class Meta(_AbstractProbability.Meta):
store_id = "R2G3Model"
ind_properties = [
PropIntel(name="W1", label="W1 (> 0.5)", math_label=r"$W_1$",
stor_name="_W1", inh_name="inherit_W1", inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
minimum=0.5, maximum=1.0, data_type=float, **PropIntel.REF_ST_WID),
PropIntel(name="P111_or_P212", label="P111 (W1 < 2/3) or\nPx1x (W1 > 2/3)",
stor_name="_P111_or_P212", inh_name="inherit_P111_or_P212",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$P_{111} %s$ or $\newline P_{x1x} %s$" % (
mt_range(0.5, "W_1", 2.0 / 3.0),
mt_range(2.0 / 3.0, "W_1", 1.0)),
minimum=0.0, maximum=1.0, data_type=float, **PropIntel.REF_ST_WID),
PropIntel(name="G1", label="W2/(W2+W3)", math_label=r"$\large\frac{W_2}{W_3 + W_2}$",
stor_name="_G1", inh_name="inherit_G1", inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
minimum=0.0, maximum=1.0, data_type=float, **PropIntel.REF_ST_WID),
PropIntel(name="G2", label="(W212+W213)/(W212+W213+W312+W313)",
stor_name="_G2", inh_name="inherit_G2", inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{212} + W_{213}}{W_{212} + W_{213} + W_{312} + W_{313}}$",
minimum=0.0, maximum=1.0, data_type=float, **PropIntel.REF_ST_WID),
PropIntel(name="G3", label="W212/(W212+W213)",
stor_name="_G3", inh_name="inherit_G3", inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{212}}{W_{212} + W_{213}}$",
minimum=0.0, maximum=1.0, data_type=float, **PropIntel.REF_ST_WID),
PropIntel(name="G4", label="W312/(W312+W313)",
stor_name="_G4", inh_name="inherit_G4", inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{312}}{W_{312} + W_{313}}$",
minimum=0.0, maximum=1.0, data_type=float, **PropIntel.REF_ST_WID),
]
inh_properties = [
PropIntel(name="inherit_%s" % prop.name, label="Inherit flag for %s" % prop.name,
data_type=bool, refinable=False, storable=True, has_widget=True,
widget_type="toggle") \
for prop in ind_properties
]
properties = ind_properties + inh_properties
class Meta(_AbstractProbability.Meta):
ind_properties = [
PropIntel(
name="W1",
label="W1",
math_label=r"$W_1$",
stor_name="_W1",
inh_name="inherit_W1",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="P11_or_P22",
label="P11_or_P22",
stor_name="_P11_or_P22",
inh_name="inherit_P11_or_P22",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$P_{11} %s$ or $\newline P_{22} %s$" %
(mt_range(0.0, "W_1", 0.5), mt_range(0.5, "W_1", 1.0)),
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
]
inh_properties = [
PropIntel(name="inherit_%s" % prop.name, label="Inherit flag for %s" % prop.name,
data_type=bool, refinable=False, storable=True, has_widget=True,
widget_type="toggle") \
for prop in ind_properties
]
properties = ind_properties + inh_properties
store_id = "R1G2Model"
class R2G3Model(_AbstractProbability):
r"""
(Restricted) probability model for Reichweite 2 with 3 components.
The (due to restrictions only) 6 independent variables are:
.. math::
:nowrap:
\begin{align*}
& W_{1}
& P_{111} \text{(if $\nicefrac{1}{2} \leq W_1 < \nicefrac{2}{3}$) or} P_{x1x} \text{(if $\nicefrac{2}{3} \leq W_1 \leq 1)$ with $x \in \left\{ {2,3} \right\}$} \\
& G_1 = \frac{W_2}{W_2 + W_3}
& G_2 = \frac{W_{212} + W_{213}}{W_{212} + W_{213} + W_{312} + W_{313}} \\
& G_3 = \frac{W_{212}}{W_{212} + W_{213}}
& G_4 = \frac{W_{312}}{W_{312} + W_{313}} \\
\end{align*}
This model can not describe mixed layers in which the last two components
occur right after each other in a stack. In other words there is always
an alternation between (one or more) layers of the first component and a
single layer of the second or third component. Therefore, the weight
fraction of the first component (:math:`W_1`) needs to be > than 1/2.
The restriction also translates in the following:
.. math::
:nowrap:
\begin{align*}
& P_{22} = P_{23} = P_{32} = P_{33} = 0 \\
& P_{21} = P_{31} = 1 \\
& \\
& P_{122} = P_{123} = P_{132} = P_{133} = 0 \\
& P_{121} = P_{131} = 1 \\
& \\
& P_{222} = P_{223} = P_{232} = P_{233} = 0 \\
& P_{221} = P_{231} = 1 \\
& \\
& P_{322} = P_{323} = P_{332} = P_{333} = 0 \\
& P_{321} = P_{331} = 1 \\
\end{align*}
Using the above, we can calculate a lot of the weight fractions of stacks:
.. math::
:nowrap:
\begin{align*}
& W_{22} = W_{23} = W_{32} = W_{33} 0 \\
& W_{21} = W_{2} \\
& W_{31} = W_{3} \\
& \\
& W_{122} = W_{123} = W_{132} = W_{133} = 0 \\
& W_{121} = W_{12} = W_{21} = W_2 \\
& W_{131} = W_{13} = W_{31} = W_3 \\
& W_{11} = W_1 - W_{12} - W_{13} \\
& \\
& W_{221} = W_{231} = W_{222} = W_{223} = W_{232} = W_{233} = 0 \\
& W_{331} = W_{331} = W_{322} = W_{323} = W_{332} = W_{333} = 0 \\
\end{align*}
Then the remaining fractions and probablities can be calculated as follows:
.. math::
:nowrap:
\begin{align*}
& W_2 = G_1 * (1 - W_1) \\
& W_3 = 1 - W_1 - W_2 \\
& \\
& W_x = W_2 + W_3 &
& \text{if $W_1 < \nicefrac{2}{3}$:} \\
& \quad \text{$P_{111}$ is given}\\
& \quad P_{x1x} =
\begin{dcases}
1 - \frac{W_1 - W_x}{W_x} \cdot (1 - P_{111}, & \text{if $W_x > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& \\
& \text{if $W_1 \geq \nicefrac{2}{3}$:} \\
& \quad \text{$P_{x1x}$ is given}\\
& \quad P_{111} =
\begin{dcases}
1 - \frac{W_x}{W_1 - W_x} \cdot (1 - P_{x1x}, & \text{if $(W_1 - W_x) > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& \\
& W_{x1x} = W_x \cdot P_{x1x} \\
& W_{21x} = G_2 \cdot W_{x1x} \\
& W_{31x} = W_{x1x} - W_{21x} \\
& \\
& W_{212} = G_3 \cdot W_{21x} \\
& W_{213} = (1 - G_3) \cdot W_{21x} \\
& W_{211} = W_{21} - W_{212} - W_{213} \\
& \\
& W_{312} = G_4 \cdot W_{31x} \\
& W_{313} = (1 - G_4) \cdot W_{31x} \\
& W_{311} = W_{31} - W_{312} - W_{313} \\
& \\
& W_{111} = W_{11} \cdot P_{111} \\
& W_{112} = W_{12} - W_{212} - W_{312} \\
& W_{112} = W_{13} - W_{213} - W_{313} \\
& \\
& \text{Calculate the remaining P using:} \\
& P_{ijk} =
\begin{dcases}
\frac{W_{ijk}}{W_{ij}}, & \text{if $W_{ij} > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
\end{align*}
"""
# MODEL METADATA:
class Meta(_AbstractProbability.Meta):
store_id = "R2G3Model"
# PROPERTIES:
_G = 3
twothirds = 2.0 / 3.0
inherit_W1 = BoolProperty(default=False,
text="Inherit flag for W1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
W1 = FloatProperty(default=0.8,
text="W1 (> 0.5)",
math_text=r"$W_1 (> 0.5)$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.5,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_W1",
inherit_from="parent.based_on.probabilities.W1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_P111_or_P212 = BoolProperty(default=False,
text="Inherit flag for P112_or_P211",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
P111_or_P212 = FloatProperty(
default=0.9,
text="P111 (W1 < 2/3) or\nPx1x (W1 > 2/3)",
math_text=r"$P_{111} %s$ or $\newline P_{x1x} %s$" %
(mt_range(0.5, "W_1", 2.0 / 3.0), mt_range(2.0 / 3.0, "W_1", 1.0)),
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_P111_or_P212",
inherit_from="parent.based_on.probabilities.P111_or_P212",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G1 = BoolProperty(default=False,
text="Inherit flag for G1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G1 = FloatProperty(default=0.9,
text="W2/(W2+W3)",
math_text=r"$\large\frac{W_2}{W_3 + W_2}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G1",
inherit_from="parent.based_on.probabilities.G1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_G2 = BoolProperty(default=False,
text="Inherit flag for G2",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G2 = FloatProperty(
default=0.9,
text="(W212+W213)/(W212+W213+W312+W313)",
math_text=
r"$\large\frac{W_{212} + W_{213}}{W_{212} + W_{213} + W_{312} + W_{313}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G2",
inherit_from="parent.based_on.probabilities.G2",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G3 = BoolProperty(default=False,
text="Inherit flag for G3",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G3 = FloatProperty(default=0.9,
text="W212/(W212+W213)",
math_text=r"$\large\frac{W_{212}}{W_{212} + W_{213}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G3",
inherit_from="parent.based_on.probabilities.G3",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_G4 = BoolProperty(default=False,
text="Inherit flag for G4",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G4 = FloatProperty(default=0.9,
text="W312/(W312+W313)",
math_text=r"$\large\frac{W_{312}}{W_{312} + W_{313}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G4",
inherit_from="parent.based_on.probabilities.G4",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
# ------------------------------------------------------------
# Initialization and other internals
# ------------------------------------------------------------
def __init__(self,
W1=0.8,
P111_or_P212=0.9,
G1=0.9,
G2=0.9,
G3=0.9,
G4=0.9,
inherit_W1=False,
inherit_P111_or_P212=False,
inherit_G1=False,
inherit_G2=False,
inherit_G3=False,
inherit_G4=False,
*args,
**kwargs):
super(R2G3Model, self).__init__(R=2, *args, **kwargs)
with self.data_changed.hold():
self.W1 = not_none(W1, 0.8)
self.inherit_W1 = inherit_W1
self.P111_or_P212 = not_none(P111_or_P212, 0.9)
self.inherit_P111_or_P212 = inherit_P111_or_P212
self.G1 = not_none(G1, 0.9)
self.inherit_G1 = inherit_G1
self.G2 = not_none(G2, 0.9)
self.inherit_G2 = inherit_G2
self.G3 = not_none(G3, 0.9)
self.inherit_G3 = inherit_G3
self.G4 = not_none(G4, 0.9)
self.inherit_G4 = inherit_G4
self.update()
# ------------------------------------------------------------
# Methods & Functions
# ------------------------------------------------------------
def update(self):
with self.monitor_changes():
# calculate Wx's:
self.mW[0] = self.W1
self.mW[1] = (1.0 - self.mW[0]) * self.G1
self.mW[2] = 1.0 - self.mW[0] - self.mW[1]
# consequences of restrictions:
self.mW[1, 1] = 0
self.mW[1, 2] = 0
self.mW[2, 1] = 0
self.mW[2, 2] = 0
self.mW[0, 1, 0] = self.mW[0, 1] = self.mW[1, 0] = self.mW[1]
self.mW[0, 2, 0] = self.mW[0, 2] = self.mW[2, 0] = self.mW[2]
self.mW[0, 0] = self.mW[0] - self.mW[0, 1] - self.mW[0, 2]
# continue calculations:
Wx = self.mW[1] + self.mW[2]
if self.mW[0] < self.twothirds:
self.mP[0, 0, 0] = self.P111_or_P212
Px0x = 1 - (self.mW[0] - Wx) / Wx * (
1 - self.mP[0, 0, 0]) if Wx != 0 else 0.0
else:
Px0x = self.P111_or_P212
self.mP[0, 0, 0] = 1 - Wx / (self.mW[0] - Wx) * (1 - Px0x) if (
self.mW[0] - Wx) != 0 else 0.0
Wx0x = Wx * Px0x
W10x = self.G2 * Wx0x
W20x = Wx0x - W10x
self.mW[1, 0, 1] = self.G3 * W10x
self.mW[1, 0, 2] = (1 - self.G3) * W10x
self.mW[1, 0,
0] = self.mW[1, 0] - self.mW[1, 0, 1] - self.mW[1, 0, 2]
self.mW[2, 0, 1] = self.G4 * W20x
self.mW[2, 0, 2] = (1 - self.G4) * W20x
self.mW[2, 0,
0] = self.mW[2, 0] - self.mW[2, 0, 1] - self.mW[2, 0, 2]
self.mW[0, 0, 0] = self.mW[0, 0] * self.mP[0, 0, 0]
self.mW[0, 0,
1] = self.mW[0, 1] - self.mW[1, 0, 1] - self.mW[2, 0, 1]
self.mW[0, 0,
2] = self.mW[0, 2] - self.mW[1, 0, 2] - self.mW[2, 0, 2]
# Calculate remaining P:
for i in range(3):
for j in range(3):
for k in range(3):
self.mP[i, j, k] = self.mW[i, j, k] / self.mW[
i, j] if self.mW[i, j] > 0 else 0.0
self.solve()
self.validate()
pass # end of class
class R2G2Model(_AbstractProbability):
r"""
Probability model for Reichweite 2 with 2 components.
