{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "947654b4", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:14.598054Z", "iopub.status.busy": "2026-10-02T14:41:14.597831Z", "iopub.status.idle": "2026-10-02T14:41:14.602466Z", "shell.execute_reply": "2026-10-02T14:41:14.601893Z" }, "papermill": { "duration": 0.007814, "end_time": "2026-10-02T14:41:14.603332+00:00", "exception": false, "start_time": "2026-10-02T14:41:14.595518+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": "a67b7694", "metadata": { "papermill": { "duration": 0.001131, "end_time": "2026-10-02T14:41:14.605889+00:00", "exception": false, "start_time": "2026-10-02T14:41:14.604758+00:00", "status": "completed" }, "tags": [] }, "source": [ "# DotProductComp\n", "\n", "`DotProductComp` performs a dot product between two compatible inputs. It may be vectorized to provide the result at one or more points simultaneously.\n", "\n", "$$\n", " c_i = \\bar{a}_i \\cdot \\bar{b}_i\n", "$$\n", "\n", "## DotProductComp Options\n", "\n", "The default `vec_size` is 1, providing the dot product of $a$ and $b$ at a single\n", "point. The lengths of $a$ and $b$ are provided by option `length`.\n", "\n", "Other options for DotProductComp 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": "4818c371", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:14.609354Z", "iopub.status.busy": "2026-10-02T14:41:14.609174Z", "iopub.status.idle": "2026-10-02T14:41:15.738053Z", "shell.execute_reply": "2026-10-02T14:41:15.737220Z" }, "papermill": { "duration": 1.131397, "end_time": "2026-10-02T14:41:15.738573+00:00", "exception": false, "start_time": "2026-10-02T14:41:14.607176+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", " \n", "
OptionDefaultAcceptable ValuesAcceptable TypesDescription
a_nameaN/A['str']The variable name for input 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 input vector b.
b_unitsN/AN/A['str']The units for vector b.
c_namecN/A['str']The variable name for output 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
length3N/A['int']The length of vectors a and b
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 dot 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.dot_product_comp.DotProductComp\")" ] }, { "cell_type": "markdown", "id": "31d5b3f7", "metadata": { "papermill": { "duration": 0.000859, "end_time": "2026-10-02T14:41:15.740630+00:00", "exception": false, "start_time": "2026-10-02T14:41:15.739771+00:00", "status": "completed" }, "tags": [] }, "source": [ "## DotProductComp Constructor\n", "\n", "The call signature for the `DotProductComp` constructor is:\n", "\n", "```{eval-rst}\n", " .. automethod:: openmdao.components.dot_product_comp.DotProductComp.__init__\n", " :noindex:\n", "```\n", "\n", "## DotProductComp 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 `DotProductComp` 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.dot_product_comp.DotProductComp.add_product\n", " :noindex:\n", "```\n", "\n", "## DotProductComp Example\n", "\n", "In the following example DotProductComp is used to compute instantaneous power as the\n", "dot product of force and velocity at 100 points simultaneously. Note the use of\n", "`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": "c1a3b078", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:15.743440Z", "iopub.status.busy": "2026-10-02T14:41:15.743055Z", "iopub.status.idle": "2026-10-02T14:41:16.986454Z", "shell.execute_reply": "2026-10-02T14:41:16.985735Z" }, "papermill": { "duration": 1.245336, "end_time": "2026-10-02T14:41:16.986923+00:00", "exception": false, "start_time": "2026-10-02T14:41:15.741587+00:00", "status": "completed" }, "tags": [ "allow-assert" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1790952076.974851] [runnervm8df0l:6401 :0] ib_iface.c:1269 UCX ERROR mana_0: iface 0x55f3baabba40 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", "[1790952076.975115] [runnervm8df0l:6401 :0] ucp_worker.c:1412 UCX ERROR uct_iface_open(ud_verbs/mana_0:1) failed: Input/output error\n", "[0.00097596 0.00168304 0.00043161 0.00018362 0.00036013 0.00083429\n", " 0.00015871 0.00034926 0.00100133 0.00115079 0.00062111 0.00049656\n", " 0.00063133 0.00060394 0.0009077 0.00079927 0.00109658 0.00033565\n", " 0.00039861 0.00067336 0.00065559 0.00108073 0.00165062 0.00055527]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[runnervm8df0l:06401] 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", "dp_comp = om.DotProductComp(vec_size=n, length=3, a_name='F', b_name='v', c_name='P',\n", " a_units='N', b_units='m/s', c_units='W')\n", "\n", "p.model.add_subsystem(name='dot_prod_comp', subsys=dp_comp,\n", " promotes_inputs=[('F', 'force'), ('v', 'vel')])\n", "\n", "p.setup()\n", "\n", "p.set_val('force', np.random.rand(n, 3))\n", "p.set_val('vel', np.random.rand(n, 3))\n", "\n", "p.run_model()\n", "\n", "# Verify the results against numpy.dot in a for loop.\n", "expected = []\n", "for i in range(n):\n", " a_i = p.get_val('force')[i, :]\n", " b_i = p.get_val('vel')[i, :]\n", " expected.append(np.dot(a_i, b_i))\n", "\n", " actual_i = p.get_val('dot_prod_comp.P')[i]\n", " rel_error = np.abs(expected[i] - actual_i)/actual_i\n", " assert rel_error < 1e-9, f\"Relative error: {rel_error}\"\n", "\n", "print(p.get_val('dot_prod_comp.P', units='kW'))" ] }, { "cell_type": "code", "execution_count": 4, "id": "1a629bcd", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:16.990747Z", "iopub.status.busy": "2026-10-02T14:41:16.990563Z", "iopub.status.idle": "2026-10-02T14:41:16.995124Z", "shell.execute_reply": "2026-10-02T14:41:16.994486Z" }, "papermill": { "duration": 0.007371, "end_time": "2026-10-02T14:41:16.995935+00:00", "exception": false, "start_time": "2026-10-02T14:41:16.988564+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(6.920306347550852e-17)" ] }, "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('dot_prod_comp.P', units='kW'), np.array(expected)/1000.)" ] }, { "cell_type": "markdown", "id": "e6c2b68f", "metadata": { "papermill": { "duration": 0.001368, "end_time": "2026-10-02T14:41:16.998851+00:00", "exception": false, "start_time": "2026-10-02T14:41:16.997483+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": "6dab0237", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:17.002192Z", "iopub.status.busy": "2026-10-02T14:41:17.002060Z", "iopub.status.idle": "2026-10-02T14:41:17.010712Z", "shell.execute_reply": "2026-10-02T14:41:17.009927Z" }, "papermill": { "duration": 0.010883, "end_time": "2026-10-02T14:41:17.011125+00:00", "exception": false, "start_time": "2026-10-02T14:41:17.000242+00:00", "status": "completed" }, "tags": [ "allow-assert" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.00143138 0.0009634 0.00101729 0.00112737 0.00097374 0.00040531\n", " 0.00065627 0.00082778 0.00026553 0.00041295 0.00017028 0.000543\n", " 0.00039183 0.00068912 0.00104271 0.00062888 0.00091903 0.00060143\n", " 0.0009909 0.0003096 0.0004878 0.00083574 0.00136847 0.00134076]\n" ] } ], "source": [ "n = 24\n", "\n", "p = om.Problem()\n", "\n", "dp_comp = om.DotProductComp(vec_size=n, length=3,\n", " a_name='F', b_name='d', c_name='W',\n", " a_units='N', b_units='m', c_units='J')\n", "\n", "dp_comp.add_product(vec_size=n, length=3,\n", " a_name='F', b_name='v', c_name='P',\n", " a_units='N', b_units='m/s', c_units='W')\n", "\n", "p.model.add_subsystem(name='dot_prod_comp', subsys=dp_comp,\n", " promotes_inputs=[('F', 'force'), ('d', 'disp'), ('v', 'vel')])\n", "\n", "p.setup()\n", "\n", "p.set_val('force', np.random.rand(n, 3))\n", "p.set_val('disp', np.random.rand(n, 3))\n", "p.set_val('vel', np.random.rand(n, 3))\n", "\n", "p.run_model()\n", "\n", "# Verify the results against numpy.dot in a for loop.\n", "expected_P = []\n", "expected_W = []\n", "for i in range(n):\n", " a_i = p.get_val('force')[i, :]\n", "\n", " b_i = p.get_val('disp')[i, :]\n", " expected_W.append(np.dot(a_i, b_i))\n", "\n", " actual_i = p.get_val('dot_prod_comp.W')[i]\n", " rel_error = np.abs(actual_i - expected_W[i])/actual_i\n", " assert rel_error < 1e-9, f\"Relative error: {rel_error}\"\n", "\n", " b_i = p.get_val('vel')[i, :]\n", " expected_P.append(np.dot(a_i, b_i))\n", "\n", " actual_i = p.get_val('dot_prod_comp.P')[i]\n", " rel_error = np.abs(expected_P[i] - actual_i)/actual_i\n", " assert rel_error < 1e-9, f\"Relative error: {rel_error}\"\n", "\n", "print(p.get_val('dot_prod_comp.W', units='kJ'))" ] }, { "cell_type": "code", "execution_count": 6, "id": "616fdb06", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:17.094453Z", "iopub.status.busy": "2026-10-02T14:41:17.094243Z", "iopub.status.idle": "2026-10-02T14:41:17.097605Z", "shell.execute_reply": "2026-10-02T14:41:17.096872Z" }, "papermill": { "duration": 0.085745, "end_time": "2026-10-02T14:41:17.098213+00:00", "exception": false, "start_time": "2026-10-02T14:41:17.012468+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.13104156e-03 9.25121439e-04 6.23233390e-04 7.38227782e-04\n", " 7.52635168e-04 9.59667553e-04 6.37173121e-04 3.26654252e-04\n", " 1.02527423e-03 5.49291574e-04 3.75761884e-04 7.61772313e-05\n", " 6.27530654e-04 1.40115680e-03 3.96347040e-04 4.34220404e-04\n", " 2.34619561e-04 2.34374713e-04 1.22189509e-03 3.30189021e-04\n", " 6.64902487e-04 8.05518207e-04 9.39292030e-04 1.36047927e-03]\n" ] } ], "source": [ "print(p.get_val('dot_prod_comp.P', units='kW'))" ] }, { "cell_type": "code", "execution_count": 7, "id": "852b2e7f", "metadata": { "execution": { "iopub.execute_input": "2026-10-02T14:41:17.101829Z", "iopub.status.busy": "2026-10-02T14:41:17.101690Z", "iopub.status.idle": "2026-10-02T14:41:17.105055Z", "shell.execute_reply": "2026-10-02T14:41:17.104389Z" }, "papermill": { "duration": 0.005891, "end_time": "2026-10-02T14:41:17.105612+00:00", "exception": false, "start_time": "2026-10-02T14:41:17.099721+00:00", "status": "completed" }, "tags": [ "remove-input", "remove-output" ] }, "outputs": [ { "data": { "text/plain": [ "np.float64(1.172333996090188e-16)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assert_near_equal(p.get_val('dot_prod_comp.W', units='kJ'), np.array(expected_W)/1000.)\n", "assert_near_equal(p.get_val('dot_prod_comp.P', units='kW'), np.array(expected_P)/1000.)" ] } ], "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": 3.812091, "end_time": "2026-10-02T14:41:17.622291+00:00", "environment_variables": {}, "exception": null, "input_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/openmdao_book/features/building_blocks/components/dot_product_comp.ipynb", "output_path": "/home/runner/work/OpenMDAO/OpenMDAO/openmdao/docs/_executed_book/features/building_blocks/components/dot_product_comp.ipynb", "parameters": {}, "start_time": "2026-10-02T14:41:13.810200+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }