def test_list_pseudo_inverse():
"Test of the pseudo-inverse"
x = ufloat((1, 0.1))
y = ufloat((2, 0.1))
mat = unumpy.matrix([[x, x], [y, 0]])
# Internal consistency: the inverse and the pseudo-inverse yield
# the same result on square matrices:
assert matrices_close(mat.I, unumpy.ulinalg.pinv(mat), 1e-4)
assert matrices_close(
unumpy.ulinalg.inv(mat),
# Support for the optional pinv argument is
# tested:
unumpy.ulinalg.pinv(mat, 1e-15),
1e-4)
# Non-square matrices:
x = ufloat((1, 0.1))
y = ufloat((2, 0.1))
mat1 = unumpy.matrix([[x, y]]) # "Long" matrix
mat2 = unumpy.matrix([[x, y], [1, 3 + x], [y, 2 * x]]) # "Tall" matrix
# Internal consistency:
assert matrices_close(mat1.I, unumpy.ulinalg.pinv(mat1, 1e-10))
assert matrices_close(mat2.I, unumpy.ulinalg.pinv(mat2, 1e-8))
def test_list_pseudo_inverse():
"Test of the pseudo-inverse"
x = ufloat((1, 0.1))
y = ufloat((2, 0.1))
mat = unumpy.matrix([[x, x], [y, 0]])
# Internal consistency: the inverse and the pseudo-inverse yield
# the same result on square matrices:
assert matrices_close(mat.I, unumpy.ulinalg.pinv(mat), 1e-4)
assert matrices_close(
unumpy.ulinalg.inv(mat),
# Support for the optional pinv argument is
# tested:
unumpy.ulinalg.pinv(mat, 1e-15),
1e-4,
)
# Non-square matrices:
x = ufloat((1, 0.1))
y = ufloat((2, 0.1))
mat1 = unumpy.matrix([[x, y]]) # "Long" matrix
mat2 = unumpy.matrix([[x, y], [1, 3 + x], [y, 2 * x]]) # "Tall" matrix
# Internal consistency:
assert matrices_close(mat1.I, unumpy.ulinalg.pinv(mat1, 1e-10))
assert matrices_close(mat2.I, unumpy.ulinalg.pinv(mat2, 1e-8))
def test_pseudo_inverse():
"Tests of the pseudo-inverse"
# Numerical version of the pseudo-inverse:
pinv_num = core.wrap_array_func(numpy.linalg.pinv)
##########
# Full rank rectangular matrix:
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))],
[1, -3.1]])
# Numerical and package (analytical) pseudo-inverses: they must be
# the same:
rcond = 1e-8 # Test of the second argument to pinv()
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
##########
# Example with a non-full rank rectangular matrix:
vector = [ufloat((10, 1)), -3.1, 11]
m = unumpy.matrix([vector, vector])
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
##########
# Example with a non-full-rank square matrix:
m = unumpy.matrix([[ufloat((10, 1)), 0], [3, 0]])
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
def test_pseudo_inverse():
"Tests of the pseudo-inverse"
# Numerical version of the pseudo-inverse:
pinv_num = core.wrap_array_func(numpy.linalg.pinv)
##########
# Full rank rectangular matrix:
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))],
[1, -3.1]])
# Numerical and package (analytical) pseudo-inverses: they must be
# the same:
rcond = 1e-8 # Test of the second argument to pinv()
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
##########
# Example with a non-full rank rectangular matrix:
vector = [ufloat((10, 1)), -3.1, 11]
m = unumpy.matrix([vector, vector])
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
##########
# Example with a non-full-rank square matrix:
m = unumpy.matrix([[ufloat((10, 1)), 0], [3, 0]])
m_pinv_num = pinv_num(m, rcond)
m_pinv_package = core._pinv(m, rcond)
assert matrices_close(m_pinv_num, m_pinv_package)
def test_wrap_array_func():
'''
Test of numpy.wrap_array_func(), with optional arguments and
keyword arguments.
'''
# Function that works with numbers with uncertainties in mat (if
# mat is an uncertainties.unumpy.matrix):
def f_unc(mat, *args, **kwargs):
return mat.I + args[0] * kwargs['factor']
# Test with optional arguments and keyword arguments:
def f(mat, *args, **kwargs):
# This function is wrapped: it should only be called with pure
# numbers:
assert not any(isinstance(v, uncert_core.UFloat) for v in mat.flat)
return f_unc(mat, *args, **kwargs)
# Wrapped function:
f_wrapped = core.wrap_array_func(f)
##########
# Full rank rectangular matrix:
m = unumpy.matrix([[ufloat(10, 1), -3.1], [0, ufloat(3, 0)], [1, -3.1]])
# Numerical and package (analytical) pseudo-inverses: they must be
# the same:
m_f_wrapped = f_wrapped(m, 2, factor=10)
m_f_unc = f_unc(m, 2, factor=10)
assert arrays_close(m_f_wrapped, m_f_unc)
def inertia_components(jay, beta):
'''Returns the 2D orthogonal inertia tensor.
When at least three moments of inertia and their axes orientations are
known relative to a common inertial frame of a planar object, the orthoganl
moments of inertia relative the frame are computed.
Parameters
----------
jay : ndarray, shape(n,)
An array of at least three moments of inertia. (n >= 3)
beta : ndarray, shape(n,)
An array of orientation angles corresponding to the moments of inertia
in jay.
Returns
-------
eye : ndarray, shape(3,)
Ixx, Ixz, Izz
'''
sb = unumpy.sin(beta)
cb = unumpy.cos(beta)
betaMat = unumpy.matrix(np.vstack((cb**2, -2 * sb * cb, sb**2)).T)
eye = np.squeeze(np.asarray(np.dot(betaMat.I, jay)))
return eye
def test_wrap_array_func():
'''
Test of numpy.wrap_array_func(), with optional arguments and
keyword arguments.
