From dda3026458c512b7c14b4fb59777b399931b2b1b Mon Sep 17 00:00:00 2001
From: mkirsz <s1351949@sms.ed.ac.uk>
Date: Sat, 8 Feb 2025 09:23:44 +0000
Subject: [PATCH] Docs
---
include/tadah/models/cutoffs.h | 39 ++++++++++++++++++++++++++++++++++
1 file changed, 39 insertions(+)
diff --git a/include/tadah/models/cutoffs.h b/include/tadah/models/cutoffs.h
index a64320b..eb66891 100644
--- a/include/tadah/models/cutoffs.h
+++ b/include/tadah/models/cutoffs.h
@@ -212,6 +212,45 @@ class Cut_Poly1 : public Cut_Base {
double calc(double r);
double calc_prime(double r);
};
+/**
+ * @class Cut_Cos_S
+ * @brief Smooth cosine cutoff function with a smoothing interval.
+ *
+ * The `Cut_Cos_S` class implements a smooth cosine cutoff function that transitions smoothly from 1 to 0 over a specified smoothing interval between the inner cutoff radius \f$ r_{\text{inner}} \f$ and the outer cutoff radius \f$ r_{\text{cut}} \f$ The function is defined as:
+ *
+ * \f[
+ * f(r) =
+ * \begin{cases}
+ * 1, & \text{if } r \leq r_{\text{inner}} \\
+ * \dfrac{1}{2}\left[1 + \cos\left( \dfrac{\pi (r - r_{\text{inner}})}{r_{\text{cut}} - r_{\text{inner}}} \right) \right], & \text{if } r_{\text{inner}} < r < r_{\text{cut}} \\
+ * 0, & \text{if } r \geq r_{\text{cut}}
+ * \end{cases}
+ * \f]
+ *
+ * and its derivative:
+ *
+ * \f[
+ * f'(r) =
+ * \begin{cases}
+ * 0, & \text{if } r \leq r_{\text{inner}} \text{ or } r \geq r_{\text{cut}} \\
+ * -\dfrac{\pi}{2 (r_{\text{cut}} - r_{\text{inner}})} \sin\left( \dfrac{\pi (r - r_{\text{inner}})}{r_{\text{cut}} - r_{\text{inner}}} \right), & \text{if } r_{\text{inner}} < r < r_{\text{cut}}
+ * \end{cases}
+ * \f]
+ *
+ * where:
+ *
+ * - \f$ r \f$ is the radial distance.
+ * - \f$ r_{\text{cut}} \f$ is the outer cutoff radius (`rcut`).
+ * - \f$ r_{\text{inner}} \f$ is the inner cutoff radius (`rcut_inner`), defined as \f$ r_{\text{inner}} = r_{\text{cut}} - 1.0 \f$.
+ *
+ * **Characteristics:**
+ *
+ * - For \f$ r \leq r_{\text{inner}} \f$ the function \f$ f(r) = 1 \f$ and \f$ f'(r) = 0 \f$
+ * - For \f$ r_{\text{inner}} < r < r_{\text{cut}} \f$, the function transitions smoothly from 1 to 0.
+ * - For \f$ r \geq r_{\text{cut}} \f$, the function \f$ f(r) = 0 \f$ and \f$ f'(r) = 0 \f$.
+ *
+ * **Note:** The function ensures continuity and smoothness in simulations or calculations where a smooth cutoff is required.
+ */
class Cut_Cos_S : public Cut_Base {
private:
std::string lab = "Cut_Cos_S";
--
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