openquake.risklib package

openquake.risklib.riskinput module

class openquake.risklib.riskinput.RiskInput(hazard_getter, asset_df)[source]

Bases: object

Site specific inputs.

Parameters:
  • hazard_getter – a callable returning the hazard data for all realizations
  • asset_df – a DataFrame of assets on the given site
openquake.risklib.riskinput.rsi2str(rlzi, sid, imt)[source]

Convert a triple (XXXX, YYYY, ZZZ) into a string of the form ‘rlz-XXXX/sid-YYYY/ZZZ’

openquake.risklib.riskinput.str2rsi(key)[source]

Convert a string of the form ‘rlz-XXXX/sid-YYYY/ZZZ’ into a triple (XXXX, YYYY, ZZZ)

openquake.risklib.riskmodels module

class openquake.risklib.riskmodels.CompositeRiskModel(oqparam, risklist, consdict=())[source]

Bases: collections.abc.Mapping

A container (riskid, kind) -> riskmodel

Parameters:
  • oqparam – an openquake.commonlib.oqvalidation.OqParam instance
  • fragdict – a dictionary riskid -> loss_type -> fragility functions
  • vulndict – a dictionary riskid -> loss_type -> vulnerability function
  • consdict – a dictionary riskid -> loss_type -> consequence functions
asset_damage_dt(float_dmg_dist)[source]
Returns:a composite dtype with damages and consequences
compute_csq(asset, fractions, loss_type)[source]
Parameters:
  • asset – asset record
  • fractions – array of probabilies of shape (E, D)
  • loss_type – loss type as a string
Returns:

a dict consequence_name -> array of length E

eid_dmg_dt()[source]
Returns:a dtype (eid, dmg)
get_attrs()[source]
get_consequences()[source]
Returns:the list of available consequences
get_dmg_csq()[source]
Returns:damage states (except no_damage) plus consequences
get_interp_ratios(taxo, gmf_df)[source]
Returns:a dictionary loss_type -> loss ratios DataFrame
get_loss_ratios()[source]
Returns:a 1-dimensional composite array with loss ratios by loss type
get_output(taxo, assets, haz, sec_losses=(), rndgen=None, rlz=None)[source]
Parameters:
  • taxo – a taxonomy index
  • assets – a DataFrame of assets of the given taxonomy
  • haz – a DataFrame of GMVs on that site
  • sec_losses – a list of SecondaryLoss instances
  • rndgen – a MultiEventRNG instance
  • rlz – a realization index (or None)
Returns:

a dictionary keyed by loss type

get_rmodels_weights(loss_type, taxidx)[source]
Returns:a list of weighted risk models for the given taxonomy index
init()[source]
make_curve_params()[source]
classmethod read(dstore, oqparam)[source]
Parameters:dstore – a DataStore instance
Returns:a CompositeRiskModel instance
reduce(taxonomies)[source]
Parameters:taxonomies – a set of taxonomies
Returns:a new CompositeRiskModel reduced to the given taxonomies
taxonomy_dict
Returns:a dict taxonomy string -> taxonomy index
to_dframe()[source]
Returns:a DataFrame containing all risk functions
class openquake.risklib.riskmodels.RiskFuncList[source]

Bases: list

A list of risk functions with attributes .id, .loss_type, .kind

groupby_id(kind=None)[source]
Parameters:kind – if not None, filter the risk functions on that kind
Returns:double dictionary id -> loss_type, kind -> risk_function
class openquake.risklib.riskmodels.RiskModel(calcmode, taxonomy, risk_functions, **kw)[source]

Bases: object

Base class. Can be used in the tests as a mock.

Parameters:
  • taxonomy – a taxonomy string
  • risk_functions – a dict (loss_type, kind) -> risk_function
classical_bcr(loss_type, assets, hazard, col=None, rng=None)[source]
Parameters:
  • loss_type – the loss type
  • assets – a list of N assets of the same taxonomy
  • hazard – a dictionary col -> hazard curve
  • _eps – dummy parameter, unused
Returns:

a list of triples (eal_orig, eal_retro, bcr_result)

classical_damage(loss_type, assets, hazard_curve, col=None, rng=None)[source]
Parameters:
  • loss_type – the loss type
  • assets – a list of N assets of the same taxonomy
  • hazard_curve – a dictionary col -> hazard curve
Returns:

an array of N x D elements

where N is the number of points and D the number of damage states.

classical_risk(loss_type, assets, hazard_curve, col=None, rng=None)[source]
Parameters:
  • loss_type (str) – the loss type considered
  • assets – assets is an iterator over A openquake.risklib.scientific.Asset instances
  • hazard_curve – an array of poes
  • eps – ignored, here only for API compatibility with other calculators
Returns:

a composite array (loss, poe) of shape (A, C)

compositemodel = None
ebrisk(loss_type, assets, gmf_df, col, rndgen)
Returns:a DataFrame with columns eid, eid, loss
event_based_damage(loss_type, assets, gmf_df, col, rng=None)
Parameters:
  • loss_type – the loss type
  • assets – a list of A assets of the same taxonomy
  • gmf_df – a DataFrame of GMFs
  • epsilons – dummy parameter, unused
Returns:

an array of shape (A, E, D) elements

where N is the number of points, E the number of events and D the number of damage states.

event_based_risk(loss_type, assets, gmf_df, col, rndgen)[source]
Returns:a DataFrame with columns eid, eid, loss
loss_types

The list of loss types in the underlying vulnerability functions, in lexicographic order

scenario(loss_type, assets, gmf_df, col, rndgen)
Returns:a DataFrame with columns eid, eid, loss
scenario_damage(loss_type, assets, gmf_df, col, rng=None)[source]
Parameters:
  • loss_type – the loss type
  • assets – a list of A assets of the same taxonomy
  • gmf_df – a DataFrame of GMFs
  • epsilons – dummy parameter, unused
Returns:

an array of shape (A, E, D) elements

where N is the number of points, E the number of events and D the number of damage states.

scenario_risk(loss_type, assets, gmf_df, col, rndgen)
Returns:a DataFrame with columns eid, eid, loss
time_event = None
exception openquake.risklib.riskmodels.ValidationError[source]

Bases: Exception

openquake.risklib.riskmodels.build_vf_node(vf)[source]

Convert a VulnerabilityFunction object into a Node suitable for XML conversion.

openquake.risklib.riskmodels.filter_vset(elem)[source]
openquake.risklib.riskmodels.get_risk_files(inputs)[source]
Parameters:inputs – a dictionary key -> path name
Returns:a pair (file_type, {risk_type: path})
openquake.risklib.riskmodels.get_risk_functions(oqparam, kind='vulnerability fragility consequence vulnerability_retrofitted')[source]
Parameters:
  • oqparam – an OqParam instance
  • kind – a space-separated string with the kinds of risk models to read
Returns:

a list of risk functions

openquake.risklib.riskmodels.get_riskmodel(taxonomy, oqparam, **extra)[source]

Return an instance of the correct risk model class, depending on the attribute calculation_mode of the object oqparam.

Parameters:
  • taxonomy – a taxonomy string
  • oqparam – an object containing the parameters needed by the RiskModel class
  • extra – extra parameters to pass to the RiskModel class
openquake.risklib.riskmodels.rescale(curves, values)[source]

Multiply the losses in each curve of kind (losses, poes) by the corresponding value.

Parameters:
  • curves – an array of shape (A, 2, C)
  • values – an array of shape (A,)

openquake.risklib.scientific module

This module includes the scientific API of the oq-risklib

class openquake.risklib.scientific.ConsequenceModel(id, assetCategory, lossCategory, description, limitStates)[source]

Bases: dict

Dictionary of consequence functions. You can access each function given its name with the square bracket notation.

Parameters:
  • id (str) – ID of the model
  • assetCategory (str) – asset category (i.e. buildings, population)
  • lossCategory (str) – loss type (i.e. structural, contents, …)
  • description (str) – description of the model
  • limitStates – a list of limit state strings
class openquake.risklib.scientific.CurveParams(index, loss_type, curve_resolution, ratios, user_provided)

Bases: tuple

curve_resolution

Alias for field number 2

index

Alias for field number 0

loss_type

Alias for field number 1

ratios

Alias for field number 3

user_provided

Alias for field number 4

class openquake.risklib.scientific.FragilityFunctionContinuous(limit_state, mean, stddev, minIML, maxIML, nodamage=0)[source]

Bases: object

class openquake.risklib.scientific.FragilityFunctionDiscrete(limit_state, imls, poes, no_damage_limit=None)[source]

Bases: object

interp
class openquake.risklib.scientific.FragilityFunctionList(array, **attrs)[source]

Bases: list

A list of fragility functions with common attributes; there is a function for each limit state.

build(limit_states, discretization, steps_per_interval)[source]
Parameters:
  • limit_states – a sequence of limit states
  • discretization – continouos fragility discretization parameter
  • steps_per_interval – steps_per_interval parameter
Returns:

a populated FragilityFunctionList instance

mean_loss_ratios_with_steps(steps)[source]

For compatibility with vulnerability functions

class openquake.risklib.scientific.FragilityModel(id, assetCategory, lossCategory, description, limitStates)[source]

Bases: dict

Container for a set of fragility functions. You can access each function given the IMT and taxonomy with the square bracket notation.

Parameters:
  • id (str) – ID of the model
  • assetCategory (str) – asset category (i.e. buildings, population)
  • lossCategory (str) – loss type (i.e. structural, contents, …)
  • description (str) – description of the model
  • limitStates – a list of limit state strings
class openquake.risklib.scientific.InsuredLosses(policy_name, policy_dict)[source]

Bases: object

There is an insured loss for each loss type in the policy dictionary.

update(lt, out, asset_df)[source]
Parameters:
  • lt – a loss type string
  • out – a dictionary of dataframes keyed by loss_type
  • asset_df – a DataFrame of assets with index “ordinal”
class openquake.risklib.scientific.LossCurvesMapsBuilder(conditional_loss_poes, return_periods, loss_dt, weights, num_events, eff_time, risk_investigation_time)[source]

Bases: object

Build losses curves and maps for all loss types at the same time.

Parameters:
  • conditional_loss_poes – a list of PoEs, possibly empty
  • return_periods – ordered array of return periods
  • loss_dt – composite dtype for the loss types
  • weights – weights of the realizations
  • num_events – number of events for each realization
  • eff_time – ses_per_logic_tree_path * hazard investigation time
build_curve(losses, rlzi=0)[source]
class openquake.risklib.scientific.MultiEventRNG(master_seed, eids, asset_correlation=0)[source]

Bases: object

An object MultiEventRNG(master_seed, eids, asset_correlation=0) has a method .get(A, eids) which returns a matrix of (A, E) normally distributed random numbers. If the asset_correlation is 1 the numbers are the same.

>>> rng = MultiEventRNG(
...     master_seed=42, eids=[0, 1, 2], asset_correlation=1)
>>> eids = numpy.array([1] * 3)
>>> means = numpy.array([.5] * 3)
>>> covs = numpy.array([.1] * 3)
>>> rng.lognormal(eids, means, covs)
array([0.38892466, 0.38892466, 0.38892466])
>>> rng.beta(eids, means, covs)
array([0.4372343 , 0.57308132, 0.56392573])
>>> fractions = numpy.array([[[.8, .1, .1]]])
>>> rng.discrete_dmg_dist([0], fractions, [10])
array([[[8, 2, 0]]], dtype=uint32)
beta(eids, means, covs)[source]
Parameters:
  • eids – event IDs
  • means – array of floats in the range 0..1
  • covs – array of floats with the same shape
Returns:

array of floats following the beta distribution

This function works properly even when some or all of the stddevs are zero: in that case it returns the means since the distribution becomes extremely peaked. It also works properly when some one or all of the means are zero, returning zero in that case.

boolean_dist(probs, num_sims)[source]

Convert E probabilities into an array of (E, S) booleans, being S the number of secondary simulations.

>>> rng = MultiEventRNG(master_seed=42, eids=[0, 1, 2])
>>> dist = rng.boolean_dist(probs=[.1, .2, 0.], num_sims=100)
>>> dist.sum(axis=1)  # around 10% and 20% respectively
array([12., 17.,  0.])
discrete_dmg_dist(eids, fractions, numbers)[source]

Converting fractions into discrete damage distributions using bincount and random.choice.

Parameters:
  • eids – E event IDs
  • fractions – array of shape (A, E, D)
  • numbers – A asset numbers
Returns:

array of integers of shape (A, E, D)

lognormal(eids, means, covs)[source]
Parameters:
  • eids – event IDs
  • means – array of floats in the range 0..1
  • covs – array of floats with the same shape
Returns:

array of floats

class openquake.risklib.scientific.Sampler(distname, rng, lratios=(), cols=None)[source]

Bases: object

get_losses(df, covs)[source]
sampleBT(df)[source]
sampleLN(df)[source]
samplePM(df)[source]
class openquake.risklib.scientific.VulnerabilityFunction(vf_id, imt, imls, mean_loss_ratios, covs=None, distribution='LN')[source]

Bases: object

dtype = dtype([('iml', '<f8'), ('loss_ratio', '<f8'), ('cov', '<f8')])
init()[source]
interpolate(gmf_df, col)[source]
Parameters:gmf_df – DataFrame of GMFs
Returns:DataFrame of interpolated loss ratios and covs
loss_ratio_exceedance_matrix[source]

Compute the LREM (Loss Ratio Exceedance Matrix).

mean_imls[source]

Compute the mean IMLs (Intensity Measure Level) for the given vulnerability function.

Parameters:vulnerability_function – the vulnerability function where the IMLs (Intensity Measure Level) are taken from.
mean_loss_ratios_with_steps(steps)[source]

Split the mean loss ratios, producing a new set of loss ratios. The new set of loss ratios always includes 0.0 and 1.0

Parameters:steps (int) –

the number of steps we make to go from one loss ratio to the next. For example, if we have [0.5, 0.7]:

steps = 1 produces [0.0,  0.5, 0.7, 1]
steps = 2 produces [0.0, 0.25, 0.5, 0.6, 0.7, 0.85, 1]
steps = 3 produces [0.0, 0.17, 0.33, 0.5, 0.57, 0.63,
                    0.7, 0.8, 0.9, 1]
seed = None
strictly_increasing()[source]
Returns:a new vulnerability function that is strictly increasing. It is built by removing piece of the function where the mean loss ratio is constant.
survival(loss_ratio, mean, stddev)[source]

Compute the survival probability based on the underlying distribution.

class openquake.risklib.scientific.VulnerabilityFunctionWithPMF(vf_id, imt, imls, loss_ratios, probs)[source]

Bases: openquake.risklib.scientific.VulnerabilityFunction

Vulnerability function with an explicit distribution of probabilities

Parameters:
  • vf_id (str) – vulnerability function ID
  • imt (str) – Intensity Measure Type
  • imls – intensity measure levels (L)
  • ratios – an array of mean ratios (M)
  • probs – a matrix of probabilities of shape (M, L)
init()[source]
interpolate(gmf_df, col)[source]
Parameters:
  • gmvs – DataFrame of GMFs
  • col – name of the column to consider
Returns:

DataFrame of interpolated probabilities

loss_ratio_exceedance_matrix[source]

Compute the LREM (Loss Ratio Exceedance Matrix). Required for the Classical Risk and BCR Calculators. Currently left unimplemented as the PMF format is used only for the Scenario and Event Based Risk Calculators.

Parameters:steps (int) – Number of steps between loss ratios.
class openquake.risklib.scientific.VulnerabilityModel(id=None, assetCategory=None, lossCategory=None)[source]

Bases: dict

Container for a set of vulnerability functions. You can access each function given the IMT and taxonomy with the square bracket notation.

Parameters:
  • id (str) – ID of the model
  • assetCategory (str) – asset category (i.e. buildings, population)
  • lossCategory (str) – loss type (i.e. structural, contents, …)

All such attributes are None for a vulnerability model coming from a NRML 0.4 file.

openquake.risklib.scientific.annual_frequency_of_exceedence(poe, t_haz)[source]
Parameters:
  • poe – array of probabilities of exceedence
  • t_haz – hazard investigation time
Returns:

array of frequencies (with +inf values where poe=1)

openquake.risklib.scientific.average_loss(lc)[source]

Given a loss curve array with poe and loss fields, computes the average loss on a period of time.

Note:As the loss curve is supposed to be piecewise linear as it is a result of a linear interpolation, we compute an exact integral by using the trapeizodal rule with the width given by the loss bin width.
openquake.risklib.scientific.bcr(eal_original, eal_retrofitted, interest_rate, asset_life_expectancy, asset_value, retrofitting_cost)[source]

Compute the Benefit-Cost Ratio.

BCR = (EALo - EALr)(1-exp(-r*t))/(r*C)

Where:

  • BCR – Benefit cost ratio
  • EALo – Expected annual loss for original asset
  • EALr – Expected annual loss for retrofitted asset
  • r – Interest rate
  • t – Life expectancy of the asset
  • C – Retrofitting cost
openquake.risklib.scientific.broadcast(func, composite_array, *args)[source]

Broadcast an array function over a composite array

openquake.risklib.scientific.build_imls(ff, continuous_fragility_discretization, steps_per_interval=0)[source]

Build intensity measure levels from a fragility function. If the function is continuous, they are produced simply as a linear space between minIML and maxIML. If the function is discrete, they are generated with a complex logic depending on the noDamageLimit and the parameter steps per interval.

Parameters:
  • ff – a fragility function object
  • continuous_fragility_discretization – .ini file parameter
  • steps_per_interval – .ini file parameter
Returns:

generated imls

openquake.risklib.scientific.build_loss_curve_dt(curve_resolution, insured_losses=False)[source]
Parameters:
  • curve_resolution – dictionary loss_type -> curve_resolution
  • insured_losses – configuration parameter
Returns:

loss_curve_dt

openquake.risklib.scientific.classical(vulnerability_function, hazard_imls, hazard_poes, loss_ratios)[source]
Parameters:
  • vulnerability_function – an instance of openquake.risklib.scientific.VulnerabilityFunction representing the vulnerability function used to compute the curve.
  • hazard_imls – the hazard intensity measure type and levels
  • loss_ratios – a tuple of C loss ratios
Returns:

an array of shape (2, C)

openquake.risklib.scientific.classical_damage(fragility_functions, hazard_imls, hazard_poes, investigation_time, risk_investigation_time, steps_per_interval=1)[source]
Parameters:
  • fragility_functions – a list of fragility functions for each damage state
  • hazard_imls – Intensity Measure Levels
  • hazard_poes – hazard curve
  • investigation_time – hazard investigation time
  • risk_investigation_time – risk investigation time
  • steps_per_interval – steps per interval
Returns:

an array of M probabilities of occurrence where M is the numbers of damage states.

openquake.risklib.scientific.conditional_loss_ratio(loss_ratios, poes, probability)[source]

Return the loss ratio corresponding to the given PoE (Probability of Exceendance). We can have four cases:

  1. If probability is in poes it takes the bigger corresponding loss_ratios.
  2. If it is in (poe1, poe2) where both poe1 and poe2 are in poes, then we perform a linear interpolation on the corresponding losses
  3. if the given probability is smaller than the lowest PoE defined, it returns the max loss ratio .
  4. if the given probability is greater than the highest PoE defined it returns zero.
Parameters:
  • loss_ratios – non-decreasing loss ratio values (float32)
  • poes – non-increasing probabilities of exceedance values (float32)
  • probability (float) – the probability value used to interpolate the loss curve
openquake.risklib.scientific.consequence(consequence, coeffs, asset, dmgdist, loss_type)[source]
Parameters:
  • consequence – kind of consequence
  • coeffs – coefficients per damage state
  • asset – asset record
  • dmgdist – an array of probabilies of shape (E, D - 1)
  • loss_type – loss type string
Returns:

array of shape E

openquake.risklib.scientific.fine_graining(points, steps)[source]
Parameters:
  • points – a list of floats
  • steps (int) – expansion steps (>= 2)
>>> fine_graining([0, 1], steps=0)
[0, 1]
>>> fine_graining([0, 1], steps=1)
[0, 1]
>>> fine_graining([0, 1], steps=2)
array([0. , 0.5, 1. ])
>>> fine_graining([0, 1], steps=3)
array([0.        , 0.33333333, 0.66666667, 1.        ])
>>> fine_graining([0, 0.5, 0.7, 1], steps=2)
array([0.  , 0.25, 0.5 , 0.6 , 0.7 , 0.85, 1.  ])

N points become S * (N - 1) + 1 points with S > 0

openquake.risklib.scientific.get_agg_value(consequence, agg_values, agg_id, loss_type)[source]
Returns:sum of the values corresponding to agg_id for the given consequence
openquake.risklib.scientific.insured_loss_curve(curve, deductible, insured_limit)[source]

Compute an insured loss ratio curve given a loss ratio curve

Parameters:
  • curve – an array 2 x R (where R is the curve resolution)
  • deductible (float) – the deductible limit in fraction form
  • insured_limit (float) – the insured limit in fraction form
>>> losses = numpy.array([3, 20, 101])
>>> poes = numpy.array([0.9, 0.5, 0.1])
>>> insured_loss_curve(numpy.array([losses, poes]), 5, 100)
array([[ 3.        , 20.        ],
       [ 0.85294118,  0.5       ]])
openquake.risklib.scientific.insured_losses(losses, deductible, insured_limit)[source]
Parameters:
  • losses – an array of ground-up loss ratios
  • deductible (float) – the deductible limit in fraction form
  • insured_limit (float) – the insured limit in fraction form

Compute insured losses for the given asset and losses, from the point of view of the insurance company. For instance:

>>> insured_losses(numpy.array([3, 20, 101]), 5, 100)
array([ 0, 15, 95])
  • if the loss is 3 (< 5) the company does not pay anything
  • if the loss is 20 the company pays 20 - 5 = 15
  • if the loss is 101 the company pays 100 - 5 = 95
openquake.risklib.scientific.loss_maps(curves, conditional_loss_poes)[source]
Parameters:
  • curves – an array of loss curves
  • conditional_loss_poes – a list of conditional loss poes
Returns:

a composite array of loss maps with the same shape

openquake.risklib.scientific.losses_by_period(losses, return_periods, num_events=None, eff_time=None)[source]
Parameters:
  • losses – simulated losses
  • return_periods – return periods of interest
  • num_events – the number of events (>= number of losses)
  • eff_time – investigation_time * ses_per_logic_tree_path
Returns:

interpolated losses for the return periods, possibly with NaN

NB: the return periods must be ordered integers >= 1. The interpolated losses are defined inside the interval min_time < time < eff_time where min_time = eff_time /num_events. On the right of the interval they have NaN values; on the left zero values. If num_events is not passed, it is inferred from the number of losses; if eff_time is not passed, it is inferred from the longest return period. Here is an example:

>>> losses = [3, 2, 3.5, 4, 3, 23, 11, 2, 1, 4, 5, 7, 8, 9, 13]
>>> losses_by_period(losses, [1, 2, 5, 10, 20, 50, 100], 20)
array([ 0. ,  0. ,  0. ,  3.5,  8. , 13. , 23. ])
openquake.risklib.scientific.make_epsilons(matrix, seed, correlation)[source]

Given a matrix of shape (A, E) returns a matrix of the same shape obtained by applying the multivariate_normal distribution to A points and E samples, by starting from the given seed and correlation.

openquake.risklib.scientific.mean_std(fractions)[source]

Given an N x M matrix, returns mean and std computed on the rows, i.e. two M-dimensional vectors.

openquake.risklib.scientific.normalize_curves_eb(curves)[source]

A more sophisticated version of normalize_curves, used in the event based calculator.

Parameters:curves – a list of pairs (losses, poes)
Returns:first losses, all_poes
openquake.risklib.scientific.pairwise(iterable)[source]

s -> (s0,s1), (s1,s2), (s2, s3), …

openquake.risklib.scientific.pairwise_diff(values)[source]

Differences between a value and the next value in a sequence

openquake.risklib.scientific.pairwise_mean(values)[source]

Averages between a value and the next value in a sequence

openquake.risklib.scientific.return_periods(eff_time, num_losses)[source]
Parameters:
  • eff_time – ses_per_logic_tree_path * investigation_time
  • num_losses – used to determine the minimum period
Returns:

an array of periods of dtype uint32

Here are a few examples:

>>> return_periods(1, 1)
Traceback (most recent call last):
   ...
ValueError: eff_time too small: 1
>>> return_periods(2, 2)
array([1, 2], dtype=uint32)
>>> return_periods(2, 10)
array([1, 2], dtype=uint32)
>>> return_periods(100, 2)
array([ 50, 100], dtype=uint32)
>>> return_periods(1000, 1000)
array([   1,    2,    5,   10,   20,   50,  100,  200,  500, 1000],
      dtype=uint32)
openquake.risklib.scientific.scenario_damage(fragility_functions, gmvs)[source]
Parameters:
  • fragility_functions – a list of D - 1 fragility functions
  • gmvs – an array of E ground motion values
Returns:

an array of (D, E) damage fractions

Module contents