'''
# Function that works with numbers with uncertainties in mat (if
# mat is an uncertainties.unumpy.matrix):
def f_unc(mat, *args, **kwargs):
return mat.I + args[0]*kwargs['factor']
# Test with optional arguments and keyword arguments:
def f(mat, *args, **kwargs):
# This function is wrapped: it should only be called with pure
# numbers:
assert not any(isinstance(v, uncert_core.UFloat) for v in mat.flat)
return f_unc(mat, *args, **kwargs)
# Wrapped function:
f_wrapped = core.wrap_array_func(f)
##########
# Full rank rectangular matrix:
m = unumpy.matrix([[ufloat(10, 1), -3.1],
[0, ufloat(3, 0)],
[1, -3.1]])
# Numerical and package (analytical) pseudo-inverses: they must be
# the same:
m_f_wrapped = f_wrapped(m, 2, factor=10)
m_f_unc = f_unc(m, 2, factor=10)
assert arrays_close(m_f_wrapped, m_f_unc)
def calculation_prutoky_ze_zony(N, ridici_index, a, P, V, W):
P_zaloha = P
P = P[:-1, :]
k = np.full(len(a), np.nan, dtype=object)
pocet_neznamych = len(k)
index1 = [ridici_index] * N
index2 = []
for j in np.arange(1, N + 2):
if j != ridici_index:
index2.append(j)
#indexovani prutoku a jejich poloha v vektoru reseni, tj. v podstate takova funkce, mapovani
prutoky_indexy = pd.DataFrame(np.array([index1, index2]).T,
index=np.arange(1, pocet_neznamych + 1),
columns=['vychozi zona', 'cilova zona'])
Z = pd.DataFrame(np.zeros((N, pocet_neznamych)),
columns=np.arange(1, pocet_neznamych + 1),
dtype=object)
Z.index += 1
for m in np.arange(1, pocet_neznamych + 1):
i, j = prutoky_indexy.loc[m]
if i != j:
Z.loc[i, m] = -a[i - 1]
if j <= N:
Z.loc[j, m] = a[i - 1]
X = Z
# print(det(unumpy.nominal_values(X)))
l = ridici_index - 1
y = np.full(len(a), np.nan, dtype=object)
for i in np.arange(len(y)):
if i == l:
y[i] = -sum(a[:] * P[:, i]) + prem_kons_Rn * a[i] * V[i] - W[i]
else:
# y[i]=a[i]*sum(P[i, :])-sum(a[:l]*P[:l, i])-sum(a[l+1:]*P[l+1:, i])+prem_kons_Rn*a[i]*V[i]-W[i]
y[i] = a[i] * sum(P[i, :]) - sum(
a[:] *
P[:, i]) + a[l] * P[l, i] + prem_kons_Rn * a[i] * V[i] - W[i]
# X=unumpy.matrix(X)
# X_inverse=X.I
# prutoky1=np.dot(X_inverse,y)
pom = unumpy.matrix(np.dot(X.T, X))
I2 = pom.I
prutoky = np.dot(I2, np.dot(X.T, y)) #toto je s nejistotami
prutoky = np.array(prutoky)[0]
# res_ols=sm.OLS(unumpy.nominal_values(y), unumpy.nominal_values(X)).fit()
# print(res_ols.summary())
# vysledek=solve(unumpy.nominal_values(X), unumpy.nominal_values(y))
prutoky = np.append(
prutoky, calculation_infiltrations(P_zaloha, prutoky[-1],
ridici_index))
return prutoky
def proc(file):
numObj = np.load(file)
[date, arr] = numObj
A = unumpy.matrix(arr.flatten())
# this SHOULD build a new array that's twice as big -
# but everything is float values instead of strings (yay) and alternates
# between nominal, std, nominal, std
A_nom = np.ravel(A.nominal_values)
outArr = np.reshape(A_nom, arr.shape)
return [date, outArr]
def process(file):
try:
numObj = np.load(data + '/' + file)
[date, arr] = numObj
A = unumpy.matrix(arr.flatten())
A_nom = np.ravel(A.nominal_values)
outArr = np.reshape(A_nom, arr.shape)
return [date, outArr]
except EOFError:
return None
def process(file):
try:
# Assumes shape of (X,X,i) for this array - otherwise unumpy array would be unable to cope
numObj = np.load(file)
[date, arr] = numObj
A = unumpy.matrix(arr.flatten())
A_nom = np.ravel(A.nominal_values)
outArr = np.reshape(A_nom, arr.shape)
return [date, outArr]
except EOFError:
return None
def process(file, path_name):
try:
numObj = np.load(path_name + '/' + file, encoding='latin1')
try:
[date, arr] = numObj
except ValueError:
return numObj
A = unumpy.matrix(arr.flatten())
A_nom = np.ravel(A.nominal_values)
outArr = np.reshape(A_nom, arr.shape)
return [date, outArr]
except EOFError:
return None
def rotation_matrix_from(A, B):
A = A / unorm(A)
B = B / unorm(B)
v = np.cross(A, B)
s = unorm(v)
c = np.dot(A, B)
ssm = np.array([[0, -v[2], v[1]], [v[2], 0, -v[0]], [-v[1], v[0], 0]])
R = np.eye(3) + ssm + np.matmul(ssm, ssm) / (1 + c)
R = unp.matrix(R)
return R
def test_matrix():
"Matrices of numbers with uncertainties"
# Matrix inversion:
# Matrix with a mix of Variable objects and regular
# Python numbers:
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))]])
m_nominal_values = unumpy.nominal_values(m)
# Test of the nominal_value attribute:
assert numpy.all(m_nominal_values == m.nominal_values)
assert type(m[0, 0]) == uncertainties.Variable
def test_component_extraction():
"Extracting the nominal values and standard deviations from an array"
arr = unumpy.uarray(([1, 2], [0.1, 0.2]))
assert numpy.all(unumpy.nominal_values(arr) == [1, 2])
assert numpy.all(unumpy.std_devs(arr) == [0.1, 0.2])
# unumpy matrices, in addition, should have nominal_values that
# are simply numpy matrices (not unumpy ones, because they have no
# uncertainties):
mat = unumpy.matrix(arr)
assert numpy.all(unumpy.nominal_values(mat) == [1, 2])
assert numpy.all(unumpy.std_devs(mat) == [0.1, 0.2])
assert type(unumpy.nominal_values(mat)) == numpy.matrix
def test_component_extraction():
"Extracting the nominal values and standard deviations from an array"
arr = unumpy.uarray(([1, 2], [0.1, 0.2]))
assert numpy.all(unumpy.nominal_values(arr) == [1, 2])
assert numpy.all(unumpy.std_devs(arr) == [0.1, 0.2])
# unumpy matrices, in addition, should have nominal_values that
# are simply numpy matrices (not unumpy ones, because they have no
# uncertainties):
mat = unumpy.matrix(arr)
assert numpy.all(unumpy.nominal_values(mat) == [1, 2])
assert numpy.all(unumpy.std_devs(mat) == [0.1, 0.2])
assert type(unumpy.nominal_values(mat)) == numpy.matrix
def GetData(self):
c = [[],[],[],[],[],[]]
for row in range(6):
for col in range(6):
try:
c[row].append(String_to_float(self.item(row,col).text()))
except:
msg = QMessageBox()
msg.setIcon(QMessageBox.Information)
msg.setText("Check number in row:" + str(row+1)+"column:" + str(col+1))
msg.setWindowTitle("MessageBox")
msg.setStandardButtons(QMessageBox.Yes | QMessageBox.No)
if msg.exec_()== QMessageBox.Yes:
return True
else:
return False
self.c = unumpy.matrix(c)
def test_matrix():
"Matrices of numbers with uncertainties"
# Matrix inversion:
# Matrix with a mix of Variable objects and regular
# Python numbers:
m = unumpy.matrix([[ufloat(10, 1), -3.1], [0, ufloat(3, 0)]])
m_nominal_values = unumpy.nominal_values(m)
# Test of the nominal_value attribute:
assert numpy.all(m_nominal_values == m.nominal_values)
assert type(m[0, 0]) == uncert_core.Variable
# Test of scalar multiplication, both sides:
3 * m
m * 3
def test_matrix():
"Matrices of numbers with uncertainties"
# Matrix inversion:
# Matrix with a mix of Variable objects and regular
# Python numbers:
m = unumpy.matrix([[ufloat(10, 1), -3.1],
[0, ufloat(3, 0)]])
m_nominal_values = unumpy.nominal_values(m)
# Test of the nominal_value attribute:
assert numpy.all(m_nominal_values == m.nominal_values)
assert type(m[0, 0]) == uncert_core.Variable
# Test of scalar multiplication, both sides:
3*m
m*3
def process(file):
try:
# Assumes shape of (X,X,i) for this array - otherwise unumpy array would be unable to cope
if args["regex"] is not None:
p = re.compile(re.escape(str(args["regex"])))
if p.search(file) is None:
return None #We need to think of a way to skip this
#print(file)
numObj = np.load(file)
[date, arr] = numObj
A = unumpy.matrix(arr.flatten())
# this SHOULD build a new array that's twice as big -
# but everything is float values instead of strings (yay) and alternates
# between nominal, std, nominal, std
A_nom = np.ravel(A.nominal_values)
outArr = np.reshape(A_nom, arr.shape)
return [date, outArr]
except EOFError:
return None
def center_of_mass(slopes, intercepts):
'''Returns the center of mass relative to the slopes and intercepts
coordinate system.
Parameters
----------
slopes : ndarray, shape(n,)
The slope of every line used to calculate the center of mass.
intercepts : ndarray, shape(n,)
The intercept of every line used to calculate the center of mass.
Returns
-------
x : float
The abscissa of the center of mass.
y : float
The ordinate of the center of mass.
'''
num = range(len(slopes))
allComb = cartesian((num, num))
comb = []
# remove doubles
for row in allComb:
if row[0] != row[1]:
comb.append(row)
comb = np.array(comb)
# initialize the matrix to store the line intersections
lineX = np.zeros((len(comb), 2), dtype='object')
# for each line intersection...
for j, row in enumerate(comb):
sl = np.array([slopes[row[0]], slopes[row[1]]])
a = unumpy.matrix(np.vstack((-sl, np.ones((2)))).T)
b = np.array([intercepts[row[0]], intercepts[row[1]]])
lineX[j] = np.dot(a.I, b)
com = np.mean(lineX, axis=0)
return com[0], com[1]
def center_of_mass(slopes, intercepts):
'''Returns the center of mass relative to the slopes and intercepts
coordinate system.
Parameters
----------
slopes : ndarray, shape(n,)
The slope of every line used to calculate the center of mass.
intercepts : ndarray, shape(n,)
The intercept of every line used to calculate the center of mass.
Returns
-------
x : float
The abscissa of the center of mass.
y : float
The ordinate of the center of mass.
