{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "f59b5184", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:30.274037Z", "iopub.status.busy": "2026-10-02T14:41:30.273825Z", "iopub.status.idle": "2026-10-02T14:41:30.278190Z", "shell.execute_reply": "2026-10-02T14:41:30.277612Z" }, "papermill": { "duration": 0.006897, "end_time": "2026-10-02T14:41:30.278830+00:00", "exception": false, "start_time": "2026-10-02T14:41:30.271933+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": "c7d87ff6", "metadata": { "papermill": { "duration": 0.001176, "end_time": "2026-10-02T14:41:30.281515+00:00", "exception": false, "start_time": "2026-10-02T14:41:30.280339+00:00", "status": "completed" }, "tags": [] }, "source": [ "# LinearSystemComp\n", "\n", "The LinearSystemComp solves the linear system Ax = b where A and b are inputs, and x is the output.\n", "\n", "## LinearSystemComp Options\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "18d2eb96", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:30.345941Z", "iopub.status.busy": "2026-10-02T14:41:30.345811Z", "iopub.status.idle": "2026-10-02T14:41:31.509003Z", "shell.execute_reply": "2026-10-02T14:41:31.508444Z" }, "papermill": { "duration": 1.227003, "end_time": "2026-10-02T14:41:31.509739+00:00", "exception": false, "start_time": "2026-10-02T14:41:30.282736+00:00", "status": "completed" }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", "\n", "\n", "

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OptionDefaultAcceptable ValuesAcceptable TypesDescription
always_optFalse[True, False]['bool']If True, force nonlinear operations on this component to be included in the optimization loop even if this component is not relevant to the design variables and responses.
assembled_jac_typeN/A['csc', 'csr', 'dense', None]N/ALinear solver(s) in this group or implicit component, if using an assembled jacobian, will use this type.
default_shape(1,)N/A['tuple']Default shape for variables that do not set val to a non-scalar value or set shape, shape_by_conn, copy_shape, or compute_shape. Default is (1,).
derivs_methodN/A['jax', 'cs', 'fd', None]N/AThe method to use for computing derivatives
distributedFalse[True, False]['bool']If True, set all variables in this component as distributed across multiple processes
run_root_onlyFalse[True, False]['bool']If True, call compute, compute_partials, linearize, apply_linear, apply_nonlinear, solve_linear, solve_nonlinear, and compute_jacvec_product only on rank 0 and broadcast the results to the other ranks.
size1N/A['int']The size of the linear system.
use_jitTrue[True, False]['bool']If True, attempt to use jit on compute_primal, assuming jax or some other AD package capable of jitting is active.
vec_size1N/A['int']Number of linear systems to solve.
vectorize_AFalse[True, False]['bool']Set to True to vectorize the A matrix.
\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import openmdao.api as om\n", "om.show_options_table(\"openmdao.components.linear_system_comp.LinearSystemComp\")" ] }, { "cell_type": "markdown", "id": "140c112d", "metadata": { "papermill": { "duration": 0.001411, "end_time": "2026-10-02T14:41:31.512805+00:00", "exception": false, "start_time": "2026-10-02T14:41:31.511394+00:00", "status": "completed" }, "tags": [] }, "source": [ "## LinearSystemComp Constructor\n", "\n", "The call signature for the `LinearSystemComp` constructor is:\n", "\n", "```{eval-rst}\n", " .. automethod:: openmdao.components.linear_system_comp.LinearSystemComp.__init__\n", " :noindex:\n", "```\n", "\n", "## LinearSystemComp Example\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "2ed92165", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:31.669095Z", "iopub.status.busy": "2026-10-02T14:41:31.668711Z", "iopub.status.idle": "2026-10-02T14:41:32.881620Z", "shell.execute_reply": "2026-10-02T14:41:32.880939Z" }, "papermill": { "duration": 1.216042, "end_time": "2026-10-02T14:41:32.882315+00:00", "exception": false, "start_time": "2026-10-02T14:41:31.666273+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1790952092.867845] [runnervm8df0l:6634 :0] ib_iface.c:1269 UCX ERROR mana_0: iface 0x5644c53664b0 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", "[1790952092.868118] [runnervm8df0l:6634 :0] ucp_worker.c:1412 UCX ERROR uct_iface_open(ud_verbs/mana_0:1) failed: Input/output error\n", "[ 0.36423841 -0.00662252 -0.4205298 ]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[runnervm8df0l:06634] pml_ucx.c:313 Error: Failed to create UCP worker\n" ] } ], "source": [ "import numpy as np\n", "import openmdao.api as om\n", "\n", "model = om.Group()\n", "\n", "A = np.array([[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])\n", "b = np.array([1.0, 2.0, -3.0])\n", "\n", "lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])\n", "lingrp.add_subsystem('lin', om.LinearSystemComp(size=3))\n", "\n", "prob = om.Problem(model)\n", "prob.setup()\n", "\n", "prob.set_val('lin.A', A)\n", "prob.set_val('lin.b', b)\n", "\n", "lingrp.linear_solver = om.ScipyKrylov()\n", "\n", "prob.run_model()\n", "\n", "print(prob.get_val('lin.x'))" ] }, { "cell_type": "code", "execution_count": 4, "id": "305e5494", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:32.885624Z", "iopub.status.busy": "2026-10-02T14:41:32.885469Z", "iopub.status.idle": "2026-10-02T14:41:32.889360Z", "shell.execute_reply": "2026-10-02T14:41:32.888716Z" }, "papermill": { "duration": 0.00618, "end_time": "2026-10-02T14:41:32.889824+00:00", "exception": false, "start_time": "2026-10-02T14:41:32.883644+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(6.71747714541678e-09)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from openmdao.utils.assert_utils import assert_near_equal\n", "\n", "assert_near_equal(prob.get_val('lin.x'), np.array([0.36423841, -0.00662252, -0.4205298 ]), .0001)" ] }, { "cell_type": "markdown", "id": "04880f1f", "metadata": { "papermill": { "duration": 0.001891, "end_time": "2026-10-02T14:41:32.905790+00:00", "exception": false, "start_time": "2026-10-02T14:41:32.903899+00:00", "status": "completed" }, "tags": [] }, "source": [ "This component can also be vectorized to either solve a single linear system with multiple right hand sides, or to solve multiple independent linear systems.\n", "\n", "You can solve multiple right hand sides by setting the \"vec_size\" argument, giving it the number of right hand sides. When you do this, the LinearSystemComp creates an input for \"b\" such that each row of b is solved independently." ] }, { "cell_type": "code", "execution_count": 5, "id": "b5cee228", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:32.965279Z", "iopub.status.busy": "2026-10-02T14:41:32.965097Z", "iopub.status.idle": "2026-10-02T14:41:32.973130Z", "shell.execute_reply": "2026-10-02T14:41:32.972412Z" }, "papermill": { "duration": 0.066319, "end_time": "2026-10-02T14:41:32.973645+00:00", "exception": false, "start_time": "2026-10-02T14:41:32.907326+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.10596026 -0.16556291 0.48675497]\n", " [ 0.19205298 -0.11258278 -0.14900662]]\n" ] } ], "source": [ "model = om.Group()\n", "\n", "A = np.array([[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])\n", "b = np.array([[2.0, -3.0, 4.0], [1.0, 0.0, -1.0]])\n", "\n", "lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])\n", "lingrp.add_subsystem('lin', om.LinearSystemComp(size=3, vec_size=2))\n", "\n", "prob = om.Problem(model)\n", "prob.setup()\n", "\n", "prob.set_val('lin.A', A)\n", "prob.set_val('lin.b', b)\n", "\n", "lingrp.linear_solver = om.ScipyKrylov()\n", "\n", "prob.run_model()\n", "\n", "print(prob.get_val('lin.x'))" ] }, { "cell_type": "code", "execution_count": 6, "id": "88e5f616", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:32.977186Z", "iopub.status.busy": "2026-10-02T14:41:32.977017Z", "iopub.status.idle": "2026-10-02T14:41:32.981121Z", "shell.execute_reply": "2026-10-02T14:41:32.980439Z" }, "papermill": { "duration": 0.006797, "end_time": "2026-10-02T14:41:32.981593+00:00", "exception": false, "start_time": "2026-10-02T14:41:32.974796+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(1.2860374400409043e-08)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assert_near_equal(prob.get_val('lin.x'), np.array([[ 0.10596026, -0.16556291, 0.48675497],\n", " [ 0.19205298, -0.11258278, -0.14900662]]), .0001)" ] }, { "cell_type": "markdown", "id": "38b9dc7a", "metadata": { "papermill": { "duration": 0.001466, "end_time": "2026-10-02T14:41:32.984589+00:00", "exception": false, "start_time": "2026-10-02T14:41:32.983123+00:00", "status": "completed" }, "tags": [] }, "source": [ "To solve multiple linear systems, you just need to set the \"vectorize_A\" option or argument to True. The A\n", "matrix is now a 3-dimensional matrix where the first dimension is the number of linear systems to solve." ] }, { "cell_type": "code", "execution_count": 7, "id": "5c3981c7", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:33.049757Z", "iopub.status.busy": "2026-10-02T14:41:33.049544Z", "iopub.status.idle": "2026-10-02T14:41:33.057732Z", "shell.execute_reply": "2026-10-02T14:41:33.057040Z" }, "papermill": { "duration": 0.072141, "end_time": "2026-10-02T14:41:33.058218+00:00", "exception": false, "start_time": "2026-10-02T14:41:32.986077+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.78807947 0.66887417 0.47350993]\n", " [ 0.7 -1.8 0.75 ]]\n" ] } ], "source": [ "model = om.Group()\n", "\n", "A = np.array([[[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]],\n", " [[2.0, 3.0, 4.0], [1.0, -1.0, -2.0], [3.0, 2.0, -2.0]]])\n", "b = np.array([[-5.0, 2.0, 3.0], [-1.0, 1.0, -3.0]])\n", "\n", "lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])\n", "lingrp.add_subsystem('lin', om.LinearSystemComp(size=3, vec_size=2, vectorize_A=True))\n", "\n", "prob = om.Problem(model)\n", "prob.setup()\n", "\n", "prob.set_val('lin.A', A)\n", "prob.set_val('lin.b', b)\n", "\n", "lingrp.linear_solver = om.ScipyKrylov()\n", "\n", "prob.run_model()\n", "\n", "print(prob.get_val('lin.x'))" ] }, { "cell_type": "code", "execution_count": 8, "id": "eaa916f1", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:33.118677Z", "iopub.status.busy": "2026-10-02T14:41:33.118441Z", "iopub.status.idle": "2026-10-02T14:41:33.123455Z", "shell.execute_reply": "2026-10-02T14:41:33.122827Z" }, "papermill": { "duration": 0.064162, "end_time": "2026-10-02T14:41:33.123981+00:00", "exception": false, "start_time": "2026-10-02T14:41:33.059819+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(1.8475641795162215e-09)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assert_near_equal(prob.get_val('lin.x'), np.array([[-0.78807947, 0.66887417, 0.47350993],\n", " [ 0.7 , -1.8 , 0.75 ]]),\n", " .0001)" ] } ], "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": 4.226448, "end_time": "2026-10-02T14:41:33.842091+00:00", "environment_variables": {}, "exception": null, "input_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/openmdao_book/features/building_blocks/components/linearsystem_comp.ipynb", "output_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/_executed_book/features/building_blocks/components/linearsystem_comp.ipynb", "parameters": {}, "start_time": "2026-10-02T14:41:29.615643+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }