A deep dive into responses.ipynb

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    "# A deep dive into PHA responses\n",
    "\n",
    "How does the RMF \"work\"? Well, we start by reading [The Formal Underpinnings of the Response Functions Used in X-Ray Spectral Analysis](https://ui.adsabs.harvard.edu/abs/2001ApJ...548.1010D/abstract), Davis, John E., 2001, ApJ, 548, 1010, where we can take equation 2 and\n",
    "\"forget about\" the spatial terms and the time dependence. This gives us\n",
    "\n",
    "$$\n",
    "S_p(h) = \\int A(\\lambda) R(h, \\lambda) S(\\lambda) d\\lambda\n",
    "$$\n",
    "\n",
    "where $A$ represents the effective area (ARF) and $R$ the response matrix (RMF). As we switch from the theoretical to the instrumental view we\n",
    "replace the integral with summations, switch from wavelength to Energy, and using [] rather than () to indicate discrete bins we get\n",
    "\n",
    "$$\n",
    "S_p[h] = \\sum_i A[E_i] R[E_i, h] S[E_i]\n",
    "$$\n",
    "\n",
    "You can (and we do) apply this formula directly, but Sherpa normally does it for you (in part because the RMF on-disk format is designed to save\n",
    "memory and so complicates the logic).I am going to try and show various ways of implementing this equation, as used by Sherpa.\n",
    "\n",
    "This notebook **needs** Sherpa 4.16 or later to run. We use the CIAO 4.16 environment as it also requires XSPEC models and they are a pain to build and configure..."
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       "{'date': '2023-10-11T08:27:13-0400',\n",
       " 'dirty': False,\n",
       " 'error': None,\n",
       " 'full-revisionid': '1aaa9c60fc6a34d91b502e178ff75383c41cf47d',\n",
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   "source": [
    "import sherpa\n",
    "\n",
    "sherpa._version.get_versions()"
   ]
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   "source": [
    "Let's start by reading in a Chandra \"imaging mode\" (i.e. not a grating observation) response:"
   ]
  },
  {
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   "id": "243a0fea-9fdd-480b-9369-e1cb31322ce6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sherpa.astro import io"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b4243a8c-a750-468a-ba78-1fc3c1e134f3",
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   "source": [
    "arf = io.read_arf(\"9774.arf\")\n",
    "rmf = io.read_rmf(\"9774.rmf\")"
   ]
  },
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   "execution_count": 4,
   "id": "905ae3f2-ee65-42d5-83b7-1188c8705ddc",
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       " it under the terms of the GNU General Public License as published by\n",
       " the Free Software Foundation; either version 3 of the License, or\n",
       " (at your option) any later version.\n",
       "\n",
       " This program is distributed in the hope that it will be useful,\n",
       " but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
       " MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
       " GNU General Public License for more details.\n",
       "\n",
       " You should have received a copy of the GNU General Public License along\n",
       " with this program; if not, write to the Free Software Foundation, Inc.,\n",
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       "Copyright (C) 2020  Smithsonian Astrophysical Observatory\n",
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       " (at your option) any later version.\n",
       "\n",
       " This program is distributed in the hope that it will be useful,\n",
       " but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
       " MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
       " GNU General Public License for more details.\n",
       "\n",
       " You should have received a copy of the GNU General Public License along\n",
       " with this program; if not, write to the Free Software Foundation, Inc.,\n",