The 4 (=g^2) independent variables are:
.. math::
:nowrap:
\begin{align*}
& W_1
& P_{112} (W_1 leq \nicefrac{2}{3})
\text{ or }P_{211} (W_1 > \nicefrac{2}{3}) \\
& P_{21}
& P_{122} (P_{21} leq \nicefrac{1}{2})
\text{ or }P_{221} (P_{21} > \nicefrac{1}{2}) \\
\end{align*}
Calculation of the other variables happens as follows:
.. math::
:nowrap:
\begin{align*}
& W_2 = 1 - W_1 \\
& P_{22} = 1 - P_{21} \\
& \\
& W_{21} = W_2 \cdot P_{21} \\
& W_{21} = W_{12} \\
& W_{11} = W_1 - W_{21} \\
& W_{22} = W_{2} \cdot P_{22} \\
& \\
& \text{if $W_1 leq \nicefrac{2}{3}$:} \\
& \quad \text{$P_{112}$ is given}\\
& \quad P_{211} =
\begin{dcases}
\frac{W_{11}}{W_{21}} \cdot P_{112} , & \text{if $W_{21} > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& \\
& \text{if $W_1 > \nicefrac{2}{3}$:} \\
& \quad \text{$P_{211}$ is given}\\
& \quad P_{112} =
\begin{dcases}
\frac{W_{21}}{W_{11}} \cdot P_{211} , & \text{if $W_{11} > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& \\
& P_{212} = 1 - P_{211} \\
& P_{111} = 1 - P_{112} \\
& \\
& \text{if $P_{21} leq \nicefrac{1}{2}$:} \\
& \quad \text{$P_{122}$ is given}\\
& \quad P_{221} =
\begin{dcases}
\frac{W_{12}}{W_{22}} \cdot P_{122} , & \text{if $W_{22} > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& \\
& \text{if $P_{21} > \nicefrac{1}{2}$:} \\
& \quad \text{$P_{221}$ is given}\\
& \quad P_{122} =
\begin{dcases}
\frac{W_{22}}{W_{12}} \cdot P_{221} , & \text{if $W_{12} > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& P_{121} = 1 - P_{122} \\
& P_{222} = 1 - P_{221} \\
\end{align*}
"""
# MODEL METADATA:
class Meta(_AbstractProbability.Meta):
store_id = "R2G2Model"
# PROPERTIES:
_G = 2
twothirds = 2.0 / 3.0
inherit_W1 = BoolProperty(default=False,
text="Inherit flag for W1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
W1 = FloatProperty(default=0.75,
text="W1 (> 0.5)",
math_text=r"$W_1 (> 0.5)$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.5,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_W1",
inherit_from="parent.based_on.probabilities.W1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_P112_or_P211 = BoolProperty(default=False,
text="Inherit flag for P112_or_P211",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
P112_or_P211 = FloatProperty(
default=0.75,
text="P112 (W1 < 2/3) or\nP211 (W1 > 2/3)",
math_text=r"$P_{112} %s$ or $\newlineP_{211} %s$" % (mt_range(
1.0 / 2.0, "W_1", 2.0 / 3.0), mt_range(2.0 / 3.0, "W_1", 1.0)),
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_P112_or_P211",
inherit_from="parent.based_on.probabilities.P112_or_P211",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_P21 = BoolProperty(default=False,
text="Inherit flag for P21",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
P21 = FloatProperty(default=0.75,
text="P21",
math_text=r"$P_{21}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_P21",
inherit_from="parent.based_on.probabilities.P21",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_P122_or_P221 = BoolProperty(default=False,
text="Inherit flag for P122_or_P221",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
P122_or_P221 = FloatProperty(
default=0.75,
text="P112 (W1 < 1/2) or\nP221 (W1 > 1/2)",
math_text=r"$P_{122} %s$ or $\newlineP_{221} %s$" %
(mt_range(0.0, "W_1", 1.0 / 2.0), mt_range(1.0 / 2.0, "W_1", 1.0)),
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_P122_or_P221",
inherit_from="parent.based_on.probabilities.P122_or_P221",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
# ------------------------------------------------------------
# Initialization and other internals
# ------------------------------------------------------------
def __init__(self,
W1=0.75,
P112_or_P211=0.75,
P21=0.75,
P122_or_P221=0.75,
inherit_W1=False,
inherit_P112_or_P211=False,
inherit_P21=False,
inherit_P122_or_P221=False,
*args,
**kwargs):
super(R2G2Model, self).__init__(R=2, *args, **kwargs)
with self.data_changed.hold():
self.W1 = not_none(W1, 0.75)
self.inherit_W1 = inherit_W1
self.P112_or_P211 = not_none(P112_or_P211, 0.75)
self.inherit_P112_or_P211 = inherit_P112_or_P211
self.P21 = not_none(P21, 0.75)
self.inherit_P21 = inherit_P21
self.P122_or_P221 = not_none(P122_or_P221, 0.75)
self.inherit_P122_or_P221 = inherit_P122_or_P221
self.update()
# ------------------------------------------------------------
# Methods & Functions
# ------------------------------------------------------------
def update(self):
with self.monitor_changes():
self.mW[0] = self.W1
self.mW[1] = 1.0 - self.mW[0]
self.mP[1, 0] = self.P21
self.mP[1, 1] = 1.0 - self.mP[1, 0]
self.mW[1, 0] = self.mW[1] * self.mP[1, 0]
self.mW[1, 1] = self.mW[1] * self.mP[1, 1]
self.mW[0, 1] = self.mW[1, 0]
self.mW[0, 0] = self.mW[0] - self.mW[1, 0]
if self.mW[0] <= self.twothirds:
self.mP[0, 0, 1] = self.P112_or_P211
if self.mW[1, 0] == 0.0:
self.mP[1, 0, 0] = 0.0
else:
self.mP[1, 0,
0] = self.mP[0, 0, 1] * self.mW[0, 0] / self.mW[1,
0]
else:
self.mP[1, 0, 0] = self.P112_or_P211
if self.mW[0, 0] == 0.0:
self.mP[0, 0, 1] = 0.0
else:
self.mP[0, 0,
1] = self.mP[1, 0, 0] * self.mW[1, 0] / self.mW[0,
0]
self.mP[1, 0, 1] = 1.0 - self.mP[1, 0, 0]
self.mP[0, 0, 0] = 1.0 - self.mP[0, 0, 1]
if self.mP[1, 0] <= 0.5:
self.mP[0, 1, 1] = self.P122_or_P221
self.mP[1, 1,
0] = self.mP[0, 1, 1] * self.mW[0, 1] / self.mW[1, 1]
else:
self.mP[1, 1, 0] = self.P122_or_P221
self.mP[0, 1,
1] = self.mP[1, 1, 0] * self.mW[1, 1] / self.mW[0, 1]
self.mP[0, 1, 0] = 1.0 - self.mP[0, 1, 1]
self.mP[1, 1, 1] = 1.0 - self.mP[1, 1, 0]
self.solve()
self.validate()
pass # end of class
class R1G4Model(_AbstractProbability):
r"""
Probability model for Reichweite 1 with 4 components.