'''
num = range(len(slopes))
allComb = cartesian((num, num))
comb = []
# remove doubles
for row in allComb:
if row[0] != row[1]:
comb.append(row)
comb = np.array(comb)
# initialize the matrix to store the line intersections
lineX = np.zeros((len(comb), 2), dtype='object')
# for each line intersection...
for j, row in enumerate(comb):
sl = np.array([slopes[row[0]], slopes[row[1]]])
a = unumpy.matrix(np.vstack((-sl, np.ones((2)))).T)
b = np.array([intercepts[row[0]], intercepts[row[1]]])
lineX[j] = np.dot(a.I, b)
com = np.mean(lineX, axis=0)
return com[0], com[1]
def test_list_inverse():
"Test of the inversion of a square matrix"
mat_list = [[1, 1], [1, 0]]
# numpy.linalg.inv(mat_list) does calculate the inverse even
# though mat_list is a list of lists (and not a matrix). Can
# ulinalg do the same? Here is a test:
mat_list_inv = unumpy.ulinalg.inv(mat_list)
# More type testing:
mat_matrix = numpy.asmatrix(mat_list)
assert isinstance(unumpy.ulinalg.inv(mat_matrix),
type(numpy.linalg.inv(mat_matrix)))
# unumpy.ulinalg should behave in the same way as numpy.linalg,
# with respect to types:
mat_list_inv_numpy = numpy.linalg.inv(mat_list)
assert type(mat_list_inv) == type(mat_list_inv_numpy)
# The resulting matrix does not have to be a matrix that can
# handle uncertainties, because the input matrix does not have
# uncertainties:
assert not isinstance(mat_list_inv, unumpy.matrix)
# Individual element check:
assert isinstance(mat_list_inv[1, 1], float)
assert mat_list_inv[1, 1] == -1
x = ufloat((1, 0.1))
y = ufloat((2, 0.1))
mat = unumpy.matrix([[x, x], [y, 0]])
# Internal consistency: ulinalg.inv() must coincide with the
# unumpy.matrix inverse, for square matrices (.I is the
# pseudo-inverse, for non-square matrices, but inv() is not).
assert matrices_close(unumpy.ulinalg.inv(mat), mat.I)
def test_list_inverse():
"Test of the inversion of a square matrix"
mat_list = [[1, 1], [1, 0]]
# numpy.linalg.inv(mat_list) does calculate the inverse even
# though mat_list is a list of lists (and not a matrix). Can
# ulinalg do the same? Here is a test:
mat_list_inv = unumpy.ulinalg.inv(mat_list)
# More type testing:
mat_matrix = numpy.asmatrix(mat_list)
assert isinstance(unumpy.ulinalg.inv(mat_matrix),
type(numpy.linalg.inv(mat_matrix)))
# unumpy.ulinalg should behave in the same way as numpy.linalg,
# with respect to types:
mat_list_inv_numpy = numpy.linalg.inv(mat_list)
assert type(mat_list_inv) == type(mat_list_inv_numpy)
# The resulting matrix does not have to be a matrix that can
# handle uncertainties, because the input matrix does not have
# uncertainties:
assert not isinstance(mat_list_inv, unumpy.matrix)
# Individual element check:
assert isinstance(mat_list_inv[1,1], float)
assert mat_list_inv[1,1] == -1
x = ufloat((1, 0.1))
y = ufloat((2, 0.1))
mat = unumpy.matrix([[x, x], [y, 0]])
# Internal consistency: ulinalg.inv() must coincide with the
# unumpy.matrix inverse, for square matrices (.I is the
# pseudo-inverse, for non-square matrices, but inv() is not).
assert matrices_close(unumpy.ulinalg.inv(mat), mat.I)
d6 = genfromtxt(f6, delimiter=',') ar8 = unumpy.uarray(d6[:,0],d6[:,1]) ar08 = unumpy.uarray(d1[:,0],d1[:,1]) ar008 = unumpy.uarray(d2[:,0],d2[:,1]) arabs = unumpy.uarray(d3[:,0],d3[:,1]) aragua = unumpy.uarray(d4[:,0],d4[:,1]) arVBC = unumpy.uarray(d5[:,0],d4[:,1]) vol = (ar8 + ar08 + ar008 + aragua + arVBC) mol = (ar8 * 0.8 + ar08 *0.08 + ar008 *0.008) conc = mol/vol mT = unumpy.matrix(conc) filename = "resconc.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') XB = arabs/(0.757) mT = unumpy.matrix(XB) filename = "resXB.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') XHB = 1 - XB mT = unumpy.matrix(XHB) filename = "resXHB.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n')
def test_inverse():
"Tests of the matrix inverse"
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))]])
m_nominal_values = unumpy.nominal_values(m)
# "Regular" inverse matrix, when uncertainties are not taken
# into account:
m_no_uncert_inv = m_nominal_values.I
# The matrix inversion should not yield numbers with uncertainties:
assert m_no_uncert_inv.dtype == numpy.dtype(float)
# Inverse with uncertainties:
m_inv_uncert = m.I # AffineScalarFunc elements
# The inverse contains uncertainties: it must support custom
# operations on matrices with uncertainties:
assert isinstance(m_inv_uncert, unumpy.matrix)
assert type(m_inv_uncert[0, 0]) == uncertainties.AffineScalarFunc
# Checks of the numerical values: the diagonal elements of the
# inverse should be the inverses of the diagonal elements of
# m (because we started with a triangular matrix):
assert _numbers_close(1/m_nominal_values[0, 0],
m_inv_uncert[0, 0].nominal_value), "Wrong value"
assert _numbers_close(1/m_nominal_values[1, 1],
m_inv_uncert[1, 1].nominal_value), "Wrong value"
####################
# Checks of the covariances between elements:
x = ufloat((10, 1))
m = unumpy.matrix([[x, x],
[0, 3+2*x]])
m_inverse = m.I
# Check of the properties of the inverse:
m_double_inverse = m_inverse.I
# The initial matrix should be recovered, including its
# derivatives, which define covariances:
assert _numbers_close(m_double_inverse[0, 0].nominal_value,
m[0, 0].nominal_value)
assert _numbers_close(m_double_inverse[0, 0].std_dev(),
m[0, 0].std_dev())
assert matrices_close(m_double_inverse, m)
# Partial test:
assert _derivatives_close(m_double_inverse[0, 0], m[0, 0])
assert _derivatives_close(m_double_inverse[1, 1], m[1, 1])
####################
# Tests of covariances during the inversion:
# There are correlations if both the next two derivatives are
# not zero:
assert m_inverse[0, 0].derivatives[x]
assert m_inverse[0, 1].derivatives[x]
# Correlations between m and m_inverse should create a perfect
# inversion:
assert matrices_close(m * m_inverse, numpy.eye(m.shape[0]))
U_CU_C, U_CU_H, U_CU_M, U_AL_C, U_AL_H, U_AL_M = np.loadtxt("Messdaten/Messung_Material.txt",
unpack=True)
# Erstellen der Fehlerbehaftete Spannungen
uU_CU_C = unp.uarray(U_CU_C, len(U_CU_C)*[U_ERR])
uU_CU_H = unp.uarray(U_CU_H, len(U_CU_H)*[U_ERR])
uU_CU_M = unp.uarray(U_CU_M, len(U_CU_M)*[U_ERR])
uU_AL_C = unp.uarray(U_AL_C, len(U_AL_C)*[U_ERR])
uU_AL_H = unp.uarray(U_AL_H, len(U_AL_H)*[U_ERR])
uU_AL_M = unp.uarray(U_AL_M, len(U_AL_M)*[U_ERR])
# Erstellen von 3x3 Matrizen für die Werte von Cu und Al
# Spalte entspricht einer Versuchsreihe, Zeile: Entspricht einer Größe
uU_CU = unp.matrix([uU_CU_C, uU_CU_H, uU_CU_M])
uU_AL = unp.matrix([uU_AL_C, uU_AL_H, uU_AL_M])
# Umrechnung der Spannungen in Temperaturen
uT_CU = TensToTemp(uU_CU)
uT_AL = TensToTemp(uU_AL)
TEST = True
if TEST:
for i in range(3):
for j in range(3):
uT_CU[i,j] = ufloat(noms(uT_CU[i,j]), stds(uT_CU[i,j]))
if TEST:
def Restframe(string, name):
dirName = f'{name}'
dirName = dirName.split('/')[0]
if not os.path.exists(dirName):
os.mkdir(dirName)
print("Directory ", dirName, " Created ")
else:
print("Directory ", dirName, " already exists")
#Creating a line dict from NIST
line_dict = {
'CIV_1548': [1548.202, 0.01, r'C \Rn{4} $\lambda$ 1548'],
'SiIV_1402': [1402.77, 0.1, r'Si \Rn{4} $\lambda$ 1403'],
'Ly_a': [1215.6701, 0.0021, r'Ly-$\alpha$ $\lambda$ 1216'],
'CIII_1897': [1897.57, 0.1, r'C \Rn{3} $\lambda$ 1898'],
'MgII_2796': [2795.528, 0.01, r'Mg \Rn{2} $\lambda$ 2796'],
'MgII_2803': [2802.705, 0.01, r'Mg \Rn{2} $\lambda$ 2803'],
'OIII_5007': [5006.843, 0.01, r'O \Rn{3} $\lambda$ 5007'],
'H_b': [4861.283363, 0.000024, r'H-$\beta$ $\lambda$ 4861'],
'H_a': [6562.85117, 0.00003, r'H-$\alpha$ $\lambda$ 6563'],
'SiII_989': [989.87, 0.1, r'Si \Rn{2} $\lambda$ 989'],
'BeIII_4487': [4487.30, 0.10, r'Be \Rn{3} $\lambda$ 4487'],
'AlII_1670': [1670.7874, 0.001, r'Al \Rn{2} $\lambda$ 1670'],
'NV_1239': [1238.8210, 0.01, r'N \Rn{5} $\lambda$ 1239'],
'CuII_10852': [10852.401, 0.004, r'Cu \Rn{2} $\lambda$ 10852'],
'CuII_5007': [5006.79978, 0.00015, r'Cu \Rn{2} $\lambda$ 5007'],