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       "</details></div><details open><summary>Summary (5)</summary><div class=\"datavals\"><div class=\"dataname\">Identifier</div><div class=\"dataval\">9774.arf</div><div class=\"dataname\">Exposure</div><div class=\"dataval\">75141.2 s</div><div class=\"dataname\">Number of bins</div><div class=\"dataval\">1078</div><div class=\"dataname\">Energy range</div><div class=\"dataval\">0.22 - 11 keV, bin size 0.0100002 keV</div><div class=\"dataname\">Area range</div><div class=\"dataval\">0.533159 - 681.944 cm<sup>2</sup></div></div></details><details><summary>Metadata (6)</summary><div class=\"datavals\"><div class=\"dataname\">Mission or Satellite</div><div class=\"dataval\">CHANDRA</div><div class=\"dataname\">Instrument or Detector</div><div class=\"dataval\">ACIS</div><div class=\"dataname\">Object</div><div class=\"dataval\">3C 186</div><div class=\"dataname\">Program description</div><div class=\"dataval\">The cluster around the powerful radio-loud quasar 3C186 at z=1.1</div><div class=\"dataname\">Observation date</div><div class=\"dataval\">2007-12-06T05:30:00</div><div class=\"dataname\">Program that created the ARF</div><div class=\"dataval\">mkarf v0.6.2-0</div></div></details></div>"
      ],
      "text/plain": [
       "<DataARF data set instance '9774.arf'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
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    }
   ],
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  {
   "cell_type": "markdown",
   "id": "1ad11307-0279-410b-9c68-689e7bcd7b44",
   "metadata": {},
   "source": [
    "It will be useful below to refer to the ARF values:"
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  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7d3e6996-16eb-4a31-b7f5-7bec3aa845bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "specresp = arf.get_y()"
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  },
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   "execution_count": 6,
   "id": "b441c7be-f956-4a34-be86-a415f8949f5d",
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       "\n",
       " You should have received a copy of the GNU General Public License along\n",
       " with this program; if not, write to the Free Software Foundation, Inc.,\n",
       " 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.\n",
       "\n",
       "*/\n",
       "\n",
       ":root {\n",
       "  --sherpa-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --sherpa-background-color: var(--jp-layout-color0, white);\n",
       "  --sherpa-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --sherpa-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "\n",
       "  /* https://medium.com/ge-design/iot-cool-gray-is-a-great-background-color-for-data-visualization-ebf18c318418 */\n",
       "  --sherpa-background-color-dark1: #EBEFF2;\n",
       "  --sherpa-background-color-dark2: #D8E0E5;\n",
       "}\n",
       "\n",
       "div.sherpa-text-fallback {\n",
       "    display: none;\n",
       "}\n",
       "\n",
       "div.sherpa {\n",
       "    display: block;\n",
       "}\n",
       "\n",
       "div.sherpa details summary {\n",
       "    display: list-item;  /* needed for notebook, not lab */\n",
       "    font-size: larger;\n",
       "}\n",
       "\n",
       "div.sherpa details div.datavals {\n",
       "    display: grid;\n",
       "    grid-template-columns: 1fr 3fr;\n",
       "    column-gap: 0.5em;\n",
       "}\n",
       "\n",
       "div.sherpa div.dataname {\n",
       "    font-weight: bold;\n",
       "    border-right: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa div.dataval { }\n",
       "\n",
       "div.sherpa div.datavals div:nth-child(4n + 1) ,\n",
       "div.sherpa div.datavals div:nth-child(4n + 2) {\n",
       "    background: var(--sherpa-background-color-row-odd);\n",
       "}\n",
       "\n",
       "div.sherpa table.model tbody {\n",
       "    border-bottom: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model tr.block {\n",
       "    border-top: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-odd ,\n",
       "div.sherpa table.model th.model-even {\n",
       "    border-right: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-odd {\n",
       "    background: var(--sherpa-background-color-dark1);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-even {\n",
       "    background: var(--sherpa-background-color-dark2);\n",
       "}\n",
       "\n",
       "div.sherpa .failed {\n",
       "    background: orange;\n",
       "    font-size: large;\n",
       "    padding: 1em;\n",
       "}\n",