The independent variables (# = g*(g-1) = 12) are:
.. math::
:nowrap:
\begin{align*}
& W_1
& P_{11} (W_1 < 0,5)\text{ or }P_{xx} (W_1 > 0,5)
with P_{xx} = \frac {W_{22} + W_{23} + W_{24} + W_{32} + W_{33} + W_{34} + W_{42} + W_{43} + W_{44}}{W_2 + W_3 + W_4} \\
& R_2 = \frac{ W_2 }{W_2 + W_3 + W_4}
& R_3 = \frac{ W_3 }{W_3 + W_4} \\
& G_2 = \frac{W_{22} + W_{23} + W_{24}}{\sum_{i=2}^{4}\sum_{j=2}^4{W_{ij}}}
& G_3 = \frac{W_{32} + W_{33} + W_{34}}{\sum_{i=3}^{4}\sum_{j=2}^4{W_{ij}}} \\
& G_{22} = \frac{W_{22}}{W_{22} + W_{23} + W_{24}}
& G_{23} = \frac{W_{23}}{W_{23} + W_{24}} \\
& G_{32} = \frac{W_{32}}{W_{32} + W_{33} + W_{34}}
& G_{33} = \frac{W_{33}}{W_{33} + W_{34}} \\
& G_{42} = \frac{W_{42}}{W_{42} + W_{43} + W_{44}}
& G_{44} = \frac{W_{43}}{W_{43} + W_{44}}
\end{align*}
Calculation of the other variables happens as follows:
.. math::
:nowrap:
\begin{align*}
& \text{Calculate the base weight fractions of each component:} \\
& W_2 = (1 - W_1) \cdot R_1 \\
& W_3 = (1 - W_1 - W_2) \cdot R_2 \\
& W_4 = (1 - W_1 - W_2 - W_3) \\
& \\
& \text{if $W_1 \leq 0.5$:} \\
& \quad \text{$P_{11}$ is given}\\
& \quad W_{xx} = W_{22} + W_{23} + W_{24} + W_{32} + W_{33} + W_{34} + W_{42} + W_{43} + W_{44} = W_1 \cdot (1 - P_{11}) + W_2 + W_3 + W_4 \\
& \text{if $W_1 > 0.5$:} \\
& \quad \text{$P_{xx}$ is given and $P_{11}$ is derived further down} \\
& \quad W_{xx} = W_{22} + W_{23} + W_{24} + W_{32} + W_{33} + W_{34} + W_{42} + W_{43} + W_{44} = P_{xx} \cdot (W_2 + W_3 + W_4) \\
& \\
& \text{Caclulate a partial sum of the $2^{nd}$ component's contributions: } \\
& W_{2x} = W_{xx} \cdot G_2 \\
& \text{Calculate a partial sum of the $3^{d}$ and $4^{th}$ component's contributions:} \\
& W_{yx} = W_{xx} - W_{2x} \\
& \text{Calculate a partial sum of the $3^{d}$ component's contributions:} \\
& W_{3x} = W_{yx} \cdot G_3 \\
& \text{Calculate a partial sum of the $4^{th}$ component's contributions:} \\
& W_{4x} = W_{yx} - W_{3x} \\
& \\
& W_{22} = G_{22} \cdot W_{2x} \\
& W_{23} = G_{23} \cdot (W_{2x} - W_{22}) \\
& W_{24} = W{2x} - W_{22} - W_{23} \\
& \\
& W_{32} = G_{32} \cdot W_{3x} \\
& W_{33} = G_{33} \cdot (W_{3x} - W_{32}) \\
& W_{34} = W{3x} - W_{32} - W_{33} \\
& \\
& W_{42} = G_{42} \cdot W_{4x} \\
& W_{43} = G_{43} \cdot (W_{4x} - W_{42}) \\
& W_{44} = W{4x} - W_{42} - W_{43} \\
& \\
& \text{ From the above weight fractions the junction probabilities
for any combination of $2^{nd}$, $3^{d}$ and $4^{th}$ type
components can be calculated. } \\
& \text{ The remaining probabilities are: } \\
& P_{12} = \begin{dcases}
\frac{W_2 - W_{22} - W_{32} - W_{42}}{W_1}, & \text{if $W_1 > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& P_{13} = \begin{dcases}
\frac{W_3 - W_{23} - W_{33} - W_{43}}{W_1}, & \text{if $W_1 > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& P_{14} = \begin{dcases}
\frac{W_4 - W_{24} - W_{34} - W_{44}}{W_1}, & \text{if $W_1 > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& \\
& \text{if $W_1 \leq 0.5$}: \\
& \quad P_{11} = 1 - P_{12} - P_{13} - P_{14} \\
& \text{Remainder of weight fraction can now be calculated as follows:} \\
& \quad W_{ij} = {W_{ii}} \cdot {P_{ij}} \quad \forall {i,j} \in \left[ {1, 4} \right] \\
\end{align*}
"""
# MODEL METADATA:
class Meta(_AbstractProbability.Meta):
store_id = "R1G4Model"
# PROPERTIES
_G = 4
inherit_W1 = BoolProperty(default=False,
text="Inherit flag for W1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
W1 = FloatProperty(default=0.6,
text="W1",
math_text=r"$W_1$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_W1",
inherit_from="parent.based_on.probabilities.W1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_P11_or_P22 = BoolProperty(default=False,
text="Inherit flag for P11_or_P22",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
P11_or_P22 = FloatProperty(
default=0.25,
text="P11_or_P22",
math_text=r"$P_{11} %s$ or $\newline P_{22} %s$" %
(mt_range(0.0, "W_1", 0.5), mt_range(0.5, "W_1", 1.0)),
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_P11_or_P22",
inherit_from="parent.based_on.probabilities.P11_or_P22",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_R1 = BoolProperty(default=False,
text="Inherit flag for R1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
R1 = FloatProperty(default=0.5,
text="W2/(W2+W3+W4)",
math_text=r"$\large\frac{W_2}{W_2 + W_3 + W_4}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_R1",
inherit_from="parent.based_on.probabilities.R1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_R2 = BoolProperty(default=False,
text="Inherit flag for R2",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
R2 = FloatProperty(default=0.5,
text="W3/(W3+W4)",
math_text=r"$\large\frac{W_3}{W_3 + W_4}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_R2",
inherit_from="parent.based_on.probabilities.R2",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_G1 = BoolProperty(default=False,
text="Inherit flag for G1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G1 = FloatProperty(
default=0.5,
text="(W22+W23+W24)/(W22+W23+W24+W32+W33+W34+W42+W43+W44)",
math_text=
r"$\large\frac{\sum_{j=2}^{4} W_{2j}}{\sum_{i=2}^{4} \sum_{j=2}^{4} W_{ij}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G1",
inherit_from="parent.based_on.probabilities.G1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G2 = BoolProperty(default=False,
text="Inherit flag for G2",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G2 = FloatProperty(
default=0.4,
text="(W32+W33+W34)/(W32+W33+W34+W42+W43+W44)",
math_text=
r"$\large\frac{\sum_{j=2}^{4} W_{3j}}{\sum_{i=3}^{4} \sum_{j=2}^{4} W_{ij}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G2",
inherit_from="parent.based_on.probabilities.G2",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G11 = BoolProperty(default=False,
text="Inherit flag for G11",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G11 = FloatProperty(
default=0.5,
text="W22/(W22+W23+W24)",
math_text=r"$\large\frac{W_{22}}{\sum_{j=2}^{4} W_{2j}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G11",
inherit_from="parent.based_on.probabilities.G11",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G12 = BoolProperty(default=False,
text="Inherit flag for G12",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G12 = FloatProperty(
default=0.5,
text="W23/(W23+W24)",
math_text=r"$\large\frac{W_{23}}{\sum_{j=3}^{4} W_{2j}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G12",
inherit_from="parent.based_on.probabilities.G12",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G21 = BoolProperty(default=False,
text="Inherit flag for G21",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G21 = FloatProperty(
default=0.8,
text="W32/(W32+W33+W34)",
math_text=r"$\large\frac{W_{32}}{\sum_{j=2}^{4} W_{3j}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G21",
inherit_from="parent.based_on.probabilities.G21",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G22 = BoolProperty(default=False,
text="Inherit flag for G22",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G22 = FloatProperty(
default=0.8,
text="W33/(W32+W34)",
math_text=r"$\large\frac{W_{33}}{\sum_{j=3}^{4} W_{3j}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G22",
inherit_from="parent.based_on.probabilities.G22",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G31 = BoolProperty(default=False,
text="Inherit flag for G31",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G31 = FloatProperty(
default=0.7,
text="W42/(W42+W43+W44)",
math_text=r"$\large\frac{W_{42}}{\sum_{j=2}^{4} W_{4j}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G31",
inherit_from="parent.based_on.probabilities.G31",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G32 = BoolProperty(default=False,
text="Inherit flag for G32",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G32 = FloatProperty(
default=0.5,
text="W43/(W43+W44)",
math_text=r"$\large\frac{W_{43}}{\sum_{j=3}^{4} W_{4j}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G32",
inherit_from="parent.based_on.probabilities.G32",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
# ------------------------------------------------------------
# Initialization and other internals
# ------------------------------------------------------------
def __init__(self,
W1=0.6,
P11_or_P22=0.25,
R1=0.5,
R2=0.5,
G1=0.5,
G2=0.4,
G11=0.5,
G12=0.5,
G21=0.8,
G22=0.75,
G31=0.7,
G32=0.5,
inherit_W1=False,
inherit_P11_or_P22=False,
inherit_R1=False,
inherit_R2=False,
inherit_G1=False,
inherit_G2=False,
inherit_G11=False,
inherit_G12=False,
inherit_G21=False,
inherit_G22=False,
inherit_G31=False,
inherit_G32=False,
*args,
**kwargs):
super(R1G4Model, self).__init__(R=1, *args, **kwargs)
with self.data_changed.hold():
self.W1 = not_none(W1, 0.6)
self.inherit_W1 = inherit_W1
self.P11_or_P22 = not_none(P11_or_P22, 0.25)
self.inherit_P11_or_P22 = inherit_P11_or_P22
self.R1 = not_none(R1, 0.5)
self.inherit_R1 = inherit_R1
self.R2 = not_none(R2, 0.5)
self.inherit_R2 = inherit_R2
self.G1 = not_none(G1, 0.5)
self.inherit_G1 = inherit_G1
self.G2 = not_none(G2, 0.4)
self.inherit_G2 = inherit_G2
self.G11 = not_none(G11, 0.5)
self.inherit_G11 = inherit_G11
self.G12 = not_none(G12, 0.5)
self.inherit_G12 = inherit_G12
self.G21 = not_none(G21, 0.8)
self.inherit_G21 = inherit_G21
self.G22 = not_none(G22, 0.75)
self.inherit_G22 = inherit_G22
self.G31 = not_none(G31, 0.7)
self.inherit_G31 = inherit_G31
self.G32 = not_none(G32, 0.5)
self.inherit_G32 = inherit_G32
self.update()
# ------------------------------------------------------------
# Methods & Functions
# ------------------------------------------------------------
def update(self):
with self.monitor_changes():
self.mW[0] = self.W1
self.mW[1] = (1.0 - self.mW[0]) * self.R1
self.mW[2] = (1.0 - self.mW[0] - self.mW[1]) * self.R2
self.mW[3] = 1.0 - self.mW[0] - self.mW[1] - self.mW[2]
W0inv = 1.0 / self.mW[0] if self.mW[0] > 0.0 else 0.0
if self.mW[0] < 0.5: # P11 is given
self.mP[0, 0] = self.P11_or_P22
Wxx = self.mW[0] * (self.mP[0, 0] -
1) + self.mW[1] + self.mW[2] + self.mW[3]
else: # P22 is given
Wxx = self.P11_or_P22 * (self.mW[1] + self.mW[2] + self.mW[3])
W1x = Wxx * self.G1 # = W11 + W12 + W13
Wyx = (Wxx - W1x) # = W21 + W22 + W23 + W31 + W32 + W33
W2x = Wyx * self.G2 # = W21 + W22 + W23
W3x = Wyx - W2x # = W31 + W32 + W33
self.mW[1, 1] = self.G11 * W1x
self.mW[1, 2] = self.G12 * (W1x - self.mW[1, 1])
self.mW[1, 3] = W1x - self.mW[1, 1] - self.mW[1, 2]
self.mW[2, 1] = self.G21 * W2x
self.mW[2, 2] = self.G22 * (W2x - self.mW[2, 1])
self.mW[2, 3] = W2x - self.mW[2, 1] - self.mW[2, 2]
self.mW[3, 1] = self.G31 * W3x
self.mW[3, 2] = self.G32 * (W3x - self.mW[3, 1])
self.mW[3, 3] = W3x - self.mW[3, 1] - self.mW[3, 2]
for i in range(1, 4):
self.mP[i, 0] = 1
for j in range(1, 4):
self.mP[i, j] = self.mW[
i, j] / self.mW[i] if self.mW[i] > 0 else 0
self.mP[i, 0] -= self.mP[i, j]
self.mW[i, 0] = self.mW[i] * self.mP[i, 0]
self.mP[0, 1] = (self.mW[1] - self.mW[1, 1] - self.mW[2, 1] -
self.mW[3, 1]) * W0inv
self.mP[0, 2] = (self.mW[2] - self.mW[1, 2] - self.mW[2, 2] -
self.mW[3, 2]) * W0inv
self.mP[0, 3] = (self.mW[3] - self.mW[1, 3] - self.mW[2, 3] -
self.mW[3, 3]) * W0inv
if self.mW[0] >= 0.5:
self.mP[0,
0] = 1 - self.mP[0, 1] - self.mP[0, 2] - self.mP[0, 3]
for i in range(4):
for j in range(4):
self.mW[i, j] = self.mW[i] * self.mP[i, j]
self.solve()
self.validate()
pass # end of class
class R1G2Model(_AbstractProbability):
r"""
Probability model for Reichweite 1 with 2 components.
The 2(=g*(g-1)) independent variables are:
.. math::
:nowrap:
\begin{flalign*}
& W_1 \\
& \text{$P_{11} (W_1 < 0.5)$ or $P_{22} (W_1 > 0.5)$}
\end{flalign*}
Calculation of the other variables happens as follows:
.. math::
:nowrap:
\begin{align*}
& W_2 = 1 – W_1 \\
& \begin{aligned}
& \text{$P_{11}$ is given:} \\
& \quad P_{12} = 1 - P_{11} \\
& \quad P_{21} = \frac{W_1 \cdot P_{12}}{W2} \\
& \quad P_{22} = 1 - P_{21} \\
\end{aligned}
\quad \quad
\begin{aligned}
& \text{$P_{22}$ is given:} \\
& \quad P_{21} = 1 - P_{22} \\
& \quad P_{12} = \frac{W_2 \cdot P_{21}}{W1} \\
& \quad P_{11} = 1 - P_{12} \\
\end{aligned} \\
\end{align*}
"""
# MODEL METADATA:
class Meta(_AbstractProbability.Meta):
store_id = "R1G2Model"
# PROPERTIES:
_G = 2
inherit_W1 = BoolProperty(default=False,
text="Inherit flag for W1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
W1 = FloatProperty(default=0.0,
text="W1",
math_text=r"$W_1$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_W1",
inherit_from="parent.based_on.probabilities.W1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_P11_or_P22 = BoolProperty(default=False,
text="Inherit flag for P11_or_P22",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
P11_or_P22 = FloatProperty(
default=0.0,
text="P11_or_P22",
math_text=r"$P_{11} %s$ or $\newline P_{22} %s$" %
(mt_range(0.0, "W_1", 0.5), mt_range(0.5, "W_1", 1.0)),
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_P11_or_P22",
inherit_from="parent.based_on.probabilities.P11_or_P22",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
# ------------------------------------------------------------
# Initialization and other internals
# ------------------------------------------------------------
def __init__(self,
W1=0.75,
P11_or_P22=0.5,
inherit_W1=False,
inherit_P11_or_P22=False,
*args,
**kwargs):
super(R1G2Model, self).__init__(R=1, *args, **kwargs)
with self.data_changed.hold():
self.W1 = not_none(W1, 0.75)
self.inherit_W1 = inherit_W1
self.P11_or_P22 = not_none(P11_or_P22, 0.5)
self.inherit_P11_or_P22 = inherit_P11_or_P22
self.update()
# ------------------------------------------------------------
# Methods & Functions
# ------------------------------------------------------------
def update(self):
with self.monitor_changes():
self.mW[0] = self.W1
self.mW[1] = 1.0 - self.mW[0]
if self.mW[0] <= 0.5:
self.mP[0, 0] = self.P11_or_P22
self.mP[0, 1] = 1.0 - self.mP[0, 0]
self.mP[1, 0] = self.mW[0] * self.mP[0, 1] / self.mW[1]
self.mP[1, 1] = 1.0 - self.mP[1, 0]
else:
self.mP[1, 1] = self.P11_or_P22
self.mP[1, 0] = 1.0 - self.mP[1, 1]
self.mP[0, 1] = self.mW[1] * self.mP[1, 0] / self.mW[0]
self.mP[0, 0] = 1.0 - self.mP[0, 1]
self.solve()
self.validate()
pass # end of class
class R1G3Model(_AbstractProbability):
r"""
Probability model for Reichweite 1 with 3 components.
The 6 (=g*(g-1)) independent variables are:
.. math::
:nowrap:
\begin{align*}
& W_1
& \text{$P_{11} (W_1 < 0.5)$ or $P_{xx} (W_1 > 0.5)$}
with P_{xx} = \frac {W_{22} + W_{23} + W_{32} + W_{33} + W_{42} + W_{43}}{W_2 + W_3} \\
& G_1 = \frac{W_2}{W_2 + W_3}
& G_2 = \frac{W_{22} + W_{23}}{W_{22} + W_{23} + W_{32} + W_{33}} \\
& G_3 = \frac{W_{22}}{W_{22} + W_{23}}
& G_4 = \frac{W_{32}}{W_{32} + W_{33}} \\
\end{align*}
Calculation of the other variables happens as follows:
.. math::
:nowrap:
\begin{align*}
& \text{Calculate the 'inverted' ratios of $G_2$, $G_3$ and $G_4$ as follows:} \\
& \quad G_i^{\text{-1}} =
\begin{cases}
G_i^{-1} - 1.0, & \text{if } G_i > 0 \\
0, & \text{otherwise}
\end{cases} \quad \forall i \in \left\{ {2, 3, 4}\right\} \\
& \\
& \text{Calculate the base weight fractions of each component:} \\
& \quad W_2 = (1 - W_1) \cdot G_1\\
& \quad W_3 = 1.0 - W_1 - W_2 \\
& \\
& \text{if $W_1 \leq 0.5$:} \\
& \quad \text{$P_{11}$ is given and W_xx is derived as} \\
& \quad W_{xx} = W_{22} + W_{23} + W_{32} + W_{23} = W_1 \cdot (1 - P_{11}) + W_2 + W_3 \\
& \\
& \text{if $W_1 > 0.5$:} \\
& \quad \text{$P_{xx}$ is given and $P_{11}$ is derived further down} \\
& \quad W_{xx} = W_{22} + W_{23} + W_{32} + W_{23} = P_{xx} \cdot (W_2 + W_3) \\
& \\
& W_{22} = W_{xx} \cdot G_2 \cdot G_3 \\
& W_{23} = W_{22} \cdot G_3^{-1} \\
& W_{32} = W_{xx} \cdot (1 - G_2) \\
& W_{33} = G_4^{-1} \cdot W_{32} \\
& \\
& P_{23} =
\begin{dcases}
\dfrac{W_{23}}{W_2}, & \text{if $W_2 > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& P_{12} = 1 - P_{22} - P_{23} \\
& \\
& P_{32} =
\begin{dcases}
\frac{W_{32}}{W_3}, & \text{if $W_3 > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& P_{33} =
\begin{dcases}
\frac{W_{33}}{W_3}, & \text{if $W_3 > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& P_{31} = 1 - P_{32} - P_{33} \\
& \\
& P_{12} =
\begin{dcases}
\frac{W_2 - W_{22} - W_{32}}{W_1}, & \text{if $W_1 > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& P_{13} =
\begin{dcases}
\frac{W_3 - W_{23} - W_{33}}{W_1}, & \text{if $W_1 > 0$} \\
0, & \text{otherwise}
\end{dcases} \\
& \\
& \text{if $W_1 > 0.5$}: \\
& \quad P_{11} = 1 - P_{12} - P_{13} \\
& \\
& \text{Remainder of weight fraction can be calculated as follows:} \\
& \quad W_{ij} = {W_{ii}} \cdot {P_{ij}} \quad \forall {i,j} \in \left[ {1, 3} \right] \\
\end{align*}
"""
# MODEL METADATA:
class Meta(_AbstractProbability.Meta):
store_id = "R1G3Model"
# PROPERTIES
_G = 3
inherit_W1 = BoolProperty(default=False,
text="Inherit flag for W1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
W1 = FloatProperty(default=0.8,
text="W1",
math_text=r"$W_1$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_W1",
inherit_from="parent.based_on.probabilities.W1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_P11_or_P22 = BoolProperty(default=False,
text="Inherit flag for P11_or_P22",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
P11_or_P22 = FloatProperty(
default=0.7,
text="P11_or_P22",
math_text=r"$P_{11} %s$ or $\newline P_{22} %s$" %
(mt_range(0.0, "W_1", 0.5), mt_range(0.5, "W_1", 1.0)),
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_P11_or_P22",
inherit_from="parent.based_on.probabilities.P11_or_P22",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G1 = BoolProperty(default=False,
text="Inherit flag for G1",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G1 = FloatProperty(default=0.7,
text="W2/(W2+W3)",
math_text=r"$\large\frac{W_2}{W_3 + W_2}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G1",
inherit_from="parent.based_on.probabilities.G1",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_G2 = BoolProperty(default=False,
text="Inherit flag for G2",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G2 = FloatProperty(
default=0.7,
text="(W22+W23)/(W22+W23+W32+W33)",
math_text=
r"$\large\frac{W_{22} + W_{23}}{W_{22} + W_{23} + W_{32} + W_{33}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G2",
inherit_from="parent.based_on.probabilities.G2",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin, InheritableMixin))
inherit_G3 = BoolProperty(default=False,
text="Inherit flag for G3",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G3 = FloatProperty(default=0.7,
text="W22/(W22+W23)",
math_text=r"$\large\frac{W_{22}}{W_{22} + W_{23}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G3",
inherit_from="parent.based_on.probabilities.G3",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
inherit_G4 = BoolProperty(default=False,
text="Inherit flag for G4",
persistent=True,
visible=True,
set_action_name="update",
mix_with=(SetActionMixin, ))
G4 = FloatProperty(default=0.7,
text="W23/(W32+W33)",
math_text=r"$\large\frac{W_{22}}{W_{22} + W_{23}}$",
persistent=True,
visible=True,
refinable=True,
store_private=True,
minimum=0.0,
maximum=1.0,
is_independent=True,
inheritable=True,
inherit_flag="inherit_G4",
inherit_from="parent.based_on.probabilities.G4",
set_action_name="update",
mix_with=(SetActionMixin, RefinableMixin,
InheritableMixin))
# ------------------------------------------------------------
# Initialization and other internals
# ------------------------------------------------------------
def __init__(self,
W1=0.8,
P11_or_P22=0.7,
G1=0.7,
G2=0.7,
G3=0.7,
G4=0.7,
