():
coeff = np.array([1.0])
# ==> f(x) = 1.0
xVals = np.array([0.0])
res = polynomial_horner(xVals, *coeff)
reference = 1.0
assert np.isclose(res, reference)
xVals = np.array([0.25])
res = polynomial_horner(xVals, *coeff)
reference = 1.0
assert np.isclose(res, reference)
xVals = np.array([0.6666667])
res = polynomial_horner(xVals, *coeff)
reference = 1.0
assert np.isclose(res, reference)
xVals = np.array([1.6666667e-9])
res = polynomial_horner(xVals, *coeff)
reference = 1.0
assert np.isclose(res, reference)
xVals = np.array([1.0])
res = polynomial_horner(xVals, *coeff)
reference = 1.0
assert np.isclose(res, reference)
def polynomialCurveFitting(mOrder, Xt, X):
nTest = X.shape[0]
res = np.zeros((len(mOrder), 3))
for m in mOrder:
# create coefficient vector (containing all fit parameters)
w = np.ones((m + 1, ))
# curve fitting
popt, pcov = curve_fit(polynomial_horner, Xt[:, 0], Xt[:, 1], p0=w)
yPredict = polynomial_horner(Xt[:, 0], *popt)
# test data set prediction
yPredictTest = polynomial_horner(X[:, 0], *popt)
# compute sum of squares deviation
sum_of_squares_error = 0.5 * np.sum(np.square(yPredict - Xt[:, 1]))
sum_of_squares_error_test = 0.5 * np.sum(
np.square(yPredictTest - X[:, 1]))
RMS = np.sqrt(2.0 * sum_of_squares_error / N)
RMS_test = np.sqrt(2.0 * sum_of_squares_error_test / nTest)
res[m, 0] = m
res[m, 1] = RMS
res[m, 2] = RMS_test
return res
def test_10():
coeff = np.array([1.0]) # i.e. f(x) = 1.0
yValue_ref = 1.0
yValue = polynomial_horner(0.0, *coeff)
assert np.isclose(yValue, yValue_ref)
yValue_ref = 1.0
yValue = polynomial_horner(-1.23456789, *coeff)
assert np.isclose(yValue, yValue_ref)
yValue_ref = 1.0
yValue = polynomial_horner(1.2e4, *coeff)
assert np.isclose(yValue, yValue_ref)
def test_01():
coeff = np.array([1.0])
# ==> f(x) = 1.0
res = polynomial_horner(0.0, *coeff)
assert np.isclose(res, 1.0)
res = polynomial_horner(0.1, *coeff)
assert np.isclose(res, 1.0)
res = polynomial_horner(-99.1, *coeff)
assert np.isclose(res, 1.0)
res = polynomial_horner(1.0e-3, *coeff)
assert np.isclose(res, 1.0)
def test_06():
nVals = 130
xVals = np.linspace(0.0, 1.0, nVals)
coeff = np.array([1.0])
yVals = polynomial_horner(xVals, *coeff)
assert xVals.shape == yVals.shape
assert np.array_equal(np.ones(nVals), yVals)
def test_05():
nVals = 120
xVals = np.linspace(0.0, 1.0, nVals)
coeff = np.array([0.0, 1.0])
yVals = polynomial_horner(xVals, *coeff)
assert xVals.shape == yVals.shape
assert np.array_equal(xVals, yVals)
def test_09():
# return type test
coeff = np.array([1.0, 1.0]) # i.e. f(x) = 1 + x
# vector in / vector out
xVals = np.array([0.15])
yVals = polynomial_horner(xVals, *coeff)
assert xVals.shape == yVals.shape
assert type(xVals) == type(yVals)
yVals_ref = np.array([1.0 + x for x in xVals])
assert np.array_equal(yVals, yVals_ref)
# scalar in / scalar out
xVals = 0.15
yVals = float(polynomial_horner(xVals, *coeff))
assert type(xVals) == type(yVals)
yVals_ref = 1.0 + 1.0 * 0.15
assert np.array_equal(yVals, yVals_ref)
def test_08():
# single value test
xVals = np.array([0.91264712])
coeff = np.array([0.15, 2.83, 3.5, -0.224, 2.9971])
yVals = polynomial_horner(xVals, *coeff)
assert xVals.shape == yVals.shape
yVals_ref = np.array([0.15 + 2.83 * x + 3.5 * x ** 2 - 0.224 * x ** 3 \
+ 2.9971 * x ** 4 for x in xVals])
assert np.array_equal(yVals, yVals_ref)
def test_07():
nVals = 140
xVals = np.linspace(0.0, 1.0, nVals)
coeff = np.array([1.0, 0.0, 0.5])
yVals = polynomial_horner(xVals, *coeff)
assert xVals.shape == yVals.shape
yVals_ref = np.array([1.0 + 0.5 * x**2 for x in xVals])
assert np.array_equal(yVals, yVals_ref)
def test_04():
coeff = np.array([1.0, 1.0])
# ==> f(x) = 1 + x
xVals = np.array([1.0, 0.0])
reference = np.array([2.0, 1.0])
res = polynomial_horner(xVals, *coeff)
assert np.array_equal(res, reference)
def test_03():
coeff = np.array([1.0])
# ==> f(x) = 1.0
res = polynomial_horner(0.0, *coeff)
reference = 1.0
assert np.isclose(res, reference)
res = polynomial_horner(0.25, *coeff)
reference = 1.0
assert np.isclose(res, reference)
res = polynomial_horner(0.6666667, *coeff)
reference = 1.0
assert np.isclose(res, reference)
