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   "source": [
    "# Usage\n",
    "\n",
    "`fourierror` propagates measurement uncertainty through a discrete Fourier transform. \n",
    "It offers three entry points, and the point of this notebook is to show what each one is for and where they agree:\n",
    "\n",
    "| Function | Method | Cost |\n",
    "|---|---|---|\n",
    "| `analytical.dft` | exact propagation through the DFT matrix | one matrix product |\n",
    "| `numerical.dft`  | Monte Carlo sampling of the input distribution | `n_samples` transforms |\n",
    "| `numerical.fft`  | Monte Carlo sampling, via the FFT | `n_samples` transforms, faster |\n",
    "\n",
    "Everything is built on [scipp](https://scipp.github.io) data objects, so inputs carry units, coordinates and variances, and the frequency axis is derived for you."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ee1d258f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T15:57:28.517737Z",
     "iopub.status.busy": "2026-08-11T15:57:28.517505Z",
     "iopub.status.idle": "2026-08-11T15:57:30.413001Z",
     "shell.execute_reply": "2026-08-11T15:57:30.411210Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipp as sc\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from fourierror import analytical, numerical"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71283140",
   "metadata": {},
   "source": [
    "## Input data\n",
    "\n",
    "A damped cosine, measured with noise that grows over time — so the input variances are *not* all equal. \n",
    "That is the interesting case: a single \"average\" error bar would not capture it.\n",
    "\n",
    "The input is a `scipp.DataArray` whose data has `variances` and whose coordinate carries a unit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b509d3b4",
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    "execution": {
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     "iopub.status.busy": "2026-08-11T15:57:30.416593Z",
     "iopub.status.idle": "2026-08-11T15:57:30.448912Z",
     "shell.execute_reply": "2026-08-11T15:57:30.447448Z"
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   "outputs": [
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!important;stroke-width:0;stroke:currentColor;fill:currentColor;}label.sc-hide-icon svg{opacity:0;}.sc-standalone-var-name{grid-column:1/3;}.sc-standalone-var-name span{padding-left:25px;padding-right:10px;}.sc-title{font-weight:bold;font-size:1.5em;}.sc-subtitle{font-weight:normal;font-style:italic;text-align:left;font-size:1.2em;padding:1px;}.sc-label{fill:var(--sc-font-color0,#444444);text-anchor:middle;}.sc-name{fill:var(--sc-font-color0,#111111);}.sc-inset-line{stroke:var(--sc-font-color1);stroke-width:0.05;stroke-dasharray:0.2,0.2;}.sc-log-wrap{height:25ex;resize:vertical;overflow-y:scroll;display:flex;flex-direction:column-reverse;border:1px solid;border-color:var(--jp-border-color2);background-color:var(--sc-background-color1);}div.sc-log{line-height:2.5ex;}table.sc-log{table-layout:auto;border-collapse:collapse;}tr.sc-log:nth-child(even){background-color:var(--sc-background-color0);}tr.sc-log > td{vertical-align:top;padding-bottom:0.5ex;}.sc-log-time-stamp{min-width:22ch;font-family:var(--jp-code-font-family);color:var(--sc-font-color2);}.sc-log-level{min-width:10ch;}tr.sc-log-debug td.sc-log-level{color:var(--jp-accent-color1);}tr.sc-log-info td.sc-log-level{color:var(--jp-info-color1);}tr.sc-log-warning td.sc-log-level{color:var(--jp-warn-color1);}tr.sc-log-error td.sc-log-level{font-weight:bold;color:var(--jp-error-color2);}tr.sc-log-critical td.sc-log-level{font-weight:bold;color:var(--sc-background-color0);background-color:var(--jp-error-color1);}.sc-log-message{white-space:pre-wrap;width:100%;}.sc-log-html-payload{white-space:normal;}.sc-log-name{padding-right:0.5em;text-align:right;white-space:pre-wrap;color:var(--sc-font-color3);}</style><div class='sc-wrap sc-root'><div class='sc-header'><div class='sc-obj-type'>scipp.DataArray (3.86 KB)</div></div><ul class='sc-sections'><li class='sc-section-item'><input id='section-31efaf23-b405-4999-b160-ec230e85369d' class='sc-section-summary-in' type='checkbox' disabled ><label for='section-31efaf23-b405-4999-b160-ec230e85369d' class='sc-section-summary' >Dimensions:</label><div class='sc-section-inline-details'><ul class='sc-dim-list'><li><span class='sc-has-index'>t</span>: 128</li></ul></div><div class='sc-section-details'></div></li><li class='sc-section-item'><input id='section-1337e3f0-99d8-4993-a9a7-6c3992bcab68' class='sc-section-summary-in' type='checkbox'  checked><label for='section-1337e3f0-99d8-4993-a9a7-6c3992bcab68' class='sc-section-summary'  title='Expand/collapse section'>Coordinates: <span>(1)</span></label><div class='sc-section-inline-details'></div><div class='sc-section-details'><ul class='sc-var-list'><li class='sc-var-item'><div class='sc-var-name'><span class='sc-aligned'>t</span></div><div class='sc-var-dims'>(t)</div><div class='sc-var-dtype'>float64</div><div class='sc-var-unit'>s</div><div class='sc-value-preview sc-preview'><span><div>0.0, 0.05, ..., 6.300, 6.350</div></span></div><input id='attrs-e8eb1a0e-3cee-4443-a03c-b279d1175052' class='sc-var-attrs-in' type='checkbox' disabled><label for='attrs-e8eb1a0e-3cee-4443-a03c-b279d1175052' class='sc-hide-icon' title='Show/Hide attributes'><svg class='icon sc-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d3e59fae-93d8-421e-865c-b318347b346d' class='sc-var-data-in' type='checkbox'><label for='data-d3e59fae-93d8-421e-865c-b318347b346d' title='Show/Hide data repr'><svg class='icon sc-icon-database'><use xlink:href='#icon-database'></use></svg></label><pre class='sc-var-data'>Values:<br>array([0.  , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35, 0.4 , 0.45, 0.5 ,\n",
