NumCosmoMathSBesselOdeOperator

Decreases the reference count of op by one and sets op to NULL.

Gets the multipole range [ell_min, ell_max] for which the operator solves. For single-ell operators, ell_min == ell_max.

Gets the interval [a, b] on which the operator is defined.

Bound on the roundoff left in the endpoint derivatives of the last solve for that multipole: $\sum_j j^2 |a_j| / h$, which multiplied by the machine epsilon bounds the absolute error of $u’(x_a)$ and $u’(x_b)$. Those are formed as $u’(\pm 1) = (1/h)\sum_j (\pm 1)^{j+1} j^2 a_j$, and under NCM_SBESSEL_ODE_CONSTRAINT_TAU any homogeneous content the truncation admitted cancels in that sum, exactly but not in floating point —- so this is what survives, and it is what limits the accuracy of a boundary functional built from the derivatives.

Largest $|a_j|$ produced by the last back-substitution for that multipole. Under NCM_SBESSEL_ODE_CONSTRAINT_TAU a value far above the forcing’s own scale $\max|x F| / \min|x^2 - \nu^2|$ means the solve admitted homogeneous content, and the panel must be redone with Dirichlet data.

Dense $n \times n$ row-major representation of op, closed the way op is closed: rows 0 and 1 carry the two constraint functionals of its NcmSBesselOdeConstraint —- the dense $(-1)^j$ and $1$ patterns of Dirichlet data, the two single entries of the pinned constraint, or nothing at all under NCM_SBESSEL_ODE_CONSTRAINT_TAU —- and rows 2 to nrows-1 are the discretized operator. For validation and for comparison with dense solvers; the solve itself never forms this matrix.

Gets the number of columns in the currently stored factorization, zero before the first solve and after a reconfiguration or a constraint change.

Gets the number of matrix rows allocated, the rows per multipole times the block’s $n_\ell$, which sizes the stored rows, rotations and transformed right-hand side. It grows when a solve needs more columns and is kept across reconfigurations.

Reads back the indices last given to ncm_sbessel_ode_operator_set_pinned_constraint(), both zero if it was never called. They act only while ncm_sbessel_ode_operator_get_constraint() is NCM_SBESSEL_ODE_CONSTRAINT_PINNED.

Number of coefficients a NCM_SBESSEL_ODE_CONSTRAINT_TAU solve of a right-hand side with rhs_len entries uses at least: the larger of the operator’s minimum and the forcing floor.

Gets the operator’s relative coefficient-decay tolerance.

Increases the reference count of op by one.

Sets the constraint of this operator alone, overriding what it inherited from the solver. The stored factorization is discarded and the resolution floor recomputed.

Overrides the floor the decay test may not stop below. Experimental: with NCM_SBESSEL_ODE_CONSTRAINT_PINNED and a floor of zero the test may stop before the pinned columns have entered the system, in which case the pins never act and the solve is closed by whatever back-substitution assigns to the trailing coefficients, which is NCM_SBESSEL_ODE_CONSTRAINT_TAU by another route. The stored factorization is discarded.

Puts op on NCM_SBESSEL_ODE_CONSTRAINT_PINNED, closing the system with $\langle T_{pin1}, u\rangle = \langle T_{pin2}, u\rangle = 0$ instead of the Dirichlet data $u(x_a) = u(x_b) = 0$.

Solves the ODE by adaptive QR in ultraspherical coefficient space. The matrix grows until the relative coefficient-decay criterion described by NcmSBesselOdeSolver is met.

Efficiently computes only the endpoint derivatives u’(a) and u’(b) without building the full solution vector. This is much more efficient when only endpoint information is needed (e.g., for integral computations via Green’s identity).

Solves the ODE and evaluates the solution and its physical-coordinate derivative at two points without constructing the complete Chebyshev coefficient vectors. For each multipole the output contains [u(x0), u'(x0), u(x1), u'(x1)].

Decreases the reference count of op by one. When the reference count reaches zero, frees all allocated memory.