uncertainty pack¶

7 nodes, in noodlelab and above.

Uncertainty¶

Add Uncertainty (Type B)¶

uncertainty.add_uncertainty

Give a value an uncertainty from a certificate, a resolution or a tolerance (GUM Type B), in the value’s unit. A half-width a becomes a/√3 for a rectangular distribution (a resolution, a tolerance) and a/√6 for a triangular one. On a value that is already uncertain, this adds another independent component.

Inputs

Name	Type	Description
`value`	`float \| Quantity`
`uncertainty`	`float`	Default `0.0`.
`given_as`	`Literal['standard uncertainty', 'expanded, k = 2', 'half-width, rectangular', 'half-width, triangular', 'relative, %']`	Default `'standard uncertainty'`.
`name`	`str`	Names this input in uncertainty budgets Default `''`.

Outputs

Name	Type	Description
`result`	`Uncertain`

Expanded Uncertainty¶

uncertainty.expanded_uncertainty

The expanded uncertainty U = k·u and the interval x ± U (GUM 6). k = 2 covers about 95 % for a normal distribution.

Inputs

Name	Type	Description
`value`	`Uncertain`
`k`	`float`	2 for about 95 % Default `2.0`.

Outputs

Name	Type	Description
`expanded`	`Any`
`lower`	`Any`
`upper`	`Any`

Mean of Repeats (Type A)¶

uncertainty.mean_of_repeats

The mean of repeated readings, with its standard uncertainty s/√n (GUM Type A, 4.2). std is the spread of single readings (s, n - 1). Readings that carry an uncertainty of their own (from an instrument’s calibration, say) pass it on to the mean too, combined with s/√n.

Inputs

Name	Type	Description
`values`	`ndarray \| list`
`name`	`str`	Names this input in uncertainty budgets Default `''`.
`unit`	`str`	Default `''`.

Outputs

Name	Type	Description
`mean`	`Uncertain`
`std`	`float`
`count`	`int`

Measurement¶

uncertainty.measurement

A measured value with its standard uncertainty, typed as text: 9.81 ± 0.02 m/s^2, 9.81 +/- 0.02 or 9.81(2).

Inputs

Name	Type	Description
`value`	`Uncertain`	Default `'9.810 ± 0.020 m/s**2'`.
`name`	`str`	Names this input in uncertainty budgets Default `''`.

Outputs

Name	Type	Description
`result`	`Uncertain`

Monte Carlo¶

uncertainty.monte_carlo

Propagate the distributions of the inputs by simulation (GUM Supplement 1, JCGM 101): everything upstream that depends on an uncertain input runs trials times, each input drawn from its own distribution (normal, rectangular, triangular, or Student’s t for a mean of few readings). Gives the mean and standard uncertainty, the coverage interval, the samples and a histogram, and says whether the linear (GUM) result agrees (JCGM 101, 8), which it may not for non-linear models. Arrays are handled element by element.

Inputs

Name	Type	Description
`value`	`Any`	The result to study: link it from any node
`trials`	`int`	Default `10000`.
`coverage`	`float`	Default `0.95`.
`seed`	`int`	Default `1`.

Outputs

Name	Type	Description
`result`	`Any`
`uncertainty`	`Any`
`lower`	`Any`
`upper`	`Any`
`samples`	`Any`
`histogram`	`Any`
`agrees_with_gum`	`bool \| None`
`gum_comparison`	`str`

Uncertainty Budget¶

uncertainty.uncertainty_budget

Which inputs the uncertainty of a result comes from: each named input’s contribution |∂y/∂xᵢ|·u(xᵢ), in the result’s unit, and its share of the variance. Connect to Add Table for the report. For an array, each input’s largest contribution over the elements, and the element where it is.

Inputs

Name	Type	Description
`value`	`Uncertain`

Outputs

Name	Type	Description
`result`	`dict[str, list[Any]]`

Value and Uncertainty¶

uncertainty.value_and_uncertainty

Split a value into its best estimate, its standard uncertainty (in the value’s unit) and the relative uncertainty u/|x|. An array is split element by element.

Inputs

Name	Type	Description
`value`	`Uncertain`

Outputs

Name	Type	Description
`value`	`Any`
`uncertainty`	`Any`
`relative`	`Any`