pyoptmat.utility: useful miscellaneous mathematical functions

Various utility functions used in the rest of the modules. This includes basic mathematical functions, routines used in the tests, and various visualization routines.

class pyoptmat.utility.ArbitraryBatchTimeSeriesInterpolator(times, data)

Bases: Module

Interpolate data located at discrete times linearly to point t.

This version handles batched of arbitrary size – only the rightmost batch dimension must agree with the input data. All other dimensions are broadcast.

Parameters:

times (torch.tensor) – input time series as a code:(ntime,nbatch) array
values (torch.tensor) – input values series as a code:(ntime,nbatch) array

forward(t)

Calculate the linearly-interpolated current values

Parameters:: t (torch.tensor) – batched times as (...,nbatch,) array
Returns:: batched values at t
Return type:: torch.tensor

class pyoptmat.utility.BatchTimeSeriesInterpolator(times, data)

Bases: Module

Interpolate data located at discrete times linearly to point t.

This version handles batched input

Precache a lot of the work required to interpolate in time vs pyoptmat.utility.timeseries_interpolate_batch_times()

Parameters:

times (torch.tensor) – input time series as a code:(ntime,nbatch) array
values (torch.tensor) – input values series as a code:(ntime,nbatch) array

forward(t)

Calculate the linearly-interpolated current values

Parameters:: t (torch.tensor) – batched times as (nbatch,) array
Returns:: batched values at t
Return type:: torch.tensor

class pyoptmat.utility.CheaterBatchTimeSeriesInterpolator(times, data)

Bases: Module

Interpolate data located at discrete times linearly to point t.

Precache a lot of the work required to interpolate in time vs pyoptmat.utility.timeseries_interpolate_batch_times()

This is the cheater version specifically for our structured problems where if you figure out where one time point index is relative to the provided time points then you can use that index for all the other points in the batch. This won’t work in general, but works fine here.

Parameters:

times (torch.tensor) – input time series as a (ntime,nbatch) array
values (torch.tensor) – input values series as a (ntime,nbatch) array

forward(t)

Calculate the linearly-interpolated current values

Parameters:: t (torch.tensor) – batched times as (nbatch,) array
Returns:: batched values at t
Return type:: torch.tensor

pyoptmat.utility.add_id(df)

Add the identity to a tensor with the shape of the Jacobian

Parameters:: df (torch.tensor) – batched (n,m,m) tensor
Returns:: df plus a batched identity of the right shape
Return type:: torch.tensor

pyoptmat.utility.batch_differentiate(fn, x0, eps=1e-06, nbatch_dim=1)

New numerical differentiation function to handle the batched-model cases

This version handles arbitrary batch sizes

Parameters:

fn (torch.tensor) – function to differentiate via finite differences
x0 (torch.tensor) – point at which to take the numerical derivative

Keyword Arguments:

eps (float) – perturbation to use

Returns:

finite difference approximation to: \(\frac{df}{dx}|_{x_0}\)

Return type:

torch.tensor

pyoptmat.utility.compose(f1, f2)

A function composition operator…

Parameters:

f1 (function) – first function
f2 (function) – second function

Returns:

f2(f1)

Return type:

function

pyoptmat.utility.differentiate(fn, x0, eps=1e-06)

Numerical differentiation used in the tests, old version does not handle batched input

Parameters:

fn (torch.tensor) – function to differentiate via finite differences
x0 (torch.tensor) – point at which to take the numerical derivative

Keyword Arguments:

eps (float) – perturbation to use

Returns:

finite difference approximation to: \(\frac{df}{dx}|_{x_0}\)

Return type:

torch.tensor

pyoptmat.utility.heaviside(X)

A pytorch-differentiable version of the Heaviside function

\[H\left(x\right) = \frac{\operatorname{sign}(x) + 1)}{2}\]

Parameters:: X (torch.tensor) – tensor input
Returns:: the Heaviside function of the input
Return type:: torch.tensor

pyoptmat.utility.jacobianize(argnums=None)

Decorator that adds the multibatched Jacobian to a function

Assumes that the function itself has only a single dimension, the last in the shape

By default provides Jacobian for all *args, but argnums can be set to limit this to certain arguments

pyoptmat.utility.macaulay(X)

A pytorch-differentiable version of the Macualay bracket

\[M\left(x\right) = x H\left(x\right)\]

Parameters:: X (torch.tensor) – tensor input
Returns:: the Macaulay bracket applied to the input
Return type:: torch.tensor

pyoptmat.utility.mbmm(A1, A2): Batched matrix-matrix multiplication with several batch dimensions

pyoptmat.utility.new_differentiate(fn, x0, eps=1e-06)

New numerical differentiation function to handle the batched-model cases

Parameters:

fn (torch.tensor) – function to differentiate via finite differences
x0 (torch.tensor) – point at which to take the numerical derivative

Keyword Arguments:

eps (float) – perturbation to use

Returns:

finite difference approximation to: \(\frac{df}{dx}|_{x_0}\)

Return type:

torch.tensor

pyoptmat.utility.timeseries_interpolate_batch_times(times, values, t)

Interpolate the time series defined by X to the times defined by t

This version handles batched input

Parameters:

times (torch.tensor) – input time series as a (ntime,nbatch) array
values (torch.tensor) – input value series as a (ntime,nbatch) array
t (torch.tensor) – batch times as a (nbatch,) array

Returns:

Interpolated values as a (nbatch,) array

Return type:

torch.tensor

pyoptmat.utility.timeseries_interpolate_single_times(times, values, t)

Interpolate the time series defined by X to the times defined by t

This version does not handle batched input

Parameters:

times (torch.tensor) – input time series as a (ntime,) array
values (torch.tensor) – input value series as a (ntime,nbatch) array
t (torch.tensor) – times as a scalar

Returns:

interpolated values as a (nbatch,) array

Return type:

torch.tensor

pyoptmat.utility.visualize_variance(strain, stress_true, stress_calc, alpha=0.05)

Visualize variance for batched examples

Parameters:

strain (torch.tensor) – input strain
stress_true (torch.tensor) – actual stress values
stress_calc (torch.tensor) – simulated stress values

Keyword Arguments:

alpha (float) – alpha value for shading