       "       0.55, 0.6 , 0.65, 0.7 , 0.75, 0.8 , 0.85, 0.9 , 0.95, 1.  , 1.05,\n",
       "       1.1 , 1.15, 1.2 , 1.25, 1.3 , 1.35, 1.4 , 1.45, 1.5 , 1.55, 1.6 ,\n",
       "       1.65, 1.7 , 1.75, 1.8 , 1.85, 1.9 , 1.95, 2.  , 2.05, 2.1 , 2.15,\n",
       "       2.2 , 2.25, 2.3 , 2.35, 2.4 , 2.45, 2.5 , 2.55, 2.6 , 2.65, 2.7 ,\n",
       "       2.75, 2.8 , 2.85, 2.9 , 2.95, 3.  , 3.05, 3.1 , 3.15, 3.2 , 3.25,\n",
       "       3.3 , 3.35, 3.4 , 3.45, 3.5 , 3.55, 3.6 , 3.65, 3.7 , 3.75, 3.8 ,\n",
       "       3.85, 3.9 , 3.95, 4.  , 4.05, 4.1 , 4.15, 4.2 , 4.25, 4.3 , 4.35,\n",
       "       4.4 , 4.45, 4.5 , 4.55, 4.6 , 4.65, 4.7 , 4.75, 4.8 , 4.85, 4.9 ,\n",
       "       4.95, 5.  , 5.05, 5.1 , 5.15, 5.2 , 5.25, 5.3 , 5.35, 5.4 , 5.45,\n",
       "       5.5 , 5.55, 5.6 , 5.65, 5.7 , 5.75, 5.8 , 5.85, 5.9 , 5.95, 6.  ,\n",
       "       6.05, 6.1 , 6.15, 6.2 , 6.25, 6.3 , 6.35])</pre></span></li></ul></div></li><li class='sc-section-item'><input id='section-ae477103-7369-48e9-87eb-c764f63dadfc' class='sc-section-summary-in' type='checkbox'  checked><label for='section-ae477103-7369-48e9-87eb-c764f63dadfc' class='sc-section-summary'  title='Expand/collapse section'>Data: <span>(1)</span></label><div class='sc-section-inline-details'></div><div class='sc-section-details'><ul class='sc-var-list'><li class='sc-var-item'><div class='sc-var-name'><span></span></div><div class='sc-var-dims'>(t)</div><div class='sc-var-dtype'>float64</div><div class='sc-var-unit'>𝟙</div><div class='sc-value-preview sc-preview'><span><div>1.015, 0.809, ..., 0.277, -0.252</div></span><span><div>σ = 0.05, 0.051, ..., 0.199, 0.2</div></span></div><input id='attrs-dfbc9d36-0cc1-40cc-8be2-2b3003b27971' class='sc-var-attrs-in' type='checkbox' disabled><label for='attrs-dfbc9d36-0cc1-40cc-8be2-2b3003b27971' class='sc-hide-icon' title='Show/Hide attributes'><svg class='icon sc-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8277bd44-27a8-40a7-8e05-a4aec218c991' class='sc-var-data-in' type='checkbox'><label for='data-8277bd44-27a8-40a7-8e05-a4aec218c991' title='Show/Hide data repr'><svg class='icon sc-icon-database'><use xlink:href='#icon-database'></use></svg></label><pre class='sc-var-data'>Values:<br>array([ 1.01523585,  0.80856832,  0.58917249,  0.1919087 , -0.37721268,\n",
       "       -0.67135198, -0.77136124, -0.80056683, -0.62064785, -0.38804442,\n",
       "        0.05435649,  0.36362863,  0.54653771,  0.71403224,  0.6275031 ,\n",
       "        0.37069363,  0.20668971, -0.15596034, -0.25998516, -0.47658027,\n",
       "       -0.52702706, -0.49339642, -0.18942248, -0.08459736,  0.10529232,\n",
       "        0.27930302,  0.44273893,  0.43149024,  0.35242448,  0.20897224,\n",
       "        0.18296753, -0.19673971, -0.32339875, -0.40117944, -0.25066536,\n",
       "       -0.1170766 , -0.10361651, -0.03315085,  0.0873915 ,  0.3053255 ,\n",
       "        0.33587422,  0.28062699,  0.0786571 ,  0.06071052, -0.05938984,\n",
       "       -0.13521921, -0.11433556, -0.18257792, -0.09090245, -0.08136413,\n",
       "        0.03152995,  0.15252741, -0.01940359,  0.13280315,  0.10368981,\n",
       "        0.03960625,  0.01583035,  0.15199307, -0.18763645, -0.00878342,\n",
       "       -0.33873726, -0.15750318, -0.054362  ,  0.05377519,  0.12592388,\n",
       "        0.18157928,  0.06075973,  0.04614588,  0.19566747,  0.0203608 ,\n",
       "       -0.16925445, -0.19428093, -0.19755462, -0.01894012, -0.06114406,\n",
       "        0.03764645, -0.08424852,  0.03435813,  0.13256956,  0.01967711,\n",
       "        0.13548208, -0.03654173, -0.01510723, -0.046674  , -0.19722568,\n",
       "        0.03164807, -0.1252535 , -0.05243724,  0.03094935,  0.04589609,\n",
       "        0.10399917,  0.00635232, -0.02948021,  0.03175221, -0.23026097,\n",
       "       -0.20492828, -0.20351416, -0.17028141,  0.04384758, -0.18401398,\n",
       "       -0.09924699,  0.1892044 , -0.0803495 ,  0.12154759, -0.15171368,\n",
       "       -0.0143966 , -0.13866299, -0.0318959 ,  0.17130967, -0.29674349,\n",
       "        0.07816205,  0.03183023, -0.12764973, -0.28814465, -0.00795747,\n",
       "       -0.11369385,  0.03704517,  0.00727887,  0.31483683, -0.028737  ,\n",
       "       -0.17792187,  0.05036901,  0.0527715 ,  0.26800869,  0.15910985,\n",
       "        0.05956833,  0.27667063, -0.25207801])<br><br>Variances (σ²):<br>array([0.0025    , 0.00261951, 0.0027418 , 0.00286689, 0.00299476,\n",
       "       0.00312543, 0.00325888, 0.00339513, 0.00353416, 0.00367599,\n",
       "       0.0038206 , 0.00396801, 0.0041182 , 0.00427119, 0.00442696,\n",
       "       0.00458553, 0.00474688, 0.00491103, 0.00507797, 0.00524769,\n",