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       "</details></div><details open><summary>Summary (5)</summary><div class=\"datavals\"><div class=\"dataname\">Identifier</div><div class=\"dataval\">9774.rmf</div><div class=\"dataname\">Number of channels</div><div class=\"dataval\">1024</div><div class=\"dataname\">Number of energies</div><div class=\"dataval\">1078</div><div class=\"dataname\">Energy range</div><div class=\"dataval\">0.22 - 11 keV, bin size 0.0100002 keV</div><div class=\"dataname\">Channel range</div><div class=\"dataval\">1 - 1024</div></div></details><details><summary>Metadata (6)</summary><div class=\"datavals\"><div class=\"dataname\">Mission or Satellite</div><div class=\"dataval\">CHANDRA</div><div class=\"dataname\">Instrument or Detector</div><div class=\"dataval\">ACIS</div><div class=\"dataname\">Program that created the RMF</div><div class=\"dataval\">mkrmf - Version CIAO 4.3</div><div class=\"dataname\">The channel type</div><div class=\"dataval\">PI</div><div class=\"dataname\">The minimum probability threshold</div><div class=\"dataval\">9.9999997e-06</div><div class=\"dataname\">Matrix contents</div><div class=\"dataval\">REDIST</div></div></details></div>"
      ],
      "text/plain": [
       "<DataRMF data set instance '9774.rmf'>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e4b7bd6-4b31-43ec-8522-a38b5108b9ea",
   "metadata": {},
   "source": [
    "The ARF is a one-dimensional array but the RMF is a 2D matrix, although stored in a compressed form since most of the data is empty. Let's look at the\n",
    "RMF as an image, using new-to-4.16 functionality:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "96e65189-44a0-4c63-b9a0-744aa26d4ee8",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sherpa.astro import instrument"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "789906e9-d933-413b-a6f6-c53f4b0d0334",
   "metadata": {},
   "source": [
    "The `rmf_to_image` routine converts a RMF into a `DataIMG` object which we can then display automatically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "076003d8-1568-4bae-8ca1-6fa74102e4c9",
   "metadata": {},
   "outputs": [
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       "Copyright (C) 2020  Smithsonian Astrophysical Observatory\n",
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Hc7M+uNUmc71J+ac219YWOHP8MY9/JoJ3YgU7nd655xWRfW+bAngXTsFfItjYojGG9QblSwOsCzmGboz0O03WZ1uV9ZaciOyQ7TuiGnYKDr+cviU3GBK7X2fhgsv9a4scLLRpfjCh99ZCWEXoLTkR2QHbmo5PXlPewVPwc0xQCyYuQbtD5nqTyk9sPnm8wJljj1n9agT31Ap2KmnMyV1E5tc2noCD3TkFz372U19/ug/2x9Mq4nKf2MUsvUmczNsN1r+SCRd6RmM7+8wisu/sXDLu9Inyy0LY8wgGQ6L36yxcmPDokwUO5Lq0PhjTeWdBA3tEZNttbwDv5il49vOf+vrpEA4m4dS09PUmlZ/aXHu0yJkjq6x91Q6riExaVYSIbJudTcUXCbOtCr4v6oRnVUStQflSj8TFNB0nQe7NOmvvp8MqIq5bESKyPbY/gDefgk2x+W05zyMYjog+qFO9MGHtygILmT6d90e0360SKWuXnIhsjx0+AdtmnII3/6NpFeF3uuHAnvMW1x8tcvrQGmsfWDhnljU7WES2xc4EsAmn4C/qgzcN7Clf6pK6kKI5SlF8o87q+yk4vKzZwSKy5Xb2BLzxgdyXnCZ3Y8uy5xH0B0Qe1KhecGhcqVBODeh/ZUjznRJ2taKBPSKypXYugL+gBthRXzS4xw2riNSNelhFPFzg1PI66x/A6MwBzQ4WkS21C3fDDPBFIexMoN6idLlD+kKKxjBN+bU6a+8nCA4vqYoQkS2zwxXEpuAz7SS5ea39cEjkQY2Fiw7NjysUkiOG7w1ovlPUGiMR2TI7fwI2tYqAJyHshrODU9drVM8H3HiwwKkD66y/D8OzS6oiRGRLmFtB7NRGjU99z9+oIoJGk9KlDtnzSdb7GRZfW2ftgwTB0WWtMRKRV7Y7AWzKKRg+P4Q9D384wnpUY+HCmM7HFbJxB+fdPo13CtiLVc0OFpFXsnsnYJNC+LMEfng1rdsjebNG9acBN+4vcGKpxvoHPoOzi9iFnN6SE5GXZm4FsZM+5z8GYRXhENSbFC+3yZ1PstbLsnJmnbWvxPGPHtDsYBF5aQrgmS/og/3hCOthjeqFMd3LZTIxB/dcj/q7+bCK0OxgEXkJCuDNvqAPDrpdkjfWWDgfcO3eEicXa9Tf9+m/sag1RiLyUswOYBNmCEM4ttKZ4NcaFD5qkTuf4HE3x6FTa6x9JYZ3/IBmB4vICzM7gHdLEHzm23LBeIz1aI2F8yN6l8skoi6826F2Lot1YEGzg0XkhSiAX0DgB/i9Pokbayz8JOD67SWOVRo0vuLRe6NKpFRUFSEiz838AN7NX+s/6xQ8cfEbTQqXmhTOx7nfLnD0xBprX4kyOX5As4NF5LmZH8C77XOqCB6vs3B+yPhSEcsKiL7dpnYuDcuLqiJE5LkogJ/HMyEceB5+r0/81hoLP/W5fWuRI6Umza+4dN+sECmXNLBHRL6UAvh5PRvCExe/2SJ/uUnxfIw7jRLHjq2x9hUb5+QBbFURIvIlFMAvYnMIz6qIR+ssXBjgfVTA820Sb7VYfy8NK5odLCJfTAH8ojaFcOB5+IMBsdtrLJz3uHdrgZV8h/Z7Du23ylpjJCJfyMwAfmpw+wtuUt4Jm0N4WkXkLtcp/zTCnXqZE0fWWP+KxfiUZgeLyOczM4Bh97cof5lZCAd+uFF5dZ3KxQHWxRwjN0rm9Sbr7yUJDi5pdrCIfCZzA3gvmIZw4Hn4/SGx26ssnHd5dH2BpVyX7rkRrbeL2JWyqggR+RTzA3iPnIQDz8Nvd8hcrVP+qc3NtQonD61Te89idGYJu5DXW3Ii8hSzA9j08N0s8PFHY1irUfmwR+xilp4TJ/96nbX3EgSHlrCTCfXBIrLB7ADeKzb1wX5/SPTuGgvnJ6x+skA1PWDw7pDm2wXNDhaRp5gbwKavLHrWrIpwJ/itNulPalR/anFjtcqJlRrrX0FrjETkKeYG8F40DWHfmcBanfJHXZIX07RHSSpn66yf0xojEXlCAbzVgiCsIgYD7HthFVG/WqGQHDF6d0Dj7Tz20oKqCBFRAG+XwPMI2h3Sn6xTPW9x82GVk0s1au8F9F9b0BojEVEAb4tNVYS/Xqd0qUP6YoraIM3i6Rrr52L4x7TGSGS/m48ANjHEplVEMBxi311j4YJD+0qFTNxh8k6P2rtaYySy35kdwM97EyIIjA3hwPPwOx1S19apng+4dX+B4wsNGu/59F8L1xjpLTmR/cnsAH4RpoYw04E9tQalSx2yF8ONyssn11l7L1xjZKdVRYjsR/MTwDOmBdmmKsK6v8rC+THDK0XiEQ/e7lJ7N1xjpNnBIvvPfAXwrLIwMIQDz8Pv9kjeWKN6PuD23QWOlJs0z3l036xgq4oQ2XfmK4DB7BCeVhGFyy0KF+I87OQ5fHyd9XNaYySyH5kfwC/zSrKxIRyuMbIerFG9OMK5XAAg8mYnrCK0xkhkXzE/gF+WiSG8cSuiR+LGGtXzPvfuVDlUbNM6N6HzRklrjET2kb0RwK86mMe0EHYn+PWwiiheiHGvWeTo0XXW37NxTi6Ga4z0lpzI3NsbAfyyntotZ1YI+6MxPFyjenGIfzmH69vE32iz/m4qXGOk2cEic2++AxgMDmEfv9cnfnOVhfM+D25Xw43K5xzab83WGGlgj8g8m/8ABjNDeFZFNFvkPm5QOh/hTr3EscPrrJ+zGJ1ews5nVUWIzLH9EcBg5oD3WRXxaI3qxQHWpRyOFyH7epP1c9M1RpodLDK39k8Ab2ZSoE2riNit6UblGwtUs316747CNUYLFVURInNqfwWwqVWE5+E3W2Q/rlM+b3NnrczxgzVq56ZrjDQ7WGQu7a8ABmND2Hcm8Hidyod9oh9l6DtxCmcb4RqjI4uaHSwyh/ZfAIOZIex7+IMB0durLJ6fsHa9Qjk9ZPj2MFxjtFDR7GCRObM/AxiMDOHA86YbletUztvcWq1wYnnTGqN8XlWEyBzZvwFsolkVsVqj8mGPxIdpWsMUS2fWtcZIZA7t7wA28BQ8qyLsu6ssnJ/Q+KRMPj5m8k6P+ttZrKWqqgiRObG/AxiMDOFZFZG5Gm5Uvv5ogVNLNerv+QzOVnUrQmROKIDBvBAOAgLHeWajcobl0+usnYvhHV1SFSEyBxTApgqCjY3K1QsOjSsV0rEJ7ts96u9oo7LIPFAAz5h2CoaNjcrpazUq5y1uPJhuVD6njcoi80ABvJlpITxdYxTUGpQud8hcTLLWy7J0ssb6OW1UFtnrFMDPMm1oT+CHtyLur7Nw0aF3tUQi4uG+2aP+9qaNygphkT1HAfxFTAi16ayIoN0hdb1G5ULAnftVDldbNM55dN+ohLODI7oVIbLXKIA/i2lVBOA7E4Jag+LlLrmP4qx1sywda1B7J4JzXGuMRPYiBfDnMSmEgyCsIoYj7IfrVC+OGV8tELF9/Dd61N9OwfKC1hiJ7DEK4L1icxVxI6wiHt6rsFzq0HzHo/N6Cbtc0uxgkT1EAfxFTDoFAwQ+gesS1JsUP+6Q/yjGWifL0tEGtXenG5W1xkhkz1AAfxmTQng2vH04wnpUo/rRGO9qLvxnr/WovZ0iWF7UGiORPUIBvAfNqojkzRqVDwNW75VYLPRoveXSeaOIXdVGZZG9QAH8PAw7BRP44a2IepPCx20KH8VYa2dZOtKg9q7F6OQidkG3IkRMpwB+XiaG8HCE9bBG9aMRwdUsfmBhn+lReztBcFBrjERMpwDeq4KAwJ0QdLskbtWoXvRZv1tiId+j89aE1huFsIrQwB4RYymAX4RJp+Ap35ng15vkr7YpfhjlcTPHgUMN6u9YDE8vYBcLGtgjYigF8IsyKYSnVUQwHGI9XKd6aUjkShbHjRA51aP2dhz/yJIG9ogYSgH8Mkwa2DO7mtbtEb+5TuVDj+bdEoXMkO7rDo03snBgQQN7RAykAH5VJoTabINGo0n+SovihzbrjRzVAx0ab8HgdBm7VNTAHhHDKIBflklVBIQblYcjeLxO5dKIxJUUo0mU+PEutbdjTI4taWCPiGEUwK/CpCoCwqtpvT7x2+tULnkMbufJJB36Z8c03kjDgaoG9ogYRAG8VUwItU1VRO5qk9Ili3otR3WhS/PNgN4ZDewRMYkC+FUZWEUE4zGs1ih/PCR1NUF/FCd5tEv9zSjOsQUN7BExhAJ4KxhWRYTLPHvE7qxT/cjFuZUjGZ8wPDui8YYG9oiYQgG81UwItelbcn6jSeZ6k9JlaKzmKZV7NN8M6J7VW3IiJlAAbxUDqwh/NIbHNcof98lejdMfJkgf7lJ/M8L4+AJ2TlWEyG5SAG8lw6qI2a2I6L0alUsTvJtZYhEP5/SQ+ptJDewR2WUK4O1iQqjNqohmi/T1BuXL0Hqco1js037do/2aqgiR3aQA3mqmVhFrNUof98hfidHtpcgc7NJ402J4sqqBPSK7RAG8HUysIvpDIvfXKV92sG6msawA99SQ+psJ/EMLGtgjsgsUwNvNhFDbVEWkbtQpXwroPsyRzw7pvObSei0HixUN7BHZYQrg7WJiFeFMoNagcLVL4UqUTjdNbrlL8w2L4amqBvaI7DAF8HYytYp4UKN8eUz0egrft/GPD6m/EcM9vICdzehqmsgOUQDvFENOwYE7wW+1Sd2sU77sM3iQJZsZ0T07ofVaFpYWNLBHZIfoo+/tFgRPwsyydv9UPK0irFqDwtU0w0qRdiFNbqlH840iqXqJTG9AMHEJJs7uPqvInNMJeCfsdug+y/fwBwOsB+tUPh6RvJbEdSNwrE/9jRiTI6oiRHaCAninGfKrfeB5GxuVyx97jO9lSSUn9M5MaL6ehuUFDewR2WaqIHaKoVUE9Sa5T9IMKyUaxTS5hR6t14qkGkVy3QGB64bjLUVky+kEvJNMu5rmexsblctXRqQ/SeA4UeyjfeqvT2cHa2CPyLZRAO9zGxuVb9coX/Fw72ZIJCYMTjk0Xk8SrCxoYI/INlEFsdMMrCICx8G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       "</details></div><details><summary>Metadata (2)</summary><div class=\"datavals\"><div class=\"dataname\">Mission or Satellite</div><div class=\"dataval\">CHANDRA</div><div class=\"dataname\">Instrument or Detector</div><div class=\"dataval\">ACIS</div></div></details></div>"
      ],
      "text/plain": [
       "<DataIMG data set instance '9774.rmf'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "instrument.rmf_to_image(rmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a69baea-929e-4d8b-a5bf-043d1ae684f7",
   "metadata": {},
   "source": [
    "However, `rmf_to_matrix` is more useful here, as it easier to get at the data we care about:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "83fc088d-9cb1-46eb-b168-87c9ae81fae6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This returns a RMFMatrix object whih has matrix, channels, and energies fields\n",
    "rmf_mat = instrument.rmf_to_matrix(rmf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6facc1bd-3ad7-4fe1-acc0-90d83277a82d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1078, 1024)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What we care about here is the matrix field\n",
    "rmf_mat.matrix.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "03e420ac-e771-4077-9741-93f18934dd69",
   "metadata": {},
   "outputs": [],
   "source": [
    "# It's also useful to get the energy scale\n",
    "elo, ehi = rmf_mat.energies.grid\n",
    "emid = (elo + ehi) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "34a67ad9-685a-440b-a18c-53d7cdc77a91",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.imshow(rmf_mat.matrix, origin='lower')\n",
    "plt.xlabel(\"Channel Axis (probably offset by one)\")\n",
    "plt.ylabel(\"Energy Axis (not in energy units!)\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2bbbdf2b-119a-43c9-9edf-7bb1e3157719",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sherpa.astro.xspec import XSgaussian\n",
