Force Harmonic Polynomial Module

The force_harmonic_polynomial module implements a harmonic oscillator force with variable stiffness represented as a polynomial function of time.

Classes

class VariableStiffnessHarmonicForcePolynomial(kappai, kappaf, tf, coef_list, continuous=False, normalized=False)

Bases: BaseHarmonicForce

Harmonic oscillator force with a variable stiffness that is a learnable parameter. The stiffness is a polynomial function of time. The center is fixed at zero.

Parameters:

• kappai (float)

• kappaf (float)

• tf (float)

• coef_list (list)

• continuous (bool)

• normalized (bool)

__init__(kappai, kappaf, tf, coef_list, continuous=False, normalized=False)

Parameters:

• kappai (float) – Initial stiffness.

• kappaf (float) – Final stiffness.

• tf (float) – final time of the protocol.

• coef_list (list) – List of coefficients for the polynomial function

• time. (of)

• continuous (bool) – If True, the stiffness is a continuous function

• t=tf. (of time at t=0 and)

• normalized (bool) – If True, the argument is normalized to be t/tf

• t. (instead of)

kappa(t)

Stiffness as a polynomial function of time. If continuous = False:

kappa(t) = sum(coef_list[i] * t^i) for i in range(len(coef_list))

If continuous = True:

kappa(t) = kappai + (t/tf) * (kappaf - kappai)

• (t/tf)*(1-t/tf)* sum(coef_list[i] * t^i) for i in range(len(coef_list))

If normalized:

use t/tf instead of t in the polynomial.

Parameters:

t – time to compute the stiffness

Returns:

the stiffness value at time t

Return type:

torch.tensor

Example Usage

Here’s an example of how to create and use a polynomial harmonic force:

import langesim_optim as lso

# Create a polynomial force with initial coefficients
force = lso.force_harmonic_polynomial.VariableStiffnessHarmonicForcePolynomial(
    kappai=1.0,  # Initial stiffness
    kappaf=2.0,  # Final stiffness
    tf=1.0,      # Final time
    coef_list=[0.0, 0.0, 1.0],  # Quadratic polynomial coefficients
    continuous=True,  # Enforce continuity at endpoints
    normalized=True   # Use normalized time t/tf
)

# Get stiffness at a specific time
t = 0.5
k = force.kappa(t)