schrodinger.application.matsci.uq_utils module

Utilities for uncertainty quantification.

Copyright Schrodinger, LLC. All rights reserved.

schrodinger.application.matsci.uq_utils.X_BIAS_F(x)

schrodinger.application.matsci.uq_utils.get_positive_definite_data(xs, ys)

Return positive definite data.

Parameters

• xs (list) – the domain

• ys (list) – the range

Return type

list, list

Returns

the domain and range

schrodinger.application.matsci.uq_utils.get_bilinear_regions(original_data)

Gets the initial early and late regions such that the R squared values are maximized.

Parameters

original_data (list) – contains pair tuples of data points

Return type

tuple, tuple

Returns

(min, max) tuples for early and late regions

schrodinger.application.matsci.uq_utils.get_points_in_region(data, region)

Determine which data points fall into a region given its lower and upper bound.

Parameters

• data (list) – contains pair tuples of data points

• region (tuple) – a tuple containing the lower and upper boundaries points of the region

Returns

all points within the region

Return type

list

schrodinger.application.matsci.uq_utils.get_bilinear_regression(data)

Return the regression information.

Parameters

data (list) – contains pair tuples of data points

Return type

tuple

Returns

(slope, intercept, R^2)

schrodinger.application.matsci.uq_utils.get_bilinear_prop(early_regression, late_regression)

Returns the bilinear property if both regressions are available.

Parameters

• early_regression (tuple) – (slope, intercept, R^2) for early part

• late_regression (tuple) – (slope, intercept, R^2) for late part

Returns

the property

Return type

float

schrodinger.application.matsci.uq_utils.get_bilinear_fit_property(x, x_intersection, early_regression, late_regression, invert_y=True)

Return the fit property given the x-value.

Parameters

• x (float) – the x-value

• x_intersection (float) – the x intersection point

• early_regression (tuple) – (slope, intercept, R^2) for early part

• late_regression (tuple) – (slope, intercept, R^2) for late part

• invert_y (bool) – whether to invert the y-values

Return type

float or None

Returns

the fit property value or None if there isn’t one

schrodinger.application.matsci.uq_utils.get_bilinear_prop_from_points(points, early_region=None, late_region=None)

Return a bilinear property using the given points.

Parameters

• points (list) – list of (x,y) tuples

• early_region (tuple or None) – (min, max) tuple for early region, if None then automatically determined

• late_region (tuple or None) – (min, max) tuple for late region, if None then automatically determined

Return type

float or None

Returns

the property or None if there isn’t one

schrodinger.application.matsci.uq_utils.get_min_max_avg(data)

Return (min, max, avg) of the given data.

Parameters

data (list) – the data

Return type

float, float, float

Returns

the min, max, avg

schrodinger.application.matsci.uq_utils.get_hyperbola_regression(data, avg_x)

Return the regression information.

Parameters

• data (list) – contains pair tuples of data points

• avg_x (float) – the average x-value

Return type

tuple

Returns

(t0, a, b, c, p0) parameters

schrodinger.application.matsci.uq_utils.calc_property(x_scaled, t0, a, b, c, p0)

Calculate the hyperbolic property.

Parameters

• x_scaled (float) – the scaled x-value

• t0 (float) – the scaled T_0 factor in polynomial

• a (float) – a factor in polynomial

• b (float) – b factor in polynomial

• c (float) – c factor in polynomial

• p0 (float) – p_0 factor in polynomial

schrodinger.application.matsci.uq_utils.get_hyperbola_fit_property(x, regression)

Return the fit property given the x-value.

Parameters

• x (float) – the x-value

• regression (tuple) – (t0, a_coeff, b_coeff, c_coeff, p0)

Return type

float or None

Returns

the fit property value or None if there isn’t one

schrodinger.application.matsci.uq_utils.get_hyperbola_prop_from_points(points)

Return a hyperbola property using the given points.

Parameters

points (list) – list of (x,y) tuples

Return type

float or None

Returns

the property or None if there isn’t one

class schrodinger.application.matsci.uq_utils.BootstrapNoiseHistogramData

Bases: object

Manage data of a histogram of a quantity derived from a parametric bootstrap analysis of uncorrelated Gaussian white noise.

SAMPLE_SIZE = 1000

__init__()

Create an instance.

setOriginalData(points)

Set the original data used to derive the histogram.

Parameters

points (list) – list of (x,y) tuples

setFitFunction(fit_function)

Set the fit function, i.e. the function that was fit to the original data.

Parameters

fit_function (function) – the fit function

setXBiasFunction(x_bias_function=None)

Set a biasing function for the original x data.

Parameters

x_bias_function (function or None) – a biasing function for the original x data or None if there isn’t one

seedRandom(seed=None)

Seed the random number generator.

Parameters

seed (int or None) – the seed

setSampleSize(size=None)

Set the sample size.

Parameters

size (int or None) – the sample size, if None then the default of SAMPLE_SIZE is used

setTargetFunction(target_function)

Set the target function, i.e. the function used to obtain the target quantity from points.

Parameters

target_function (function) – the target function

getHistogramData()

Return the histogram data which is just a list of sampled target values.

Raises

RuntimeError – if required variables are not defined

Return type

list or None

Returns

list of sampled target values or None if there isn’t one

static getSampleHistogram(points, fit_function, target_function, x_bias_function=None, seed=None, size=None)

Return a sample of histogram data using the given points, fit function, and target function.

Parameters

• points (list) – list of (x,y) tuples

• fit_function (function) – the fit function

• target_function (function) – the target function

• x_bias_function (function or None) – a biasing function for the original x data or None if there isn’t one

• seed (int or None) – the seed

• size (int or None) – the sample size, if None then the default of SAMPLE_SIZE is used

Return type

list or None

Returns

list of sampled target values or None if there isn’t one

static getNormalParameters(data)

Return the mean, standard deviation, covariance matrix, and figure of merit parameters from a normal fit of the given data.

Parameters

data (list) – contains (x, y) tuples

Return type

float, float, numpy.array, float or None, None, None, and None

Returns

the mean, standard deviation, covariance matrix, and figure of merit or None, None, None, and None if there aren’t any

class schrodinger.application.matsci.uq_utils.BilinearHistogramData(invert_y=True)

Bases: schrodinger.application.matsci.uq_utils.BootstrapNoiseHistogramData

Manage a histogram using bilinear data.

__init__(invert_y=True)

Create an instance.

Parameters

invert_y (bool) – whether to invert the y-values

static getSampleHistogram(points, fit_function, target_function, x_bias_function=None, seed=None, size=None, invert_y=True)

Return a sample of histogram data using the given points, fit function, and target function.

Parameters

• points (list) – list of (x,y) tuples, if using invert_y then this data should be uninverted

• fit_function (function) – the fit function, if using invert_y then expected to return uninverted data

• target_function (function) – the target function, if using invert_y then expects the input data to already be inverted

• x_bias_function (function or None) – a biasing function for the original x data or None if there isn’t one

• seed (int or None) – the seed

• size (int or None) – the sample size, if None then the default of SAMPLE_SIZE is used

• invert_y (bool) – whether to invert the y-values

Return type

list or None

Returns

list of sampled target values or None if there isn’t one

SAMPLE_SIZE = 1000

getHistogramData()

Return the histogram data which is just a list of sampled target values.

Raises

RuntimeError – if required variables are not defined

Return type

list or None

Returns

list of sampled target values or None if there isn’t one

static getNormalParameters(data)

Return the mean, standard deviation, covariance matrix, and figure of merit parameters from a normal fit of the given data.

Parameters

data (list) – contains (x, y) tuples

Return type

float, float, numpy.array, float or None, None, None, and None

Returns

the mean, standard deviation, covariance matrix, and figure of merit or None, None, None, and None if there aren’t any

seedRandom(seed=None)

Seed the random number generator.

Parameters

seed (int or None) – the seed

setFitFunction(fit_function)

Set the fit function, i.e. the function that was fit to the original data.

Parameters

fit_function (function) – the fit function

setOriginalData(points)

Set the original data used to derive the histogram.

Parameters

points (list) – list of (x,y) tuples

setSampleSize(size=None)

Set the sample size.

Parameters

size (int or None) – the sample size, if None then the default of SAMPLE_SIZE is used

setTargetFunction(target_function)

Set the target function, i.e. the function used to obtain the target quantity from points.

Parameters

target_function (function) – the target function

setXBiasFunction(x_bias_function=None)

Set a biasing function for the original x data.

Parameters

x_bias_function (function or None) – a biasing function for the original x data or None if there isn’t one

class schrodinger.application.matsci.uq_utils.HyperbolaHistogramData

Bases: schrodinger.application.matsci.uq_utils.BootstrapNoiseHistogramData

Manage a histogram using hyperbola data.

static getSampleHistogram(points, fit_function, target_function, x_bias_function=None, seed=None, size=None)

Return a sample of histogram data using the given points, fit function, and target function.

Parameters

• points (list) – list of (x,y) tuples

• fit_function (function) – the fit function

• target_function (function) – the target function

• x_bias_function (function or None) – a biasing function for the original x data or None if there isn’t one

• seed (int or None) – the seed

• size (int or None) – the sample size, if None then the default of SAMPLE_SIZE is used

Return type

list or None

Returns

list of sampled target values or None if there isn’t one

SAMPLE_SIZE = 1000

__init__()

Create an instance.

getHistogramData()

Return the histogram data which is just a list of sampled target values.

Raises

RuntimeError – if required variables are not defined

Return type

list or None

Returns

list of sampled target values or None if there isn’t one

static getNormalParameters(data)

Return the mean, standard deviation, covariance matrix, and figure of merit parameters from a normal fit of the given data.

Parameters

data (list) – contains (x, y) tuples

Return type

float, float, numpy.array, float or None, None, None, and None

Returns

the mean, standard deviation, covariance matrix, and figure of merit or None, None, None, and None if there aren’t any

seedRandom(seed=None)

Seed the random number generator.

Parameters

seed (int or None) – the seed

setFitFunction(fit_function)

Set the fit function, i.e. the function that was fit to the original data.

Parameters

fit_function (function) – the fit function

setOriginalData(points)

Set the original data used to derive the histogram.

Parameters

points (list) – list of (x,y) tuples

setSampleSize(size=None)

Set the sample size.

Parameters

size (int or None) – the sample size, if None then the default of SAMPLE_SIZE is used

setTargetFunction(target_function)

Set the target function, i.e. the function used to obtain the target quantity from points.

Parameters

target_function (function) – the target function

setXBiasFunction(x_bias_function=None)

Set a biasing function for the original x data.

Parameters

x_bias_function (function or None) – a biasing function for the original x data or None if there isn’t one