{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "7fc4d3a7", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:10.281632Z", "iopub.status.busy": "2026-10-02T14:41:10.281269Z", "iopub.status.idle": "2026-10-02T14:41:10.286312Z", "shell.execute_reply": "2026-10-02T14:41:10.285500Z" }, "papermill": { "duration": 0.00808, "end_time": "2026-10-02T14:41:10.286958+00:00", "exception": false, "start_time": "2026-10-02T14:41:10.278878+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": "92038a6c", "metadata": { "papermill": { "duration": 0.001246, "end_time": "2026-10-02T14:41:10.289788+00:00", "exception": false, "start_time": "2026-10-02T14:41:10.288542+00:00", "status": "completed" }, "tags": [] }, "source": [ "# CrossProductComp\n", "\n", "`CrossProductComp` performs a cross product between two 3-vector inputs. It may be vectorized to provide the result at one or more points simultaneously.\n", "\n", "$$\n", " c_i = \\bar{a}_i \\times \\bar{b}_i\n", "$$\n", "\n", "The first dimension of the inputs holds the vectorized dimension.\n", "The default `vec_size` is 1, providing the cross product of $a$ and $b$ at a single\n", "point. The lengths of $a$ and $b$ at each point must be 3.\n", "\n", "The shape of $a$ and $b$ will always be `(vec_size, 3)`, but the connection rules\n", "of OpenMDAO allow the incoming connection to have shape `(3,)` when `vec_size` is 1, since\n", "the storage order of the underlying data is the same. The output vector `c` of\n", "CrossProductComp will always have shape `(vec_size, 3)`.\n", "\n", "## CrossProductComp Options\n", "\n", "Options for CrossProductComp allow the user to rename the input variables $a$ and $b$ and the output $c$, as well as specifying their units." ] }, { "cell_type": "code", "execution_count": 2, "id": "55519766", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:10.293305Z", "iopub.status.busy": "2026-10-02T14:41:10.293125Z", "iopub.status.idle": "2026-10-02T14:41:11.661006Z", "shell.execute_reply": "2026-10-02T14:41:11.660402Z" }, "papermill": { "duration": 1.37056, "end_time": "2026-10-02T14:41:11.661530+00:00", "exception": false, "start_time": "2026-10-02T14:41:10.290970+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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
OptionDefaultAcceptable ValuesAcceptable TypesDescription
a_nameaN/A['str']The variable name for vector a.
a_unitsN/AN/A['str']The units for vector a.
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.
b_namebN/A['str']The variable name for vector b.
b_unitsN/AN/A['str']The units for vector b.
c_namecN/A['str']The variable name for vector c.
c_unitsN/AN/A['str']The units for vector c.
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.
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']The number of points at which the cross product is computed
\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import openmdao.api as om\n", "om.show_options_table(\"openmdao.components.cross_product_comp.CrossProductComp\")" ] }, { "cell_type": "markdown", "id": "c00855f8", "metadata": { "papermill": { "duration": 0.00088, "end_time": "2026-10-02T14:41:11.663598+00:00", "exception": false, "start_time": "2026-10-02T14:41:11.662718+00:00", "status": "completed" }, "tags": [] }, "source": [ "## CrossProductComp Constructor\n", "\n", "The call signature for the `CrossProductComp` constructor is:\n", "\n", "```{eval-rst}\n", " .. automethod:: openmdao.components.cross_product_comp.CrossProductComp.__init__\n", " :noindex:\n", "```\n", "\n", "## CrossProductComp Usage\n", "\n", "There are often situations when numerous products need to be computed, essentially in parallel.\n", "You can reduce the number of components required by having one `CrossProductComp` perform multiple operations.\n", "This is also convenient when the different operations have common inputs.