'TiIII_4971': [4971.194, 0.010, r'Ti \Rn{3} $\lambda$ 4971'],
'ZnII_2026': [2025.4845, 0.001, r'Zn \Rn{2} $\lambda$ 2026'],
'ZnII_2062': [2062.0011, 0.0010, r'Zn \Rn{2} $\lambda$ 2062'],
'ZnII_2064': [2064.2266, 0.0010, r'Zn \Rn{2} $\lambda$ 2064'],
'SiII_1808': [1808.00, 0.10, r'Si \Rn{2} $\lambda$ 1808'],
'FeII_1611': [1610.9229, 0.0005, r'Fe \Rn{2} $\lambda$ 1611'],
'FeII_2249': [2249.05864, 0.00011, r'Fe \Rn{2} $\lambda$ 2249'],
'FeII_2260': [2260.5173, 0.0019, r'Fe \Rn{2} $\lambda$ 2260'],
'SiII_1526': [1526.734, 0.10, r'Si \Rn{2} $\lambda$ 1526'],
'FeI_3021': [3021.0725, 0.0003, r'Fe \Rn{2} $\lambda$ 3021'],
'FeII_2344': [2344.9842, 0.0001, r'Fe \Rn{2} $\lambda$ 2344'],
'FeII_2374': [2374.6530, 0.0001, r'Fe \Rn{2} $\lambda$ 2374'],
'FeII_2382': [2382.0373, 0.0001, r'Fe \Rn{2} $\lambda$ 2382'],
'FeII_2586': [2585.8756, 0.0001, r'Fe \Rn{2} $\lambda$ 2586'],
'CrII_2026': [2025.6186, 0.0001, r'Cr \Rn{2} $\lambda$ 2026'],
'CrII_2062': [2061.57673, 0.00007, r'Cr \Rn{2} $\lambda$ 2062'],
'CrII_2056': [2055.59869, 0.00006, r'Cr \Rn{2} $\lambda$ 2056'],
'CrII_2066': [2065.50389, 0.00007, r'Cr \Rn{2} $\lambda$ 2066'],
'MnII_1162': [1162.0150, 0.0001, r'Mn \Rn{2} $\lambda$ 1162'],
'MnII_1197': [1197.1840, 0.0001, r'Mn \Rn{2} $\lambda$ 1197'],
'MnII_1199': [1199.3910, 0.0001, r'Mn \Rn{2} $\lambda$ 1199'],
'MnII_1201': [1201.1180, 0.0001, r'Mn \Rn{2} $\lambda$ 1201'],
'MnII_2576': [2576.8770, 0.0001, r'Mn \Rn{2} $\lambda$ 2576'],
'MnII_2594': [2594.4990, 0.0001, r'Mn \Rn{2} $\lambda$ 2594'],
'MnII_2606': [2606.4630, 0.0001, r'Mn \Rn{2} $\lambda$ 2606'],
'NiII_1317': [1317.2170, 0.0001, r'Ni \Rn{2} $\lambda$ 1317'],
'NiII_1345': [1345.8780, 0.0001, r'Ni \Rn{2} $\lambda$ 1345'],
'NiII_1370': [1370.1320, 0.0001, r'Ni \Rn{2} $\lambda$ 1370'],
'NiII_1393': [1393.3240, 0.0001, r'Ni \Rn{2} $\lambda$ 1393'],
'NiII_1454': [1454.8420, 0.0001, r'Ni \Rn{2} $\lambda$ 1454'],
'NiII_1502': [1502.1480, 0.0001, r'Ni \Rn{2} $\lambda$ 1502'],
'NiII_1703': [1703.4050, 0.0001, r'Ni \Rn{2} $\lambda$ 1703'],
'NiII_1709': [1709.6000, 0.0001, r'Ni \Rn{2} $\lambda$ 1709'],
'NiII_1741': [1741.5490, 0.0001, r'Ni \Rn{2} $\lambda$ 1741'],
'NiII_1751': [1751.9100, 0.0001, r'Ni \Rn{2} $\lambda$ 1751'],
'NiII_1773': [1773.9490, 0.0001, r'Ni \Rn{2} $\lambda$ 1773'],
'NiII_1804': [1804.4730, 0.0001, r'Ni \Rn{2} $\lambda$ 1804'],
'CrII_1058': [1058.7320, 0.0001, r'Cr \Rn{2} $\lambda$ 1058'],
'CrII_1059': [1059.7320, 0.0001, r'Cr \Rn{2} $\lambda$ 1059'],
'CrII_1064': [1064.1240, 0.0001, r'Cr \Rn{2} $\lambda$ 1064'],
'CrII_1066': [1066.7760, 0.0001, r'Cr \Rn{2} $\lambda$ 1066'],
'SiII_1020': [1020.6989, 0.1, r'Si \Rn{2} $\lambda$ 1020'],
'SiIV_1062': [1062.66, 0.1, r'Si \Rn{4} $\lambda$ 1062'],
'SiII_1190': [1190.4158, 0.1, r'Si \Rn{2} $\lambda$ 1190'],
'SiII_1193': [1193.2897, 0.1, r'Si \Rn{2} $\lambda$ 1193'],
'SiIII_1206': [1206.5000, 0.1, r'Si \Rn{3} $\lambda$ 1206'],
'SiII_1260': [1260.4221, 0.1, r'Si \Rn{2} $\lambda$ 1260'],
'SiII_1304': [1304.3702, 0.1, r'Si \Rn{2} $\lambda$ 1304'],
'SiI_1554': [1554.2960, 0.1, r'Si \Rn{1} $\lambda$ 1554'],
'SiI_1562': [1562.0020, 0.1, r'Si \Rn{1} $\lambda$ 1562'],
'SiI_1625': [1625.7051, 0.1, r'Si \Rn{1} $\lambda$ 1625'],
'SiI_1631': [1631.1705, 0.1, r'Si \Rn{1} $\lambda$ 1631'],
'SiIV_1693': [1693.2935, 0.1, r'Si \Rn{4} $\lambda$ 1693'],
'SiI_2515': [2515.0725, 0.1, r'Si \Rn{1} $\lambda$ 2515'],
'SiI_2208': [2208.6665, 0.1, r'Si \Rn{1} $\lambda$ 2208'],
'SiIII_1892': [1892.0300, 0.1, r'Si \Rn{3} $\lambda$ 1892'],
'SiI_1845': [1845.5202, 0.1, r'Si \Rn{1} $\lambda$ 1845'],
'FeII_935': [935.5175, 0.001, r'Fe \Rn{2} $\lambda$ 935'],
'FeII_937': [937.6520, 0.001, r'Fe \Rn{2} $\lambda$ 937'],
'FeII_1055': [1055.2617, 0.001, r'Fe \Rn{2} $\lambda$ 1055'],
'FeII_1062': [1062.1520, 0.001, r'Fe \Rn{2} $\lambda$ 1062'],
'FeII_1081': [1081.8750, 0.001, r'Fe \Rn{2} $\lambda$ 1081'],
'FeII_1083': [1083.4200, 0.001, r'Fe \Rn{2} $\lambda$ 1083'],
'FeII_1096': [1096.8769, 0.001, r'Fe \Rn{2} $\lambda$ 1096'],
'FeIII_1122': [1122.5360, 0.001, r'Fe \Rn{3} $\lambda$ 1122'],
'FeII_1144': [1144.9379, 0.001, r'Fe \Rn{2} $\lambda$ 1144'],
'FeII_1260': [1260.5330, 0.001, r'Fe \Rn{2} $\lambda$ 1260'],
'FeII_1608': [1608.4511, 0.001, r'Fe \Rn{2} $\lambda$ 1608'],
'FeII_1611': [1611.2005, 0.001, r'Fe \Rn{2} $\lambda$ 1611'],
'FeI_1934': [1934.5351, 0.001, r'Fe \Rn{1} $\lambda$ 1934'],
'FeI_1937': [1937.2682, 0.001, r'Fe \Rn{1} $\lambda$ 1937'],
'FeI_2167': [2167.4531, 0.001, r'Fe \Rn{1} $\lambda$ 2167'],
'FeII_2344': [2344.2140, 0.001, r'Fe \Rn{2} $\lambda$ 2344'],
'FeII_2382': [2382.7650, 0.001, r'Fe \Rn{2} $\lambda$ 2382'],
'FeII_2484': [2484.0211, 0.001, r'Fe \Rn{2} $\lambda$ 2484'],
'FeI_2523': [2523.6083, 0.001, r'Fe \Rn{1} $\lambda$ 2523'],
'FeII_2600': [2600, 0.001, r'Fe \Rn{2} $\lambda$ 2600'],
'FeI_2719': [2719.8331, 0.001, r'Fe \Rn{1} $\lambda$ 2719'],
'FeI_3021': [3021.5189, 0.001, r'Fe \Rn{1} $\lambda$ 3021'],
'AlIII_1854': [1854.7164, 0.1, r'Al \Rn{3} $\lambda$ 1854'],
'AlIII_1862': [1862.7895, 0.1, r'Al \Rn{3} $\lambda$ 1862'],
'MgI_2852': [2852.1370, 0.1, r'Mg \Rn{1} $\lambda$ 2852'],
'MgI_2026': [2026.4768, 0.1, r'Mg \Rn{1} $\lambda$ 2026'],
'PII_1152': [1152.8180, 0.001, r'P \Rn{2} $\lambda$ 1152'],
'CuII_1358': [1358.7730, 0.001, r'Cu \Rn{2} $\lambda$ 1358']
}
time_signature = datetime.now().strftime("%m%d-%H%M")
name = name.replace('.txt', '')
output_name = f'Final_table_{time_signature}_{dirName}.txt'
numify = lambda x: float(''.join(
char for char in x if char.isdigit() or char == "." or char == "-"))
tex_table = string
tex_document = r"""
\begin{table}[H]
\begin{tabular}{cccccccc}
Transition & EW$_r$ [Å] & Redshift\\
\hline
"""
approx_z = float(input('What is the approximate redshift?'))
lines = tex_table.split(r"\\")[0:-1]
data = []
text = []
# Interactive way of categorising the lines
for line in lines:
[_, wave, eq, _] = line.strip().split("&")
[wave, wave_err] = wave.split(r"\pm")
[eq, eq_err] = eq.split(r"\pm")
line_exp = unc.ufloat(numify(wave), numify(wave_err)) / (1 + approx_z)
ordered_dict = collections.OrderedDict(
sorted(line_dict.items(), key=lambda v: v[1]))
line_true = input(
f'\n What is this line {line_exp}? Please choose from: \n {ordered_dict.keys()}: '
)
data.append([
unc.ufloat(numify(wave), numify(wave_err)),
unc.ufloat(numify(eq), numify(eq_err)),
unc.ufloat(line_dict[f'{line_true}'][0],
line_dict[f'{line_true}'][1])
])
text.append(line_dict[f'{line_true}'][2])
data = unumpy.matrix(data)
z = (data[:, 0] / data[:, 2] - 1)
# The errors and their contribution to the weighted redshift avarage
z_avg = np.mean(z)
var = sum(pow(i - z_avg, 2) for i in z) / len(z)
var = var[0, 0]
z_avg_std = math.sqrt(var.nominal_value)
ew_r = (data[:, 1] / (z_avg + 1))
# Creating a LaTeX table for the results
tex_begin = "\\noindent The weighted avarage of the redshift is $z = {:.1uL}$".format(
z_avg)
for i in range(len(z)):
eq_value = ew_r[i, 0]
z_value = z[i, 0]
tex_document += " {0} & ${1:.1uL}$ & ${2:.1uL}$ \\\\".format(
text[i], eq_value, z_value)
tex_footer = r"""
\hline
\end{tabular}
\end{table}
"""
output_name = dirName + "/" + output_name
with open(output_name, "w+") as outfile:
outfile.write(tex_begin + tex_document + tex_footer)
# When the file is saved, it is also printed and inserted in the clip board
print(tex_begin + tex_document + tex_footer)
copy(tex_begin + tex_document + tex_footer)
Z_s.loc[(k, i), m] = -C.loc[k, i].s
if j <= N:
Z.loc[(k, j), m] = C.loc[k, i]
Z_n.loc[(k, j), m] = C.loc[k, i].n
Z_s.loc[(k, j), m] = C.loc[k, i].s
#nalezeni prutoku metodou nejmensich ctvercu
X = Z_n
y = -M
X2 = Z
y2 = -M
#rucne
I1 = np.linalg.inv(np.dot(X.T, X))
pom = unumpy.matrix(np.dot(X2.T, X2))
I2 = pom.I
prutoky1 = np.dot(I1, np.dot(X.T, y)) #bez nejistot
prutoky2 = np.dot(I2, np.dot(X2.T, y)) #toto je s nejistotami
prutoky2 = np.array(prutoky2)[0]
#scipy lsq_linear
# prutoky2=lsq_linear(X, y)
# prutoky2_n=prutoky2.x
#statsmodel
res_ols = sm.OLS(y, X).fit()
print(res_ols.summary())
prutoky3_n = res_ols.params
# prutoky3_s=res_ols.bse
def test_inverse():
"Tests of the matrix inverse"
m = unumpy.matrix([[ufloat((10, 1)), -3.1],
[0, ufloat((3, 0))]])
m_nominal_values = unumpy.nominal_values(m)
# "Regular" inverse matrix, when uncertainties are not taken
# into account:
m_no_uncert_inv = m_nominal_values.I
# The matrix inversion should not yield numbers with uncertainties:
assert m_no_uncert_inv.dtype == numpy.dtype(float)
# Inverse with uncertainties:
m_inv_uncert = m.I # AffineScalarFunc elements
# The inverse contains uncertainties: it must support custom
# operations on matrices with uncertainties:
assert isinstance(m_inv_uncert, unumpy.matrix)
assert type(m_inv_uncert[0, 0]) == uncertainties.AffineScalarFunc
# Checks of the numerical values: the diagonal elements of the
# inverse should be the inverses of the diagonal elements of
# m (because we started with a triangular matrix):
assert _numbers_close(1/m_nominal_values[0, 0],
m_inv_uncert[0, 0].nominal_value), "Wrong value"
assert _numbers_close(1/m_nominal_values[1, 1],
m_inv_uncert[1, 1].nominal_value), "Wrong value"
####################
# Checks of the covariances between elements:
x = ufloat((10, 1))
m = unumpy.matrix([[x, x],
[0, 3+2*x]])
m_inverse = m.I
# Check of the properties of the inverse:
m_double_inverse = m_inverse.I
# The initial matrix should be recovered, including its
# derivatives, which define covariances:
assert _numbers_close(m_double_inverse[0, 0].nominal_value,
m[0, 0].nominal_value)
assert _numbers_close(m_double_inverse[0, 0].std_dev(),
m[0, 0].std_dev())
assert matrices_close(m_double_inverse, m)
# Partial test:
assert _derivatives_close(m_double_inverse[0, 0], m[0, 0])
assert _derivatives_close(m_double_inverse[1, 1], m[1, 1])
####################
# Tests of covariances during the inversion:
# There are correlations if both the next two derivatives are
# not zero:
assert m_inverse[0, 0].derivatives[x]
assert m_inverse[0, 1].derivatives[x]
# Correlations between m and m_inverse should create a perfect
# inversion:
assert matrices_close(m * m_inverse, numpy.eye(m.shape[0]))
d5 = genfromtxt(f5, delimiter=',') d6 = genfromtxt(f6, delimiter=',') ar8 = unumpy.uarray(d6[:, 0], d6[:, 1]) ar08 = unumpy.uarray(d1[:, 0], d1[:, 1]) ar008 = unumpy.uarray(d2[:, 0], d2[:, 1]) arabs = unumpy.uarray(d3[:, 0], d3[:, 1]) aragua = unumpy.uarray(d4[:, 0], d4[:, 1]) arVBC = unumpy.uarray(d5[:, 0], d4[:, 1]) vol = (ar8 + ar08 + ar008 + aragua + arVBC) mol = (ar8 * 0.8 + ar08 * 0.08 + ar008 * 0.008) conc = mol / vol mT = unumpy.matrix(conc) filename = "resconc.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') XB = arabs / (0.757) mT = unumpy.matrix(XB) filename = "resXB.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n') XHB = 1 - XB mT = unumpy.matrix(XHB) filename = "resXHB.csv" numpy.savetxt(filename, mT, fmt='%r', delimiter='\n')
def calculation_OAR_rucne(K, Q):
K = K[:, :-1]
K = unumpy.matrix(K)
K_inverse = K.I
return -np.dot(K_inverse, Q)
U_CU_C, U_CU_H, U_CU_M, U_AL_C, U_AL_H, U_AL_M = np.loadtxt(
"Messdaten/Messung_Material.txt", unpack=True)
# Erstellen der Fehlerbehaftete Spannungen
uU_CU_C = unp.uarray(U_CU_C, len(U_CU_C) * [U_ERR])
uU_CU_H = unp.uarray(U_CU_H, len(U_CU_H) * [U_ERR])
uU_CU_M = unp.uarray(U_CU_M, len(U_CU_M) * [U_ERR])
uU_AL_C = unp.uarray(U_AL_C, len(U_AL_C) * [U_ERR])
uU_AL_H = unp.uarray(U_AL_H, len(U_AL_H) * [U_ERR])
uU_AL_M = unp.uarray(U_AL_M, len(U_AL_M) * [U_ERR])
# Erstellen von 3x3 Matrizen für die Werte von Cu und Al
# Spalte entspricht einer Versuchsreihe, Zeile: Entspricht einer Größe
uU_CU = unp.matrix([uU_CU_C, uU_CU_H, uU_CU_M])
uU_AL = unp.matrix([uU_AL_C, uU_AL_H, uU_AL_M])
# Umrechnung der Spannungen in Temperaturen
uT_CU = TensToTemp(uU_CU)
uT_AL = TensToTemp(uU_AL)
TEST = True
if TEST:
for i in range(3):
for j in range(3):
uT_CU[i, j] = ufloat(noms(uT_CU[i, j]), stds(uT_CU[i, j]))
if TEST:
for i in range(3):