    "\n",
    "gauss = XSgaussian()\n",
    "gauss.linee = 3\n",
    "gauss.sigma = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ad2bcf4-20ce-4660-a462-26fe8789c20a",
   "metadata": {},
   "source": [
    "The model can be evaluated directly, and the values depend on the model, but for XSPEC additive models (such as `XSgaussian`)\n",
    "it creates values of photon per square cm per second:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "aa2979f2-80f3-4440-adc4-8a279e3dec88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_raw = gauss(elo, ehi)\n",
    "\n",
    "plt.plot(emid, model_raw)\n",
    "plt.xlabel(\"Energy (keV)\")\n",
    "plt.ylabel(\"Photon / cm$^2$ / s\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ef15de4-1fc5-469b-9988-7f1df06c2ebb",
   "metadata": {},
   "source": [
    "We can \"convert\" this into a \"predicted\" spectrum by convoling this with the RMF and mutiplying by the ARF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ee73bbe9-e5b4-425e-888f-2076555dd754",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_pred = (model_raw * specresp) @ rmf_mat.matrix\n",
    "\n",
    "channels = rmf_mat.channels.grid[0]\n",
    "plt.plot(channels, model_pred)\n",
    "\n",
    "plt.xlabel(\"Channel\")\n",
    "plt.ylabel(\"Counts / s\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ef2ca82-07e9-426e-a530-f4aae9461761",
   "metadata": {},
   "source": [
    "This is direct application of the response, but in Sherpa we hide this with the various classes (`DataARF` and `DataRMF` for representing\n",
    "the data and `Response1D`, `ARF1d`, `RMF1D` and family to apply these to the models), which can be applied in different situations (the documentation for these\n",
    "classes is lacking and something we hope to improve in 2024).\n",
    "\n",
    "We can \"apply\" the ARF from the `DataARF` (or `ARF1D`) - even though technically this is just simple matrix multiplication:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e0d661f5-1f74-49c5-bb9f-9f4590233266",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00525531, 0.00623099, 0.00729793, ..., 0.        , 0.        ,\n",
       "       0.        ])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arf.apply_arf(model_raw)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34dbbc7a-3800-4fd5-8d6a-c4c81f8009fc",
   "metadata": {},
   "source": [
    "This applies to `apply_rmf` to from `DataRMF` (or `RMF1D`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a60787bd-d53b-43e1-93dd-fd738391b0d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_pred2 = rmf.apply_rmf(arf.apply_arf(model_raw))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "420eb7a8-d71d-461c-8111-a473d2a8aada",
   "metadata": {},
   "source": [
    "and we can see that we get almost the same results as the manual result\n",
    "above (`apply_rmf` applies the sparse matrix rather than use the full matrix used to create `model_raw`);\n",
    "the numeric values are not the same, but they are close:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "df84afba-caa2-45b0-9acf-f121c9c0afb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(model_pred == model_pred2).all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "dace5810-bac3-496a-b917-8ad046269934",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-6.661338147750939e-15\n",
      "8.43769498715119e-15\n"
     ]
    }
   ],
   "source": [
    "# The absolute differences are <~ 10^-14\n",
    "delta = model_pred2 - model_pred\n",
    "print(delta.min())\n",
    "print(delta.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b10cbc29-57f3-4c4d-90f9-cbcaa71a199d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.8592894001845593e-13\n",
      "3.972674642545171e-13\n"
     ]
    }
   ],
   "source": [
    "# The percentage differences are <~ 10^-12\n",
    "pdelta = 100 * delta[model_pred > 0] / model_pred[model_pred > 0]\n",
    "print(pdelta.min())\n",
    "print(pdelta.max())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e5fb31f-da10-4814-97b1-3d8058c8d6b7",
   "metadata": {},
   "source": [
    "The `apply_xxx` routines require the user sending in model values evaluated on the correct grid. The more Sherpa approach is to include the\n",
    "response in the model definition. Normally we would include the PHA data (via the `sherpa.astro.instrument.Response1D` factory) but here we shall\n",