res = polynomial_horner(1.6666667e-9, *coeff)
reference = 1.0
assert np.isclose(res, reference)
res = polynomial_horner(1.0, *coeff)
reference = 1.0
assert np.isclose(res, reference)
def polynomialCurveFitting(mOrder, Xt):
res = np.zeros((len(mOrder), 2))
for m in mOrder:
# create coefficient vector (containing all fit parameters)
w = np.ones((m + 1, ))
# curve fitting
popt, pcov = curve_fit(polynomial_horner, Xt[:, 0], Xt[:, 1], p0=w)
yPredict = polynomial_horner(Xt[:, 0], *popt)
# compute sum of squares deviation
sum_of_squares_error = 0.5 * np.sum(np.square(yPredict - Xt[:, 1]))
RMS = np.sqrt(2.0 * sum_of_squares_error / N)
res[m, 0] = m
res[m, 1] = RMS
return res
outname = f'prml_ch_01_figure_1.2_training_data_PRNG-seed_{seedValue}.txt'
np.savetxt(os.path.join(RAWDIR, outname), Xt, fmt = '%.8f')
######################################################################################
######################################################################################
# polynomial least squares fitting
m = 3
w = polyLeastSquares(m, Xt)
print("fitted weights =", w)
######################################################################################
######################################################################################
# create fitted model
nModelPoints = 800
xVals = np.linspace(0.0, 1.0, nModelPoints)
yVals = polynomial_horner(xVals, *w)
Xm = np.zeros((nModelPoints, 2))
Xm[:, 0] = xVals
Xm[:, 1] = yVals
######################################################################################
# file i/o
outname = f'prml_ch_01_figure_1.2_training_data_PRNG-seed_{seedValue}_m_{m}_fit.txt'
np.savetxt(os.path.join(RAWDIR, outname), Xm, fmt = '%.8f')
######################################################################################
######################################################################################
# call the plotting function
outname = f'prml_ch_01_figure_1.4_PRNG-seed_{seedValue}_m_{m}_fit_polynomial_leastSq'
######################################################################################
# polynomial curve fitting (learning the model)
m_order = np.arange(0, 10, 1).astype('int')
res = np.zeros((len(m_order), 3))
for m in m_order:
# create coefficient vector (containing all fit parameters)
w = np.ones((m + 1, ))
# curve fitting
popt, pcov = curve_fit(polynomial_horner, Xt[:, 0], Xt[:, 1], p0=w)
yPredict = polynomial_horner(Xt[:, 0], *popt)
# test data set prediction
yPredictTest = polynomial_horner(X[:, 0], *popt)
# compute sum of squares deviation
sum_of_squares_error = 0.5 * np.sum(np.square(yPredict - Xt[:, 1]))
sum_of_squares_error_test = 0.5 * np.sum(
np.square(yPredictTest - X[:, 1]))
RMS = np.sqrt(2.0 * sum_of_squares_error / n_train)
RMS_test = np.sqrt(2.0 * sum_of_squares_error_test / n_test)
res[m, 0] = m
res[m, 1] = RMS
######################################################################################
# file i/o
outname = f'figure_1.6_training_data_N_{n_train}_PRNG_seed_{seed_value}.txt'
np.savetxt(os.path.join(RAWDIR, outname), Xt, fmt = '%.8f')
######################################################################################
######################################################################################
# polynomial curve fitting (learning the model)
m = 9
w = np.ones((m + 1,))
popt, pcov = curve_fit(polynomial_horner, Xt[:, 0], Xt[:, 1], p0 = w)
# create fitted model
n_modelpoints = 800
xVals = np.linspace(0.0, 1.0, n_modelpoints)
yVals = polynomial_horner(xVals, *popt)
Xm = np.zeros((n_modelpoints, 2))
Xm[:, 0] = xVals
Xm[:, 1] = yVals
######################################################################################
# file i/o
outname = f'figure_1.6_fitted_model_N_{n_train}_PRNG_seed_{seed_value}.txt'
np.savetxt(os.path.join(RAWDIR, outname), X, fmt = '%.8f')
######################################################################################
######################################################################################
# call the plotting function
outname = f'figure_1.6_N_{n_train}_PRNG_seed_{seed_value}'
outname += '_Python_' + platform.python_version() + \
