{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "9cfc09f6", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:28.880064Z", "iopub.status.busy": "2026-10-02T14:42:28.879830Z", "iopub.status.idle": "2026-10-02T14:42:28.884801Z", "shell.execute_reply": "2026-10-02T14:42:28.884003Z" }, "papermill": { "duration": 0.007612, "end_time": "2026-10-02T14:42:28.885333+00:00", "exception": false, "start_time": "2026-10-02T14:42:28.877721+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": "d11eb76c", "metadata": { "papermill": { "duration": 0.000745, "end_time": "2026-10-02T14:42:28.887072+00:00", "exception": false, "start_time": "2026-10-02T14:42:28.886327+00:00", "status": "completed" }, "tags": [] }, "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": 2, "id": "e8cf498e", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:28.889955Z", "iopub.status.busy": "2026-10-02T14:42:28.889779Z", "iopub.status.idle": "2026-10-02T14:42:31.287922Z", "shell.execute_reply": "2026-10-02T14:42:31.287203Z" }, "papermill": { "duration": 2.400436, "end_time": "2026-10-02T14:42:31.288519+00:00", "exception": false, "start_time": "2026-10-02T14:42:28.888083+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "application/papermill.record/text/html": "
class SellarDerivatives(om.Group):\n    """\n    Group containing the Sellar MDA. This version uses the disciplines with derivatives.\n    """\n\n    def setup(self):\n        self.add_subsystem('d1', SellarDis1withDerivatives(), promotes=['x', 'z', 'y1', 'y2'])\n        self.add_subsystem('d2', SellarDis2withDerivatives(), promotes=['z', 'y1', 'y2'])\n\n        self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', obj=0.0,\n                                                  x=0.0, z=np.array([0.0, 0.0]), y1=0.0, y2=0.0),\n                           promotes=['obj', 'x', 'z', 'y1', 'y2'])\n\n        self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1', con1=0.0, y1=0.0),\n                           promotes=['con1', 'y1'])\n        self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0', con2=0.0, y2=0.0),\n                           promotes=['con2', 'y2'])\n\n        self.set_input_defaults('x', 1.0)\n        self.set_input_defaults('z', np.array([5.0, 2.0]))\n
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This version uses the disciplines with derivatives.\n \"\"\"\n\n def setup(self):\n self.add_subsystem('d1', SellarDis1withDerivatives(), promotes=['x', 'z', 'y1', 'y2'])\n self.add_subsystem('d2', SellarDis2withDerivatives(), promotes=['z', 'y1', 'y2'])\n\n self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', obj=0.0,\n x=0.0, z=np.array([0.0, 0.0]), y1=0.0, y2=0.0),\n promotes=['obj', 'x', 'z', 'y1', 'y2'])\n\n self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1', con1=0.0, y1=0.0),\n promotes=['con1', 'y1'])\n self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0', con2=0.0, y2=0.0),\n promotes=['con2', 'y2'])\n\n self.set_input_defaults('x', 1.0)\n self.set_input_defaults('z', np.array([5.0, 2.0]))" }, "metadata": { "scrapbook": { "mime_prefix": "application/papermill.record/", "name": "code_src23" } }, "output_type": "display_data" } ], "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", "id": "7cf7165e", "metadata": { "papermill": { "duration": 0.139785, "end_time": "2026-10-02T14:42:31.429541+00:00", "exception": false, "start_time": "2026-10-02T14:42:31.289756+00:00", "status": "completed" }, "tags": [] }, "source": [ ":::{dropdown} `SellarDerivatives` class definition \n", "\n", "{glue:}`code_src23`\n", ":::" ] }, { "cell_type": "code", "execution_count": 3, "id": "74553eb5", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:31.433422Z", "iopub.status.busy": "2026-10-02T14:42:31.433162Z", "iopub.status.idle": "2026-10-02T14:42:32.705009Z", "shell.execute_reply": "2026-10-02T14:42:32.704271Z" }, "papermill": { "duration": 1.274442, "end_time": "2026-10-02T14:42:32.705511+00:00", "exception": false, "start_time": "2026-10-02T14:42:31.431069+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1790952152.658878] [runnervm8df0l:7145 :0] ib_iface.c:1269 UCX ERROR mana_0: iface 0x55c815883ca0 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", "[1790952152.659139] [runnervm8df0l:7145 :0] ucp_worker.c:1412 UCX ERROR uct_iface_open(ud_verbs/mana_0:1) failed: Input/output error\n", "NL: NLBGS Converged in 8 iterations\n", "9.61001055698995\n", "1.7844853356313652\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[runnervm8df0l:07145] pml_ucx.c:313 Error: Failed to create UCP worker\n", "/home/runner/work/OpenMDAO/OpenMDAO/.pixi/envs/dev/lib/python3.13/site-packages/openmdao/utils/relevance.py:1232: OpenMDAOWarning:The top level group has a nonlinear solver that computes gradients, so the entire model will be included in the optimization iteration.\n" ] } ], "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": 4, "id": "c5919a34", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:32.708920Z", "iopub.status.busy": "2026-10-02T14:42:32.708586Z", "iopub.status.idle": "2026-10-02T14:42:32.714259Z", "shell.execute_reply": "2026-10-02T14:42:32.713199Z" }, "papermill": { "duration": 0.008395, "end_time": "2026-10-02T14:42:32.715166+00:00", "exception": false, "start_time": "2026-10-02T14:42:32.706771+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(2.448120300755809e-09)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "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", "id": "fd642ff5", "metadata": { "papermill": { "duration": 0.001107, "end_time": "2026-10-02T14:42:32.717402+00:00", "exception": false, "start_time": "2026-10-02T14:42:32.716295+00:00", "status": "completed" }, "tags": [] }, "source": [ "## DirectSolver Options" ] }, { "cell_type": "code", "execution_count": 5, "id": "c95a6f56", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:42:32.720444Z", "iopub.status.busy": "2026-10-02T14:42:32.720276Z", "iopub.status.idle": "2026-10-02T14:42:32.724341Z", "shell.execute_reply": "2026-10-02T14:42:32.723628Z" }, "papermill": { "duration": 0.006286, "end_time": "2026-10-02T14:42:32.724835+00:00", "exception": false, "start_time": "2026-10-02T14:42:32.718549+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", "
OptionDefaultAcceptable ValuesAcceptable TypesDescription
assemble_jacTrue[True, False]['bool']Activates use of assembled jacobian by this solver.
err_on_singularTrue[True, False]['bool']Raise an error if LU decomposition is singular.
iprint1N/A['int']whether to print output
rhs_checkingFalseN/A['bool', 'dict']If True, check RHS vs. cache and/or zero to avoid some solves.Can also be set to a dict of options for the LinearRHSChecker to allow finer control over it. Allowed options are: ('check_zero', 'rtol', 'atol', 'max_cache_entries', 'collect_stats', 'auto', 'verbose')
\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "om.show_options_table(\"openmdao.solvers.linear.direct.DirectSolver\")" ] }, { "cell_type": "markdown", "id": "708f513b", "metadata": { "papermill": { "duration": 0.00144, "end_time": "2026-10-02T14:42:32.727425+00:00", "exception": false, "start_time": "2026-10-02T14:42:32.725985+00:00", "status": "completed" }, "tags": [] }, "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": "3.13.14" }, "orphan": true, "papermill": { "default_parameters": {}, "duration": 5.239461, "end_time": "2026-10-02T14:42:33.444856+00:00", "environment_variables": {}, "exception": null, "input_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/openmdao_book/features/building_blocks/solvers/direct_solver.ipynb", "output_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/_executed_book/features/building_blocks/solvers/direct_solver.ipynb", "parameters": {}, "start_time": "2026-10-02T14:42:28.205395+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }