tensorquant.numericalhandles package

Submodules

tensorquant.numericalhandles.interpolation module

class tensorquant.numericalhandles.interpolation.LinearInterp(x, y)

Bases: object

Linear interpolation.

This class provides a simple linear interpolation method for a given set of x and y values. It computes interpolated values for a given term by linearly interpolating between the known data points.

Parameters:

• x (list or numpy array) – Known x-values (independent variable).

• y (list or numpy array) – Known y-values (dependent variable).

interpolate(term)

Interpolates a value at the specified term using linear interpolation.

For a given term (input value), this method finds the two adjacent x-values that bound the term and computes the corresponding interpolated y-value.

Parameters:

term (float) – The x-value at which interpolation is desired.

Returns:

The interpolated y-value.

Return type:

float

Raises:

ValueError – If the term is outside the range of x-values.

tensorquant.numericalhandles.newton module

tensorquant.numericalhandles.newton.newton(func, x0, tol=1e-08, max_iter=100)

Solves a system of nonlinear equations using Newton’s method.

Parameters:

• func (callable) – A function that returns (f(x), jacobian), where f(x) is the vector of residuals and jacobian is the NxN Jacobian matrix evaluated at x.

• x0 (numpy.ndarray) – Initial guess for the root.

• tol (float, optional) – Convergence tolerance. The method stops when both ‖f(x)‖ and ‖Δx‖ are below tol. Defaults to 1e-8.

• max_iter (int, optional) – Maximum number of iterations. Defaults to 100.

Returns:

• numpy.ndarray: Solution vector x satisfying func(x) ≈ 0.

• numpy.ndarray: Jacobian matrix at the solution.

Return type:

tuple

Raises:

ValueError – If the method fails to converge after max_iter iterations.

tensorquant.numericalhandles.newton.newton_1d(func, i: int, r0: float, tol: float = 1e-08, max_iter: int = 100) → float

Scalar Newton’s method for a single pillar in curve bootstrapping.

Finds r such that func(i, r) = 0 using the analytic derivative returned by func (typically computed via autodiff).

Parameters:

• func (callable) – Callable with signature func(i, r) -> (f, df_dr), where f is the NPV of instrument i and df_dr is its derivative w.r.t. the rate at pillar i.

• i (int) – Pillar index being solved.

• r0 (float) – Initial guess for the rate at pillar i.

• tol (float, optional) – Convergence tolerance on both |f| and the Newton step |Δr|. Defaults to 1e-8.

• max_iter (int, optional) – Maximum number of iterations. Defaults to 100.

Returns:

The bootstrapped rate at pillar i.

Return type:

float

Raises:

ValueError – If the derivative is numerically zero or if the method fails to converge within max_iter iterations.

Module contents