inherit_W1=False,
inherit_P11_or_P22=False,
inherit_G1=False,
inherit_G2=False,
inherit_G3=False,
inherit_G4=False,
*args,
**kwargs):
super(R1G3Model, self).__init__(R=1, *args, **kwargs)
with self.data_changed.hold():
self.W1 = not_none(W1, 0.8)
self.inherit_W1 = bool(inherit_W1)
self.P11_or_P22 = not_none(P11_or_P22, 0.7)
self.inherit_P11_or_P22 = bool(inherit_P11_or_P22)
self.G1 = not_none(G1, 0.7)
self.inherit_G1 = bool(inherit_G1)
self.G2 = not_none(G2, 0.7)
self.inherit_G2 = bool(inherit_G2)
self.G3 = not_none(G3, 0.7)
self.inherit_G3 = bool(inherit_G3)
self.G4 = not_none(G4, 0.7)
self.inherit_G4 = bool(inherit_G4)
self.update()
# ------------------------------------------------------------
# Methods & Functions
# ------------------------------------------------------------
def update(self):
with self.monitor_changes():
self.mW[0] = self.W1
self.mW[1] = (1 - self.mW[0]) * self.G1
self.mW[2] = 1.0 - self.mW[0] - self.mW[1]
W0inv = 1.0 / self.mW[0] if self.mW[0] > 0.0 else 0.0
Wxx = 0
if self.mW[0] <= 0.5: # P00 given
self.mP[0, 0] = self.P11_or_P22
# Wxx = W11 + W12 + W21 + W22
Wxx = self.mW[0] * (self.mP[0, 0] -
1) + self.mW[1] + self.mW[2]
else: # Pxx given
# Wxx = W11 + W12 + W21 + W22
Wxx = (1.0 - self.mW[0]) * self.P11_or_P22
# W11 + W12 = Wxx * G2:
self.mW[1, 1] = Wxx * self.G2 * self.G3
self.mW[1, 2] = Wxx * self.G2 * (1 - self.G3)
self.mP[1,
1] = self.mW[1,
1] / self.mW[1] if self.mW[1] > 0.0 else 0.0
self.mW[2, 1] = Wxx * (1 - self.G2) * self.G4
self.mW[2, 2] = Wxx * (1 - self.G2) * (1 - self.G4)
self.mP[1, 2] = (self.mW[1, 2] /
self.mW[1]) if self.mW[1] > 0.0 else 0.0
self.mP[1, 0] = 1 - self.mP[1, 1] - self.mP[1, 2]
self.mP[2, 1] = (self.mW[2, 1] /
self.mW[2]) if self.mW[2] > 0.0 else 0.0
self.mP[2, 2] = (self.mW[2, 2] /
self.mW[2]) if self.mW[2] > 0.0 else 0.0
self.mP[2, 0] = 1 - self.mP[2, 1] - self.mP[2, 2]
self.mP[0,
1] = (self.mW[1] - self.mW[1, 1] - self.mW[2, 1]) * W0inv
self.mP[0,
2] = (self.mW[2] - self.mW[1, 2] - self.mW[2, 2]) * W0inv
if self.mW[0] > 0.5:
self.mP[0, 0] = 1 - self.mP[0, 1] - self.mP[0, 2]
for i in range(3):
for j in range(3):
self.mW[i, j] = self.mW[i, i] * self.mP[i, j]
self.solve()
self.validate()
pass # end of class
class Meta(_AbstractProbability.Meta):
ind_properties = [
PropIntel(
name="W1",
label="W1",
math_label=r"$W_1$",
stor_name="_W1",
inh_name="inherit_W1",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="P11_or_P22",
label="P11_or_P22",
stor_name="_P11_or_P22",
inh_name="inherit_P11_or_P22",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$P_{11} %s$ or $\newline P_{22} %s$" %
(mt_range(0.0, "W_1", 0.5), mt_range(0.5, "W_1", 1.0)),
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="R1",
label="W2/(W2+W3+W4)",
math_label=r"$\large\frac{W_2}{W_2 + W_3 + W_4}$",
stor_name="_R1",
inh_name="inherit_R1",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="R2",
label="W3)/(W3+W4)",
math_label=r"$\large\frac{W_3}{W_3 + W_4}$",
stor_name="_R2",
inh_name="inherit_R2",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="G1",
label="(W22+W23+W24)/(W22+W23+W24+W32+W33+W34+W42+W43+W44)",
stor_name="_G1",
inh_name="inherit_G1",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=
r"$\large\frac{\sum_{j=2}^{4} W_{2j}}{\sum_{i=2}^{4} \sum_{j=2}^{4} W_{ij}}$",
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="G2",
label="(W32+W33+W34)/(W32+W33+W34+W42+W43+W44)",
stor_name="_G2",
inh_name="inherit_G2",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=
r"$\large\frac{\sum_{j=2}^{4} W_{3j}}{\sum_{i=3}^{4} \sum_{j=2}^{4} W_{ij}}$",
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="G11",
label="W22/(W22+W23+W24)",
stor_name="_G11",
inh_name="inherit_G11",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{22}}{\sum_{j=2}^{4} W_{2j}}$",
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="G12",
label="W23/(W23+W24)",
stor_name="_G12",
inh_name="inherit_G12",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{23}}{\sum_{j=3}^{4} W_{2j}}$",
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="G21",
label="W32/(W32+W33+W34)",
stor_name="_G21",
inh_name="inherit_G21",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{32}}{\sum_{j=2}^{4} W_{3j}}$",
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="G22",
label="W33/(W32+W34)",
stor_name="_G22",
inh_name="inherit_G22",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{33}}{\sum_{j=3}^{4} W_{3j}}$",
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="G31",
label="W42/(W42+W43+W44)",
stor_name="_G31",
inh_name="inherit_G31",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{42}}{\sum_{j=2}^{4} W_{4j}}$",
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID),
PropIntel(
name="G32",
label="W43/(W43+W44)",
stor_name="_G32",
inh_name="inherit_G32",
inh_from="parent.based_on.probabilities",
is_independent=True, # flag for the view creation
math_label=r"$\large\frac{W_{43}}{\sum_{j=3}^{4} W_{4j}}$",
minimum=0.0,
maximum=1.0,
data_type=float,
**PropIntel.REF_ST_WID)
]
inh_properties = [
PropIntel(name="inherit_%s" % prop.name, label="Inherit flag for %s" % prop.name,
data_type=bool, refinable=False, storable=True, has_widget=True,
widget_type="toggle") \
for prop in ind_properties
]
properties = ind_properties + inh_properties
store_id = "R1G4Model"
