{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "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",
   "metadata": {},
   "source": [
    "# DirectSolver\n",
    "\n",
    "DirectSolver is a linear solver that assembles the system Jacobian and solves the linear\n",
    "system with LU factorization and back substitution. It can handle any system topology. Since it\n",
    "assembles a global Jacobian for all of its subsystems, any linear solver that is assigned in\n",
    "any of its subsystems does not participate in this calculation (though they may be used in other\n",
    "ways such as in subsystem Newton solves.)\n",
    "\n",
    "Here we calculate the total derivatives of the Sellar system objective with respect to the design\n",
    "variable 'z'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "from openmdao.utils.notebook_utils import get_code\n",
    "from myst_nb import glue\n",
    "glue(\"code_src23\", get_code(\"openmdao.test_suite.components.sellar_feature.SellarDerivatives\"), display=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{Admonition} `SellarDerivatives` class definition \n",
    ":class: dropdown\n",
    "\n",
    "{glue:}`code_src23`\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import openmdao.api as om\n",
    "from openmdao.test_suite.components.sellar_feature import SellarDerivatives\n",
    "\n",
    "prob = om.Problem()\n",
    "model = prob.model = SellarDerivatives()\n",
    "\n",
    "model.nonlinear_solver=om.NonlinearBlockGS()\n",
    "model.linear_solver = om.DirectSolver()\n",
    "\n",
    "prob.setup()\n",
    "prob.run_model()\n",
    "\n",
    "wrt = ['z']\n",
    "of = ['obj']\n",
    "\n",
    "J = prob.compute_totals(of=of, wrt=wrt, return_format='flat_dict')\n",
    "print(J['obj', 'z'][0][0])\n",
    "print(J['obj', 'z'][0][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input",
     "remove-output"
    ]
   },
   "outputs": [],
   "source": [
    "from openmdao.utils.assert_utils import assert_near_equal\n",
    "\n",
    "assert_near_equal(J['obj', 'z'][0][0], 9.61001056, .00001)\n",
    "assert_near_equal(J['obj', 'z'][0][1], 1.78448534, .00001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DirectSolver Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "om.show_options_table(\"openmdao.solvers.linear.direct.DirectSolver\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DirectSolver Constructor\n",
    "\n",
    "The call signature for the `DirectSolver` constructor is:\n",
    "\n",
    "```{eval-rst}\n",
    "    .. automethod:: openmdao.solvers.linear.direct.DirectSolver.__init__\n",
    "        :noindex:\n",
    "```"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.5"
  },
  "orphan": true
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
