{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "6162f304", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:36.938353Z", "iopub.status.busy": "2026-10-02T14:42:36.938070Z", "iopub.status.idle": "2026-10-02T14:42:36.944058Z", "shell.execute_reply": "2026-10-02T14:42:36.942862Z" }, "papermill": { "duration": 0.00945, "end_time": "2026-10-02T14:42:36.944768+00:00", "exception": false, "start_time": "2026-10-02T14:42:36.935318+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": "837ff7e1", "metadata": { "papermill": { "duration": 0.001191, "end_time": "2026-10-02T14:42:36.947471+00:00", "exception": false, "start_time": "2026-10-02T14:42:36.946280+00:00", "status": "completed" }, "tags": [] }, "source": [ "# LinearRunOnce\n", "\n", "The simplest linear solver in OpenMDAO is LinearRunOnce, which sequentially calls `apply_linear`\n", "and `solve_linear` once on each subsystem. It is directly analogous to applying a single pass of the\n", "chain rule to the whole system without any iteration at the top level. This linear solver can only be\n", "used in systems where the following conditions are satisfied:\n", "\n", "1. System does not contain a cycle, though subsystems may.\n", "2. System does not contain any implicit states, though subsystems may.\n", "\n", "However, subsystems can contain cycles or implicit states, provided that they are using the appropriate\n", "solver such as [ScipyKrylov](../../../_srcdocs/packages/solvers.linear/scipy_iter_solver).\n", "\n", "Here is an example of using LinearRunOnce to calculate the derivatives across a simple model with\n", "the `Paraboloid` component." ] }, { "cell_type": "code", "execution_count": 2, "id": "346323a9", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:37.004718Z", "iopub.status.busy": "2026-10-02T14:42:37.004424Z", "iopub.status.idle": "2026-10-02T14:42:38.894628Z", "shell.execute_reply": "2026-10-02T14:42:38.893922Z" }, "papermill": { "duration": 1.946324, "end_time": "2026-10-02T14:42:38.895119+00:00", "exception": false, "start_time": "2026-10-02T14:42:36.948795+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "application/papermill.record/text/html": "
class Paraboloid(om.ExplicitComponent):\n    """\n    Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3.\n    """\n\n    def setup(self):\n        self.add_input('x', val=0.0)\n        self.add_input('y', val=0.0)\n\n        self.add_output('f_xy', val=0.0)\n\n    def setup_partials(self):\n        self.declare_partials('*', '*')\n\n    def compute(self, inputs, outputs):\n        """\n        f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3\n\n        Optimal solution (minimum): x = 6.6667; y = -7.3333\n        """\n        x = inputs['x']\n        y = inputs['y']\n\n        outputs['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0\n\n    def compute_partials(self, inputs, partials):\n        """\n        Jacobian for our paraboloid.\n        """\n        x = inputs['x']\n        y = inputs['y']\n\n        partials['f_xy', 'x'] = 2.0*x - 6.0 + y\n        partials['f_xy', 'y'] = 2.0*y + 8.0 + x\n
\n", "application/papermill.record/text/latex": "\\begin{Verbatim}[commandchars=\\\\\\{\\}]\n\\PY{k}{class}\\PY{+w}{ }\\PY{n+nc}{Paraboloid}\\PY{p}{(}\\PY{n}{om}\\PY{o}{.}\\PY{n}{ExplicitComponent}\\PY{p}{)}\\PY{p}{:}\n\\PY{+w}{ }\\PY{l+s+sd}{\\PYZdq{}\\PYZdq{}\\PYZdq{}}\n\\PY{l+s+sd}{ Evaluates the equation f(x,y) = (x\\PYZhy{}3)\\PYZca{}2 + xy + (y+4)\\PYZca{}2 \\PYZhy{} 3.}\n\\PY{l+s+sd}{ \\PYZdq{}\\PYZdq{}\\PYZdq{}}\n\n \\PY{k}{def}\\PY{+w}{ }\\PY{n+nf}{setup}\\PY{p}{(}\\PY{n+nb+bp}{self}\\PY{p}{)}\\PY{p}{:}\n \\PY{n+nb+bp}{self}\\PY{o}{.}\\PY{n}{add\\PYZus{}input}\\PY{p}{(}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{n}{val}\\PY{o}{=}\\PY{l+m+mf}{0.0}\\PY{p}{)}\n \\PY{n+nb+bp}{self}\\PY{o}{.}\\PY{n}{add\\PYZus{}input}\\PY{p}{(}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{y}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{n}{val}\\PY{o}{=}\\PY{l+m+mf}{0.0}\\PY{p}{)}\n\n \\PY{n+nb+bp}{self}\\PY{o}{.}\\PY{n}{add\\PYZus{}output}\\PY{p}{(}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f\\PYZus{}xy}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{n}{val}\\PY{o}{=}\\PY{l+m+mf}{0.0}\\PY{p}{)}\n\n \\PY{k}{def}\\PY{+w}{ }\\PY{n+nf}{setup\\PYZus{}partials}\\PY{p}{(}\\PY{n+nb+bp}{self}\\PY{p}{)}\\PY{p}{:}\n \\PY{n+nb+bp}{self}\\PY{o}{.}\\PY{n}{declare\\PYZus{}partials}\\PY{p}{(}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{*}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{*}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{)}\n\n \\PY{k}{def}\\PY{+w}{ }\\PY{n+nf}{compute}\\PY{p}{(}\\PY{n+nb+bp}{self}\\PY{p}{,} \\PY{n}{inputs}\\PY{p}{,} \\PY{n}{outputs}\\PY{p}{)}\\PY{p}{:}\n\\PY{+w}{ }\\PY{l+s+sd}{\\PYZdq{}\\PYZdq{}\\PYZdq{}}\n\\PY{l+s+sd}{ f(x,y) = (x\\PYZhy{}3)\\PYZca{}2 + xy + (y+4)\\PYZca{}2 \\PYZhy{} 3}\n\n\\PY{l+s+sd}{ Optimal solution (minimum): x = 6.6667; y = \\PYZhy{}7.3333}\n\\PY{l+s+sd}{ \\PYZdq{}\\PYZdq{}\\PYZdq{}}\n \\PY{n}{x} \\PY{o}{=} \\PY{n}{inputs}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]}\n \\PY{n}{y} \\PY{o}{=} \\PY{n}{inputs}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{y}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]}\n\n \\PY{n}{outputs}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f\\PYZus{}xy}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]} \\PY{o}{=} \\PY{p}{(}\\PY{n}{x}\\PY{o}{\\PYZhy{}}\\PY{l+m+mf}{3.0}\\PY{p}{)}\\PY{o}{*}\\PY{o}{*}\\PY{l+m+mi}{2} \\PY{o}{+} \\PY{n}{x}\\PY{o}{*}\\PY{n}{y} \\PY{o}{+} \\PY{p}{(}\\PY{n}{y}\\PY{o}{+}\\PY{l+m+mf}{4.0}\\PY{p}{)}\\PY{o}{*}\\PY{o}{*}\\PY{l+m+mi}{2} \\PY{o}{\\PYZhy{}} \\PY{l+m+mf}{3.0}\n\n \\PY{k}{def}\\PY{+w}{ }\\PY{n+nf}{compute\\PYZus{}partials}\\PY{p}{(}\\PY{n+nb+bp}{self}\\PY{p}{,} \\PY{n}{inputs}\\PY{p}{,} \\PY{n}{partials}\\PY{p}{)}\\PY{p}{:}\n\\PY{+w}{ }\\PY{l+s+sd}{\\PYZdq{}\\PYZdq{}\\PYZdq{}}\n\\PY{l+s+sd}{ Jacobian for our paraboloid.}\n\\PY{l+s+sd}{ \\PYZdq{}\\PYZdq{}\\PYZdq{}}\n \\PY{n}{x} \\PY{o}{=} \\PY{n}{inputs}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]}\n \\PY{n}{y} \\PY{o}{=} \\PY{n}{inputs}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{y}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]}\n\n \\PY{n}{partials}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f\\PYZus{}xy}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{x}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]} \\PY{o}{=} \\PY{l+m+mf}{2.0}\\PY{o}{*}\\PY{n}{x} \\PY{o}{\\PYZhy{}} \\PY{l+m+mf}{6.0} \\PY{o}{+} \\PY{n}{y}\n \\PY{n}{partials}\\PY{p}{[}\\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{f\\PYZus{}xy}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{,} \\PY{l+s+s1}{\\PYZsq{}}\\PY{l+s+s1}{y}\\PY{l+s+s1}{\\PYZsq{}}\\PY{p}{]} \\PY{o}{=} \\PY{l+m+mf}{2.0}\\PY{o}{*}\\PY{n}{y} \\PY{o}{+} \\PY{l+m+mf}{8.0} \\PY{o}{+} \\PY{n}{x}\n\\end{Verbatim}\n", "application/papermill.record/text/plain": "class Paraboloid(om.ExplicitComponent):\n \"\"\"\n Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3.\n \"\"\"\n\n def setup(self):\n self.add_input('x', val=0.0)\n self.add_input('y', val=0.0)\n\n self.add_output('f_xy', val=0.0)\n\n def setup_partials(self):\n self.declare_partials('*', '*')\n\n def compute(self, inputs, outputs):\n \"\"\"\n f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3\n\n Optimal solution (minimum): x = 6.6667; y = -7.3333\n \"\"\"\n x = inputs['x']\n y = inputs['y']\n\n outputs['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0\n\n def compute_partials(self, inputs, partials):\n \"\"\"\n Jacobian for our paraboloid.\n \"\"\"\n x = inputs['x']\n y = inputs['y']\n\n partials['f_xy', 'x'] = 2.0*x - 6.0 + y\n partials['f_xy', 'y'] = 2.0*y + 8.0 + x" }, "metadata": { "scrapbook": { "mime_prefix": "application/papermill.record/", "name": "code_src28" } }, "output_type": "display_data" } ], "source": [ "from openmdao.utils.notebook_utils import get_code\n", "from myst_nb import glue\n", "glue(\"code_src28\", get_code(\"openmdao.test_suite.components.paraboloid.Paraboloid\"), display=False)" ] }, { "cell_type": "markdown", "id": "d81ad03b", "metadata": { "papermill": { "duration": 0.000907, "end_time": "2026-10-02T14:42:38.897222+00:00", "exception": false, "start_time": "2026-10-02T14:42:38.896315+00:00", "status": "completed" }, "tags": [] }, "source": [ ":::{dropdown} `Paraboloid` class definition \n", "\n", "{glue:}`code_src28`\n", ":::" ] }, { "cell_type": "code", "execution_count": 3, "id": "fbb3c81d", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:38.900672Z", "iopub.status.busy": "2026-10-02T14:42:38.900495Z", "iopub.status.idle": "2026-10-02T14:42:40.162033Z", "shell.execute_reply": "2026-10-02T14:42:40.161206Z" }, "papermill": { "duration": 1.265481, "end_time": "2026-10-02T14:42:40.164402+00:00", "exception": false, "start_time": "2026-10-02T14:42:38.898921+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1790952160.110898] [runnervm8df0l:7209 :0] ib_iface.c:1269 UCX ERROR mana_0: iface 0x556a251a8100 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", "[1790952160.111148] [runnervm8df0l:7209 :0] ucp_worker.c:1412 UCX ERROR uct_iface_open(ud_verbs/mana_0:1) failed: Input/output error\n", "[[-6.]] [[-6.0]]\n", "[[8.]] [[8.0]]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[runnervm8df0l:07209] pml_ucx.c:313 Error: Failed to create UCP worker\n" ] } ], "source": [ "import openmdao.api as om\n", "from openmdao.test_suite.components.paraboloid import Paraboloid\n", "\n", "prob = om.Problem()\n", "model = prob.model\n", "\n", "model.add_subsystem('comp', Paraboloid(), promotes=['x', 'y', 'f_xy'])\n", "\n", "model.linear_solver = om.LinearRunOnce()\n", "\n", "prob.setup(check=False, mode='fwd')\n", "\n", "prob.set_val('x', 0.0)\n", "prob.set_val('y', 0.0)\n", "\n", "prob.run_model()\n", "\n", "of = ['f_xy']\n", "wrt = ['x', 'y']\n", "derivs = prob.compute_totals(of=of, wrt=wrt, return_format='dict')\n", "\n", "print(derivs['f_xy']['x'], [[-6.0]])\n", "print(derivs['f_xy']['y'], [[8.0]])" ] }, { "cell_type": "code", "execution_count": 4, "id": "060e952c", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:40.169045Z", "iopub.status.busy": "2026-10-02T14:42:40.168618Z", "iopub.status.idle": "2026-10-02T14:42:40.175295Z", "shell.execute_reply": "2026-10-02T14:42:40.174543Z" }, "papermill": { "duration": 0.009842, "end_time": "2026-10-02T14:42:40.176054+00:00", "exception": false, "start_time": "2026-10-02T14:42:40.166212+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.0)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from openmdao.utils.assert_utils import assert_near_equal\n", "\n", "assert_near_equal(derivs['f_xy']['x'], [[-6.0]], 1e-6)\n", "assert_near_equal(derivs['f_xy']['y'], [[8.0]], 1e-6)" ] }, { "cell_type": "markdown", "id": "f8a6ae38", "metadata": { "papermill": { "duration": 0.002429, "end_time": "2026-10-02T14:42:40.180167+00:00", "exception": false, "start_time": "2026-10-02T14:42:40.177738+00:00", "status": "completed" }, "tags": [] }, "source": [ "## LinearRunOnce Options" ] }, { "cell_type": "code", "execution_count": 5, "id": "cfe03110", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:40.183842Z", "iopub.status.busy": "2026-10-02T14:42:40.183637Z", "iopub.status.idle": "2026-10-02T14:42:40.188684Z", "shell.execute_reply": "2026-10-02T14:42:40.188108Z" }, "papermill": { "duration": 0.007672, "end_time": "2026-10-02T14:42:40.189194+00:00", "exception": false, "start_time": "2026-10-02T14:42:40.181522+00:00", "status": "completed" }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", "\n", "\n", "

\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
OptionDefaultAcceptable ValuesAcceptable TypesDescription
aitken_initial_factor1.0N/AN/Ainitial value for Aitken relaxation factor
aitken_max_factor1.5N/AN/Aupper limit for Aitken relaxation factor
aitken_min_factor0.1N/AN/Alower limit for Aitken relaxation factor
assemble_jacFalse[True, False]['bool']Activates use of assembled jacobian by this solver.
iprint1N/A['int']whether to print output
use_aitkenFalse[True, False]['bool']set to True to use Aitken relaxation
\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "om.show_options_table(\"openmdao.solvers.linear.linear_runonce.LinearRunOnce\")" ] }, { "cell_type": "markdown", "id": "828fe8d0", "metadata": { "papermill": { "duration": 0.001815, "end_time": "2026-10-02T14:42:40.192554+00:00", "exception": false, "start_time": "2026-10-02T14:42:40.190739+00:00", "status": "completed" }, "tags": [] }, "source": [ "## LinearRunOnce Constructor\n", "\n", "The call signature for the `LinearRunOnce` constructor is:\n", "\n", "```{eval-rst}\n", " .. automethod:: openmdao.solvers.linear.linear_runonce.LinearRunOnce.__init__\n", " :noindex:\n", "```" ] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3", "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": "3.13.14" }, "orphan": true, "papermill": { "default_parameters": {}, "duration": 4.704035, "end_time": "2026-10-02T14:42:41.010073+00:00", "environment_variables": {}, "exception": null, "input_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/openmdao_book/features/building_blocks/solvers/linear_runonce.ipynb", "output_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/_executed_book/features/building_blocks/solvers/linear_runonce.ipynb", "parameters": {}, "start_time": "2026-10-02T14:42:36.306038+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }