amici.import_utils

Miscellaneous functions related to model import, independent of any specific model format

Functions

cast_to_sym(value, input_name)	Typecasts the value to sympy.Float if possible, and ensures the value is a symbolic expression.
generate_flux_symbol(reaction_index[, name])	Generate identifier symbol for a reaction flux.
generate_measurement_symbol(observable_id)	Generates the appropriate measurement symbol for the provided observable
generate_regularization_symbol(observable_id)	Generates the appropriate regularization symbol for the provided observable
grouper(iterable, n[, fillvalue])	Collect data into fixed-length chunks or blocks
noise_distribution_to_cost_function(...)	Parse noise distribution string to a cost function definition amici can work with.
noise_distribution_to_observable_transformation(...)	Parse noise distribution string and extract observable transformation
smart_subs(element, old, new)	Optimized substitution that checks whether anything needs to be done first
smart_subs_dict(sym, subs[, field, reverse])	Substitutes expressions completely flattening them out.
strip_pysb(symbol)	Strips pysb info from a pysb.Component object
symbol_with_assumptions(name)	Central function to create symbols with consistent, canonical assumptions
toposort_symbols(symbols[, field])	Topologically sort symbol definitions according to their interdependency
unique_preserve_order(seq)	Return a list of unique elements in Sequence, keeping only the first occurrence of each element

Classes

ObservableTransformation(value[, names, ...])

Different modes of observable transformation.

Exceptions

CircularDependencyError(data)
SBMLException

exception amici.import_utils.CircularDependencyError(data)

__init__(data)

class amici.import_utils.ObservableTransformation(value, names=None, *, module=None, qualname=None, type=None, start=1, boundary=None)

Different modes of observable transformation.

LIN = 'lin'

LOG = 'log'

LOG10 = 'log10'

__init__(*args, **kwds)

static maketrans()

Return a translation table usable for str.translate().

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters to Unicode ordinals, strings or None. Character keys will be then converted to ordinals. If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

exception amici.import_utils.SBMLException

amici.import_utils.cast_to_sym(value, input_name)

Typecasts the value to sympy.Float if possible, and ensures the value is a symbolic expression.

Parameters:

• value (typing.SupportsFloat | sympy.core.expr.Expr | sympy.logic.boolalg.BooleanAtom) – value to be cast

• input_name (str) – name of input variable

Return type:

sympy.core.expr.Expr

Returns:

typecast value

amici.import_utils.generate_flux_symbol(reaction_index, name=None)

Generate identifier symbol for a reaction flux. This function will always return the same unique python object for a given entity.

Parameters:

• reaction_index (int) – index of the reaction to which the flux corresponds

• name (str | None) – an optional identifier of the reaction to which the flux corresponds

Return type:

sympy.core.symbol.Symbol

Returns:

identifier symbol

amici.import_utils.generate_measurement_symbol(observable_id)

Generates the appropriate measurement symbol for the provided observable

Parameters:

observable_id (str | sympy.core.symbol.Symbol) – symbol (or string representation) of the observable

Returns:

symbol for the corresponding measurement

amici.import_utils.generate_regularization_symbol(observable_id)

Generates the appropriate regularization symbol for the provided observable

Parameters:

observable_id (str | sympy.core.symbol.Symbol) – symbol (or string representation) of the observable

Returns:

symbol for the corresponding regularization

amici.import_utils.grouper(iterable, n, fillvalue=None)

Collect data into fixed-length chunks or blocks

grouper(‘ABCDEFG’, 3, ‘x’) –> ABC DEF Gxx”

Parameters:

• iterable (collections.abc.Iterable) – any iterable

• n (int) – chunk length

• fillvalue (typing.Any) – padding for last chunk if length < n

Return type:

collections.abc.Iterable[tuple[typing.Any]]

Returns:

itertools.zip_longest of requested chunks

amici.import_utils.noise_distribution_to_cost_function(noise_distribution)

Parse noise distribution string to a cost function definition amici can work with.

The noise distributions listed in the following are supported. \(m\) denotes the measurement, \(y\) the simulation, and \(\sigma\) a distribution scale parameter (currently, AMICI only supports a single distribution parameter).

• ‘normal’, ‘lin-normal’: A normal distribution:

  \[\pi(m|y,\sigma) = \frac{1}{\sqrt{2\pi}\sigma}\ exp\left(-\frac{(m-y)^2}{2\sigma^2}\right)\]

• ‘log-normal’: A log-normal distribution (i.e. log(m) is normally distributed):

  \[\pi(m|y,\sigma) = \frac{1}{\sqrt{2\pi}\sigma m}\ exp\left(-\frac{(\log m - \log y)^2}{2\sigma^2}\right)\]

• ‘log10-normal’: A log10-normal distribution (i.e. log10(m) is normally distributed):

  \[\pi(m|y,\sigma) = \frac{1}{\sqrt{2\pi}\sigma m \log(10)}\ exp\left(-\frac{(\log_{10} m - \log_{10} y)^2}{2\sigma^2}\right)\]

• ‘laplace’, ‘lin-laplace’: A laplace distribution:

  \[\pi(m|y,\sigma) = \frac{1}{2\sigma} \exp\left(-\frac{|m-y|}{\sigma}\right)\]

• ‘log-laplace’: A log-Laplace distribution (i.e. log(m) is Laplace distributed):

  \[\pi(m|y,\sigma) = \frac{1}{2\sigma m} \exp\left(-\frac{|\log m - \log y|}{\sigma}\right)\]

• ‘log10-laplace’: A log10-Laplace distribution (i.e. log10(m) is Laplace distributed):

  \[\pi(m|y,\sigma) = \frac{1}{2\sigma m \log(10)} \exp\left(-\frac{|\log_{10} m - \log_{10} y|}{\sigma}\right)\]

• ‘binomial’, ‘lin-binomial’: A (continuation of a discrete) binomial distribution, parameterized via the success probability \(p=\sigma\):

  \[\pi(m|y,\sigma) = \operatorname{Heaviside}(y-m) \cdot \frac{\Gamma(y+1)}{\Gamma(m+1) \Gamma(y-m+1)} \sigma^m (1-\sigma)^{(y-m)}\]

• ‘negative-binomial’, ‘lin-negative-binomial’: A (continuation of a discrete) negative binomial distribution, with with mean = y, parameterized via success probability p:

  \[\pi(m|y,\sigma) = \frac{\Gamma(m+r)}{\Gamma(m+1) \Gamma(r)} (1-\sigma)^m \sigma^r\]

  where

  \[r = \frac{1-\sigma}{\sigma} y\]

The distributions above are for a single data point. For a collection \(D=\{m_i\}_i\) of data points and corresponding simulations \(Y=\{y_i\}_i\) and noise parameters \(\Sigma=\{\sigma_i\}_i\), AMICI assumes independence, i.e. the full distributions is

\[\pi(D|Y,\Sigma) = \prod_i\pi(m_i|y_i,\sigma_i)\]

AMICI uses the logarithm \(\log(\pi(m|y,\sigma)\).

In addition to the above mentioned distributions, it is also possible to pass a function taking a symbol string and returning a log-distribution string with variables ‘{str_symbol}’, ‘m{str_symbol}’, ‘sigma{str_symbol}’ for y, m, sigma, respectively.

Parameters:

noise_distribution (str | collections.abc.Callable) –

An identifier specifying a noise model. Possible values are

{‘normal’, ‘lin-normal’, ‘log-normal’, ‘log10-normal’, ‘laplace’, ‘lin-laplace’, ‘log-laplace’, ‘log10-laplace’, ‘binomial’, ‘lin-binomial’, ‘negative-binomial’, ‘lin-negative-binomial’, <Callable>}

For the meaning of the values see above.

Return type:

collections.abc.Callable[[str], str]

Returns:

A function that takes a strSymbol and then creates a cost function string (negative log-likelihood) from it, which can be sympified.

amici.import_utils.noise_distribution_to_observable_transformation(noise_distribution)

Parse noise distribution string and extract observable transformation

Parameters:

noise_distribution (str | collections.abc.Callable) – see noise_distribution_to_cost_function()

Return type:

amici.import_utils.ObservableTransformation

Returns:

observable transformation

amici.import_utils.smart_subs(element, old, new)

Optimized substitution that checks whether anything needs to be done first

Parameters:

• element (sympy.core.expr.Expr) – substitution target

• old (sympy.core.symbol.Symbol) – to be substituted

• new (sympy.core.expr.Expr) – subsitution value

Return type:

sympy.core.expr.Expr

Returns:

substituted expression

amici.import_utils.smart_subs_dict(sym, subs, field=None, reverse=True)

Substitutes expressions completely flattening them out. Requires sorting of expressions with toposort.

Parameters:

• sym (sympy.core.expr.Expr) – Symbolic expression in which expressions will be substituted

• subs (dict[sympy.core.symbol.Symbol, typing.Union[dict[str, sympy.core.expr.Expr], sympy.core.expr.Expr]]) – Substitutions

• field (str | None) – Field of substitution expressions in subs.values(), if applicable

• reverse (bool) – Whether ordering in subs should be reversed. Note that substitution requires the reverse order of what is required for evaluation.

Return type:

sympy.core.expr.Expr

Returns:

Substituted symbolic expression

amici.import_utils.strip_pysb(symbol)

Strips pysb info from a pysb.Component object

Parameters:

symbol (sympy.core.basic.Basic) – symbolic expression

Return type:

sympy.core.basic.Basic

Returns:

stripped expression

amici.import_utils.symbol_with_assumptions(name)

Central function to create symbols with consistent, canonical assumptions

Parameters:

name (str) – name of the symbol

Returns:

symbol with canonical assumptions

amici.import_utils.toposort_symbols(symbols, field=None)

Topologically sort symbol definitions according to their interdependency

Parameters:

• symbols (dict[sympy.core.symbol.Symbol, typing.Union[dict[str, sympy.core.expr.Expr], sympy.core.expr.Expr]]) – symbol definitions

• field (str | None) – field of definition.values() that is used to compute interdependency

Return type:

dict[sympy.core.symbol.Symbol, typing.Union[dict[str, sympy.core.expr.Expr], sympy.core.expr.Expr]]

Returns:

ordered symbol definitions

amici.import_utils.unique_preserve_order(seq)

Return a list of unique elements in Sequence, keeping only the first occurrence of each element

Parameters:

seq (collections.abc.Sequence) – Sequence to prune

Return type:

list

Returns:

List of unique elements in seq