    "use `sherpa.astro.instrument.RSPModelNoPHA`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6f831919-f0af-429b-b093-ed0a27ab5559",
   "metadata": {},
   "outputs": [],
   "source": [
    "model_with_response = instrument.RSPModelNoPHA(arf, rmf, gauss)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18f2e97f-c33f-4e93-a73c-966d460b94ee",
   "metadata": {},
   "source": [
    "This is actually a Sherpa \"model\", so we can print it out and see the model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "11e4d90e-4060-47e8-b171-c5428ae31e76",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "apply_rmf(apply_arf(gaussian))\n",
      "   Param        Type          Value          Min          Max      Units\n",
      "   -----        ----          -----          ---          ---      -----\n",
      "   gaussian.LineE thawed            3            0        1e+06        keV\n",
      "   gaussian.Sigma thawed            1            0           20        keV\n",
      "   gaussian.norm thawed            1            0        1e+24           \n"
     ]
    }
   ],
   "source": [
    "print(model_with_response)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "984618f2-8de7-4c29-a4dd-2a8c112e2f3a",
   "metadata": {},
   "source": [
    "As this model is now \"in counts space\" we send in the channel array (rather than the energy array used with the `gauss` model):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a45889e0-1069-4f5f-9f78-38cf3d653b4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_pred3 = model_with_response(channels)\n",
    "\n",
    "# Note we now compare against model_pred2 not model_pred\n",
    "(model_pred3 == model_pred2).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0161fe59-c568-4b58-a321-ed07fb0d47ae",
   "metadata": {},
   "source": [
    "If the above has too much overhead we can get down to the \"raw\" routine, which for RMF handling is the `sherpa.astro.utils.rmf_fold`\n",
    "routine **but** this is a very low-level code which we don't guarantee is stable (but it hasn't changed in a *long* time) or well documented.\n",
    "\n",
    "The `rmf_fold` routine applies the sparse-matrix data to an array (it provides the functionality of the `apply_rmf` method of the `DataRMF`\n",
    "class). It takes the RMF matrix from the file, after some small tweaking. I am going to read the data in using AstroPy, but you can\n",
    "also use Crates (the CIAO I/O layer) if you want (the data is the same, the data access is just a bit different):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c5b2694e-580c-425b-8d83-563c4746af65",
   "metadata": {},
   "outputs": [],
   "source": [
    "from astropy.io import fits\n",
    "\n",
    "hdus = fits.open(\"9774.rmf\")\n",
    "hdu = hdus[1]  # I know the ordering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "181a4728-5e89-4510-b62f-9d819f3e1248",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ColDefs(\n",
       "    name = 'ENERG_LO'; format = 'E'; unit = 'keV'\n",
       "    name = 'ENERG_HI'; format = 'E'; unit = 'keV'\n",
       "    name = 'N_GRP'; format = 'I'\n",
       "    name = 'F_CHAN'; format = 'PI(3)'\n",
       "    name = 'N_CHAN'; format = 'PI(3)'\n",
       "    name = 'MATRIX'; format = 'PE(1023)'\n",
       ")"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hdu.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "167d0e88-1dc1-4b03-983e-b62ffb0d2c94",
   "metadata": {},
   "source": [
    "Here is the data we need:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "38fc24ae-ebd0-48ea-9071-1fbec54c84c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_grp = hdu.data[\"N_GRP\"]\n",
    "f_chan = hdu.data[\"F_CHAN\"]\n",
    "n_chan = hdu.data[\"N_CHAN\"]\n",
    "matrix = hdu.data[\"MATRIX\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee385852-484a-4444-92f7-387a193acaef",
   "metadata": {},
   "source": [
    "However, as hinted by the format settings in the `ColDefs` output above, RMF files play games and the data can be stored as \"variable length arrays\",\n",
    "which means each row can have a different length - this is used for the `F_CHAN`, `N_CHAN`, and `MATRIX` blocks above - which means the overall array has a \"object\" datatype, even though each row has the correct data type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bb0a2dcc-03c0-41c4-9253-857997919f7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('O')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_chan.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ec02064a-eaa1-4d89-a213-a44f93bed3eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([27], dtype=int16), array([46, 46, 58], dtype=int16))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_chan[0], n_chan[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34abcc81-ae20-498d-bc42-28671d50d0ae",
   "metadata": {},
   "source": [
    "We also need some other metadata (the number of channels and the \"starting point\" of the channel array):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8e3213eb-9d15-45d7-bb93-2f5f4fc82711",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1024"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "detchans = hdu.header[\"DETCHANS\"]\n",
    "detchans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "161e2185-8612-4ae2-847b-d690f3722720",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This requires knowing the FITS file structure\n",
    "offset = hdu.header[\"TLMIN4\"]\n",
    "offset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "5aaa20cc-4a68-47b2-8b53-9cde348b4fcf",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sherpa.astro.utils import rmf_fold"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9448c2e8-b097-44c1-95d2-00776e71a4d2",
   "metadata": {},
   "source": [
    "As mentioned, `rmf_fold` is low-level code and doesn't provide many safety checks. So, for instance, if you were to\n",
    "try to run\n",
    "\n",
    "    rmf_fold(model_raw, n_grp, f_chan, n_chan, matrix, detchans, offset)\n",
    "\n",
    "you'd find the code would crash the interpreter. We need to \"flatten out\" the data into a form that `rmf_fold` understands\n",
    "(and is currently poorly documented).\n",
    "\n",
    "Now, the `N_GRP` column lists the number of elements in each row (at least for `F_CHAN` and `N_CHAN` columns) and this data may be stored as \n",
    "a normal array rather than the variable-length approach used here - that is each column is a 2D matrix - so we would need to remove the 0 elements.\n",
    "\n",
    "The following will hopefully be sufficient but is not optimised (but it only needs to be done when reading in the data from the RMF):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f8d5bc9a-fdd6-4198-acb2-cd19472002ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "fchans = []\n",
    "nchans = []\n",
    "for ng, fc, nc in zip(n_grp, f_chan, n_chan):\n",
    "    if ng == 0:\n",
    "        # some files have this\n",
    "        continue\n",
    "\n",
    "    fchans.append(fc[:ng])\n",
    "    nchans.append(nc[:ng])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "52507aea-6328-43dd-bd45-bd50a7c11ab1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "fchan_clean = np.concatenate(fchans)\n",
    "nchan_clean = np.concatenate(nchans)\n",
    "\n",
    "# I don't think we have to do anything special with the matrix, but I can not guarantee that\n",
    "matrix_clean = np.concatenate(matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a10b8814-23f6-47e4-b64e-dcb8c79f7274",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_pred4 = rmf_fold(model_raw * specresp, n_grp, fchan_clean, nchan_clean, matrix_clean, detchans, offset)\n",
    "\n",
    "# Note we now compare against model_pred2 not model_pred\n",
    "(model_pred4 == model_pred2).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60411a38-204b-445f-a600-5e4e14d6a91a",
   "metadata": {},
   "source": [
    "Rather than doing this yourself you can use `io.read_rmf` and then use the RMF fields directly since"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "98f9ab16-6c36-46a7-98b5-d911696bdd75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, True, True, True)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(rmf.n_grp == n_grp).all(), (rmf.f_chan == fchan_clean).all(), (rmf.n_chan == nchan_clean).all(), (rmf.matrix == matrix_clean).all() "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec1e7a4c-aed9-4a93-8a57-64f958612abb",
   "metadata": {},
   "source": [
    "It is interesting to see what the different approaches \"cost\". Hwever, it's not a fair comparison as the different approaches do not\n",
    "provide the same functionality, and you also have to be careful in interpreting the results as Sherpa does some model caching **and**\n",
    "you have to be careful with data types (e.g.`model_pred4` is the slowest version but can become the fastest if you fix the ndarray\n",
    "data types):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "f4532ee6-bd9e-42c3-95ba-597e7e7e2d04",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's try to turn off the model cache on the gauss model; there has to be a better way to do this\n",
    "gauss._use_caching = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "3d925a6a-5274-4efb-88bd-d97e62cabc81",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "290 µs ± 121 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# model_pred\n",
    "%timeit (model_raw * specresp) @ rmf_mat.matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "9b94df10-bd5e-4676-bde1-280f5c4c4305",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "238 µs ± 711 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# model_pred2\n",
    "%timeit rmf.apply_rmf(arf.apply_arf(model_raw))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "f6e03bb9-8c4f-472e-8f32-e0e10c22d38c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "307 µs ± 828 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# model_pred3\n",
    "%timeit model_with_response(channels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "ebe4a0fb-4e78-4413-8857-d52d2d95b647",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "499 µs ± 3.26 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# model_pred4\n",
    "%timeit rmf_fold(model_raw * specresp, n_grp, fchan_clean, nchan_clean, matrix_clean, detchans, offset)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd028f93-f2b3-4700-b9a4-37a3f0518bcb",
   "metadata": {},
   "source": [
    "Some of it comes down to data types, as the `rmf_fold` code needs to convert the types to send to the C++ code. Switching\n",
    "to more-appropriate types does make a difference, and at least gets it below the times for `model_pred3` and `model_pred4`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "16c2e80f-6799-416d-830e-17b159b19ef1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(dtype('>i2'), dtype('int16'), dtype('int16'), dtype('float32'))"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_grp.dtype, fchan_clean.dtype, nchan_clean.dtype, matrix_clean.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "2925b315-23a8-4851-9fad-7f1557441677",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_grp2 = n_grp.astype(np.int64)\n",
    "fchan_clean2 = fchan_clean.astype(np.int64)\n",
    "nchan_clean2 = nchan_clean.astype(np.int64)\n",
    "matrix_clean2 = matrix_clean.astype(np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "570b088a-2281-4dd5-b003-2432db8427f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "240 µs ± 1.22 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit rmf_fold(model_raw * specresp, n_grp2, fchan_clean2, nchan_clean2, matrix_clean2, detchans, offset)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71d3339b-18b5-4fe6-94db-fb944ee16114",
   "metadata": {},
   "source": [
    "I just want to check that this does give the desired results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "c16ebdb0-1aa4-4459-8816-acf034526789",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_pred5 = rmf_fold(model_raw * specresp, n_grp2, fchan_clean2, nchan_clean2, matrix_clean2, detchans, offset)\n",
    "\n",
    "# Note we now compare against model_pred2 not model_pred\n",
    "(model_pred5 == model_pred2).all()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d73f86d-a1cf-4be9-843b-3ca11dae6bb9",
   "metadata": {},
   "source": [
    "So the moral may be that using the actual RMF matrix, rather than the compressed one, may be faster, but it depends on the matrix **and**\n",
    "it may lead to extra memory use since the compressed form is only about 40% of the matrix in this case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "bf5f4db6-5404-4b05-9964-c5a114f4259f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3972217793367347"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_clean2.size / rmf_mat.matrix.size"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b84fce61-0beb-44f5-926d-d83beb92be5d",
   "metadata": {},
   "source": [
    "As a final warning, as you delve deeper into the Sherpa internals the more likelihood to come across interfaces that will be changed across versions!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
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    "name": "ipython",
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