diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 346f780d..5039715b 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-11-24T08:50:29","documenter_version":"1.1.2"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-11-24T08:51:06","documenter_version":"1.1.2"}} \ No newline at end of file diff --git a/dev/export/export/index.html b/dev/export/export/index.html index de391fd2..9d65bb5d 100644 --- a/dev/export/export/index.html +++ b/dev/export/export/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Exporting to Other Systems

Here we put some helpful utilities to export your code to other identifiability software.

StructuralIdentifiability.print_for_maple — Function
print_for_maple(ode, package)

Prints the ODE in the format accepted by maple packages

  • SIAN (https://github.com/pogudingleb/SIAN) if package=:SIAN
  • DifferentialAlgebra if package=:DifferentialAlgebra
  • DifferentialThomas if package=:DifferentialThomas
source
+
GitHub

Exporting to Other Systems

Here we put some helpful utilities to export your code to other identifiability software.

StructuralIdentifiability.print_for_maple — Function
print_for_maple(ode, package)

Prints the ODE in the format accepted by maple packages

  • SIAN (https://github.com/pogudingleb/SIAN) if package=:SIAN
  • DifferentialAlgebra if package=:DifferentialAlgebra
  • DifferentialThomas if package=:DifferentialThomas
source
diff --git a/dev/identifiability/identifiability/index.html b/dev/identifiability/identifiability/index.html index be84ce26..7e37461c 100644 --- a/dev/identifiability/identifiability/index.html +++ b/dev/identifiability/identifiability/index.html @@ -3,12 +3,12 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Functions to Assess Identifiability

Assessing All Types of Identifiability

StructuralIdentifiability.assess_identifiability — Function
assess_identifiability(ode; funcs_to_check = [], p=0.99, loglevel=Logging.Info)

Input:

  • ode - the ODE model
  • funcs_to_check - list of functions to check identifiability for; if empty, all parameters and states are taken
  • p - probability of correctness.
  • loglevel - the minimal level of log messages to display (Logging.Info by default)

Assesses identifiability of a given ODE model. The result is guaranteed to be correct with the probability at least p. The function returns an (ordered) dictionary from the functions to check to their identifiability properties (one of :nonidentifiable, :locally, :globally).

source
assess_identifiability(ode::ModelingToolkit.ODESystem; measured_quantities=Array{ModelingToolkit.Equation}[], funcs_to_check=[], p = 0.99, loglevel=Logging.Info)

Input:

  • ode - the ModelingToolkit.ODESystem object that defines the model
  • measured_quantities - the output functions of the model
  • funcs_to_check - functions of parameters for which to check the identifiability
  • p - probability of correctness.
  • loglevel - the minimal level of log messages to display (Logging.Info by default)

Assesses identifiability (both local and global) of a given ODE model (parameters detected automatically). The result is guaranteed to be correct with the probability at least p.

source

Assessing Local Identifiability

StructuralIdentifiability.assess_local_identifiability — Function
function assess_local_identifiability(ode::ModelingToolkit.ODESystem; measured_quantities=Array{ModelingToolkit.Equation}[], funcs_to_check=Array{}[], p::Float64=0.99, type=:SE, loglevel=Logging.Info)

Input:

  • ode - the ODESystem object from ModelingToolkit
  • measured_quantities - the measurable outputs of the model
  • funcs_to_check - functions of parameters for which to check identifiability
  • p - probability of correctness
  • type - identifiability type (:SE for single-experiment, :ME for multi-experiment)
  • loglevel - the minimal level of log messages to display (Logging.Info by default)

Output:

  • for type=:SE, the result is an (ordered) dictionary from each parameter to boolean;
  • for type=:ME, the result is a tuple with the dictionary as in :SE case and array of number of experiments.

The function determines local identifiability of parameters in funcs_to_check or all possible parameters if funcs_to_check is empty

The result is correct with probability at least p.

type can be either :SE (single-experiment identifiability) or :ME (multi-experiment identifiability). The return value is a tuple consisting of the array of bools and the number of experiments to be performed.

source
assess_local_identifiability(ode::ODE{P}; funcs_to_check::Array{<: Any, 1}, p::Float64=0.99, type=:SE, loglevel=Logging.Info) where P <: MPolyElem{Nemo.fmpq}

Checks the local identifiability/observability of the functions in funcs_to_check. The result is correct with probability at least p.

Call this function if you have a specific collection of parameters of which you would like to check local identifiability.

type can be either :SE (single-experiment identifiability) or :ME (multi-experiment identifiability). If the type is :ME, states are not allowed to appear in the funcs_to_check.

source
function assess_local_identifiability(
+
GitHub
Functions to Assess Identifiability
Assessing All Types of Identifiability
StructuralIdentifiability.assess_identifiability — Function
assess_identifiability(ode; funcs_to_check = [], p=0.99, loglevel=Logging.Info)
Input:
  • ode - the ODE model
  • funcs_to_check - list of functions to check identifiability for; if empty, all parameters  and states are taken
  • p - probability of correctness.
  • loglevel - the minimal level of log messages to display (Logging.Info by default)
Assesses identifiability of a given ODE model. The result is guaranteed to be correct with the probability at least p. The function returns an (ordered) dictionary from the functions to check to their identifiability properties  (one of :nonidentifiable, :locally, :globally).
source
assess_identifiability(ode::ModelingToolkit.ODESystem; measured_quantities=Array{ModelingToolkit.Equation}[], funcs_to_check=[], p = 0.99, loglevel=Logging.Info)
Input:
  • ode - the ModelingToolkit.ODESystem object that defines the model
  • measured_quantities - the output functions of the model
  • funcs_to_check - functions of parameters for which to check the identifiability
  • p - probability of correctness.
  • loglevel - the minimal level of log messages to display (Logging.Info by default)
Assesses identifiability (both local and global) of a given ODE model (parameters detected automatically). The result is guaranteed to be correct with the probability at least p.
source
Assessing Local Identifiability
StructuralIdentifiability.assess_local_identifiability — Function
function assess_local_identifiability(ode::ModelingToolkit.ODESystem; measured_quantities=Array{ModelingToolkit.Equation}[], funcs_to_check=Array{}[], p::Float64=0.99, type=:SE, loglevel=Logging.Info)
Input:
  • ode - the ODESystem object from ModelingToolkit
  • measured_quantities - the measurable outputs of the model
  • funcs_to_check - functions of parameters for which to check identifiability
  • p - probability of correctness
  • type - identifiability type (:SE for single-experiment, :ME for multi-experiment)
  • loglevel - the minimal level of log messages to display (Logging.Info by default)
Output:
  • for type=:SE, the result is an (ordered) dictionary from each parameter to boolean;
  • for type=:ME, the result is a tuple with the dictionary as in :SE case and array of number of experiments.
The function determines local identifiability of parameters in funcs_to_check or all possible parameters if funcs_to_check is empty
The result is correct with probability at least p.
type can be either :SE (single-experiment identifiability) or :ME (multi-experiment identifiability). The return value is a tuple consisting of the array of bools and the number of experiments to be performed.
source
assess_local_identifiability(ode::ODE{P}; funcs_to_check::Array{<: Any, 1}, p::Float64=0.99, type=:SE, loglevel=Logging.Info) where P <: MPolyElem{Nemo.fmpq}
Checks the local identifiability/observability of the functions in funcs_to_check. The result is correct with probability at least p.
Call this function if you have a specific collection of parameters of which you would like to check local identifiability.
type can be either :SE (single-experiment identifiability) or :ME (multi-experiment identifiability). If the type is :ME, states are not allowed to appear in the funcs_to_check.
source
function assess_local_identifiability(
     dds::ModelingToolkit.DiscreteSystem; 
     measured_quantities=Array{ModelingToolkit.Equation}[], 
     funcs_to_check=Array{}[], 
     known_ic=Array{}[],
-    p::Float64=0.99)
Input:
  • dds - the DiscreteSystem object from ModelingToolkit (with difference operator in the right-hand side)
  • measured_quantities - the measurable outputs of the model
  • funcs_to_check - functions of parameters for which to check identifiability (all parameters and states if not specified)
  • known_ic - functions (of states and parameter) whose initial conditions are assumed to be known
  • p - probability of correctness
Output:
  • the result is an (ordered) dictionary from each function to to boolean;
The result is correct with probability at least p.
source
Finding Identifiable Functions
StructuralIdentifiability.find_identifiable_functions — Function
find_identifiable_functions(ode::ODE; options...)
Finds all functions of parameters/states that are identifiable in the given ODE system.
Options
This functions takes the following optional arguments:
  • with_states: When true, also reports the identifiabile functions in the   ODE states. Default is false.
  • simplify: The extent to which the output functions are simplified. Stronger simplification may require more time. Possible options are:
    • :standard: Default simplification.
    • :weak: Weak simplification. This option is the fastest, but the output functions can be quite complex.
    • :strong: Strong simplification. This option is the slowest, but the output
    functions are nice and simple.
    • :absent: No simplification.
  • p: A float in the range from 0 to 1, the probability of correctness. Default is 0.99.
  • seed: The rng seed. Default value is 42.
  • loglevel - the minimal level of log messages to display (Logging.Info by default)
Example
using StructuralIdentifiability
+    p::Float64=0.99)
Input:
  • dds - the DiscreteSystem object from ModelingToolkit (with difference operator in the right-hand side)
  • measured_quantities - the measurable outputs of the model
  • funcs_to_check - functions of parameters for which to check identifiability (all parameters and states if not specified)
  • known_ic - functions (of states and parameter) whose initial conditions are assumed to be known
  • p - probability of correctness
Output:
  • the result is an (ordered) dictionary from each function to to boolean;
The result is correct with probability at least p.
source
Finding Identifiable Functions
StructuralIdentifiability.find_identifiable_functions — Function
find_identifiable_functions(ode::ODE; options...)
Finds all functions of parameters/states that are identifiable in the given ODE system.
Options
This functions takes the following optional arguments:
  • with_states: When true, also reports the identifiabile functions in the   ODE states. Default is false.
  • simplify: The extent to which the output functions are simplified. Stronger simplification may require more time. Possible options are:
    • :standard: Default simplification.
    • :weak: Weak simplification. This option is the fastest, but the output functions can be quite complex.
    • :strong: Strong simplification. This option is the slowest, but the output
    functions are nice and simple.
    • :absent: No simplification.
  • p: A float in the range from 0 to 1, the probability of correctness. Default is 0.99.
  • seed: The rng seed. Default value is 42.
  • loglevel - the minimal level of log messages to display (Logging.Info by default)
Example
using StructuralIdentifiability
 
 ode = @ODEmodel(
     x0'(t) = -(a01 + a21) * x0(t) + a12 * x1(t),
@@ -21,7 +21,7 @@
 # prints
 3-element Vector{AbstractAlgebra.Generic.Frac{Nemo.fmpq_mpoly}}:
  a12 + a01 + a21
- a12*a01
source
find_identifiable_functions(ode::ModelingToolkit.ODESystem; measured_quantities=[], options...)
Finds all functions of parameters/states that are identifiable in the given ODE system.
Options
This functions takes the following optional arguments:
  • measured_quantities - the output functions of the model.
  • loglevel - the verbosity of the logging  (can be Logging.Error, Logging.Warn, Logging.Info, Logging.Debug)
Example
using StructuralIdentifiability
+ a12*a01
source
find_identifiable_functions(ode::ModelingToolkit.ODESystem; measured_quantities=[], options...)
Finds all functions of parameters/states that are identifiable in the given ODE system.
Options
This functions takes the following optional arguments:
  • measured_quantities - the output functions of the model.
  • loglevel - the verbosity of the logging  (can be Logging.Error, Logging.Warn, Logging.Info, Logging.Debug)
Example
using StructuralIdentifiability
 using ModelingToolkit
 
 @parameters a01 a21 a12
@@ -39,4 +39,4 @@
 # prints
 2-element Vector{Num}:
          a01*a12
- a01 + a12 + a21
source

+ a01 + a12 + a21
source
diff --git a/dev/index.html b/dev/index.html index 2d1a5fa9..7de540f6 100644 --- a/dev/index.html +++ b/dev/index.html @@ -264,4 +264,4 @@ [3f19e933] p7zip_jll v17.4.0+0 Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`You can also download the manifest file and the -project file. +project file. diff --git a/dev/input/input/index.html b/dev/input/input/index.html index 3fbde79b..ef93b35f 100644 --- a/dev/input/input/index.html +++ b/dev/input/input/index.html @@ -9,4 +9,4 @@ x1'(t) = a * x1(t) + u(t), x2'(t) = b * x2(t) + c*x1(t)*x2(t), y(t) = x1(t) -)

Here,

source
StructuralIdentifiability.ODE — Type

The main structure that represents input ODE system.

Stores information about states (x_vars), outputs (y_vars), inputs (u_vars), parameters (parameters) and the equations.

This structure is constructed via @ODEmodel macro.

source
StructuralIdentifiability.set_parameter_values — Function
set_parameter_values(ode, param_values)

Input:

  • ode - an ODE as above
  • param_values - values for (possibly, some of) the parameters as dictionary parameter => value

Output:

  • new ode with the parameters in param_values plugged with the given numbers
source

Create Compartmental Model

StructuralIdentifiability.linear_compartment_model — Function
linear_compartment_model(graph, inputs, outputs, leaks)

Input: defines a linear compartment model with nodes numbered from 1 to n by

  • graph - and array of integer arrays representing the adjacency lists of the graph
  • inputs - array of input nodes
  • outputs - array of output nodes
  • leaks - array of sink nodes

Output:

  • the corresponding ODE system in the notation of https://doi.org/10.1007/s11538-015-0098-0
source
+)

Here,

source
StructuralIdentifiability.ODE — Type

The main structure that represents input ODE system.

Stores information about states (x_vars), outputs (y_vars), inputs (u_vars), parameters (parameters) and the equations.

This structure is constructed via @ODEmodel macro.

source
StructuralIdentifiability.set_parameter_values — Function
set_parameter_values(ode, param_values)

Input:

  • ode - an ODE as above
  • param_values - values for (possibly, some of) the parameters as dictionary parameter => value

Output:

  • new ode with the parameters in param_values plugged with the given numbers
source

Create Compartmental Model

StructuralIdentifiability.linear_compartment_model — Function
linear_compartment_model(graph, inputs, outputs, leaks)

Input: defines a linear compartment model with nodes numbered from 1 to n by

  • graph - and array of integer arrays representing the adjacency lists of the graph
  • inputs - array of input nodes
  • outputs - array of output nodes
  • leaks - array of sink nodes

Output:

  • the corresponding ODE system in the notation of https://doi.org/10.1007/s11538-015-0098-0
source
diff --git a/dev/ioequations/ioequations/index.html b/dev/ioequations/ioequations/index.html index e61d9f7b..bd8cb8e3 100644 --- a/dev/ioequations/ioequations/index.html +++ b/dev/ioequations/ioequations/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Finding Input-Output Equations

StructuralIdentifiability.find_ioequations — Function
find_ioequations(ode, [var_change_policy=:default])

Finds the input-output equations of an ODE system Input:

  • ode - the ODE system
  • var_change_policy - whether to perform automatic variable change, can be one of :default, :yes, :no
  • loglevel - logging level (default: Logging.Info)

Output:

  • a dictionary from “leaders” to the corresponding input-output equations; if an extra projection is needed, it will be the value corresponding to rand_proj_var
source

Reducing with respect to Input-Output Equations

StructuralIdentifiability.PBRepresentation — Type

The structure for storing a projection-based representation of differential ideal (see Section 2.3 https://arxiv.org/abs/2111.00991). Contains the following fields:

  • y_names - the names of the variables with finite order in the profile (typically, outputs)
  • u_names - the names of the variables with infinite order in the profile (typically, inputs)
  • param_names - the names of the parameters
  • profile - the profile of the PB-representation (see Definition 2.13) as a dict from y_names with finite orders to the orders
  • projections - the corresponding projections (see Definition 2.15) as a dict from y_names to the projections
source
StructuralIdentifiability.pseudodivision — Function
pseudodivision(f, g, x)

Computes the result of pseudodivision of f by g as univariate polynomials in x Input:

  • f - the polynomial to be divided
  • g - the polynomial to divide by
  • x - the variable for the division

Output: the pseudoremainder of f divided by g w.r.t. x

source
StructuralIdentifiability.diffreduce — Function
diffreduce(diffpoly, pbr)

Computes the result of differential reduction of a differential polynomial diffpoly with respect to the charset defined by a PB-representation pbr Input:

  • diffpoly - a polynomial representing a differential polynomial to be reduced
  • pbr - a projection-based representation

Output: the result of differential reduction of diffpoly by pbr considered as a characteristic set (see Remark 2.20 in the paper)

source
+
GitHub

Finding Input-Output Equations

StructuralIdentifiability.find_ioequations — Function
find_ioequations(ode, [var_change_policy=:default])

Finds the input-output equations of an ODE system Input:

  • ode - the ODE system
  • var_change_policy - whether to perform automatic variable change, can be one of :default, :yes, :no
  • loglevel - logging level (default: Logging.Info)

Output:

  • a dictionary from “leaders” to the corresponding input-output equations; if an extra projection is needed, it will be the value corresponding to rand_proj_var
source

Reducing with respect to Input-Output Equations

StructuralIdentifiability.PBRepresentation — Type

The structure for storing a projection-based representation of differential ideal (see Section 2.3 https://arxiv.org/abs/2111.00991). Contains the following fields:

  • y_names - the names of the variables with finite order in the profile (typically, outputs)
  • u_names - the names of the variables with infinite order in the profile (typically, inputs)
  • param_names - the names of the parameters
  • profile - the profile of the PB-representation (see Definition 2.13) as a dict from y_names with finite orders to the orders
  • projections - the corresponding projections (see Definition 2.15) as a dict from y_names to the projections
source
StructuralIdentifiability.pseudodivision — Function
pseudodivision(f, g, x)

Computes the result of pseudodivision of f by g as univariate polynomials in x Input:

  • f - the polynomial to be divided
  • g - the polynomial to divide by
  • x - the variable for the division

Output: the pseudoremainder of f divided by g w.r.t. x

source
StructuralIdentifiability.diffreduce — Function
diffreduce(diffpoly, pbr)

Computes the result of differential reduction of a differential polynomial diffpoly with respect to the charset defined by a PB-representation pbr Input:

  • diffpoly - a polynomial representing a differential polynomial to be reduced
  • pbr - a projection-based representation

Output: the result of differential reduction of diffpoly by pbr considered as a characteristic set (see Remark 2.20 in the paper)

source
diff --git a/dev/tutorials/creating_ode/index.html b/dev/tutorials/creating_ode/index.html index 4a35654f..57609d14 100644 --- a/dev/tutorials/creating_ode/index.html +++ b/dev/tutorials/creating_ode/index.html @@ -57,4 +57,4 @@ c2 => :nonidentifiable chi2 => :globally r2 => :globally - beta2 => :globally
+ beta2 => :globally
diff --git a/dev/tutorials/discrete_time/index.html b/dev/tutorials/discrete_time/index.html index 9045c8eb..b3d49a01 100644 --- a/dev/tutorials/discrete_time/index.html +++ b/dev/tutorials/discrete_time/index.html @@ -35,4 +35,4 @@ R(t) => 0 β => 1 α => 1

The assess_local_identifiability function has three important keyword arguments:

assess_local_identifiability(sir; measured_quantities = [I], funcs_to_check = [β * S])
OrderedCollections.OrderedDict{Symbolics.Num, Bool} with 1 entry:
-  S(t)*β => 1

As other main functions in the package, assess_local_identifiability accepts an optional parameter loglevel (default: Logging.Info) to adjust the verbosity of logging.

The implementation is based on a version of the observability rank criterion and will be described in a forthcoming paper.

+ S(t)*β => 1

As other main functions in the package, assess_local_identifiability accepts an optional parameter loglevel (default: Logging.Info) to adjust the verbosity of logging.

The implementation is based on a version of the observability rank criterion and will be described in a forthcoming paper.

diff --git a/dev/tutorials/identifiability/index.html b/dev/tutorials/identifiability/index.html index 2c85c904..2fe1fad5 100644 --- a/dev/tutorials/identifiability/index.html +++ b/dev/tutorials/identifiability/index.html @@ -48,4 +48,4 @@ gama => :nonidentifiable sigma => :globally

As a result, each parameter/state is assigned one of the labels :globally (globally identifiable), :locally (locally but not globally identifiable), or :nonidentifiable (not identifiable, even locally). The algorithm behind this computation follows [4].

Similarly to assess_local_identifiability, this function has optional parameters:

Using funcs_to_check parameter, one can further inverstigate the nature of the lack of identifiability in the model at hand. For example, for the Goodwin oscillator, we can check if beta + delta and beta * delta are identifiable:

assess_identifiability(ode, funcs_to_check = [beta + delta, beta * delta])
OrderedCollections.OrderedDict{Any, Symbol} with 2 entries:
   beta + delta => :globally
-  beta*delta   => :globally

And we see that they indeed are. This means, in particular, that the reason why beta and delta are not identifiable is because their values can be exchanged. One may wonder how could we guess these functions beta + delta, beta * delta. In fact, they can be just computed using find_identifiable_functions function as we will explain in the next tutorial. Stay tuned!

+ beta*delta => :globally

And we see that they indeed are. This means, in particular, that the reason why beta and delta are not identifiable is because their values can be exchanged. One may wonder how could we guess these functions beta + delta, beta * delta. In fact, they can be just computed using find_identifiable_functions function as we will explain in the next tutorial. Stay tuned!

diff --git a/dev/tutorials/identifiable_functions/index.html b/dev/tutorials/identifiable_functions/index.html index a3717ffe..e44aef01 100644 --- a/dev/tutorials/identifiable_functions/index.html +++ b/dev/tutorials/identifiable_functions/index.html @@ -22,4 +22,4 @@ p1*p3 p1 + p3 x1(t)*p4 + x2(t)*p2 - (-p1 + p3)//(x1(t)*p4 - x2(t)*p2)

By default, find_identifiable_functions tries to simplify the output functions as much as possible, and it has simplify keyword responsible for the degree of simplification. The default value is :standard but one could use :strong to try to simplify further (at the expense of heavier computation) or use :weak to simplify less (but compute faster).

As assess_identifiability and assess_local_identifiability, find_identifiable_functions accepts an optional parameter loglevel (default: Logging.Info) to adjust the verbosity of logging.

+ (-p1 + p3)//(x1(t)*p4 - x2(t)*p2)

By default, find_identifiable_functions tries to simplify the output functions as much as possible, and it has simplify keyword responsible for the degree of simplification. The default value is :standard but one could use :strong to try to simplify further (at the expense of heavier computation) or use :weak to simplify less (but compute faster).

As assess_identifiability and assess_local_identifiability, find_identifiable_functions accepts an optional parameter loglevel (default: Logging.Info) to adjust the verbosity of logging.

diff --git a/dev/utils/elimination/index.html b/dev/utils/elimination/index.html index 5e2b2e23..41ba1890 100644 --- a/dev/utils/elimination/index.html +++ b/dev/utils/elimination/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Elimination

StructuralIdentifiability.Bezout_matrix — Method
Bezout_matrix(f, g, var_elim)

Compute the Bezout matrix of two polynomials f, g with respect to var_elim

Inputs:

  • f - first polynomial
  • g - second polynomial
  • var_elim - variable, of which f and g are considered as polynomials

Output:

  • M::MatrixElem - The Bezout matrix
source
StructuralIdentifiability.Sylvester_matrix — Method
Sylvester_matrix(f, g, var_elim)

Compute the Sylvester matrix of two polynomials f, g with respect to var_elim Inputs:

  • f - first polynomial
  • g - second polynomial
  • var_elim - variable, of which f and g are considered as polynomials

Output:

  • M::MatrixElem - The Sylvester matrix
source
StructuralIdentifiability.choose — Method
choose(polys, generic_point_generator)

Input:

  • polys - an array of distinct irreducible polynomials in the same ring
  • generic_point_generator - a generic point generator as described above for one of polys

Output:

  • the polynomial that vanishes at the generic_point_generator
source
StructuralIdentifiability.eliminate_var — Method
eliminate_var(f, g, var_elim, generic_point_generator)

Eliminate a variable from a pair of polynomials

Input:

  • f and g - polynomials
  • var_elim - variable to be eliminated
  • generic_point_generator - a generic point generator object for the factor of the resultant of f and g of interest

Output:

  • polynomial - the desired factor of the resultant of f and g
source
StructuralIdentifiability.simplify_matrix — Method
simplify_matrix(M)

Eliminate GCD of entries of every row and column

Input:

  • M::MatrixElem - matrix to be simplified

Output:

  • M::MatrixElem - Simplified matrix
  • extra_factors::Vector{AbstractAlgebra.MPolyElem} - array of GCDs eliminated from M.
source
+
GitHub

Elimination

StructuralIdentifiability.Bezout_matrix — Method
Bezout_matrix(f, g, var_elim)

Compute the Bezout matrix of two polynomials f, g with respect to var_elim

Inputs:

  • f - first polynomial
  • g - second polynomial
  • var_elim - variable, of which f and g are considered as polynomials

Output:

  • M::MatrixElem - The Bezout matrix
source
StructuralIdentifiability.Sylvester_matrix — Method
Sylvester_matrix(f, g, var_elim)

Compute the Sylvester matrix of two polynomials f, g with respect to var_elim Inputs:

  • f - first polynomial
  • g - second polynomial
  • var_elim - variable, of which f and g are considered as polynomials

Output:

  • M::MatrixElem - The Sylvester matrix
source
StructuralIdentifiability.choose — Method
choose(polys, generic_point_generator)

Input:

  • polys - an array of distinct irreducible polynomials in the same ring
  • generic_point_generator - a generic point generator as described above for one of polys

Output:

  • the polynomial that vanishes at the generic_point_generator
source
StructuralIdentifiability.eliminate_var — Method
eliminate_var(f, g, var_elim, generic_point_generator)

Eliminate a variable from a pair of polynomials

Input:

  • f and g - polynomials
  • var_elim - variable to be eliminated
  • generic_point_generator - a generic point generator object for the factor of the resultant of f and g of interest

Output:

  • polynomial - the desired factor of the resultant of f and g
source
StructuralIdentifiability.simplify_matrix — Method
simplify_matrix(M)

Eliminate GCD of entries of every row and column

Input:

  • M::MatrixElem - matrix to be simplified

Output:

  • M::MatrixElem - Simplified matrix
  • extra_factors::Vector{AbstractAlgebra.MPolyElem} - array of GCDs eliminated from M.
source
diff --git a/dev/utils/global_identifiability/index.html b/dev/utils/global_identifiability/index.html index fa1e744a..ee1e8dd4 100644 --- a/dev/utils/global_identifiability/index.html +++ b/dev/utils/global_identifiability/index.html @@ -12,4 +12,4 @@ rff = RationalFunctionField([x // y, y // z]) # Constructs a subfield generated by y / x, 1 / x, z / y -rff = RationalFunctionField([[x, y, R(1)], [y, z]])source
StructuralIdentifiability.field_contains — Function
field_contains(field, ratfuncs, p)

Checks whether given rational function field field contains given rational functions ratfuncs (represented as a list of lists). The result is correct with probability at least p

Inputs:

  • field - a rational function field
  • ratfuncs - a list of lists of polynomials. Each of the lists, say, [f1, ..., fn], defines generators f2/f1, ..., fn/f1.
  • p real number from (0, 1)

Output:

  • a list L[i] of bools of length length(rat_funcs) such that L[i] is true iff the i-th function belongs to field
source
StructuralIdentifiability.get_degree_and_coeffsize — Function
get_degree_and_coeffsize(f)

for f being a polynomial/rational function over rationals (QQ) returns a tuple (degree, max_coef_size)

source
+rff = RationalFunctionField([[x, y, R(1)], [y, z]])source
StructuralIdentifiability.field_contains — Function
field_contains(field, ratfuncs, p)

Checks whether given rational function field field contains given rational functions ratfuncs (represented as a list of lists). The result is correct with probability at least p

Inputs:

  • field - a rational function field
  • ratfuncs - a list of lists of polynomials. Each of the lists, say, [f1, ..., fn], defines generators f2/f1, ..., fn/f1.
  • p real number from (0, 1)

Output:

  • a list L[i] of bools of length length(rat_funcs) such that L[i] is true iff the i-th function belongs to field
source
StructuralIdentifiability.get_degree_and_coeffsize — Function
get_degree_and_coeffsize(f)

for f being a polynomial/rational function over rationals (QQ) returns a tuple (degree, max_coef_size)

source
diff --git a/dev/utils/local_identifiability/index.html b/dev/utils/local_identifiability/index.html index 25248b21..b35d1009 100644 --- a/dev/utils/local_identifiability/index.html +++ b/dev/utils/local_identifiability/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Local Identifiability Tools

StructuralIdentifiability.differentiate_solution — Function
differentiate_solution(ode, params, ic, inputs, prec)

Input:

  • the same as for power_series_solutions

Output:

  • a tuple consisting of the power series solution and a dictionary of the form (u, v) => power series, where u is a state variable v is a state or parameter, and the power series is the partial derivative of the function u w.r.t. v evaluated at the solution
source
StructuralIdentifiability.differentiate_output — Function
differentiate_output(ode, params, ic, inputs, prec)

Similar to differentiate_solution but computes partial derivatives of prescribed outputs returns a dictionary of the form y_function => Dict(var => dy/dvar) where dy/dvar is the derivative of y_function with respect to var.

source
+
GitHub

Local Identifiability Tools

StructuralIdentifiability.differentiate_solution — Function
differentiate_solution(ode, params, ic, inputs, prec)

Input:

  • the same as for power_series_solutions

Output:

  • a tuple consisting of the power series solution and a dictionary of the form (u, v) => power series, where u is a state variable v is a state or parameter, and the power series is the partial derivative of the function u w.r.t. v evaluated at the solution
source
StructuralIdentifiability.differentiate_output — Function
differentiate_output(ode, params, ic, inputs, prec)

Similar to differentiate_solution but computes partial derivatives of prescribed outputs returns a dictionary of the form y_function => Dict(var => dy/dvar) where dy/dvar is the derivative of y_function with respect to var.

source
diff --git a/dev/utils/ode/index.html b/dev/utils/ode/index.html index 1689fdfb..2aa72d52 100644 --- a/dev/utils/ode/index.html +++ b/dev/utils/ode/index.html @@ -3,8 +3,8 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Functions to work with the ODE structure

StructuralIdentifiability.__mtk_to_si — Method
function __mtk_to_si(de::ModelingToolkit.AbstractTimeDependentSystem, measured_quantities::Array{Tuple{String, SymbolicUtils.BasicSymbolic}})

Input:

  • de - ModelingToolkit.AbstractTimeDependentSystem, a system for identifiability query
  • measured_quantities - array of input function in the form (name, expression)

Output:

  • ODE object containing required data for identifiability assessment
  • conversion dictionary from the symbols in the input MTK model to the variable involved in the produced ODE object
source
StructuralIdentifiability.mtk_to_si — Method
function mtk_to_si(de::ModelingToolkit.AbstractTimeDependentSystem, measured_quantities::Array{ModelingToolkit.Equation})
-function mtk_to_si(de::ModelingToolkit.AbstractTimeDependentSystem, measured_quantities::Array{SymbolicUtils.BasicSymbolic})

Input:

  • de - ModelingToolkit.AbstractTimeDependentSystem, a system for identifiability query
  • measured_quantities - array of output functions (as equations of just functions)

Output:

  • ODE object containing required data for identifiability assessment
  • conversion dictionary from the symbols in the input MTK model to the variable involved in the produced ODE object
source
StructuralIdentifiability.power_series_solution — Method
power_series_solution(ode, param_values, initial_conditions, input_values, prec)

Input:

  • ode - an ode to solve
  • param_values - parameter values, must be a dictionary mapping parameter to a value
  • initial_conditions - initial conditions of ode, must be a dictionary mapping state variable to a value
  • input_values - power series for the inputs presented as a dictionary variable => list of coefficients
  • prec - the precision of solutions

Output:

  • computes a power series solution with precision prec presented as a dictionary variable => corresponding coordinate of the solution
source
StructuralIdentifiability.set_parameter_values — Method
set_parameter_values(ode, param_values)

Input:

  • ode - an ODE as above
  • param_values - values for (possibly, some of) the parameters as dictionary parameter => value

Output:

  • new ode with the parameters in param_values plugged with the given numbers
source
StructuralIdentifiability.find_submodels — Method
find_submodels(ode)

The function calculates and returns all valid submodels given a system of ODEs.

Input:

  • ode - an ODEs system to be studied

Output:

  • A list of submodels represented as ode objects

Example:

>ode = @ODEmodel(x1'(t) = x1(t)^2, 
+
GitHub
Functions to work with the ODE structure
StructuralIdentifiability.__mtk_to_si — Method
function __mtk_to_si(de::ModelingToolkit.AbstractTimeDependentSystem, measured_quantities::Array{Tuple{String, SymbolicUtils.BasicSymbolic}})
Input:
  • de - ModelingToolkit.AbstractTimeDependentSystem, a system for identifiability query
  • measured_quantities - array of input function in the form (name, expression)
Output:
  • ODE object containing required data for identifiability assessment
  • conversion dictionary from the symbols in the input MTK model to the variable involved in the produced ODE object
source
StructuralIdentifiability.mtk_to_si — Method
function mtk_to_si(de::ModelingToolkit.AbstractTimeDependentSystem, measured_quantities::Array{ModelingToolkit.Equation})
+function mtk_to_si(de::ModelingToolkit.AbstractTimeDependentSystem, measured_quantities::Array{SymbolicUtils.BasicSymbolic})
Input:
  • de - ModelingToolkit.AbstractTimeDependentSystem, a system for identifiability query
  • measured_quantities - array of output functions (as equations of just functions)
Output:
  • ODE object containing required data for identifiability assessment
  • conversion dictionary from the symbols in the input MTK model to the variable involved in the produced ODE object
source
StructuralIdentifiability.power_series_solution — Method
power_series_solution(ode, param_values, initial_conditions, input_values, prec)
Input:
  • ode - an ode to solve
  • param_values - parameter values, must be a dictionary mapping parameter to a value
  • initial_conditions - initial conditions of ode, must be a dictionary mapping state variable to a value
  • input_values - power series for the inputs presented as a dictionary variable => list of coefficients
  • prec - the precision of solutions
Output:
  • computes a power series solution with precision prec presented as a dictionary variable => corresponding coordinate of the solution
source
StructuralIdentifiability.set_parameter_values — Method
set_parameter_values(ode, param_values)
Input:
  • ode - an ODE as above
  • param_values - values for (possibly, some of) the parameters as dictionary parameter => value
Output:
  • new ode with the parameters in param_values plugged with the given numbers
source
StructuralIdentifiability.find_submodels — Method
find_submodels(ode)
The function calculates and returns all valid submodels given a system of ODEs.
Input:
  • ode - an ODEs system to be studied
Output: 
  • A list of submodels represented as ode objects
Example:
>ode = @ODEmodel(x1'(t) = x1(t)^2, 
                  x2'(t) = x1(t) * x2(t), 
                  y1(t) = x1(t), 
                  y2(t) = x2(t))
@@ -13,4 +13,4 @@
         
         x1'(t) = a(t)*x2(t)^2 + x1(t)
         y1(t) = x1(t)
-    ]
source

+    ]
source
diff --git a/dev/utils/power_series_utils/index.html b/dev/utils/power_series_utils/index.html index 740ad54e..c9c367d8 100644 --- a/dev/utils/power_series_utils/index.html +++ b/dev/utils/power_series_utils/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Power Series Utilities

StructuralIdentifiability.ps_matrix_homlinear_de — Method
ps_matrix_homlinear_de(A, Y0, prec)

Input:

  • A - a square matrix with entries in a univariate power series ring
  • Y0 - a square invertible matrix over the base field

Output:

  • matrix Y such that Y' = AY up to precision of A - 1 and Y(0) = Y0
source
StructuralIdentifiability.ps_matrix_inv — Function
ps_matrix_inv(M, prec)

Input:

  • M - a square matrix with entries in a univariate power series ring it is assumed that M(0) is invertible and all entries having the same precision
  • prec - an integer, precision, if -1 then defaults to precision of M

Output:

  • the inverse of M computed up to prec
source
StructuralIdentifiability.ps_matrix_linear_de — Method
ps_matrix_linear_de(A, B, Y0, prec)

Input:

  • A, B - square matrices with entries in a univariate power series ring
  • Y0 - a matrix over the base field with the rows number the same as A

Output:

  • matrix Y such that Y' = AY + B up to precision of A - 1 and Y(0) = Y0
source
StructuralIdentifiability.ps_ode_solution — Method
ps_ode_solution(equations, ic, inputs, prec)

Input:

  • equations - a system of the form $A(x, u, mu)x' - B(x, u, mu) = 0$, where A is a generically nonsingular square matrix. Assumption: A is nonzero at zero
  • ic - initial conditions for x's (dictionary)
  • inputs - power series for inputs represented as arrays (dictionary)
  • prec - precision of the solution

Output:

  • power series solution of the system
source
+
GitHub

Power Series Utilities

StructuralIdentifiability.ps_matrix_homlinear_de — Method
ps_matrix_homlinear_de(A, Y0, prec)

Input:

  • A - a square matrix with entries in a univariate power series ring
  • Y0 - a square invertible matrix over the base field

Output:

  • matrix Y such that Y' = AY up to precision of A - 1 and Y(0) = Y0
source
StructuralIdentifiability.ps_matrix_inv — Function
ps_matrix_inv(M, prec)

Input:

  • M - a square matrix with entries in a univariate power series ring it is assumed that M(0) is invertible and all entries having the same precision
  • prec - an integer, precision, if -1 then defaults to precision of M

Output:

  • the inverse of M computed up to prec
source
StructuralIdentifiability.ps_matrix_linear_de — Method
ps_matrix_linear_de(A, B, Y0, prec)

Input:

  • A, B - square matrices with entries in a univariate power series ring
  • Y0 - a matrix over the base field with the rows number the same as A

Output:

  • matrix Y such that Y' = AY + B up to precision of A - 1 and Y(0) = Y0
source
StructuralIdentifiability.ps_ode_solution — Method
ps_ode_solution(equations, ic, inputs, prec)

Input:

  • equations - a system of the form $A(x, u, mu)x' - B(x, u, mu) = 0$, where A is a generically nonsingular square matrix. Assumption: A is nonzero at zero
  • ic - initial conditions for x's (dictionary)
  • inputs - power series for inputs represented as arrays (dictionary)
  • prec - precision of the solution

Output:

  • power series solution of the system
source
diff --git a/dev/utils/primality/index.html b/dev/utils/primality/index.html index 43ba87f8..b8142daf 100644 --- a/dev/utils/primality/index.html +++ b/dev/utils/primality/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Primality Checks

StructuralIdentifiability.check_primality — Function
check_primality(polys::Dict{fmpq_mpoly, fmpq_mpoly}, extra_relations::Array{fmpq_mpoly, 1})

The function checks if the ideal generated by the polynomials and saturated at the leading coefficient with respect to the corresponding variables is prime over rationals.

The extra_relations allows adding more polynomials to the generators (not affecting the saturation).

source
check_primality(polys::Dict{fmpq_mpoly, fmpq_mpoly})

The function checks if the ideal generated by the polynomials and saturated at the leading coefficient with respect to the corresponding variables is prime over rationals.

source
+
GitHub

Primality Checks

StructuralIdentifiability.check_primality — Function
check_primality(polys::Dict{fmpq_mpoly, fmpq_mpoly}, extra_relations::Array{fmpq_mpoly, 1})

The function checks if the ideal generated by the polynomials and saturated at the leading coefficient with respect to the corresponding variables is prime over rationals.

The extra_relations allows adding more polynomials to the generators (not affecting the saturation).

source
check_primality(polys::Dict{fmpq_mpoly, fmpq_mpoly})

The function checks if the ideal generated by the polynomials and saturated at the leading coefficient with respect to the corresponding variables is prime over rationals.

source
diff --git a/dev/utils/reparametrization/index.html b/dev/utils/reparametrization/index.html index f55bd1be..11e702e3 100644 --- a/dev/utils/reparametrization/index.html +++ b/dev/utils/reparametrization/index.html @@ -23,4 +23,4 @@ X1 => x1 a2 => d a3 => a - a1 => c

Notice that the new_ode is fully identifiabile, and has 1 less parameter compared to the original one.

source + a1 => c

Notice that the new_ode is fully identifiabile, and has 1 less parameter compared to the original one.

source diff --git a/dev/utils/util/index.html b/dev/utils/util/index.html index a2bd773b..6bc14265 100644 --- a/dev/utils/util/index.html +++ b/dev/utils/util/index.html @@ -3,5 +3,5 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Other Helpful Functions

StructuralIdentifiability.dennums_to_fractions — Method
dennums_to_fractions(dennums)

Returns the field generators represented by fractions.

Input: an array of arrays of polynomials, as in [[f1, f2, f3, ...], [g1, g2, g3, ...], ...]

Output: an array of fractions [f2/f1, f3/f1, ..., g2/g1, g3/g1, ...]

source
StructuralIdentifiability.extract_coefficients — Method
extract_coefficients(poly, variables)

Input:

  • poly - multivariate polynomial
  • variables - a list of variables from the generators of the ring of p

Output:

  • dictionary with keys being tuples of length lenght(variables) and values being polynomials in the variables other than those which are the coefficients at the corresponding monomials (in a smaller polynomial ring)
source
StructuralIdentifiability.fractions_to_dennums — Method
fractions_to_dennums(fractions)

Returns the field generators represented by lists of denominators and numerators.

Input: an array of fractions, as in [f2/f1, f3/f1, ..., g2/g1, g3/g1, ...]

Output: an array of arrays of polynomials, [[f1, f2, f3, ...], [g1, g2, g3, ...], ...]

source
StructuralIdentifiability.gen_tag_name — Function
gen_tag_name(base; stop_words)
-gen_tag_names(n, base; stop_words)

Generates a string which will not collide with the words in stop_words.

Arguments

  • n: Generates a sequence of unique strings of length n
  • base: A string or a vector of strings, the base for the generated sequence
  • stop_words: A vector of strings, stop words
source
StructuralIdentifiability.make_substitution — Method
make_substitution(f, var_sub, val_numer, val_denom)

Substitute a variable in a polynomial with an expression

Input:

  • f - the polynomial
  • var_sub - the variable to be substituted
  • var_numer - numerator of the substitution expression
  • var_denom - denominator of the substitution expression

Output:

  • polynomial - result of substitution
source
StructuralIdentifiability.parent_ring_change — Method
parent_ring_change(poly, new_ring)

Converts a polynomial to a different polynomial ring Input

  • poly - a polynomial to be converted
  • new_ring - a polynomial ring such that every variable name appearing in poly appears among the generators

Output:

  • a polynomial in new_ring “equal” to poly
source
StructuralIdentifiability.uncertain_factorization — Method
uncertain_factorization(f)

Input:

  • f - polynomial with rational coefficients

Output:

  • list of pairs (div, certainty) where
    • div's are divisors of f such that f is their product with certain powers
    • if certainty is true, div is $Q$-irreducible
source
+
GitHub

Other Helpful Functions

StructuralIdentifiability.dennums_to_fractions — Method
dennums_to_fractions(dennums)

Returns the field generators represented by fractions.

Input: an array of arrays of polynomials, as in [[f1, f2, f3, ...], [g1, g2, g3, ...], ...]

Output: an array of fractions [f2/f1, f3/f1, ..., g2/g1, g3/g1, ...]

source
StructuralIdentifiability.extract_coefficients — Method
extract_coefficients(poly, variables)

Input:

  • poly - multivariate polynomial
  • variables - a list of variables from the generators of the ring of p

Output:

  • dictionary with keys being tuples of length lenght(variables) and values being polynomials in the variables other than those which are the coefficients at the corresponding monomials (in a smaller polynomial ring)
source
StructuralIdentifiability.fractions_to_dennums — Method
fractions_to_dennums(fractions)

Returns the field generators represented by lists of denominators and numerators.

Input: an array of fractions, as in [f2/f1, f3/f1, ..., g2/g1, g3/g1, ...]

Output: an array of arrays of polynomials, [[f1, f2, f3, ...], [g1, g2, g3, ...], ...]

source
StructuralIdentifiability.gen_tag_name — Function
gen_tag_name(base; stop_words)
+gen_tag_names(n, base; stop_words)

Generates a string which will not collide with the words in stop_words.

Arguments

  • n: Generates a sequence of unique strings of length n
  • base: A string or a vector of strings, the base for the generated sequence
  • stop_words: A vector of strings, stop words
source
StructuralIdentifiability.make_substitution — Method
make_substitution(f, var_sub, val_numer, val_denom)

Substitute a variable in a polynomial with an expression

Input:

  • f - the polynomial
  • var_sub - the variable to be substituted
  • var_numer - numerator of the substitution expression
  • var_denom - denominator of the substitution expression

Output:

  • polynomial - result of substitution
source
StructuralIdentifiability.parent_ring_change — Method
parent_ring_change(poly, new_ring)

Converts a polynomial to a different polynomial ring Input

  • poly - a polynomial to be converted
  • new_ring - a polynomial ring such that every variable name appearing in poly appears among the generators

Output:

  • a polynomial in new_ring “equal” to poly
source
StructuralIdentifiability.uncertain_factorization — Method
uncertain_factorization(f)

Input:

  • f - polynomial with rational coefficients

Output:

  • list of pairs (div, certainty) where
    • div's are divisors of f such that f is their product with certain powers
    • if certainty is true, div is $Q$-irreducible
source
diff --git a/dev/utils/wronskian/index.html b/dev/utils/wronskian/index.html index 4bfcf7f6..fb419024 100644 --- a/dev/utils/wronskian/index.html +++ b/dev/utils/wronskian/index.html @@ -3,4 +3,4 @@ function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'UA-90474609-3', {'page_path': location.pathname + location.search + location.hash}); -
GitHub

Wronskian Tools

StructuralIdentifiability.get_max_below — Method
get_max_below(t, vect)

Input:

  • t - a trie with exponent vectors
  • vect - yet another exponent vector

Output:

  • a pair (d, v) where v is a vector in the trie which is componentwise ≤ vect and the difference d is as small as possible
source
StructuralIdentifiability.massive_eval — Method
massive_eval(polys, eval_dict)

Input:

  • polys - a list of polynomials
  • eval_dict - dictionary from variables to the values. Missing values are treated as zeroes

Output:

  • a list of values of the polynomials

Evaluates a list of polynomials at a point. Assumes that multiplications are relatively expensive (like in truncated power series) so all the monomials are precomputed first and the values of monomials of lower degree are cached and used to compute the values of the monomials of higher degree

source
StructuralIdentifiability.monomial_compress — Method
monomial_compress(io_equation, ode)

Compresses an input-output equation for the rank computation Input:

  • io_equation - input-output equation
  • ode - the corresponding ODE model

Output:

  • pair (coeffs, terms) such that:
    • sum of coeffs[i] * terms[i] = io_equation
    • coeffs involve only parameters, terms involve only inputs and outputs
    • length of the representation is the smallest possible
source
StructuralIdentifiability.wronskian — Method
wronskian(io_equations, ode)

Input:

  • io_equations - a set of io-equations in the form of the Dict as returned by find_ioequations
  • ode - the ODE object

Output:

  • a list of Wronskians evaluated at a point modulo prime

Computes the Wronskians of io_equations

source
+
GitHub

Wronskian Tools

StructuralIdentifiability.get_max_below — Method
get_max_below(t, vect)

Input:

  • t - a trie with exponent vectors
  • vect - yet another exponent vector

Output:

  • a pair (d, v) where v is a vector in the trie which is componentwise ≤ vect and the difference d is as small as possible
source
StructuralIdentifiability.massive_eval — Method
massive_eval(polys, eval_dict)

Input:

  • polys - a list of polynomials
  • eval_dict - dictionary from variables to the values. Missing values are treated as zeroes

Output:

  • a list of values of the polynomials

Evaluates a list of polynomials at a point. Assumes that multiplications are relatively expensive (like in truncated power series) so all the monomials are precomputed first and the values of monomials of lower degree are cached and used to compute the values of the monomials of higher degree

source
StructuralIdentifiability.monomial_compress — Method
monomial_compress(io_equation, ode)

Compresses an input-output equation for the rank computation Input:

  • io_equation - input-output equation
  • ode - the corresponding ODE model

Output:

  • pair (coeffs, terms) such that:
    • sum of coeffs[i] * terms[i] = io_equation
    • coeffs involve only parameters, terms involve only inputs and outputs
    • length of the representation is the smallest possible
source
StructuralIdentifiability.wronskian — Method
wronskian(io_equations, ode)

Input:

  • io_equations - a set of io-equations in the form of the Dict as returned by find_ioequations
  • ode - the ODE object

Output:

  • a list of Wronskians evaluated at a point modulo prime

Computes the Wronskians of io_equations

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