{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "16528e77", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:06.898516Z", "iopub.status.busy": "2026-08-26T15:43:06.898292Z", "iopub.status.idle": "2026-08-26T15:43:10.684252Z", "shell.execute_reply": "2026-08-26T15:43:10.682953Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Matrix mirror_example: nnz=4 neqs=4\n", " (col, row) = value\n", " (0, 0) = (1+0j) : I_In1 mode=0 -> I_In1 mode=0\n", " (1, 1) = (1+0j) : I_Out1 mode=0 -> I_Out1 mode=0\n", " (2, 2) = (1+0j) : I_In2 mode=0 -> I_In2 mode=0\n", " (3, 3) = (1+0j) : I_Out2 mode=0 -> I_Out2 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "import numpy as np\n", "from finesse.cymath.cmatrix import KLUMatrix\n", "\n", "mat = KLUMatrix(name=\"mirror_example\")\n", "In1 = mat.declare_equations(Neqs=1, index=0, name=\"I_In1\", is_diagonal=True)\n", "Out1 = mat.declare_equations(Neqs=1, index=1, name=\"I_Out1\", is_diagonal=True)\n", "In2 = mat.declare_equations(Neqs=1, index=2, name=\"I_In2\", is_diagonal=True)\n", "Out2 = mat.declare_equations(Neqs=1, index=3, name=\"I_Out2\", is_diagonal=True)\n", "\n", "mat.construct()\n", "mat.print_matrix()" ] }, { "cell_type": "code", "execution_count": 2, "id": "a1e3ebd5", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:10.686646Z", "iopub.status.busy": "2026-08-26T15:43:10.686168Z", "iopub.status.idle": "2026-08-26T15:43:10.692586Z", "shell.execute_reply": "2026-08-26T15:43:10.692087Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Matrix mirror_example: nnz=8 neqs=4\n", " (col, row) = value\n", " (0, 0) = (1+0j) : I_In1 mode=0 -> I_In1 mode=0\n", " (0, 1) = 0j : I_In1 mode=0 -> I_Out1 mode=0\n", " (0, 3) = 0j : I_In1 mode=0 -> I_Out2 mode=0\n", " (1, 1) = (1+0j) : I_Out1 mode=0 -> I_Out1 mode=0\n", " (2, 1) = 0j : I_In2 mode=0 -> I_Out1 mode=0\n", " (2, 2) = (1+0j) : I_In2 mode=0 -> I_In2 mode=0\n", " (2, 3) = 0j : I_In2 mode=0 -> I_Out2 mode=0\n", " (3, 3) = (1+0j) : I_Out2 mode=0 -> I_Out2 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "a11.shape=(1, 1)" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "a11 = mat.declare_submatrix_view(In1.from_idx, Out1.from_idx, \"_In1->Out1\", False)\n", "a22 = mat.declare_submatrix_view(In2.from_idx, Out2.from_idx, \"_In2->Out2\", False)\n", "\n", "a12 = mat.declare_submatrix_view(In1.from_idx, Out2.from_idx, \"_In1->Out2\", False)\n", "a21 = mat.declare_submatrix_view(In2.from_idx, Out1.from_idx, \"_In2->Out1\", False)\n", "\n", "mat.construct()\n", "mat.print_matrix()\n", "\n", "print(f\"{a11.shape=}\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "0f3f3a2e", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:10.695342Z", "iopub.status.busy": "2026-08-26T15:43:10.695086Z", "iopub.status.idle": "2026-08-26T15:43:10.703647Z", "shell.execute_reply": "2026-08-26T15:43:10.702510Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Matrix mirror_example: nnz=8 neqs=4\n", " (col, row) = value\n", " (0, 0) = (1+0j) : I_In1 mode=0 -> I_In1 mode=0\n", " (0, 1) = (-0.9486832980505138+0j) : I_In1 mode=0 -> I_Out1 mode=0\n", " (0, 3) = (-0-0.31622776601683794j) : I_In1 mode=0 -> I_Out2 mode=0\n", " (1, 1) = (1+0j) : I_Out1 mode=0 -> I_Out1 mode=0\n", " (2, 1) = (-0-0.31622776601683794j) : I_In2 mode=0 -> I_Out1 mode=0\n", " (2, 2) = (1+0j) : I_In2 mode=0 -> I_In2 mode=0\n", " (2, 3) = (-0.9486832980505138+0j) : I_In2 mode=0 -> I_Out2 mode=0\n", " (3, 3) = (1+0j) : I_Out2 mode=0 -> I_Out2 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[[ 1. +0.j 0. +0.j 0. +0.j 0. +0.j ]\n", " [-0.9+0.j 1. +0.j 0. -0.3j 0. +0.j ]\n", " [ 0. +0.j 0. +0.j 1. +0.j 0. +0.j ]\n", " [ 0. -0.3j 0. +0.j -0.9+0.j 1. +0.j ]]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "r = np.sqrt(0.9)\n", "t = np.sqrt(0.1)\n", "\n", "a11[:] = r\n", "a22[:] = r\n", "a12[:] = 1j * t\n", "a21[:] = 1j * t\n", "\n", "mat.print_matrix()\n", "\n", "# print in dense format\n", "np.set_printoptions(precision=1, linewidth=250)\n", "print(mat.to_scipy_csc().todense())" ] }, { "cell_type": "code", "execution_count": 4, "id": "0ba2787e", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:10.705423Z", "iopub.status.busy": "2026-08-26T15:43:10.705209Z", "iopub.status.idle": "2026-08-26T15:43:10.708351Z", "shell.execute_reply": "2026-08-26T15:43:10.707674Z" } }, "outputs": [], "source": [ "mat.set_rhs(In1.from_idx, 1.0)" ] }, { "cell_type": "code", "execution_count": 5, "id": "03341eb0", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:10.715886Z", "iopub.status.busy": "2026-08-26T15:43:10.715513Z", "iopub.status.idle": "2026-08-26T15:43:10.721523Z", "shell.execute_reply": "2026-08-26T15:43:10.720914Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Vector mirror_example: neqs=4\n", " (row) = value\n", " (0) = (1+0j) : I_In1 mode=0\n", " (1) = 0j : I_Out1 mode=0\n", " (2) = 0j : I_In2 mode=0\n", " (3) = 0j : I_Out2 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Vector mirror_example: neqs=4\n", " (row) = value\n", " (0) = (1+0j) : I_In1 mode=0\n", " (1) = (0.9486832980505138+0j) : I_Out1 mode=0\n", " (2) = 0j : I_In2 mode=0\n", " (3) = 0.31622776601683794j : I_Out2 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "mat.print_rhs()\n", "\n", "mat.factor()\n", "mat.solve()\n", "\n", "mat.print_rhs()" ] }, { "cell_type": "code", "execution_count": 6, "id": "1b2913cc", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:10.730629Z", "iopub.status.busy": "2026-08-26T15:43:10.730369Z", "iopub.status.idle": "2026-08-26T15:43:10.862698Z", "shell.execute_reply": "2026-08-26T15:43:10.861707Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Matrix carrier: nnz=12 neqs=6\n", " (col, row) = value\n", " (0, 0) = (1+0j) : I,node=l1.p1.i,f=0,fidx=0,Neq=1 mode=0 -> I,node=l1.p1.i,f=0,fidx=0,Neq=1 mode=0\n", " (1, 1) = (1+0j) : I,node=l1.p1.o,f=0,fidx=1,Neq=1 mode=0 -> I,node=l1.p1.o,f=0,fidx=1,Neq=1 mode=0\n", " (1, 2) = (-1-0j) : I,node=l1.p1.o,f=0,fidx=1,Neq=1 mode=0 -> I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0\n", " (2, 2) = (1+0j) : I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0 -> I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0\n", " (2, 3) = (-0.9486832980505138-0j) : I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0 -> I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0\n", " (2, 5) = -0.31622776601683794j : I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0 -> I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0\n", " (3, 0) = (-1-0j) : I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0 -> I,node=l1.p1.i,f=0,fidx=0,Neq=1 mode=0\n", " (3, 3) = (1+0j) : I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0 -> I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0\n", " (4, 3) = -0.31622776601683794j : I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0 -> I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0\n", " (4, 4) = (1+0j) : I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0 -> I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0\n", " (4, 5) = (-0.9486832980505138+0j) : I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0 -> I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0\n", " (5, 5) = (1+0j) : I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0 -> I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Matrix in dense format:\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[[ 1. +0.j 0. +0.j 0. +0.j -1. +0.j 0. +0.j 0. +0.j ]\n", " [ 0. +0.j 1. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j ]\n", " [ 0. +0.j -1. +0.j 1. +0.j 0. +0.j 0. +0.j 0. +0.j ]\n", " [ 0. +0.j 0. +0.j -0.9+0.j 1. +0.j 0. -0.3j 0. +0.j ]\n", " [ 0. +0.j 0. +0.j 0. +0.j 0. +0.j 1. +0.j 0. +0.j ]\n", " [ 0. +0.j 0. +0.j 0. -0.3j 0. +0.j -0.9+0.j 1. +0.j ]]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Right hand side vector:" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Vector carrier: neqs=6\n", " (row) = value\n", " (0) = (1.3416407864998738+0j) : I,node=l1.p1.i,f=0,fidx=0,Neq=1 mode=0\n", " (1) = (1.4142135623730951+0j) : I,node=l1.p1.o,f=0,fidx=1,Neq=1 mode=0\n", " (2) = (1.4142135623730951+0j) : I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0\n", " (3) = (1.3416407864998738+0j) : I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0\n", " (4) = 0j : I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0\n", " (5) = 0.447213595499958j : I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "import finesse\n", "import numpy as np\n", "\n", "model = finesse.Model()\n", "\n", "np.set_printoptions(linewidth=200, precision=1)\n", "\n", "model.parse(\n", " \"\"\"\n", " l l1\n", " s s1 l1.p1 m1.p1\n", " m m1 R=0.9 T=0.1\n", " \"\"\"\n", ")\n", "model.run(simulation_options={\"debug_mode\": True});" ] }, { "cell_type": "code", "execution_count": 7, "id": "db0c9b3e", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:10.865321Z", "iopub.status.busy": "2026-08-26T15:43:10.864704Z", "iopub.status.idle": "2026-08-26T15:43:10.892121Z", "shell.execute_reply": "2026-08-26T15:43:10.890038Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Matrix carrier: nnz=12 neqs=6\n", " (col, row) = value\n", " (0, 0) = (1+0j) : I,node=l1.p1.i,f=0,fidx=0,Neq=1 mode=0 -> I,node=l1.p1.i,f=0,fidx=0,Neq=1 mode=0\n", " (1, 1) = (1+0j) : I,node=l1.p1.o,f=0,fidx=1,Neq=1 mode=0 -> I,node=l1.p1.o,f=0,fidx=1,Neq=1 mode=0\n", " (1, 2) = (-1-0j) : I,node=l1.p1.o,f=0,fidx=1,Neq=1 mode=0 -> I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0\n", " (2, 2) = (1+0j) : I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0 -> I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0\n", " (2, 3) = (-0.9486832980505138-0j) : I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0 -> I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0\n", " (2, 5) = -0.31622776601683794j : I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0 -> I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0\n", " (3, 0) = (-1-0j) : I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0 -> I,node=l1.p1.i,f=0,fidx=0,Neq=1 mode=0\n", " (3, 3) = (1+0j) : I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0 -> I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0\n", " (4, 3) = -0.31622776601683794j : I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0 -> I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0\n", " (4, 4) = (1+0j) : I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0 -> I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0\n", " (4, 5) = (-0.9486832980505138+0j) : I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0 -> I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0\n", " (5, 5) = (1+0j) : I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0 -> I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Vector carrier: neqs=6\n", " (row) = value\n", " (0) = (1.3416407864998738+0j) : I,node=l1.p1.i,f=0,fidx=0,Neq=1 mode=0\n", " (1) = (1.4142135623730951+0j) : I,node=l1.p1.o,f=0,fidx=1,Neq=1 mode=0\n", " (2) = (1.4142135623730951+0j) : I,node=m1.p1.i,f=0,fidx=2,Neq=1 mode=0\n", " (3) = (1.3416407864998738+0j) : I,node=m1.p1.o,f=0,fidx=3,Neq=1 mode=0\n", " (4) = 0j : I,node=m1.p2.i,f=0,fidx=4,Neq=1 mode=0\n", " (5) = 0.447213595499958j : I,node=m1.p2.o,f=0,fidx=5,Neq=1 mode=0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "with model.built() as sim:\n", " carrier_solver = sim.carrier\n", " klu_mat = carrier_solver.M()\n", " klu_mat.print_matrix()\n", " klu_mat.print_rhs()" ] }, { "cell_type": "code", "execution_count": 8, "id": "7dd567e8", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:10.894588Z", "iopub.status.busy": "2026-08-26T15:43:10.894345Z", "iopub.status.idle": "2026-08-26T15:43:11.333247Z", "shell.execute_reply": "2026-08-26T15:43:11.331384Z" } }, "outputs": [ { "ename": "Exception", "evalue": "An error occurred in KLU during factoring: STATUS=1 (KLU_SINGULAR)\n", "output_type": "error", "traceback": [ "\u001b[31m---------------------------------------------------------------------------\u001b[39m", "\u001b[31mException\u001b[39m Traceback (most recent call last)", "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[8]\u001b[39m\u001b[32m, line 14\u001b[39m\n\u001b[32m 10\u001b[39m \n\u001b[32m 11\u001b[39m a12[:] = \u001b[32m1\u001b[39m\n\u001b[32m 12\u001b[39m a21[:] = \u001b[32m1\u001b[39m\n\u001b[32m 13\u001b[39m \n\u001b[32m---> \u001b[39m\u001b[32m14\u001b[39m mat.factor()\n", "\u001b[36mFile \u001b[39m\u001b[32msrc/finesse/cymath/cmatrix.pyx:1741\u001b[39m, in \u001b[36mfinesse.cymath.cmatrix.KLUMatrix.factor\u001b[39m\u001b[34m()\u001b[39m\n\u001b[32m-> \u001b[39m\u001b[32m1741\u001b[39m \u001b[33m'Could not get source, probably due dynamically evaluated source code.'\u001b[39m\n", "\u001b[36mFile \u001b[39m\u001b[32msrc/finesse/cymath/cmatrix.pyx:1776\u001b[39m, in \u001b[36mfinesse.cymath.cmatrix.KLUMatrix.factor\u001b[39m\u001b[34m()\u001b[39m\n\u001b[32m-> \u001b[39m\u001b[32m1776\u001b[39m \u001b[33m'Could not get source, probably due dynamically evaluated source code.'\u001b[39m\n", "\u001b[31mException\u001b[39m: An error occurred in KLU during factoring: STATUS=1 (KLU_SINGULAR)\n" ] } ], "source": [ "from finesse.cymath.cmatrix import KLUMatrix\n", "\n", "mat = KLUMatrix(name=\"singular_example\")\n", "In1 = mat.declare_equations(Neqs=1, index=0, name=\"I_In1\", is_diagonal=True)\n", "Out1 = mat.declare_equations(Neqs=1, index=1, name=\"I_Out1\", is_diagonal=True)\n", "a12 = mat.declare_submatrix_view(In1.from_idx, Out1.from_idx, \"_In1->Out1\", False)\n", "a21 = mat.declare_submatrix_view(Out1.from_idx, In1.from_idx, \"_Out1->In1\", False)\n", "\n", "mat.construct()\n", "\n", "a12[:] = 1\n", "a21[:] = 1\n", "\n", "mat.factor()" ] }, { "cell_type": "code", "execution_count": 9, "id": "ba8ce244", "metadata": { "execution": { "iopub.execute_input": "2026-08-26T15:43:11.335720Z", "iopub.status.busy": "2026-08-26T15:43:11.335465Z", "iopub.status.idle": "2026-08-26T15:43:11.410475Z", "shell.execute_reply": "2026-08-26T15:43:11.409137Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "l1.p1.i" ] }, { "name": "stdout", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "(0.447213595499958+0j)" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "l1.p1.o" ] }, { "name": "stdout", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "(1.4142135623730951+0j)" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "m1.p1.i" ] }, { "name": "stdout", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "(1.4142135623730951+0j)" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "m1.p1.o" ] }, { "name": "stdout", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "(0.447213595499958+0j)" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "m1.p2.i" ] }, { "name": "stdout", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "0j" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "m1.p2.o" ] }, { "name": "stdout", "output_type": "stream", "text": [ " " ] }, { "name": "stdout", "output_type": "stream", "text": [ "1.3416407864998738j" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "import numpy as np\n", "import finesse\n", "\n", "\n", "model = finesse.Model()\n", "\n", "model.parse(\n", " \"\"\"\n", " l l1 P=1\n", " s s1 l1.p1 m1.p1\n", " m m1 R=0.1 T=0.9\n", " \"\"\"\n", ")\n", "with model.built() as sim:\n", " sim.run_carrier()\n", " for node, val in zip(\n", " sim.carrier.nodes.keys(), np.array(sim.carrier.M().rhs_view[0, :]),\n", " strict=True\n", " ):\n", " print(node, val)" ] } ], "metadata": { "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": "3.13.15" } }, "nbformat": 4, "nbformat_minor": 5 }