       "       0.00542021, 0.00559551, 0.00577361, 0.00595449, 0.00613817,\n",
       "       0.00632463, 0.00651389, 0.00670593, 0.00690077, 0.00709839,\n",
       "       0.00729881, 0.00750202, 0.00770801, 0.0079168 , 0.00812837,\n",
       "       0.00834274, 0.00855989, 0.00877984, 0.00900257, 0.0092281 ,\n",
       "       0.00945641, 0.00968752, 0.00992141, 0.0101581 , 0.01039758,\n",
       "       0.01063984, 0.0108849 , 0.01113274, 0.01138338, 0.0116368 ,\n",
       "       0.01189302, 0.01215202, 0.01241382, 0.01267841, 0.01294578,\n",
       "       0.01321595, 0.0134889 , 0.01376465, 0.01404318, 0.01432451,\n",
       "       0.01460862, 0.01489553, 0.01518523, 0.01547771, 0.01577299,\n",
       "       0.01607105, 0.01637191, 0.01667555, 0.01698199, 0.01729121,\n",
       "       0.01760323, 0.01791804, 0.01823563, 0.01855602, 0.01887919,\n",
       "       0.01920516, 0.01953391, 0.01986546, 0.0201998 , 0.02053692,\n",
       "       0.02087684, 0.02121954, 0.02156504, 0.02191332, 0.0222644 ,\n",
       "       0.02261827, 0.02297492, 0.02333437, 0.0236966 , 0.02406163,\n",
       "       0.02442944, 0.02480005, 0.02517345, 0.02554963, 0.02592861,\n",
       "       0.02631037, 0.02669493, 0.02708227, 0.02747241, 0.02786534,\n",
       "       0.02826105, 0.02865956, 0.02906085, 0.02946494, 0.02987181,\n",
       "       0.03028148, 0.03069394, 0.03110918, 0.03152722, 0.03194804,\n",
       "       0.03237166, 0.03279807, 0.03322726, 0.03365925, 0.03409402,\n",
       "       0.03453159, 0.03497194, 0.03541509, 0.03586103, 0.03630975,\n",
       "       0.03676127, 0.03721557, 0.03767267, 0.03813256, 0.03859523,\n",
       "       0.0390607 , 0.03952895, 0.04      ])</pre></li></ul></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<scipp.DataArray>\n",
       "Dimensions: Sizes[t:128, ]\n",
       "Coordinates:\n",
       "* t                         float64              [s]  (t)  [0, 0.05, ..., 6.3, 6.35]\n",
       "Data:\n",
       "                            float64  [dimensionless]  (t)  [1.01524, 0.808568, ..., 0.276671, -0.252078]  [0.0025, 0.00261951, ..., 0.039529, 0.04]\n"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.default_rng(42)\n",
    "\n",
    "N, dt = 128, 0.05\n",
    "t = np.arange(N) * dt\n",
    "truth = np.exp(-t / 1.5) * np.cos(2 * np.pi * 1.5 * t)\n",
    "\n",
    "sigma = 0.05 + 0.15 * (t / t.max())  # noise grows with time\n",
    "measured = truth + rng.normal(0.0, sigma)\n",
    "\n",
    "data = sc.DataArray(\n",
    "    data=sc.array(dims=[\"t\"], values=measured, variances=sigma**2),\n",
    "    coords={\"t\": sc.array(dims=[\"t\"], values=t, unit=\"s\")},\n",
    ")\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6a4c7237",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T15:57:30.452023Z",
     "iopub.status.busy": "2026-08-11T15:57:30.451038Z",
     "iopub.status.idle": "2026-08-11T15:57:30.718397Z",
     "shell.execute_reply": "2026-08-11T15:57:30.716939Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 3))\n",
    "ax.errorbar(t, measured, yerr=sigma, fmt=\"o\", ms=3, lw=1, alpha=0.7, label=\"measured\")\n",
    "ax.plot(t, truth, \"k-\", lw=1.5, label=\"truth\")\n",
    "ax.set(xlabel=\"t / s\", ylabel=\"signal\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36205c15",
   "metadata": {},
   "source": [
    "## Exact propagation\n",
    "\n",
    "The DFT is linear, so an input covariance maps onto the output exactly: `cos @ cov @ cos.T` for the real part and `sin @ cov @ sin.T` for the imaginary part. \n",
    "No sampling, no tuning parameter — just one matrix product.\n",
    "\n",
    "The result is a `scipp.Dataset` with `real` and `imag` entries, each carrying its own variances, on an `omega` axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "76f76c7e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T15:57:30.730658Z",
     "iopub.status.busy": "2026-08-11T15:57:30.730436Z",
     "iopub.status.idle": "2026-08-11T15:57:30.749599Z",
     "shell.execute_reply": "2026-08-11T15:57:30.748168Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "</symbol>\n",
       "</defs>\n",
       "</svg><style id=\"scipp-style-sheet\">.sc-root{--sc-background-color0:var(--jp-layout-color0,#fff);--sc-background-color1:var(--jp-layout-color1,#fcfcfc);--sc-background-color2:var(--jp-layout-color2,#efefef);--sc-inverse-background-color0:var(--jp-inverse-layout-color4,#111);--sc-font-color0:var(--jp-content-font-color0,#000);--sc-font-color1:var(--jp-content-font-color1,#555);--sc-font-color2:var(--jp-content-font-color2,#888);--sc-font-color3:var(--jp-content-font-color3,#ccc);}body.vscode-dark .sc-root{--sc-font-color0:rgba(255,255,255,1);--sc-font-color1:rgba(255,255,255,0.70);--sc-font-color2:rgba(255,255,255,0.54);--sc-font-color3:rgba(255,255,255,0.38);--sc-border-color:#1F1F1F;--sc-disabled-color:#515151;--sc-background-color0:#111111;--sc-background-color1:#111111;--sc-background-color2:#313131;}.sc-wrap{font-size:14px;min-width:300px;max-width:800px;}.sc-var-attrs 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span{background-color:var(--sc-background-color2);}.sc-var-name{grid-column:1;}.sc-var-dims{grid-column:2;}.sc-var-dtype{grid-column:3;text-align:right;color:var(--sc-font-color2);}.sc-var-unit{grid-column:4;text-align:left;color:var(--sc-font-color1);max-width:50pt;text-overflow:ellipsis;}.sc-value-preview{grid-column:5;}.sc-var-preview-variances{text-align:right;}.sc-sections .sc-section-item .sc-section-summary,.sc-sections .sc-section-item .sc-section-inline-details,.sc-section-item .sc-var-list .sc-var-item > div,.sc-section-item .sc-var-list .sc-var-item > label,.sc-section-details .sc-var-list .sc-var-item > div,.sc-section-details .sc-var-list .sc-var-item > label{margin-top:0;margin-bottom:0;}.sc-var-name,.sc-var-dims,.sc-var-dtype,.sc-var-unit,.sc-preview,.sc-attrs dt{white-space:nowrap;overflow:hidden;text-overflow:ellipsis;padding-right:10px;}.sc-var-name:hover,.sc-var-dims:hover,.sc-var-dtype:hover,.sc-var-unit:hover,.sc-attrs dt:hover{overflow:visible;width:auto;z-index:1;}.sc-var-attrs{display:block;}.sc-var-data,.reveal .sc-var-data{display:none;}.sc-var-attrs,.sc-var-data{background-color:var(--sc-background-color0) !important;padding-bottom:5px !important;}.sc-var-attrs-in:checked ~ .sc-var-attrs{display:none;}.sc-var-data-in:checked ~ .sc-var-data{display:block;}.sc-var-data > table{float:right;}.sc-var-name span,.sc-var-data{padding-left:25px !important;}.sc-var-attrs,.sc-var-data{grid-column:1 / -1;}dl.sc-attrs{padding:0;margin:0;display:grid;grid-template-columns:125px auto;}.sc-attrs dt,dd{padding:0;margin:0;float:left;padding-right:10px;width:auto;}.sc-attrs dt{font-weight:normal;grid-column:1;}.sc-attrs dt:hover span{display:inline-block;padding-right:10px;}.sc-attrs dd{grid-column:2;white-space:pre-wrap;word-break:break-all;}.sc-icon-database,.sc-icon-file-text2{display:inline-block;vertical-align:middle;width:1em;height:1.5em !important;stroke-width:0;stroke:currentColor;fill:currentColor;}label.sc-hide-icon svg{opacity:0;}.sc-standalone-var-name{grid-column:1/3;}.sc-standalone-var-name span{padding-left:25px;padding-right:10px;}.sc-title{font-weight:bold;font-size:1.5em;}.sc-subtitle{font-weight:normal;font-style:italic;text-align:left;font-size:1.2em;padding:1px;}.sc-label{fill:var(--sc-font-color0,#444444);text-anchor:middle;}.sc-name{fill:var(--sc-font-color0,#111111);}.sc-inset-line{stroke:var(--sc-font-color1);stroke-width:0.05;stroke-dasharray:0.2,0.2;}.sc-log-wrap{height:25ex;resize:vertical;overflow-y:scroll;display:flex;flex-direction:column-reverse;border:1px solid;border-color:var(--jp-border-color2);background-color:var(--sc-background-color1);}div.sc-log{line-height:2.5ex;}table.sc-log{table-layout:auto;border-collapse:collapse;}tr.sc-log:nth-child(even){background-color:var(--sc-background-color0);}tr.sc-log > td{vertical-align:top;padding-bottom:0.5ex;}.sc-log-time-stamp{min-width:22ch;font-family:var(--jp-code-font-family);color:var(--sc-font-color2);}.sc-log-level{min-width:10ch;}tr.sc-log-debug td.sc-log-level{color:var(--jp-accent-color1);}tr.sc-log-info td.sc-log-level{color:var(--jp-info-color1);}tr.sc-log-warning td.sc-log-level{color:var(--jp-warn-color1);}tr.sc-log-error td.sc-log-level{font-weight:bold;color:var(--jp-error-color2);}tr.sc-log-critical td.sc-log-level{font-weight:bold;color:var(--sc-background-color0);background-color:var(--jp-error-color1);}.sc-log-message{white-space:pre-wrap;width:100%;}.sc-log-html-payload{white-space:normal;}.sc-log-name{padding-right:0.5em;text-align:right;white-space:pre-wrap;color:var(--sc-font-color3);}</style><div class='sc-wrap sc-root'><div class='sc-header'><div class='sc-obj-type'>scipp.Dataset (6.67 KB)</div></div><ul class='sc-sections'><li class='sc-section-item'><input id='section-a424a7dd-bf92-4f1b-9898-cc47610d83ba' class='sc-section-summary-in' type='checkbox' disabled ><label for='section-a424a7dd-bf92-4f1b-9898-cc47610d83ba' class='sc-section-summary' >Dimensions:</label><div class='sc-section-inline-details'><ul class='sc-dim-list'><li><span class='sc-has-index'>omega</span>: 128</li></ul></div><div class='sc-section-details'></div></li><li class='sc-section-item'><input id='section-890279a9-8b8e-44fb-a3de-6116e9216791' class='sc-section-summary-in' type='checkbox'  checked><label for='section-890279a9-8b8e-44fb-a3de-6116e9216791' class='sc-section-summary'  title='Expand/collapse section'>Coordinates: <span>(1)</span></label><div class='sc-section-inline-details'></div><div class='sc-section-details'><ul class='sc-var-list'><li class='sc-var-item'><div class='sc-var-name'><span class='sc-aligned'>omega</span></div><div class='sc-var-dims'>(omega)</div><div class='sc-var-dtype'>float64</div><div class='sc-var-unit'>Hz</div><div class='sc-value-preview sc-preview'><span><div>0.0, 0.982, ..., -1.963, -0.982</div></span></div><input id='attrs-d3b496a7-305f-41bb-a72f-cad84da1a21a' class='sc-var-attrs-in' type='checkbox' disabled><label for='attrs-d3b496a7-305f-41bb-a72f-cad84da1a21a' class='sc-hide-icon' title='Show/Hide attributes'><svg class='icon sc-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bf70a503-dbe1-4368-b5f7-767fb426015f' class='sc-var-data-in' type='checkbox'><label for='data-bf70a503-dbe1-4368-b5f7-767fb426015f' title='Show/Hide data repr'><svg class='icon sc-icon-database'><use xlink:href='#icon-database'></use></svg></label><pre class='sc-var-data'>Values:<br>array([  0.        ,   0.9817477 ,   1.96349541,   2.94524311,\n",
       "         3.92699082,   4.90873852,   5.89048623,   6.87223393,\n",
       "         7.85398163,   8.83572934,   9.81747704,  10.79922475,\n",
       "        11.78097245,  12.76272016,  13.74446786,  14.72621556,\n",
       "        15.70796327,  16.68971097,  17.67145868,  18.65320638,\n",
       "        19.63495408,  20.61670179,  21.59844949,  22.5801972 ,\n",
       "        23.5619449 ,  24.54369261,  25.52544031,  26.50718801,\n",
       "        27.48893572,  28.47068342,  29.45243113,  30.43417883,\n",
       "        31.41592654,  32.39767424,  33.37942194,  34.36116965,\n",
       "        35.34291735,  36.32466506,  37.30641276,  38.28816047,\n",
       "        39.26990817,  40.25165587,  41.23340358,  42.21515128,\n",
       "        43.19689899,  44.17864669,  45.1603944 ,  46.1421421 ,\n",
       "        47.1238898 ,  48.10563751,  49.08738521,  50.06913292,\n",
       "        51.05088062,  52.03262833,  53.01437603,  53.99612373,\n",
       "        54.97787144,  55.95961914,  56.94136685,  57.92311455,\n",
       "        58.90486225,  59.88660996,  60.86835766,  61.85010537,\n",
       "       -62.83185307, -61.85010537, -60.86835766, -59.88660996,\n",
       "       -58.90486225, -57.92311455, -56.94136685, -55.95961914,\n",
       "       -54.97787144, -53.99612373, -53.01437603, -52.03262833,\n",
       "       -51.05088062, -50.06913292, -49.08738521, -48.10563751,\n",
       "       -47.1238898 , -46.1421421 , -45.1603944 , -44.17864669,\n",
       "       -43.19689899, -42.21515128, -41.23340358, -40.25165587,\n",
       "       -39.26990817, -38.28816047, -37.30641276, -36.32466506,\n",
       "       -35.34291735, -34.36116965, -33.37942194, -32.39767424,\n",
       "       -31.41592654, -30.43417883, -29.45243113, -28.47068342,\n",
       "       -27.48893572, -26.50718801, -25.52544031, -24.54369261,\n",
       "       -23.5619449 , -22.5801972 , -21.59844949, -20.61670179,\n",
       "       -19.63495408, -18.65320638, -17.67145868, -16.68971097,\n",
       "       -15.70796327, -14.72621556, -13.74446786, -12.76272016,\n",
       "       -11.78097245, -10.79922475,  -9.81747704,  -8.83572934,\n",
       "        -7.85398163,  -6.87223393,  -5.89048623,  -4.90873852,\n",
       "        -3.92699082,  -2.94524311,  -1.96349541,  -0.9817477 ])</pre></span></li></ul></div></li><li class='sc-section-item'><input id='section-48a9ddd2-f6cf-4234-9f6d-5a598862c3cc' class='sc-section-summary-in' type='checkbox'  checked><label for='section-48a9ddd2-f6cf-4234-9f6d-5a598862c3cc' class='sc-section-summary'  title='Expand/collapse section'>Data: <span>(2)</span></label><div class='sc-section-inline-details'></div><div class='sc-section-details'><ul class='sc-var-list'><li class='sc-var-item'><div class='sc-var-name'><span>imag</span></div><div class='sc-var-dims'>(omega)</div><div class='sc-var-dtype'>float64</div><div class='sc-var-unit'>𝟙</div><div class='sc-value-preview sc-preview'><span><div>0.0, -0.024, ..., -0.007, 0.024</div></span><span><div>σ = 0.0, 0.016, ..., 0.017, 0.016</div></span></div><input id='attrs-c6aa80d2-e2c1-4411-92e9-abdde8bb44c4' class='sc-var-attrs-in' type='checkbox' disabled><label for='attrs-c6aa80d2-e2c1-4411-92e9-abdde8bb44c4' class='' title='Show/Hide attributes'><svg class='icon sc-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f46291c2-c398-4563-9c61-c635095a43fc' class='sc-var-data-in' type='checkbox'><label for='data-f46291c2-c398-4563-9c61-c635095a43fc' title='Show/Hide data repr'><svg class='icon sc-icon-database'><use xlink:href='#icon-database'></use></svg></label><pre class='sc-var-data'>Values:<br>array([ 0.00000000e+00, -2.42925147e-02,  7.37462838e-03,  2.77815430e-02,\n",
       "        2.76505479e-02,  3.12804638e-02,  4.76239324e-02,  7.12011227e-02,\n",
       "        9.68103674e-02,  9.22395917e-02, -9.72072332e-02, -7.41970465e-02,\n",
       "       -8.28404732e-02, -4.63209916e-02, -4.38481221e-02, -1.22799039e-02,\n",
       "       -3.19985584e-02, -2.13160033e-02, -2.96641985e-02, -4.06257881e-02,\n",
       "       -3.17651843e-02, -3.22528574e-02, -1.09772966e-02, -5.07539748e-02,\n",
       "       -1.26344654e-02, -1.37505555e-02, -3.73460073e-03, -1.58720648e-02,\n",
       "       -6.45967210e-03, -1.01083472e-02, -1.00863624e-02, -4.76137106e-04,\n",
       "       -5.63879972e-03,  1.59355169e-03, -1.04705132e-02, -1.59965004e-02,\n",
       "       -3.29952277e-02, -1.16480707e-02, -5.49759290e-03,  6.63451509e-03,\n",
       "        2.29316465e-03, -9.15515531e-03, -2.07503792e-02, -9.89378473e-03,\n",
       "       -1.33797594e-02,  2.22176624e-03, -1.25902096e-02, -5.55705149e-04,\n",
       "       -1.73897171e-02, -1.48574012e-02, -4.07827332e-02, -1.74806208e-02,\n",
       "        6.83935236e-03, -1.40633381e-02, -1.20596750e-03, -1.53921595e-02,\n",
       "       -1.29611289e-03,  1.72316958e-03,  1.93167602e-02, -4.61407396e-03,\n",
       "       -3.61461822e-03, -2.09518991e-02,  8.44340597e-04,  2.91968896e-03,\n",
       "       -1.77308425e-16, -2.91968896e-03, -8.44340597e-04,  2.09518991e-02,\n",
       "        3.61461822e-03,  4.61407396e-03, -1.93167602e-02, -1.72316958e-03,\n",
       "        1.29611289e-03,  1.53921595e-02,  1.20596750e-03,  1.40633381e-02,\n",
       "       -6.83935236e-03,  1.74806208e-02,  4.07827332e-02,  1.48574012e-02,\n",
       "        1.73897171e-02,  5.55705149e-04,  1.25902096e-02, -2.22176624e-03,\n",
       "        1.33797594e-02,  9.89378473e-03,  2.07503792e-02,  9.15515531e-03,\n",
       "       -2.29316465e-03, -6.63451509e-03,  5.49759290e-03,  1.16480707e-02,\n",
       "        3.29952277e-02,  1.59965004e-02,  1.04705132e-02, -1.59355169e-03,\n",
       "        5.63879972e-03,  4.76137106e-04,  1.00863624e-02,  1.01083472e-02,\n",
       "        6.45967210e-03,  1.58720648e-02,  3.73460073e-03,  1.37505555e-02,\n",
       "        1.26344654e-02,  5.07539748e-02,  1.09772966e-02,  3.22528574e-02,\n",
       "        3.17651843e-02,  4.06257881e-02,  2.96641985e-02,  2.13160033e-02,\n",
       "        3.19985584e-02,  1.22799039e-02,  4.38481221e-02,  4.63209916e-02,\n",
       "        8.28404732e-02,  7.41970465e-02,  9.72072332e-02, -9.22395917e-02,\n",
       "       -9.68103674e-02, -7.12011227e-02, -4.76239324e-02, -3.12804638e-02,\n",
       "       -2.76505479e-02, -2.77815430e-02, -7.37462838e-03,  2.42925147e-02])<br><br>Variances (σ²):<br>array([0.00000000e+00, 2.71689986e-04, 2.75082221e-04, 2.75710404e-04,\n",
       "       2.75930259e-04, 2.76032011e-04, 2.76087272e-04, 2.76120581e-04,\n",
       "       2.76142188e-04, 2.76156989e-04, 2.76167562e-04, 2.76175372e-04,\n",
       "       2.76181298e-04, 2.76185895e-04, 2.76189527e-04, 2.76192442e-04,\n",
       "       2.76194810e-04, 2.76196756e-04, 2.76198368e-04, 2.76199714e-04,\n",
       "       2.76200843e-04, 2.76201793e-04, 2.76202595e-04, 2.76203271e-04,\n",
       "       2.76203839e-04, 2.76204313e-04, 2.76204706e-04, 2.76205025e-04,\n",
       "       2.76205277e-04, 2.76205469e-04, 2.76205603e-04, 2.76205682e-04,\n",
       "       2.76205709e-04, 2.76205682e-04, 2.76205603e-04, 2.76205469e-04,\n",
       "       2.76205277e-04, 2.76205025e-04, 2.76204706e-04, 2.76204313e-04,\n",
       "       2.76203839e-04, 2.76203271e-04, 2.76202595e-04, 2.76201793e-04,\n",
       "       2.76200843e-04, 2.76199714e-04, 2.76198368e-04, 2.76196756e-04,\n",
       "       2.76194810e-04, 2.76192442e-04, 2.76189527e-04, 2.76185895e-04,\n",
       "       2.76181298e-04, 2.76175372e-04, 2.76167562e-04, 2.76156989e-04,\n",
       "       2.76142188e-04, 2.76120581e-04, 2.76087272e-04, 2.76032011e-04,\n",
       "       2.75930259e-04, 2.75710404e-04, 2.75082221e-04, 2.71689986e-04,\n",
       "       1.81171480e-31, 2.71689986e-04, 2.75082221e-04, 2.75710404e-04,\n",
       "       2.75930259e-04, 2.76032011e-04, 2.76087272e-04, 2.76120581e-04,\n",
       "       2.76142188e-04, 2.76156989e-04, 2.76167562e-04, 2.76175372e-04,\n",
       "       2.76181298e-04, 2.76185895e-04, 2.76189527e-04, 2.76192442e-04,\n",
       "       2.76194810e-04, 2.76196756e-04, 2.76198368e-04, 2.76199714e-04,\n",
       "       2.76200843e-04, 2.76201793e-04, 2.76202595e-04, 2.76203271e-04,\n",
       "       2.76203839e-04, 2.76204313e-04, 2.76204706e-04, 2.76205025e-04,\n",
       "       2.76205277e-04, 2.76205469e-04, 2.76205603e-04, 2.76205682e-04,\n",
       "       2.76205709e-04, 2.76205682e-04, 2.76205603e-04, 2.76205469e-04,\n",
       "       2.76205277e-04, 2.76205025e-04, 2.76204706e-04, 2.76204313e-04,\n",
       "       2.76203839e-04, 2.76203271e-04, 2.76202595e-04, 2.76201793e-04,\n",
       "       2.76200843e-04, 2.76199714e-04, 2.76198368e-04, 2.76196756e-04,\n",
       "       2.76194810e-04, 2.76192442e-04, 2.76189527e-04, 2.76185895e-04,\n",
       "       2.76181298e-04, 2.76175372e-04, 2.76167562e-04, 2.76156989e-04,\n",
       "       2.76142188e-04, 2.76120581e-04, 2.76087272e-04, 2.76032011e-04,\n",
       "       2.75930259e-04, 2.75710404e-04, 2.75082221e-04, 2.71689986e-04])</pre></li><li class='sc-var-item'><div class='sc-var-name'><span>real</span></div><div class='sc-var-dims'>(omega)</div><div class='sc-var-dtype'>float64</div><div class='sc-var-unit'>𝟙</div><div class='sc-value-preview sc-preview'><span><div>-0.004, 0.017, ..., 0.026, 0.017</div></span><span><div>σ = 0.023, 0.017, ..., 0.017, 0.017</div></span></div><input id='attrs-9a548c40-37f4-462f-9d4e-3b3bf738d031' class='sc-var-attrs-in' type='checkbox' disabled><label for='attrs-9a548c40-37f4-462f-9d4e-3b3bf738d031' class='' title='Show/Hide attributes'><svg class='icon sc-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8b0cc29b-012b-41a4-bd9e-1e78e419f94d' class='sc-var-data-in' type='checkbox'><label for='data-8b0cc29b-012b-41a4-bd9e-1e78e419f94d' title='Show/Hide data repr'><svg class='icon sc-icon-database'><use xlink:href='#icon-database'></use></svg></label><pre class='sc-var-data'>Values:<br>array([-4.34913327e-03,  1.70044689e-02,  2.61698261e-02,  2.47495808e-02,\n",
       "        1.21130717e-02,  1.58014536e-02,  2.74687203e-02,  3.75093372e-03,\n",
       "        3.40242829e-02,  1.35808242e-01,  2.11891923e-01,  3.67639399e-02,\n",
       "        1.54801213e-02,  2.87611653e-02,  2.39673096e-02, -8.63325519e-03,\n",
       "       -4.36247226e-03, -1.60338161e-02, -2.51248172e-04, -1.47334190e-03,\n",
       "        5.85973102e-04,  6.69438609e-03,  1.80919304e-02,  8.68461768e-03,\n",
       "        9.01966344e-03,  1.06860341e-02,  2.10825463e-02, -1.55139779e-02,\n",
       "        3.72799128e-03,  1.41298161e-02,  1.54831104e-02, -1.31056705e-02,\n",
       "       -1.40841388e-02,  6.48144273e-04, -5.44669579e-03, -4.82316152e-03,\n",
       "        1.16764933e-02,  1.33493433e-02,  2.64095015e-02,  1.90241199e-02,\n",
       "       -1.45994720e-04,  3.02035304e-03, -2.66816509e-03,  1.84130850e-02,\n",
       "       -7.27181377e-04,  1.25843150e-02,  2.44027451e-03,  1.43517773e-02,\n",
       "        1.84708667e-02, -1.04645671e-02,  2.22793188e-02,  4.29117503e-02,\n",
       "        2.01287398e-02,  8.94655554e-03,  9.00253056e-03,  8.69989906e-03,\n",
       "        4.44619373e-02,  1.55398008e-02,  1.21964807e-02,  5.44681874e-03,\n",
       "       -1.65680772e-03,  9.49447943e-03,  8.90079732e-03,  3.94386994e-02,\n",
       "        1.40474515e-02,  3.94386994e-02,  8.90079732e-03,  9.49447943e-03,\n",
       "       -1.65680772e-03,  5.44681874e-03,  1.21964807e-02,  1.55398008e-02,\n",
       "        4.44619373e-02,  8.69989906e-03,  9.00253056e-03,  8.94655554e-03,\n",
       "        2.01287398e-02,  4.29117503e-02,  2.22793188e-02, -1.04645671e-02,\n",
       "        1.84708667e-02,  1.43517773e-02,  2.44027451e-03,  1.25843150e-02,\n",
       "       -7.27181377e-04,  1.84130850e-02, -2.66816509e-03,  3.02035304e-03,\n",
       "       -1.45994720e-04,  1.90241199e-02,  2.64095015e-02,  1.33493433e-02,\n",
       "        1.16764933e-02, -4.82316152e-03, -5.44669579e-03,  6.48144273e-04,\n",
       "       -1.40841388e-02, -1.31056705e-02,  1.54831104e-02,  1.41298161e-02,\n",
       "        3.72799128e-03, -1.55139779e-02,  2.10825463e-02,  1.06860341e-02,\n",
       "        9.01966344e-03,  8.68461768e-03,  1.80919304e-02,  6.69438609e-03,\n",
       "        5.85973102e-04, -1.47334190e-03, -2.51248172e-04, -1.60338161e-02,\n",
       "       -4.36247226e-03, -8.63325519e-03,  2.39673096e-02,  2.87611653e-02,\n",
       "        1.54801213e-02,  3.67639399e-02,  2.11891923e-01,  1.35808242e-01,\n",
       "        3.40242829e-02,  3.75093372e-03,  2.74687203e-02,  1.58014536e-02,\n",
       "        1.21130717e-02,  2.47495808e-02,  2.61698261e-02,  1.70044689e-02])<br><br>Variances (σ²):<br>array([0.0005478 , 0.00027611, 0.00027272, 0.00027209, 0.00027187,\n",
       "       0.00027177, 0.00027171, 0.00027168, 0.00027166, 0.00027164,\n",
       "       0.00027163, 0.00027162, 0.00027162, 0.00027161, 0.00027161,\n",
       "       0.00027161, 0.0002716 , 0.0002716 , 0.0002716 , 0.0002716 ,\n",
       "       0.0002716 , 0.0002716 , 0.0002716 , 0.00027159, 0.00027159,\n",
       "       0.00027159, 0.00027159, 0.00027159, 0.00027159, 0.00027159,\n",
       "       0.00027159, 0.00027159, 0.00027159, 0.00027159, 0.00027159,\n",
       "       0.00027159, 0.00027159, 0.00027159, 0.00027159, 0.00027159,\n",
       "       0.00027159, 0.00027159, 0.0002716 , 0.0002716 , 0.0002716 ,\n",
       "       0.0002716 , 0.0002716 , 0.0002716 , 0.0002716 , 0.00027161,\n",
       "       0.00027161, 0.00027161, 0.00027162, 0.00027162, 0.00027163,\n",
       "       0.00027164, 0.00027166, 0.00027168, 0.00027171, 0.00027177,\n",
       "       0.00027187, 0.00027209, 0.00027272, 0.00027611, 0.0005478 ,\n",
       "       0.00027611, 0.00027272, 0.00027209, 0.00027187, 0.00027177,\n",
       "       0.00027171, 0.00027168, 0.00027166, 0.00027164, 0.00027163,\n",
       "       0.00027162, 0.00027162, 0.00027161, 0.00027161, 0.00027161,\n",
       "       0.0002716 , 0.0002716 , 0.0002716 , 0.0002716 , 0.0002716 ,\n",
       "       0.0002716 , 0.0002716 , 0.00027159, 0.00027159, 0.00027159,\n",
       "       0.00027159, 0.00027159, 0.00027159, 0.00027159, 0.00027159,\n",
       "       0.00027159, 0.00027159, 0.00027159, 0.00027159, 0.00027159,\n",
       "       0.00027159, 0.00027159, 0.00027159, 0.00027159, 0.00027159,\n",
       "       0.00027159, 0.0002716 , 0.0002716 , 0.0002716 , 0.0002716 ,\n",
       "       0.0002716 , 0.0002716 , 0.0002716 , 0.00027161, 0.00027161,\n",
       "       0.00027161, 0.00027162, 0.00027162, 0.00027163, 0.00027164,\n",
       "       0.00027166, 0.00027168, 0.00027171, 0.00027177, 0.00027187,\n",
       "       0.00027209, 0.00027272, 0.00027611])</pre></li></ul></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<scipp.Dataset>\n",
       "Dimensions: Sizes[omega:128, ]\n",
       "Coordinates:\n",
       "* omega                     float64             [Hz]  (omega)  [0, 0.981748, ..., -1.9635, -0.981748]\n",
       "Data:\n",
       "  imag                      float64  [dimensionless]  (omega)  [0, -0.0242925, ..., -0.00737463, 0.0242925]  [0, 0.00027169, ..., 0.000275082, 0.00027169]\n",
       "  real                      float64  [dimensionless]  (omega)  [-0.00434913, 0.0170045, ..., 0.0261698, 0.0170045]  [0.000547798, 0.000276108, ..., 0.000272716, 0.000276108]\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ana = analytical.dft(data, \"t\")\n",
    "ana"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1b8c5564",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T15:57:30.751679Z",
     "iopub.status.busy": "2026-08-11T15:57:30.751455Z",
     "iopub.status.idle": "2026-08-11T15:57:31.022339Z",
     "shell.execute_reply": "2026-08-11T15:57:31.020953Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_spectrum(ds, ax, label, **kw):\n",
    "    \"\"\"Plot the positive-frequency real part with a 1-sigma band.\"\"\"\n",
    "    w = ds.coords[\"omega\"].values\n",
    "    keep = w >= 0\n",
    "    v = ds[\"real\"].values[keep]\n",
    "    e = np.sqrt(ds[\"real\"].variances[keep])\n",
    "    ax.plot(w[keep], v, label=label, **kw)\n",
    "    ax.fill_between(w[keep], v - e, v + e, alpha=0.25, lw=0, **kw)\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 3))\n",
    "plot_spectrum(ana, ax, \"analytical\", color=\"C0\")\n",
    "ax.set(xlabel=\"omega / rad s$^{-1}$\", ylabel=\"Re[F]\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7334682",
   "metadata": {},
   "source": [
    "## Monte Carlo\n",
    "\n",
    "The numerical route draws `n_samples` realisations from a multivariate normal built from the input values and variances, transforms every one of them, and\n",
    "takes the mean and covariance of the results.\n",
    "\n",
    "It is (usually) slower and stochastic, but it makes no assumptions about how the uncertainty propagates — which is what makes it the reference when you want to *check* the analytical result, or when the analytical assumptions do not hold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0c2b3796",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T15:57:31.024641Z",
     "iopub.status.busy": "2026-08-11T15:57:31.024418Z",
     "iopub.status.idle": "2026-08-11T15:57:31.496538Z",
     "shell.execute_reply": "2026-08-11T15:57:31.495134Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x320 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num = numerical.dft(data, \"t\", n_samples=5_000)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 3.2))\n",
    "plot_spectrum(ana, axes[0], \"analytical\", color=\"C0\")\n",
    "plot_spectrum(num, axes[0], \"numerical\", color=\"C1\")\n",
    "axes[0].set(xlabel=\"omega / rad s$^{-1}$\", ylabel=\"Re[F]\")\n",
    "axes[0].legend()\n",
    "\n",
    "w = ana.coords[\"omega\"].values\n",
    "keep = w >= 0\n",
    "axes[1].plot(\n",
    "    w[keep], np.sqrt(ana[\"real\"].variances[keep]), \"o-\", ms=3, label=\"analytical\"\n",
    ")\n",
    "axes[1].plot(\n",
    "    w[keep], np.sqrt(num[\"real\"].variances[keep]), \"x-\", ms=4, label=\"numerical\"\n",
    ")\n",
    "axes[1].set(xlabel=\"omega / rad s$^{-1}$\", ylabel=\"sigma(Re[F])\")\n",
    "axes[1].legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f56bda66",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T15:57:31.499247Z",
     "iopub.status.busy": "2026-08-11T15:57:31.498175Z",
     "iopub.status.idle": "2026-08-11T15:57:31.505140Z",
     "shell.execute_reply": "2026-08-11T15:57:31.504089Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max relative difference in sigma: 2.44%\n"
     ]
    }
   ],
   "source": [
    "sd_a = np.sqrt(ana[\"real\"].variances)\n",
    "sd_n = np.sqrt(num[\"real\"].variances)\n",
    "print(f\"max relative difference in sigma: {np.abs(sd_n / sd_a - 1).max():.2%}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c4d62cb",
   "metadata": {},
   "source": [
    "The two agree to within Monte Carlo noise, and the sampling error shrinks as `n_samples` grows — the usual $1/\\sqrt{n}$ convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3ddf2031",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T15:57:31.507090Z",
     "iopub.status.busy": "2026-08-11T15:57:31.506828Z",
     "iopub.status.idle": "2026-08-11T15:57:32.063493Z",
     "shell.execute_reply": "2026-08-11T15:57:32.062078Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_samples =    100   max relative difference = 15.38%\n",
      "n_samples =    500   max relative difference = 9.37%\n",
      "n_samples =   2500   max relative difference = 3.45%\n",
      "n_samples =  12500   max relative difference = 1.58%\n"
     ]
    }
   ],
   "source": [
    "for n in (100, 500, 2_500, 12_500):\n",
    "    sd = np.sqrt(numerical.dft(data, \"t\", n_samples=n)[\"real\"].variances)\n",
    "    print(\n",
    "        f\"n_samples = {n:6d}   max relative difference = {np.abs(sd / sd_a - 1).max():.2%}\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9b048bf",
   "metadata": {},
   "source": [
    "## Fast Fourier transform\n",
    "\n",
    "`numerical.fft` samples in exactly the same way but uses `np.fft.fft` instead of an explicit DFT matrix, which is the difference between O(N²) and O(N log N) per sample.\n",
    "\n",
    "*We are in the process of developing an FFT analytical form*.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c3fa694c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T15:57:32.292629Z",
     "iopub.status.busy": "2026-08-11T15:57:32.292336Z",
     "iopub.status.idle": "2026-08-11T15:57:32.361671Z",
     "shell.execute_reply": "2026-08-11T15:57:32.360460Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fast = numerical.fft(data, \"t\", n_samples=5_000)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 3))\n",
    "plot_spectrum(fast, ax, \"fft\", color=\"C2\")\n",
    "ax.set(xlabel=\"omega / rad s$^{-1}$\", ylabel=\"Re[F]\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "kinisi-dev",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}