🥮 mooncakes.io

    moondiffraction

    Bounded constant-scatterer reciprocal diffraction and powder spectra

    diffraction
    reciprocal
    crystallography
    Download zip
    Author
    Version
    0.1.1
    License
    MIT
    Repository
    Last updated
    13 hours ago
    Downloads
    4

    #MoonDiffraction

    Verify diffraction

    源代码版本：0.1.1；GitHub Releases。

    MoonBit 常数散射点倒易衍射内核：已有晶胞参数与分数坐标 → 完整有限反射 → 复结构因子/消光 → Bragg 角 → 粉末峰与有限采样谱。

    这不是 MoonINI 的改名版本，也不是 CIF/通用晶体解析器。面向教学工具与离线数值原型；不是元素相关 X 射线仿真、实验标定、结构精修或完整空间群库。

    #为什么独立建设：与已有项目的互补边界

    MoonCakes 已有 IvanAXu/BioSeqs@0.1.9 的晶胞/原子模型、CIF、坐标转换。我们不重复这些 API，接收其已有模型的六个晶胞标量和 fractional atom 标量，新增倒易反射计算下游。没有强制依赖或复制 BioSeqs 源码；桥接契约见 上游接入。

    相对于旧 MoonINI，本项目核心数据是 hkl / reciprocal Gram matrix / complex amplitudes / multiplicities，不是配置 AST。查重包含多个不同领域候选、MoonCakes 搜索、相邻源码和全登记表：查重报告。只对已检索范围作判断，保留中等相邻风险，不承诺报名通过。

    #本地安装与运行

    安装 MoonBit 官方工具链后：

    git clone https://github.com/shangwuxi/moondiffraction.git
cd moondiffraction
moon test --deny-warn
moon run cmd/cubic
moon run cmd/extinction
moon run cmd/powder
python scripts/oracle.py wasm-gc

    当前代码仅依赖 moonbitlang/core/math 及标准库内建能力。已以 shangwuxi 身份发布到 MoonCakes。在已有 MoonBit 工程中运行：

    moon add shangwuxi/moondiffraction

    0.1.1 为发布说明同步版本，数值实现与 0.1.0 相同。GitHub 对应标签 v0.1.1；v0.1.0 保留其历史发布说明，不改写标签。

    已本地验证工具链：moon 0.1.20260904；moonc v0.10.12+1634b282e（2026-09-07）。不修改其他项目/全局工具链。原生构建需要 C 编译器；本机仅验证 native check，native build 因缺少 cl/cc/gcc/clang 未运行成功；CI 已使用 Ubuntu C 工具链完成 native check/build/test、三个示例和独立 oracle；这不等同于本地 native 构建通过。

    #三个分别可运行的完整场景

    #1. 教学工具：立方晶面间距和区轴

    moon run cmd/cubic：输入 a=b=c=3 Å、(122)、波长 1 Å，验证 d=1 Å、2θ=60°，并验证 [001] 区轴第一反射壳层含 4 个点。失败会 abort，不是只打印预设答案。

    #2. 点阵课程：BCC/FCC 消光

    moon run cmd/extinction：把体心和面心平移显式转换为散射点，分别对 26 个带符号反射求复振幅；验证 14/18 个消光，并与独立整数选择规则逐项一致。规则只预测平移消光，不能预测全部基元或滑移/螺旋消光。

    #3. 原型开发者：三斜晶胞到粉末谱与峰位比较

    moon run cmd/powder：输入三斜六参数和两个带占据率/常数权重的点，生成 70 个反射、35 个峰组与 7201 个谱采样，检查积分强度守恒；一个合成观测峰匹配、179° 观测保持未匹配。输出可读摘要和带单位 CSV，不强制把观测分配给“最近的”峰。

    #最小 API 使用

    在子包 moon.pkg 中：

    import { "shangwuxi/moondiffraction" @diff }
    pkgtype(kind: "executable")

    fn main {
      let m = @diff.reciprocal(3.0, 3.0, 3.0, 90.0, 90.0, 90.0).unwrap()
      let points = [@diff.site(0.0, 0.0, 0.0, 1.0).unwrap()]
      let reflections = m.simulate(points, 1.0, 1.0).unwrap()
      let peaks = @diff.powder(reflections).unwrap()
      println(peaks.length())
    }

    以上 unwrap 仅用于固定演示输入。生产调用须处理 Err(Invalid(message)) 与 Err(Budget(message))；不能自动忽略失败或截断后声称完整。

    API语义
    reciprocal / hkl / site验证输入并构造只读字段模型
    Metric.q2 / spacing / plane_angle倒易度量、间距、带方向晶面角
    reflections / zone有界完整枚举、整数区轴过滤
    amplitude / sensitivity补偿求和复振幅；单点六参数强度局部导数
    Centering.allows / translationsP/I/F/A/B/C/R（R obverse hex）平移规则/点
    two_theta / spacing_from_angle一阶 Bragg；不可达返回 Ok(None)
    simulate同时限制候选数和相位项数；保留相消/不可达反射
    powder拒绝重复 hkl 和混合波长；锚点分组，不做链式聚类
    gaussian_profile / Profile.area单位连续面积 Gaussian；有限窗口梯形积分
    match_peaks所有容差内候选及残差；不做物相识别
    reflections_csv / reflections_json / Profile.csv数值导出，JSON 带版本和模型声明

    完整签名：pkg.generated.mbti。数值与复杂度边界：架构。

    #重要约定和限制

    • 长度/波长 Å，B_iso Ų，角度 degree；q²=1/d²，没有 2π 因子。
    • F=Σ occ*w*exp(-B*q²/4)*exp(2πi(hx+ky+lz))；w 是实常数，可为负。没有元素散射表或异常色散。
    • 默认枚举保留 Friedel 两侧；粉末强度为成员强度之和，不再额外乘多重度。显式设置 Friedel 唯一时，应理解多重度减半；simulate 固定保留两侧。
    • centering 参数只过滤，不扩增 site；使用 translations 创建完整点阵，或自己输入完整 conventional-cell 点。没有空间群对称扩增。
    • d_min 边界允许 1e-12 相对 q² 容差，拒绝归一化 Gram determinant ≤1e-10 的近奇异晶胞。
    • Gaussian 的 sigma 是标准差，不是 FWHM；要求 step ≤ sigma/4。窗外面积丢失会如实反映，不重归一化、不加背景/仪器校正。
    • 峰组使用最小角为锚点（不是强度质心），width 报告组内角跨度。数组字段是调用者可变容器，改动输出后不再代表原始仿真结果。

    #验证

    moon fmt --check
moon check --target wasm-gc --deny-warn
moon build --target wasm-gc --deny-warn
moon test --target wasm-gc --deny-warn
python scripts/oracle.py wasm-gc

    把 target 换成 wasm / js / native 做相同验证（native 需 C 编译器）。2026-09-11 四目标 CI 首次全部通过（验证记录）。当前 24 个 MoonBit 测试组；其中含 2394 个平移规则交叉检查、立方壳计数、NaN/Infinity、非对称三斜、资源失败及六维导数差分。另有 496 组独立 Python 标准库 oracle，以笛卡尔叉积重建倒易基，避免与被测余子式公式共用同一算法。测试组数不等于断言数，不能混报。

    #开源与发布

    MIT；唯一项目 Git 提交身份 shangwuxi。AI 协助范围见 AI_USAGE.md，数学/生态来源及未复制声明见 THIRD_PARTY.md。开发快照 21 个非空提交，经逐提交重跑保守计入 20 个，另 1 个粉末修复不单独计入；后续发布文档提交不用于凑门槛，见 逐 SHA 审计。CI、发布版本以 GitHub 实际状态为准。MoonCakes 发布和组委会复核是独立步骤。

    Amplitude

    source
    pub struct Amplitude {
      real : Double
      imag : Double
    } derive(
    Debug    )

    Amplitude::intensity

    source
    fn Amplitude::intensity(self : Amplitude) -> Double

    Centering

    source
    pub(all) enum Centering {
      Primitive
      Body
      Face
      AFace
      BFace
      CFace
      RhombohedralHex
    } derive(Eq, 
    Debug    )

    Translational centering only, not a full space-group absence predictor.

    Centering::allows

    source
    fn Centering::allows(self : Centering, i : Hkl) -> Bool

    Centering::translations

    source
    fn Centering::translations(self : Centering) -> Array[(Double, Double, Double)]

    Fractional translations in conventional cell; R uses obverse hexagonal setting.

    Hkl

    source
    pub struct Hkl {
      h : Int
      k : Int
      l : Int
    } derive(Eq, 
    Debug    )

    Integer plane indices, bounded to avoid overflow in combinatorial operations.

    Hkl::canonical

    source
    fn Hkl::canonical(self : Hkl) -> Hkl

    Select one of a Friedel pair without changing index magnitude.

    Hkl::opposite

    source
    fn Hkl::opposite(self : Hkl) -> Hkl

    Metric

    source
    pub struct Metric {
      aa : Double
      bb : Double
      cc : Double
      ab : Double
      ac : Double
      bc : Double
      a : Double
      b : Double
      c : Double
    } derive(
    Debug    )

    Reciprocal metric in inverse square angstroms (no 2*pi factor).

    Metric::amplitude

    source
    fn Metric::amplitude(self : Metric, index : Hkl, sites : Array[Site]) -> Result[Amplitude, Problem]

    A real signed constant weight obeys Friedel conjugacy; no anomalous scattering.

    Metric::plane_angle

    source
    fn Metric::plane_angle(self : Metric, x : Hkl, y : Hkl) -> Double

    Reciprocal plane angle; signed hkl retains angle in [0,180].

    Metric::q2

    source
    fn Metric::q2(self : Metric, index : Hkl) -> Double

    Squared reciprocal length, 1/d^2; NOT (2*pi/d)^2.

    Metric::reflections

    source
    fn Metric::reflections(self : Metric, d_min : Double, max_candidates? : Int, friedel_unique? : Bool) -> Result[Array[Hkl], Problem]

    Complete enumeration, or an error before traversal; never a truncated success.

    Metric::sensitivity

    source
    fn Metric::sensitivity(self : Metric, index : Hkl, sites : Array[Site], selected : Int) -> Result[Sensitivity, Problem]

    Metric::simulate

    source
    fn Metric::simulate(self : Metric, sites : Array[Site], d_min : Double, wavelength : Double, centering? : Centering, max_candidates? : Int, max_terms? : Int) -> Result[Array[Reflection], Problem]

    Simulate a complete bounded reciprocal sphere. Centering is a filter, NOT expansion.

    Metric::spacing

    source
    fn Metric::spacing(self : Metric, index : Hkl) -> Double

    Metric::zone

    source
    fn Metric::zone(self : Metric, d_min : Double, u : Int, v : Int, w : Int, max_candidates? : Int) -> Result[Array[Hkl], Problem]

    Zone-filter a complete finite reflection sphere.

    Peak

    source
    pub struct Peak {
      angle : Double
      intensity : Double
      members : Array[Hkl]
      width : Double
    } derive(
    Debug    )

    Accessible powder group; intensity SUMS members, multiplicity counts supplied reflections.

    Peak::multiplicity

    source
    fn Peak::multiplicity(self : Peak) -> Int

    PeakMatch

    source
    pub struct PeakMatch {
      observed : Double
      candidates : Array[Int]
      residuals : Array[Double]
    } derive(
    Debug    )

    All compatible simulated groups for one observed angle; no forced assignment.

    Problem

    source
    pub(all) enum Problem {
      Invalid(String)
      Budget(String)
    } derive(Eq, 
    Debug    )

    Common typed failures; numerical inputs never silently clamp invalid cells.

    Profile

    source
    pub struct Profile {
      start : Double
      step : Double
      values : Array[Double]
    } derive(
    Debug    )

    Uniform 2theta grid, density per degree; finite window is not renormalized.

    Profile::area

    source
    fn Profile::area(self : Profile) -> Double

    Trapezoidal integral over the sampled window only.

    Profile::csv

    source
    fn Profile::csv(self : Profile) -> String

    Profile density per degree, not counts per bin.

    Reflection

    source
    pub struct Reflection {
      index : Hkl
      d : Double
      intensity : Double
      angle : Double?
      wavelength : Double
    } derive(
    Debug    )

    Individual reciprocal reflection. Both Friedel partners are retained.

    Sensitivity

    source
    pub struct Sensitivity {
      dx : Double
      dy : Double
      dz : Double
      occupancy : Double
      weight : Double
      b_iso : Double
    } derive(
    Debug    )

    constant weight and B_iso. This is local sensitivity, NOT structure refinement.

    Site

    source
    pub struct Site {
      x : Double
      y : Double
      z : Double
      weight : Double
      occupancy : Double
      b_iso : Double
    } derive(
    Debug    )

    Fractional point scatterer. Weight is user-supplied constant, not an element table.

    Site::translated

    source
    fn Site::translated(self : Site, dx : Double, dy : Double, dz : Double) -> Result[Site, Problem]

    A global fractional translation preserves intensities, not complex phase.

    gaussian_profile

    source
    fn gaussian_profile(peaks : Array[Peak], start : Double, end : Double, samples : Int, sigma : Double, max_terms? : Int) -> Result[Profile, Problem]

    Gaussian lines with unit continuous area. Requires >=4 samples per sigma.

    hkl

    source
    fn hkl(h : Int, k : Int, l : Int) -> Result[Hkl, Problem]

    in_zone

    source
    fn in_zone(index : Hkl, u : Int, v : Int, w : Int) -> Result[Bool, Problem]

    Zone law hu+kv+l*w = 0. Direction is a nonzero bounded integer triple.

    match_peaks

    source
    fn match_peaks(observed : Array[Double], peaks : Array[Peak], tolerance : Double, max_pairs? : Int) -> Result[Array[PeakMatch], Problem]

    Independent bounded matching. Ambiguities and unmatched observations remain visible.

    powder

    source
    fn powder(reflections : Array[Reflection], tolerance? : Double) -> Result[Array[Peak], Problem]

    Caller must supply one wavelength and each hkl once; duplicates and mixed wavelengths are rejected.

    reciprocal

    source
    fn reciprocal(a : Double, b : Double, c : Double, alpha : Double, beta : Double, gamma : Double) -> Result[Metric, Problem]

    Positive lengths in angstroms; angles in degrees. Reject ill-conditioned cells.

    reflections_csv

    source
    fn reflections_csv(reflections : Array[Reflection]) -> Result[String, Problem]

    Numeric CSV only, no free-text labels and no user formula cells.

    reflections_json

    source
    fn reflections_json(reflections : Array[Reflection]) -> Result[Json, Problem]

    Versioned structured output; null angles explicitly mark inaccessible reflections.

    site

    source
    fn site(x : Double, y : Double, z : Double, weight : Double, occupancy? : Double, b_iso? : Double) -> Result[Site, Problem]

    spacing_from_angle

    source
    fn spacing_from_angle(angle : Double, wavelength : Double) -> Result[Double, Problem]

    Inverse first-order Bragg relation; excludes forward direction.

    two_theta

    source
    fn two_theta(d : Double, wavelength : Double) -> Result[Double?, Problem]

    First-order Bragg 2theta in degrees; None means inaccessible at this wavelength.

    Source Files

    Powered by MoonBit

    Site sourceReport issuePackagesBuild queueSkillsStatistics

    © 2026 mooncakes.io