\n", "\n", "The `add_product` method is used to create additional products after instantiation.\n", "\n", "```{eval-rst}\n", " .. automethod:: openmdao.components.cross_product_comp.CrossProductComp.add_product\n", " :noindex:\n", "```\n", "\n", "## CrossProductComp Example\n", "\n", "In the following example CrossProductComp is used to compute torque as the\n", "cross product of force ($F$) and radius ($r$) at 100 points simultaneously.\n", "Note the use of `a_name`, `b_name`, and `c_name` to assign names to the inputs and outputs.\n", "Units are assigned using `a_units`, `b_units`, and `c_units`.\n", "Note that no internal checks are performed to ensure that `c_units` are consistent\n", "with `a_units` and `b_units`.\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "27421b8e", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:11.666266Z", "iopub.status.busy": "2026-10-02T14:41:11.666021Z", "iopub.status.idle": "2026-10-02T14:41:12.883052Z", "shell.execute_reply": "2026-10-02T14:41:12.882231Z" }, "papermill": { "duration": 1.219476, "end_time": "2026-10-02T14:41:12.883974+00:00", "exception": false, "start_time": "2026-10-02T14:41:11.664498+00:00", "status": "completed" }, "tags": [ "allow-assert" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1790952072.870789] [runnervm8df0l:6371 :0] ib_iface.c:1269 UCX ERROR mana_0: iface 0x5570c4a28800 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", "[1790952072.871019] [runnervm8df0l:6371 :0] ucp_worker.c:1412 UCX ERROR uct_iface_open(ud_verbs/mana_0:1) failed: Input/output error\n", "[[-8.37364803e-02 2.16320867e-01 -9.06059063e-02]\n", " [ 1.10815363e-01 7.03287006e-02 -6.56732664e-01]\n", " [-3.81875927e-01 1.46799881e-01 3.38641640e-01]\n", " [-7.56291417e-02 2.66839901e-01 -9.16212283e-02]\n", " [-1.30347239e-02 -8.90145437e-02 1.73824930e-02]\n", " [ 8.76564740e-03 5.29334368e-01 -1.85523437e-01]\n", " [ 6.60438287e-02 -9.69407456e-02 1.81493494e-01]\n", " [ 1.26416565e-04 -3.17697186e-02 1.35442348e-01]\n", " [-1.96886280e-01 9.19928194e-02 1.15383850e-01]\n", " [ 4.98981050e-02 1.25379854e-01 -1.38891019e-01]\n", " [-1.48594038e-01 1.43494619e-01 -2.94527112e-01]\n", " [ 1.11642372e-01 -2.56949456e-01 3.71293213e-01]\n", " [ 5.80214209e-02 1.24073755e-01 -1.53957745e-01]\n", " [ 2.19581952e-01 2.27415256e-01 -3.90943514e-01]\n", " [ 2.54987570e-01 -3.46410542e-01 4.57729660e-02]\n", " [ 2.18657800e-02 -1.17431560e-01 1.06874706e-01]\n", " [ 1.65884667e-01 -4.04852516e-01 3.11524562e-01]\n", " [ 3.13622661e-01 -3.72515287e-01 2.68620294e-01]\n", " [ 1.16682459e-01 1.01697379e-02 -1.12797236e-01]\n", " [-1.18111022e-01 4.17869032e-02 1.27500710e-01]\n", " [-1.15757280e-01 1.12122454e-01 5.82130972e-02]\n", " [-2.59304312e-01 2.00007201e-01 2.51275637e-02]\n", " [-1.34970018e-01 2.85872098e-01 -2.30068695e-01]\n", " [ 1.02321420e-01 -1.54955741e-01 9.81674752e-03]]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[runnervm8df0l:06371] pml_ucx.c:313 Error: Failed to create UCP worker\n" ] } ], "source": [ "import numpy as np\n", "import openmdao.api as om\n", "\n", "n = 24\n", "\n", "p = om.Problem()\n", "\n", "p.model.add_subsystem(name='cross_prod_comp',\n", " subsys=om.CrossProductComp(vec_size=n,\n", " a_name='r', b_name='F', c_name='torque',\n", " a_units='m', b_units='N', c_units='N*m'),\n", " promotes_inputs=['r', 'F'])\n", "\n", "p.setup()\n", "\n", "p.set_val('r', np.random.rand(n, 3))\n", "p.set_val('F', np.random.rand(n, 3))\n", "\n", "p.run_model()\n", "\n", "# Check the output in units of ft*lbf to ensure that our units work as expected.