diff --git a/previews/PR374/.documenter-siteinfo.json b/previews/PR374/.documenter-siteinfo.json index 6868400f..57d26586 100644 --- a/previews/PR374/.documenter-siteinfo.json +++ b/previews/PR374/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-19T07:19:27","documenter_version":"1.8.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-19T07:24:45","documenter_version":"1.8.0"}} \ No newline at end of file diff --git a/previews/PR374/export/export/index.html b/previews/PR374/export/export/index.html index 46a5ad33..17e18bf3 100644 --- a/previews/PR374/export/export/index.html +++ b/previews/PR374/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/previews/PR374/identifiability/identifiability/index.html b/previews/PR374/identifiability/identifiability/index.html index 34cd385f..f4ab186d 100644 --- a/previews/PR374/identifiability/identifiability/index.html +++ b/previews/PR374/identifiability/identifiability/index.html @@ -3,7 +3,7 @@ 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 = [], prob_threshold=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
  • known_ic: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).
  • prob_threshold - 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 prob_threshold. The function returns an (ordered) dictionary from the functions to check to their identifiability properties (one of :nonidentifiable, :locally, :globally).

source

Assessing Local Identifiability

StructuralIdentifiability.assess_local_identifiability — Function
assess_local_identifiability(ode::ODE{P}; funcs_to_check::Array{<: Any, 1}, prob_threshold::Float64=0.99, type=:SE, loglevel=Logging.Info) where P <: MPolyRingElem{Nemo.QQFieldElem}

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

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
assess_local_identifiability(dds::DDS{P}; funcs_to_check::Array{<: Any, 1}, known_ic, prob_threshold::Float64=0.99, loglevel=Logging.Info) where P <: MPolyRingElem{Nemo.QQFieldElem}

Checks the local identifiability/observability of the functions in funcs_to_check. The result is correct with probability at least prob_threshold. A list of quantities can be provided as known_ic for which the initial conditions can be assumed to be known and generic.

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.
  • known_ic: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).
  • prob_threshold: 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
+
GitHub
Functions to Assess Identifiability
Assessing All Types of Identifiability
StructuralIdentifiability.assess_identifiability — Function
assess_identifiability(ode; funcs_to_check = [], prob_threshold=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
  • known_ic: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).
  • prob_threshold - 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 prob_threshold. The function returns an (ordered) dictionary from the functions to check to their identifiability properties  (one of :nonidentifiable, :locally, :globally).
source
Assessing Local Identifiability
StructuralIdentifiability.assess_local_identifiability — Function
assess_local_identifiability(ode::ODE{P}; funcs_to_check::Array{<: Any, 1}, prob_threshold::Float64=0.99, type=:SE, loglevel=Logging.Info) where P <: MPolyRingElem{Nemo.QQFieldElem}
Checks the local identifiability/observability of the functions in funcs_to_check. The result is correct with probability at least prob_threshold.
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
assess_local_identifiability(dds::DDS{P}; funcs_to_check::Array{<: Any, 1}, known_ic, prob_threshold::Float64=0.99, loglevel=Logging.Info) where P <: MPolyRingElem{Nemo.QQFieldElem}
Checks the local identifiability/observability of the functions in funcs_to_check. The result is correct with probability at least prob_threshold. A list of quantities can be provided as known_ic for which the initial conditions can be assumed to be known and generic.
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.
  • known_ic: a list of functions whose initial conditions are assumed to be known, then the returned identifiable functions will be functions of parameters and initial conditions, not states (this is an experimental functionality).
  • prob_threshold: 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),
@@ -16,4 +16,4 @@
 # prints
 3-element Vector{AbstractAlgebra.Generic.FracFieldElem{Nemo.QQMPolyRingElem}}:
  a12 + a01 + a21
- a12*a01
source

+ a12*a01
source
diff --git a/previews/PR374/index.html b/previews/PR374/index.html index 4928e81e..f8b8cda6 100644 --- a/previews/PR374/index.html +++ b/previews/PR374/index.html @@ -281,4 +281,4 @@ [3f19e933] p7zip_jll v17.4.0+2 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/previews/PR374/input/input/index.html b/previews/PR374/input/input/index.html index 3e0928a1..0a4076e3 100644 --- a/previews/PR374/input/input/index.html +++ b/previews/PR374/input/input/index.html @@ -9,10 +9,10 @@ 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

Discrete-time systems

StructuralIdentifiability.@DDSmodel — Macro
macro DDSmodel

Macro for creating a DDS (discrete dynamical system) from a list of equations. It also injects all variables into the global scope.

Example

Creating a simple DDS:

using StructuralIdentifiability
+)

Here,

  • x1, x2 are state variables
  • y is an output variable
  • u is an input variable
  • a, b, c are time-independent parameters
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

Discrete-time systems

StructuralIdentifiability.@DDSmodel — Macro
macro DDSmodel

Macro for creating a DDS (discrete dynamical system) from a list of equations. It also injects all variables into the global scope.

Example

Creating a simple DDS:

using StructuralIdentifiability
 
 dds = @DDSmodel(
     x1(t + 1) = a * x1(t) + u(t),
     x2(t + 1) = b * x2(t) + c*x1(t)*x2(t),
     y(t) = x1(t)
-)

Here,

  • x1, x2 are state variables
  • y is an output variable
  • u is an input variable
  • a, b, c are time-independent parameters
source
+)

Here,

source diff --git a/previews/PR374/ioequations/ioequations/index.html b/previews/PR374/ioequations/ioequations/index.html index 2faab6f7..063f5779 100644 --- a/previews/PR374/ioequations/ioequations/index.html +++ b/previews/PR374/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/previews/PR374/tutorials/creating_ode/index.html b/previews/PR374/tutorials/creating_ode/index.html index b4ee9434..38d2c56c 100644 --- a/previews/PR374/tutorials/creating_ode/index.html +++ b/previews/PR374/tutorials/creating_ode/index.html @@ -56,4 +56,4 @@ c2 => :nonidentifiable chi2 => :globally r2 => :globally - beta2 => :globally
+ beta2 => :globally
diff --git a/previews/PR374/tutorials/discrete_time/index.html b/previews/PR374/tutorials/discrete_time/index.html index 67915881..2fbc3b74 100644 --- a/previews/PR374/tutorials/discrete_time/index.html +++ b/previews/PR374/tutorials/discrete_time/index.html @@ -49,4 +49,4 @@ I(t) => 1 R(t) => 0 β => 1 - α => 1

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

+ α => 1

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

diff --git a/previews/PR374/tutorials/identifiability/index.html b/previews/PR374/tutorials/identifiability/index.html index c826c916..e9ca8a6f 100644 --- a/previews/PR374/tutorials/identifiability/index.html +++ b/previews/PR374/tutorials/identifiability/index.html @@ -59,4 +59,4 @@ c => :globally delta => :locally gama => :locally - sigma => :globally

And we see that now alpha and gama become locally identifiable.

+ sigma => :globally

And we see that now alpha and gama become locally identifiable.

diff --git a/previews/PR374/tutorials/identifiable_functions/index.html b/previews/PR374/tutorials/identifiable_functions/index.html index 8cd4ffef..57569d68 100644 --- a/previews/PR374/tutorials/identifiable_functions/index.html +++ b/previews/PR374/tutorials/identifiable_functions/index.html @@ -30,4 +30,4 @@ p1*p3 p1 + p3 p2*x2(0) + p4*x1(0) - (-p1*x2(0) + p3*x2(0))//(p2*x2(0) - p4*x1(0))

We see that x2(0) becomes an identifiable function as well, which is natural since x1(t) * x2(t) was an identifiable function before.

+ (-p1*x2(0) + p3*x2(0))//(p2*x2(0) - p4*x1(0))

We see that x2(0) becomes an identifiable function as well, which is natural since x1(t) * x2(t) was an identifiable function before.

diff --git a/previews/PR374/tutorials/reparametrization/index.html b/previews/PR374/tutorials/reparametrization/index.html index 115495b8..1e4a9c7e 100644 --- a/previews/PR374/tutorials/reparametrization/index.html +++ b/previews/PR374/tutorials/reparametrization/index.html @@ -60,4 +60,4 @@ X4(t) => :globally a1 => :globally a2 => :globally - a3 => :globally
+ a3 => :globally
diff --git a/previews/PR374/utils/elimination/index.html b/previews/PR374/utils/elimination/index.html index 67b6687e..63f455b1 100644 --- a/previews/PR374/utils/elimination/index.html +++ b/previews/PR374/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.MPolyRingElem} - 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.MPolyRingElem} - array of GCDs eliminated from M.
source
diff --git a/previews/PR374/utils/global_identifiability/index.html b/previews/PR374/utils/global_identifiability/index.html index 3895a72e..d1acf9b4 100644 --- a/previews/PR374/utils/global_identifiability/index.html +++ b/previews/PR374/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, prob_threshold)

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 prob_threshold

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.
  • prob_threshold 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, prob_threshold)

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 prob_threshold

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.
  • prob_threshold 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/previews/PR374/utils/local_identifiability/index.html b/previews/PR374/utils/local_identifiability/index.html index 58c4f51a..86b15114 100644 --- a/previews/PR374/utils/local_identifiability/index.html +++ b/previews/PR374/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/previews/PR374/utils/ode/index.html b/previews/PR374/utils/ode/index.html index 3f58d74d..bb9a6cfa 100644 --- a/previews/PR374/utils/ode/index.html +++ b/previews/PR374/utils/ode/index.html @@ -3,7 +3,7 @@ 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.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.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))
@@ -12,4 +12,4 @@
         
         x1'(t) = a(t)*x2(t)^2 + x1(t)
         y1(t) = x1(t)
-    ]
source

+    ]
source
diff --git a/previews/PR374/utils/power_series_utils/index.html b/previews/PR374/utils/power_series_utils/index.html index 6c71168c..2cf83ee6 100644 --- a/previews/PR374/utils/power_series_utils/index.html +++ b/previews/PR374/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/previews/PR374/utils/primality/index.html b/previews/PR374/utils/primality/index.html index d7d39664..c649a9a2 100644 --- a/previews/PR374/utils/primality/index.html +++ b/previews/PR374/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{QQMPolyRingElem, QQMPolyRingElem}, extra_relations::Array{QQMPolyRingElem, 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{QQMPolyRingElem, QQMPolyRingElem})

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{QQMPolyRingElem, QQMPolyRingElem}, extra_relations::Array{QQMPolyRingElem, 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{QQMPolyRingElem, QQMPolyRingElem})

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/previews/PR374/utils/reparametrization/index.html b/previews/PR374/utils/reparametrization/index.html index 7632877f..af606adc 100644 --- a/previews/PR374/utils/reparametrization/index.html +++ b/previews/PR374/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/previews/PR374/utils/util/index.html b/previews/PR374/utils/util/index.html index 08428bf9..97bb4e47 100644 --- a/previews/PR374/utils/util/index.html +++ b/previews/PR374/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 length(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.replace_with_ic — Method
replace_with_ic(ode::ODE, funcs)

Takes an ode and a list of functions in the states and parameters and makes a change of variable names x(t) -> x(0). Function is used to prepare the output for the case of known initial conditions

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 length(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.replace_with_ic — Method
replace_with_ic(ode::ODE, funcs)

Takes an ode and a list of functions in the states and parameters and makes a change of variable names x(t) -> x(0). Function is used to prepare the output for the case of known initial conditions

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/previews/PR374/utils/wronskian/index.html b/previews/PR374/utils/wronskian/index.html index 6a7645ed..4fe11b4c 100644 --- a/previews/PR374/utils/wronskian/index.html +++ b/previews/PR374/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

source