{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e569d931",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:11.786613Z",
     "iopub.status.busy": "2026-10-02T14:42:11.786374Z",
     "iopub.status.idle": "2026-10-02T14:42:11.792344Z",
     "shell.execute_reply": "2026-10-02T14:42:11.791703Z"
    },
    "papermill": {
     "duration": 0.010353,
     "end_time": "2026-10-02T14:42:11.793305+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:11.782952+00:00",
     "status": "completed"
    },
    "tags": [
     "remove-input",
     "active-ipynb",
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "try:\n",
    "    from openmdao.utils.notebook_utils import notebook_mode  # noqa: F401\n",
    "except ImportError:\n",
    "    !python -m pip install openmdao[notebooks]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "111e8af7",
   "metadata": {
    "papermill": {
     "duration": 0.001953,
     "end_time": "2026-10-02T14:42:11.797500+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:11.795547+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "(sec:openmdao_jax_subpackage)=\n",
    "# Composable functions via `jax` (`openmdao.jax`)\n",
    "\n",
    "Certain functions are useful in a gradient-based optimization context, such as smooth activation \n",
    "functions or differentiable maximum/minimum functions.\n",
    "\n",
    "Rather than provide a component that forces a user to structure their system in a certain way and \n",
    "add more components than necessary, the `openmdao.jax` package is intended to provide a universal \n",
    "source for _composable_ functions that users can use within their own components.\n",
    "\n",
    "Functions in `openmdao.jax` are built using the [jax](https://github.com/google/jax) Python package.\n",
    "This allows users to develop components that use these functions, along with other code written with \n",
    "`jax`, and leverage capabilities of `jax` like automatic differentiation, vectorization, and \n",
    "just-in-time compilation.  For most users, these functions will be used within the `compute_primal` \n",
    "method of a [JaxExplicitComponent](../../experimental/jax_explicitcomp_api.ipynb) or \n",
    "[JaxImplicitComponent](../../experimental/jax_implicitcomp_api.ipynb), but users who are proficient in jax \n",
    "can also write their own custom components using these functions if necessary.\n",
    "\n",
    "Many of these functions are focused on providing differentiable forms of strictly non-differentiable \n",
    "functions, such as step responses, absolute value, and minimums or maximums. Near regions where the \n",
    "nominal functions would have invalid derivatives, these functions are smooth but will not perfectly \n",
    "match their non-smooth counterparts."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86efbe58",
   "metadata": {
    "papermill": {
     "duration": 0.001907,
     "end_time": "2026-10-02T14:42:11.801764+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:11.799857+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Available Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a201b2ba",
   "metadata": {
    "papermill": {
     "duration": 0.001801,
     "end_time": "2026-10-02T14:42:11.805492+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:11.803691+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "```{eval-rst}\n",
    "    .. autofunction:: openmdao.jax.act_tanh\n",
    "        :noindex:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "613fa1f1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:11.810783Z",
     "iopub.status.busy": "2026-10-02T14:42:11.810564Z",
     "iopub.status.idle": "2026-10-02T14:42:13.233018Z",
     "shell.execute_reply": "2026-10-02T14:42:13.232388Z"
    },
    "papermill": {
     "duration": 1.4266,
     "end_time": "2026-10-02T14:42:13.233952+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:11.807352+00:00",
     "status": "completed"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import openmdao.jax_funcs as omj\n",
    "\n",
    "fig, ax = plt.subplots(2, 2, figsize=(8, 8))\n",
    "fig.suptitle('Impact of different parameters on act_tanh')\n",
    "x = np.linspace(0, 1, 1000)\n",
    "\n",
    "mup001 = omj.act_tanh(x, mu=0.001, z=0.5, a=0, b=1)\n",
    "mup01 = omj.act_tanh(x, mu=0.01, z=0.5, a=0, b=1)\n",
    "mup1 = omj.act_tanh(x, mu=0.1, z=0.5, a=0, b=1)\n",
    "\n",
    "ax[0, 0].plot(x, mup001, label=r'$\\mu$ = 0.001')\n",
    "ax[0, 0].plot(x, mup01, label=r'$\\mu$ = 0.01')\n",
    "ax[0, 0].plot(x, mup1, label=r'$\\mu$ = 0.1')\n",
    "ax[0, 0].legend()\n",
    "ax[0, 0].grid()\n",
    "\n",
    "zp5 = omj.act_tanh(x, mu=0.01, z=0.5, a=0, b=1)\n",
    "zp4 = omj.act_tanh(x, mu=0.01, z=0.4, a=0, b=1)\n",
    "zp6 = omj.act_tanh(x, mu=0.01, z=0.6, a=0, b=1)\n",
    "\n",
    "ax[0, 1].plot(x, zp4, label=r'$z$ = 0.4')\n",
    "ax[0, 1].plot(x, zp5, label=r'$z$ = 0.5')\n",
    "ax[0, 1].plot(x, zp6, label=r'$z$ = 0.6')\n",
    "ax[0, 1].legend()\n",
    "ax[0, 1].grid()\n",
    "\n",
    "a0 = omj.act_tanh(x, mu=0.01, z=0.5, a=0, b=1)\n",
    "ap2 = omj.act_tanh(x, mu=0.01, z=0.5, a=0.2, b=1)\n",
    "ap4 = omj.act_tanh(x, mu=0.01, z=0.5, a=0.4, b=1)\n",
    "\n",
    "ax[1, 0].plot(x, a0, label=r'$a$ = 0.0')\n",
    "ax[1, 0].plot(x, ap2, label=r'$a$ = 0.2')\n",
    "ax[1, 0].plot(x, ap4, label=r'$a$ = 0.4')\n",
    "ax[1, 0].legend()\n",
    "ax[1, 0].grid()\n",
    "\n",
    "bp6 = omj.act_tanh(x, mu=0.01, z=0.5, a=0, b=.6)\n",
    "bp8 = omj.act_tanh(x, mu=0.01, z=0.5, a=0, b=.8)\n",
    "b1 = omj.act_tanh(x, mu=0.01, z=0.5, a=0, b=1)\n",
    "\n",
    "ax[1, 1].plot(x, bp6, label=r'$b$ = 0.6')\n",
    "ax[1, 1].plot(x, bp8, label=r'$b$ = 0.8')\n",
    "ax[1, 1].plot(x, b1, label=r'$b$ = 1.0')\n",
    "ax[1, 1].legend()\n",
    "ax[1, 1].grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "716b50cc",
   "metadata": {
    "papermill": {
     "duration": 0.00237,
     "end_time": "2026-10-02T14:42:13.238951+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:13.236581+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "```{eval-rst}\n",
    "    .. autofunction:: openmdao.jax.smooth_abs\n",
    "        :noindex:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "308f5047",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:13.268232Z",
     "iopub.status.busy": "2026-10-02T14:42:13.267982Z",
     "iopub.status.idle": "2026-10-02T14:42:13.432092Z",
     "shell.execute_reply": "2026-10-02T14:42:13.429922Z"
    },
    "papermill": {
     "duration": 0.167926,
     "end_time": "2026-10-02T14:42:13.432896+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:13.264970+00:00",
     "status": "completed"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "fig.suptitle('Impact of different parameters on smooth_abs')\n",
    "x = np.linspace(-0.2, 0.2, 1000)\n",
    "\n",
    "mup001 = omj.smooth_abs(x, mu=0.001)\n",
    "mup01 = omj.smooth_abs(x, mu=0.01)\n",
    "mup1 = omj.smooth_abs(x, mu=0.1)\n",
    "\n",
    "ax.plot(x, mup001, label=r'$\\mu$ = 0.001')\n",
    "ax.plot(x, mup01, label=r'$\\mu$ = 0.01')\n",
    "ax.plot(x, mup1, label=r'$\\mu$ = 0.1')\n",
    "ax.legend()\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "268fc9f7",
   "metadata": {
    "papermill": {
     "duration": 0.058094,
     "end_time": "2026-10-02T14:42:13.494651+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:13.436557+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "```{eval-rst}\n",
    "    .. autofunction:: openmdao.jax.smooth_max\n",
    "        :noindex:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "810cb8c2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:13.512519Z",
     "iopub.status.busy": "2026-10-02T14:42:13.512292Z",
     "iopub.status.idle": "2026-10-02T14:42:13.743823Z",
     "shell.execute_reply": "2026-10-02T14:42:13.743187Z"
    },
    "papermill": {
     "duration": 0.247669,
     "end_time": "2026-10-02T14:42:13.744894+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:13.497225+00:00",
     "status": "completed"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "fig.suptitle('Impact of different parameters on smooth_max of sin and cos')\n",
    "x = np.linspace(0.5, 1, 1000)\n",
    "\n",
    "sin = np.sin(x)\n",
    "cos = np.cos(x)\n",
    "\n",
    "mup001 = omj.smooth_max(sin, cos, mu=0.001)\n",
    "mup01 = omj.smooth_max(sin, cos, mu=0.01)\n",
    "mup1 = omj.smooth_max(sin, cos, mu=0.1)\n",
    "\n",
    "ax.plot(x, sin, '--', label=r'$\\sin{x}$')\n",
    "ax.plot(x, cos, '--', label=r'$\\cos{x}$')\n",
    "ax.plot(x, mup01, label=r'$\\mu$ = 0.01')\n",
    "ax.plot(x, mup1, label=r'$\\mu$ = 0.1')\n",
    "ax.legend()\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77b3f93a",
   "metadata": {
    "papermill": {
     "duration": 0.002503,
     "end_time": "2026-10-02T14:42:13.750786+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:13.748283+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "```{eval-rst}\n",
    "    .. autofunction:: openmdao.jax.smooth_min\n",
    "        :noindex:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7322fd31",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:13.757007Z",
     "iopub.status.busy": "2026-10-02T14:42:13.756853Z",
     "iopub.status.idle": "2026-10-02T14:42:13.902895Z",
     "shell.execute_reply": "2026-10-02T14:42:13.902404Z"
    },
    "papermill": {
     "duration": 0.150549,
     "end_time": "2026-10-02T14:42:13.903814+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:13.753265+00:00",
     "status": "completed"
    },
    "scrolled": true,
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "fig.suptitle('Impact of different parameters on smooth_min of sin and cos')\n",
    "x = np.linspace(0.5, 1, 1000)\n",
    "\n",
    "sin = np.sin(x)\n",
    "cos = np.cos(x)\n",
    "\n",
    "mup001 = omj.smooth_min(sin, cos, mu=0.001)\n",
    "mup01 = omj.smooth_min(sin, cos, mu=0.01)\n",
    "mup1 = omj.smooth_min(sin, cos, mu=0.1)\n",
    "\n",
    "ax.plot(x, sin, '--', label=r'$\\sin{x}$')\n",
    "ax.plot(x, cos, '--', label=r'$\\cos{x}$')\n",
    "ax.plot(x, mup01, label=r'$\\mu$ = 0.01')\n",
    "ax.plot(x, mup1, label=r'$\\mu$ = 0.1')\n",
    "ax.legend(ncol=2)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5087f654",
   "metadata": {
    "papermill": {
     "duration": 0.001842,
     "end_time": "2026-10-02T14:42:13.907875+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:13.906033+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "```{eval-rst}\n",
    "    .. autofunction:: openmdao.jax.smooth_round\n",
    "        :noindex:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b8a697c2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:13.912272Z",
     "iopub.status.busy": "2026-10-02T14:42:13.912118Z",
     "iopub.status.idle": "2026-10-02T14:42:14.090126Z",
     "shell.execute_reply": "2026-10-02T14:42:14.089642Z"
    },
    "papermill": {
     "duration": 0.180995,
     "end_time": "2026-10-02T14:42:14.090637+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:13.909642+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n",
    "fig.suptitle('Impact of different parameters on smooth_round of a step function')\n",
    "x = np.linspace(2, -2, 1000)\n",
    "x_round = np.round(x)\n",
    "\n",
    "mup01 = omj.smooth_round(x, mu=0.05)\n",
    "mup1 = omj.smooth_round(x, mu=0.1)\n",
    "\n",
    "ax.plot(x, x_round, '--', label=r'$np.round(x)$')\n",
    "\n",
    "ax.plot(x, mup01, label=r'$\\mu$ = 0.05')\n",
    "ax.plot(x, mup1, label=r'$\\mu$ = 0.1')\n",
    "ax.legend(ncol=2)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5828da93",
   "metadata": {
    "papermill": {
     "duration": 0.001937,
     "end_time": "2026-10-02T14:42:14.094898+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:14.092961+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "```{eval-rst}\n",
    "    .. autofunction:: openmdao.jax.ks_max\n",
    "        :noindex:\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cf24ddab",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:14.099250Z",
     "iopub.status.busy": "2026-10-02T14:42:14.099096Z",
     "iopub.status.idle": "2026-10-02T14:42:14.289824Z",
     "shell.execute_reply": "2026-10-02T14:42:14.289382Z"
    },
    "papermill": {
     "duration": 0.193479,
     "end_time": "2026-10-02T14:42:14.290257+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:14.096778+00:00",
     "status": "completed"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from openmdao.jax_funcs import ks_max\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "fig.suptitle('Impact of different parameters on ks_max')\n",
    "y = np.random.random(100)\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "rho1 = ks_max(y, rho=10.)\n",
    "rho10 = ks_max(y, rho=100.)\n",
    "rho100 = ks_max(y, rho=1000.)\n",
    "\n",
    "ax.plot(x, y, '.', label='y')\n",
    "ax.plot(x, rho1 * np.ones_like(x), label='ks_max(y, rho=10)')\n",
    "ax.plot(x, rho10 * np.ones_like(x), label='ks_max(y, rho=100)')\n",
    "ax.legend(ncol=1)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "13ea9f69",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:14.296349Z",
     "iopub.status.busy": "2026-10-02T14:42:14.296067Z",
     "iopub.status.idle": "2026-10-02T14:42:14.503100Z",
     "shell.execute_reply": "2026-10-02T14:42:14.502649Z"
    },
    "papermill": {
     "duration": 0.211571,
     "end_time": "2026-10-02T14:42:14.504593+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:14.293022+00:00",
     "status": "completed"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from openmdao.jax_funcs import ks_min\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(4, 4))\n",
    "fig.suptitle('Impact of different parameters on ks_min')\n",
    "y = np.random.random(100) + 5\n",
    "x = np.linspace(0, 1, 100)\n",
    "\n",
    "rho1 = ks_min(y, rho=10.)\n",
    "rho10 = ks_min(y, rho=100.)\n",
    "rho100 = ks_min(y, rho=1000.)\n",
    "\n",
    "ax.plot(x, y, '.', label='y')\n",
    "ax.plot(x, rho1 * np.ones_like(x), label='ks_min(y, rho=10)')\n",
    "ax.plot(x, rho10 * np.ones_like(x), label='ks_min(y, rho=100)')\n",
    "ax.legend(ncol=1)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ed36a21",
   "metadata": {
    "papermill": {
     "duration": 0.037792,
     "end_time": "2026-10-02T14:42:14.560794+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:14.523002+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Getting derivatives from jax-composed functions\n",
    "\n",
    "If the user writes a function that is composed entirely using jax-based functions (from `jax.numpy`, etc.), then `jax` will in most cases be able to provide derivatives of those functions automatically.\n",
    "\n",
    "The library has several ways of doing this and the best approach will likely depend on the specific use-case at hand.\n",
    "Rather than provide a component to wrap a `jax` function and provide derivatives automatically, consider the following example as a template for how to utilize `jax` in combination with OpenMDAO components.\n",
    "\n",
    "The following component uses the `jax` library's numpy implementation to compute the root-mean-square (rms) of an array of data.  It then passes this data through the `openmdao.jax.act_tanh` activation function.\n",
    "\n",
    "The arguments to `act_tanh` are such that it will return a value of approximately 1.0 if the rms is greater than a threshold value of 0.5, or approximately 0.0 if the rms is less than this value.  This `act_tanh` function is an activation function that smoothly transitions from 0.0 to 1.0 such that it is differentiable. Near the threhold value it will return some value between 0.0 and 1.0.\n",
    "\n",
    "\\begin{align}\n",
    "\\mathrm{rms\\_switch} = \\mathrm{act\\_tanh}\\left(\\sqrt{\\frac{1}{n}\\sum{\\left(x^2\\right)}}\\right)\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "### compute_primal\n",
    "\n",
    "If OpenMDAO sees a Component method with the name `compute_primal`, it assumes that the method takes \n",
    "the component's inputs as positional arguments and returns the component's outputs as a tuple. \n",
    "JaxExplicitComponent and JaxImplicitComponent both require a `compute_primal` method to be defined,\n",
    "but any OpenMDAO component may declare `compute_primal` instead of `compute`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ac28484d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:14.568072Z",
     "iopub.status.busy": "2026-10-02T14:42:14.567879Z",
     "iopub.status.idle": "2026-10-02T14:42:15.664535Z",
     "shell.execute_reply": "2026-10-02T14:42:15.663438Z"
    },
    "papermill": {
     "duration": 1.101052,
     "end_time": "2026-10-02T14:42:15.665079+00:00",
     "exception": false,
     "start_time": "2026-10-02T14:42:14.564027+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/runner/work/OpenMDAO/OpenMDAO/.pixi/envs/dev/lib/python3.13/site-packages/modopt/core/visualization.py:11: UserWarning: matplotlib not found, plotting disabled.\n",
      "  warnings.warn(\"matplotlib not found, plotting disabled.\")\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import jax.numpy as jnp\n",
    "\n",
    "import openmdao.api as om\n",
    "from openmdao.jax_funcs import act_tanh\n",
    "\n",
    "\n",
    "class RootMeanSquareSwitchComp(om.JaxExplicitComponent):\n",
    "\n",
    "    def initialize(self):\n",
    "        self.options.declare('vec_size', types=(int,))\n",
    "        self.options.declare('mu', types=(float,), default=0.01)\n",
    "        self.options.declare('threshold', types=(float,), default=0.5)\n",
    "\n",
    "    def setup(self):\n",
    "        n = self.options['vec_size']\n",
    "        self.add_input('x', shape=(n,))\n",
    "        self.add_output('rms', shape=())\n",
    "        self.add_output('rms_switch', shape=())\n",
    "\n",
    "        # we can declare partials here if we know them, but in most cases it's best just to\n",
    "        # let the component determine them (and any sparsity) automatically.\n",
    "\n",
    "    # because our compute_primal references 'static' data, i.e. data that won't change during\n",
    "    # the execution of the component, we need to provide a way to let jax know about this data.\n",
    "    # This is important in order to cause jax to recompile the function if any of the static data\n",
    "    # changes, between runs for example.\n",
    "    def get_self_statics(self):\n",
    "        return (self.options['vec_size'], self.options['mu'], self.options['threshold'])\n",
    "\n",
    "    def compute_primal(self, x):\n",
    "        n = self.options['vec_size']\n",
    "        mu = self.options['mu']\n",
    "        z = self.options['threshold']\n",
    "        rms = jnp.sqrt(jnp.sum(x**2) / n)\n",
    "        return rms, act_tanh(rms, mu, z, 0.0, 1.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7d19c963",
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     "shell.execute_reply": "2026-10-02T14:42:17.373214Z"
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     "exception": false,
     "start_time": "2026-10-02T14:42:15.667636+00:00",
     "status": "completed"
    },
    "scrolled": false,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1790952136.926902] [runnervm8df0l:7012 :0]        ib_iface.c:1269 UCX  ERROR mana_0: iface 0x5654af563750 failed to create UD QP TX wr:256 sge:6 inl:64 resp:0 RX wr:4096 sge:1 resp:0 failed: Operation not supported\n",
      "[1790952136.927168] [runnervm8df0l:7012 :0]      ucp_worker.c:1412 UCX  ERROR uct_iface_open(ud_verbs/mana_0:1) failed: Input/output error\n",
      "Derivative method: {deriv_method}\n",
      "rms =  0.5746942321200503\n",
      "rms_switch =  0.9999996748069234\n",
      "\n",
      "checking partials\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[runnervm8df0l:07012] pml_ucx.c:313  Error: Failed to create UCP worker\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">----------------------------------------------------------------------------------\n",
       "Component: RootMeanSquareSwitchComp '<span style=\"color: #00ffff; text-decoration-color: #00ffff; font-weight: bold\">counter</span>'\n",
       "----------------------------------------------------------------------------------\n",
       "\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+-------------------+\n",
       "| 'of' variable | 'wrt' variable | calc val @ max viol | fd val @ max viol | (calc-fd) - (a + r*fd) | error desc        |\n",
       "+===============+================+=====================+===================+========================+===================+\n",
       "| rms           | x              |        1.997398e-04 |      1.997486e-04 |           8.504969e-09 |  8.504969e-09&gt;TOL |\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+-------------------+\n",
       "| rms_switch    | x              |        8.181628e-07 |      8.183454e-07 |           1.817999e-10 |  1.817999e-10&gt;TOL |\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+-------------------+\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "----------------------------------------------------------------------------------\n",
       "Component: RootMeanSquareSwitchComp '\u001b[1;96mcounter\u001b[0m'\n",
       "----------------------------------------------------------------------------------\n",
       "\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+-------------------+\n",
       "| 'of' variable | 'wrt' variable | calc val @ max viol | fd val @ max viol | (calc-fd) - (a + r*fd) | error desc        |\n",
       "+===============+================+=====================+===================+========================+===================+\n",
       "| rms           | x              |        1.997398e-04 |      1.997486e-04 |           8.504969e-09 |  8.504969e-09>TOL |\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+-------------------+\n",
       "| rms_switch    | x              |        8.181628e-07 |      8.183454e-07 |           1.817999e-10 |  1.817999e-10>TOL |\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+-------------------+\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "#################################################################################\n",
      "Sub Jacobian with Largest Tolerance Violation: RootMeanSquareSwitchComp 'counter'\n",
      "#################################################################################\n",
      "+---------------+----------------+---------------------+-------------------+------------------------+-------------------+\n",
      "| 'of' variable | 'wrt' variable | calc val @ max viol | fd val @ max viol | (calc-fd) - (a + r*fd) | error desc        |\n",
      "+===============+================+=====================+===================+========================+===================+\n",
      "| rms           | x              |        1.997398e-04 |      1.997486e-04 |           8.504969e-09 |  8.504969e-09>TOL |\n",
      "+---------------+----------------+---------------------+-------------------+------------------------+-------------------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "N = 100\n",
    "np.random.seed(16)\n",
    "\n",
    "p = om.Problem()\n",
    "p.model.add_subsystem('counter', RootMeanSquareSwitchComp(vec_size=N),\n",
    "                      promotes_inputs=['x'], promotes_outputs=['rms', 'rms_switch'])\n",
    "\n",
    "\n",
    "p.setup(force_alloc_complex=True)\n",
    "p.set_val('x', np.random.random(N))\n",
    "p.run_model()\n",
    "\n",
    "print('Derivative method: {deriv_method}')\n",
    "print('rms = ', p.get_val('rms'))\n",
    "print('rms_switch = ', p.get_val('rms_switch'))\n",
    "\n",
    "print('\\nchecking partials')\n",
    "with np.printoptions(linewidth=1024):\n",
    "    cpd = p.check_partials(method='fd', compact_print=True)\n",
    "print()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aef56f31",
   "metadata": {
    "execution": {
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     "iopub.status.idle": "2026-10-02T14:42:17.405066Z",
     "shell.execute_reply": "2026-10-02T14:42:17.404306Z"
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     "end_time": "2026-10-02T14:42:17.405990+00:00",
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     "status": "completed"
    },
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "from openmdao.utils.assert_utils import assert_check_partials\n",
    "\n",
    "assert_check_partials(cpd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc8aae02",
   "metadata": {
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Example 2: A component with vector inputs and outputs\n",
    "\n",
    "A common pattern is to have a vectorized input and a corresponding vectorized output.\n",
    "For a simple vectorized calculation this will typically result in a diagonal jacobian, where the\n",
    "n-th element of the input only impacts the n-th element of the output.  JaxExplicitComponent\n",
    "will automatically detect the sparsity of the partial jacobian if we don't declare any partials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ef4be7f7",
   "metadata": {
    "execution": {
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     "status": "completed"
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   "outputs": [],
   "source": [
    "class SinCosComp(om.JaxExplicitComponent):\n",
    "\n",
    "    def initialize(self):\n",
    "        self.options.declare('vec_size', types=(int,))\n",
    "\n",
    "    def setup(self):\n",
    "        n = self.options['vec_size']\n",
    "        self.add_input('x', shape=(n,))\n",
    "        self.add_output('sin_cos_x', shape=(n,))\n",
    "\n",
    "        # We'll let jax automatically detect our partials and their sparsity by not declaring\n",
    "        # any partials.\n",
    "\n",
    "    # because we don't reference any static data in our compute_primal, we don't need to provide\n",
    "    # a get_self_statics method.\n",
    "\n",
    "    def compute_primal(self, x):\n",
    "        return jnp.sin(jnp.cos(x))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "55b8389e",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-10-02T14:42:17.652433Z"
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sin(cos(x)) =  [0.82779949 0.76190096 0.75270268 0.84090884 0.80497885 0.82782559\n",
      " 0.69760996 0.8341699 ]\n",
      "\n",
      "checking partials\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">----------------------------------------------------------------\n",
       "Component: SinCosComp '<span style=\"color: #00ffff; text-decoration-color: #00ffff; font-weight: bold\">scx</span>'\n",
       "----------------------------------------------------------------\n",
       "\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+------------+\n",
       "| 'of' variable | 'wrt' variable | calc val @ max viol | fd val @ max viol | (calc-fd) - (a + r*fd) | error desc |\n",
       "+===============+================+=====================+===================+========================+============+\n",
       "| sin_cos_x     | x              |       -0.000000e+00 |      0.000000e+00 |         (0.000000e+00) |            |\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+------------+\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "----------------------------------------------------------------\n",
       "Component: SinCosComp '\u001b[1;96mscx\u001b[0m'\n",
       "----------------------------------------------------------------\n",
       "\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+------------+\n",
       "| 'of' variable | 'wrt' variable | calc val @ max viol | fd val @ max viol | (calc-fd) - (a + r*fd) | error desc |\n",
       "+===============+================+=====================+===================+========================+============+\n",
       "| sin_cos_x     | x              |       -0.000000e+00 |      0.000000e+00 |         (0.000000e+00) |            |\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+------------+\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 8\n",
    "np.random.seed(16)\n",
    "\n",
    "p = om.Problem()\n",
    "scx = p.model.add_subsystem('scx', SinCosComp(vec_size=N),\n",
    "                             promotes_inputs=['x'], promotes_outputs=['sin_cos_x'])\n",
    "\n",
    "\n",
    "p.setup(force_alloc_complex=True)\n",
    "p.set_val('x', np.random.random(N))\n",
    "p.run_model()\n",
    "\n",
    "print('sin(cos(x)) = ', p.get_val('sin_cos_x'))\n",
    "\n",
    "print('\\nchecking partials')\n",
    "with np.printoptions(linewidth=1024):\n",
    "    cpd = p.check_partials(method='cs', compact_print=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c29a361b",
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     "status": "completed"
    },
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "assert_check_partials(cpd, atol=1.0E-5, rtol=1.0E-5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dddcf7dc",
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Example 3: A component with dynamically shaped inputs and outputs\n",
    "\n",
    "Jax can determine output shapes based on input shapes at runtime, so if no shape information is\n",
    "'hard wired' into your `compute_primal` method, you can use OpenMDAO's dynamic shaping capability\n",
    "to figure out the shapes automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bdf9fcfc",
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2026-10-02T14:42:17.673874Z",
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     "shell.execute_reply": "2026-10-02T14:42:17.892277Z"
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sin(cos(x)) =  [[0.69399366 0.77967794 0.82880194 0.78445882]\n",
      " [0.83750606 0.57094689 0.74718296 0.77748193]\n",
      " [0.81395648 0.84096616 0.66688464 0.75524207]]\n",
      "\n",
      "checking partials\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">-----------------------------------------------------------------------\n",
       "Component: SinCosDynamicComp '<span style=\"color: #00ffff; text-decoration-color: #00ffff; font-weight: bold\">scx</span>'\n",
       "-----------------------------------------------------------------------\n",
       "\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+------------+\n",
       "| 'of' variable | 'wrt' variable | calc val @ max viol | fd val @ max viol | (calc-fd) - (a + r*fd) | error desc |\n",
       "+===============+================+=====================+===================+========================+============+\n",
       "| sin_cos_x     | x              |       -0.000000e+00 |      0.000000e+00 |         (0.000000e+00) |            |\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+------------+\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "-----------------------------------------------------------------------\n",
       "Component: SinCosDynamicComp '\u001b[1;96mscx\u001b[0m'\n",
       "-----------------------------------------------------------------------\n",
       "\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+------------+\n",
       "| 'of' variable | 'wrt' variable | calc val @ max viol | fd val @ max viol | (calc-fd) - (a + r*fd) | error desc |\n",
       "+===============+================+=====================+===================+========================+============+\n",
       "| sin_cos_x     | x              |       -0.000000e+00 |      0.000000e+00 |         (0.000000e+00) |            |\n",
       "+---------------+----------------+---------------------+-------------------+------------------------+------------+\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "class SinCosDynamicComp(om.JaxExplicitComponent):\n",
    "\n",
    "    def setup(self):\n",
    "        self.add_input('x')\n",
    "        self.add_output('sin_cos_x')\n",
    "\n",
    "    def compute_primal(self, x):\n",
    "        return jnp.sin(jnp.cos(x))\n",
    "\n",
    "p = om.Problem()\n",
    "# by setting default_to_dyn_shapes to True, we tell OpenMDAO to use dynamic shapes by default\n",
    "# for any variables where we don't set a shape. Note that if you want to use this option and it is\n",
    "# not passed in when creating the component as it is in this case, you must set it BEFORE adding\n",
    "# any variables in your component's setup method. Otherwise it will be ignored.\n",
    "p.model.add_subsystem('scx', SinCosDynamicComp(default_to_dyn_shapes=True),\n",
    "                      promotes_inputs=['x'],\n",
    "                      promotes_outputs=['sin_cos_x'])\n",
    "\n",
    "p.setup(force_alloc_complex=True)\n",
    "p.set_val('x', np.random.random((3, 4)))\n",
    "p.run_model()\n",
    "\n",
    "print('sin(cos(x)) = ', p.get_val('sin_cos_x'))\n",
    "\n",
    "print('\\nchecking partials')\n",
    "with np.printoptions(linewidth=1024):\n",
    "    cpd = p.check_partials(method='cs', compact_print=True)\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "15aafa71",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-02T14:42:17.899732Z",
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     "shell.execute_reply": "2026-10-02T14:42:17.901784Z"
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     "status": "completed"
    },
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "from openmdao.utils.assert_utils import assert_check_partials\n",
    "\n",
    "assert_check_partials(cpd)"
   ]
  }
 ],
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