\n", "expected = []\n", "for i in range(n):\n", " a_i = p.get_val('r')[i, :]\n", " b_i = p.get_val('F')[i, :]\n", " expected.append(np.cross(a_i, b_i) * 0.73756215)\n", "\n", " actual_i = p.get_val('cross_prod_comp.torque', units='ft*lbf')[i]\n", " rel_error = np.abs(expected[i] - actual_i)/actual_i\n", " assert np.all(rel_error < 1e-8), f\"Relative error: {rel_error}\"\n", "\n", "print(p.get_val('cross_prod_comp.torque', units='ft*lbf'))" ] }, { "cell_type": "code", "execution_count": 4, "id": "12b1f36b", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:12.887937Z", "iopub.status.busy": "2026-10-02T14:41:12.887785Z", "iopub.status.idle": "2026-10-02T14:41:12.892093Z", "shell.execute_reply": "2026-10-02T14:41:12.891410Z" }, "papermill": { "duration": 0.006855, "end_time": "2026-10-02T14:41:12.892543+00:00", "exception": false, "start_time": "2026-10-02T14:41:12.885688+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(2.04537869907584e-09)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from openmdao.utils.assert_utils import assert_near_equal\n", "\n", "assert_near_equal(p.get_val('cross_prod_comp.torque', units='ft*lbf'), np.array(expected), tolerance=1e-8)" ] }, { "cell_type": "markdown", "id": "a62739dd", "metadata": { "papermill": { "duration": 0.006471, "end_time": "2026-10-02T14:41:12.900104+00:00", "exception": false, "start_time": "2026-10-02T14:41:12.893633+00:00", "status": "completed" }, "tags": [] }, "source": [ "## DotProductComp Example with Multiple Products\n", "\n", "When defining multiple products:\n", "\n", "- An input name in one call to `add_product` may not be an output name in another call, and vice-versa.\n", "- The units and shape of variables used across multiple products must be the same in each one." ] }, { "cell_type": "code", "execution_count": 5, "id": "d60706b7", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:12.903576Z", "iopub.status.busy": "2026-10-02T14:41:12.903448Z", "iopub.status.idle": "2026-10-02T14:41:12.913128Z", "shell.execute_reply": "2026-10-02T14:41:12.912465Z" }, "papermill": { "duration": 0.012403, "end_time": "2026-10-02T14:41:12.913905+00:00", "exception": false, "start_time": "2026-10-02T14:41:12.901502+00:00", "status": "completed" }, "tags": [ "allow-assert" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 5.39420338e-01 -5.27679823e-01 7.62122276e-02]\n", " [-4.16897261e-01 4.89412928e-01 2.13322687e-01]\n", " [-2.55644704e-01 1.87887887e-01 5.99171914e-01]\n", " [-4.80844975e-02 2.03534018e-01 -2.94102949e-01]\n", " [ 2.67874546e-01 -7.34877039e-01 2.11913429e-01]\n", " [-3.58426682e-01 7.57501941e-02 2.63215257e-02]\n", " [ 3.09468401e-01 -2.88329607e-01 2.75817887e-01]\n", " [-5.05339362e-01 2.54591527e-01 1.64740986e-01]\n", " [-1.14929535e-01 5.37064892e-01 -4.97357938e-01]\n", " [-6.61968334e-01 3.18501470e-02 3.47389982e-01]\n", " [-4.22171351e-01 -2.34917200e-01 4.58073710e-01]\n", " [ 5.25918045e-01 -6.17009233e-01 4.36110194e-01]\n", " [ 2.22264198e-01 -8.71431800e-02 -6.20686651e-02]\n", " [-2.25728862e-01 1.31583422e-01 6.23781266e-02]\n", " [ 2.86065996e-01 -7.18558956e-04 -1.68030235e-02]\n", " [-5.90733550e-02 1.79214865e-01 -1.31225354e-01]\n", " [-9.96864417e-02 4.45945802e-01 -1.44338585e-02]\n", " [ 3.31315466e-01 2.46914001e-01 -4.91735447e-01]\n", " [ 1.52668643e-01 -1.00785609e-01 -5.38916650e-01]\n", " [-1.49342583e-01 2.96160271e-02 7.48028438e-02]\n", " [ 6.56959918e-02 1.43694397e-01 -1.80248800e-01]\n", " [-8.45752671e-02 -7.30126291e-02 1.06783330e-01]\n", " [-4.76158678e-01 3.83939807e-01 2.97037709e-01]\n", " [-3.20925039e-01 -3.37558885e-01 7.00093521e-01]]\n" ] } ], "source": [ "n = 24\n", "\n", "p = om.Problem()\n", "\n", "cpc = om.CrossProductComp(vec_size=n,\n", " a_name='r', b_name='F', c_name='torque',\n", " a_units='m', b_units='N', c_units='N*m')\n", "\n", "cpc.add_product(vec_size=n,\n", " a_name='r', b_name='p', c_name='L',\n", " a_units='m', b_units='kg*m/s', c_units='kg*m**2/s')\n", "\n", "p.model.add_subsystem(name='cross_prod_comp', subsys=cpc,\n", " promotes_inputs=['r', 'F', 'p'])\n", "\n", "p.setup()\n", "\n", "p.set_val('r', np.random.rand(n, 3))\n", "p.set_val('F', np.random.rand(n, 3))\n", "p.set_val('p', np.random.rand(n, 3))\n", "\n", "p.run_model()\n", "\n", "# Check the output.\n", "expected_T = []\n", "expected_L = []\n", "for i in range(n):\n", " a_i = p.get_val('r')[i, :]\n", " b_i = p.get_val('F')[i, :]\n", " expected_T.append(np.cross(a_i, b_i))\n", "\n", " actual_i = p.get_val('cross_prod_comp.torque')[i]\n", " rel_error = np.abs(expected_T[i] - actual_i)/actual_i\n", " assert np.all(rel_error < 1e-8), f\"Relative error: {rel_error}\"\n", "\n", " b_i = p.get_val('p')[i, :]\n", " expected_L.append(np.cross(a_i, b_i))\n", "\n", " actual_i = p.get_val('cross_prod_comp.L')[i]\n", " rel_error = np.abs(expected_L[i] - actual_i)/actual_i\n", " assert np.all(rel_error < 1e-8), f\"Relative error: {rel_error}\"\n", "\n", "print(p.get_val('cross_prod_comp.torque'))" ] }, { "cell_type": "code", "execution_count": 6, "id": "e5d0c0cd", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:12.917756Z", "iopub.status.busy": "2026-10-02T14:41:12.917609Z", "iopub.status.idle": "2026-10-02T14:41:12.920443Z", "shell.execute_reply": "2026-10-02T14:41:12.919728Z" }, "papermill": { "duration": 0.005166, "end_time": "2026-10-02T14:41:12.920884+00:00", "exception": false, "start_time": "2026-10-02T14:41:12.915718+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.02976415 -0.1346321 0.17520703]\n", " [-0.27229264 0.58952198 0.07570326]\n", " [-0.30623091 -0.12934774 0.81499972]\n", " [-0.25606549 0.15863341 0.03900362]\n", " [ 0.22806284 -0.56502059 0.13770608]\n", " [-0.05372327 0.3687119 -0.07623891]\n", " [ 0.23586482 -0.18977517 -0.37125858]\n", " [ 0.20539231 -0.31833756 0.11132083]\n", " [ 0.11385881 0.29644518 -0.28328328]\n", " [-0.38000296 -0.02971061 0.21790282]\n", " [-0.71896125 0.06685563 0.5944584 ]\n", " [ 0.56252114 -0.65527971 0.05167142]\n", " [ 0.48540713 -0.17097331 -0.47762516]\n", " [-0.23754146 0.1800353 0.03608386]\n", " [ 0.20501553 0.00450646 -0.05503295]\n", " [-0.587529 0.43483075 -0.01407459]\n", " [-0.19111024 0.09874218 0.0044351 ]\n", " [-0.48732466 0.34198887 -0.23578373]\n", " [ 0.2432161 -0.24359209 0.07011508]\n", " [-0.07513793 -0.00701538 0.03811882]\n", " [ 0.14246738 -0.12945128 -0.07339697]\n", " [-0.15223063 0.38830663 -0.24180632]\n", " [-0.66804135 0.08848046 0.48512098]\n", " [-0.51309516 0.13806604 0.35682369]]\n" ] } ], "source": [ "print(p.get_val('cross_prod_comp.L'))" ] }, { "cell_type": "code", "execution_count": 7, "id": "cdf1882c", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:12.923836Z", "iopub.status.busy": "2026-10-02T14:41:12.923646Z", "iopub.status.idle": "2026-10-02T14:41:12.927100Z", "shell.execute_reply": "2026-10-02T14:41:12.926516Z" }, "papermill": { "duration": 0.00569, "end_time": "2026-10-02T14:41:12.927667+00:00", "exception": false, "start_time": "2026-10-02T14:41:12.921977+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.0)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assert_near_equal(p.get_val('cross_prod_comp.torque'), np.array(expected_T), tolerance=1e-8)\n", "assert_near_equal(p.get_val('cross_prod_comp.L'), np.array(expected_L), tolerance=1e-8)" ] } ], "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": 3.82649, "end_time": "2026-10-02T14:41:13.445303+00:00", "environment_variables": {}, "exception": null, "input_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/openmdao_book/features/building_blocks/components/cross_product_comp.ipynb", "output_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/_executed_book/features/building_blocks/components/cross_product_comp.ipynb", "parameters": {}, "start_time": "2026-10-02T14:41:09.618813+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }