Richard-stream-coords.ipynb

{"metadata":{"kernelspec":{"display_name":"Python [conda env:root] *","language":"python","name":"conda-root-py"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.10.12"}},"nbformat_minor":5,"nbformat":4,"cells":[{"id":"bc730dd8-c51c-4bf0-aa0e-49decf160413","cell_type":"code","source":"import astropy.coordinates as coord\nimport astropy.table as at\nimport astropy.units as u\nimport gala.dynamics as gd\nimport h5py as hp\nimport matplotlib as mpl\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom scipy.spatial.transform import Rotation\n\n%matplotlib inline","metadata":{"execution":{"iopub.status.busy":"2024-03-08T21:28:08.592781Z","iopub.execute_input":"2024-03-08T21:28:08.593324Z","iopub.status.idle":"2024-03-08T21:28:10.038358Z","shell.execute_reply.started":"2024-03-08T21:28:08.593292Z","shell.execute_reply":"2024-03-08T21:28:10.038003Z"},"trusted":true},"outputs":[],"execution_count":1},{"id":"d8e2a60c-5659-4fba-8f20-e97b232849e3","cell_type":"code","source":"t_idx = -1\nwith hp.File(\"/Users/apricewhelan/Downloads/stream_550.hdf5\", mode=\"r\") as f:\n    prog = gd.PhaseSpacePosition(\n        f[\"positions\"][t_idx, 0] * u.kpc, f[\"velocities\"][t_idx, 0] * u.km / u.s\n    )\n    stream = gd.PhaseSpacePosition(\n        f[\"positions\"][t_idx, 1:].T * u.kpc, f[\"velocities\"][t_idx, 1:].T * u.km / u.s\n    )","metadata":{"execution":{"iopub.status.busy":"2024-03-08T21:28:10.039392Z","iopub.execute_input":"2024-03-08T21:28:10.039555Z","iopub.status.idle":"2024-03-08T21:28:10.044369Z","shell.execute_reply.started":"2024-03-08T21:28:10.039546Z","shell.execute_reply":"2024-03-08T21:28:10.044114Z"},"trusted":true},"outputs":[],"execution_count":2},{"id":"1bd3d28d-eb51-4c4f-802d-a1155ac6cc1e","cell_type":"code","source":"plt.plot(\n    stream.x.value,\n    stream.y.value,\n    marker=\"o\",\n    ls=\"none\",\n    alpha=0.5,\n    mew=0,\n    ms=1.5,\n)\nplt.scatter(prog.x.value, prog.y.value, color=\"tab:red\", s=100, zorder=100)\nplt.xlim(-50, 50)\nplt.ylim(-50, 50)","metadata":{"execution":{"iopub.status.busy":"2024-03-08T21:28:10.044827Z","iopub.execute_input":"2024-03-08T21:28:10.044947Z","iopub.status.idle":"2024-03-08T21:28:10.270165Z","shell.execute_reply.started":"2024-03-08T21:28:10.044939Z","shell.execute_reply":"2024-03-08T21:28:10.268463Z"},"trusted":true},"outputs":[{"execution_count":3,"output_type":"execute_result","data":{"text/plain":"(-50.0, 50.0)"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x432 with 1 Axes>","image/png":"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"},"metadata":{"image/png":{"width":440,"height":440}}}],"execution_count":3},{"id":"ec03b1de-26fa-4afc-8459-918fb97cc19f","cell_type":"code","source":"R1 = Rotation.from_euler(\"z\", -prog.spherical.lon.degree, degrees=True)\nR2 = Rotation.from_euler(\"y\", prog.spherical.lat.degree, degrees=True)\nR_prog0 = R2.as_matrix() @ R1.as_matrix()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2024-03-08T21:28:10.274237Z","iopub.execute_input":"2024-03-08T21:28:10.286320Z","iopub.status.idle":"2024-03-08T21:28:10.318125Z","shell.execute_reply.started":"2024-03-08T21:28:10.286267Z","shell.execute_reply":"2024-03-08T21:28:10.314592Z"}},"outputs":[],"execution_count":4},{"id":"4df979e5-04c8-430e-a60e-15a20be1ad03","cell_type":"code","source":"new_vxyz = R_prog0 @ prog.v_xyz\nv_angle = np.arctan2(new_vxyz[2], new_vxyz[1])\nR3 = Rotation.from_euler(\"x\", -v_angle.to_value(u.degree), degrees=True)\nR = (R3 * R2 * R1).as_matrix()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2024-03-08T21:28:10.319881Z","iopub.execute_input":"2024-03-08T21:28:10.320396Z","iopub.status.idle":"2024-03-08T21:28:10.325817Z","shell.execute_reply.started":"2024-03-08T21:28:10.320372Z","shell.execute_reply":"2024-03-08T21:28:10.324461Z"}},"outputs":[],"execution_count":5},{"id":"267933f2-b164-4ba2-9b44-821fa95e2aba","cell_type":"code","source":"new_vxyz = R @ prog.v_xyz\nassert np.isclose(new_vxyz[2], 0)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2024-03-08T21:28:10.327053Z","iopub.execute_input":"2024-03-08T21:28:10.327460Z","iopub.status.idle":"2024-03-08T21:28:10.335585Z","shell.execute_reply.started":"2024-03-08T21:28:10.327438Z","shell.execute_reply":"2024-03-08T21:28:10.334635Z"}},"outputs":[],"execution_count":6},{"id":"080de677-dcd3-44e5-ae30-64a108289bc2","cell_type":"code","source":"stream_rot = gd.PhaseSpacePosition(stream.data.transform(R))","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2024-03-08T21:28:10.339957Z","iopub.execute_input":"2024-03-08T21:28:10.340367Z","iopub.status.idle":"2024-03-08T21:28:10.347540Z","shell.execute_reply.started":"2024-03-08T21:28:10.340354Z","shell.execute_reply":"2024-03-08T21:28:10.347016Z"}},"outputs":[],"execution_count":7},{"id":"1c1b7587-421d-4d20-9fc9-0fa5c5e127e8","cell_type":"code","source":"stream_sph = stream_rot.spherical","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2024-03-08T21:28:10.348483Z","iopub.execute_input":"2024-03-08T21:28:10.348589Z","iopub.status.idle":"2024-03-08T21:28:10.359012Z","shell.execute_reply.started":"2024-03-08T21:28:10.348579Z","shell.execute_reply":"2024-03-08T21:28:10.358449Z"}},"outputs":[{"name":"stderr","text":"/Users/apricewhelan/anaconda3/lib/python3.10/site-packages/astropy/units/quantity.py:666: RuntimeWarning: invalid value encountered in divide\n  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n/Users/apricewhelan/anaconda3/lib/python3.10/site-packages/astropy/units/quantity.py:666: RuntimeWarning: divide by zero encountered in divide\n  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n/Users/apricewhelan/anaconda3/lib/python3.10/site-packages/astropy/units/quantity.py:666: RuntimeWarning: invalid value encountered in pdp\n  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n","output_type":"stream"}],"execution_count":8},{"id":"3559c6b6-4c9b-4d5f-a185-b296f3d06195","cell_type":"code","source":"plt.figure(figsize=(12, 5))\nplt.plot(stream_sph.lon.wrap_at(180*u.deg).degree, stream_sph.lat.degree, ls='none')\nplt.xlim(-180, 180)\nplt.ylim(-25, 25)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2024-03-08T21:28:10.360366Z","iopub.execute_input":"2024-03-08T21:28:10.360748Z","iopub.status.idle":"2024-03-08T21:28:10.520127Z","shell.execute_reply.started":"2024-03-08T21:28:10.360732Z","shell.execute_reply":"2024-03-08T21:28:10.519656Z"}},"outputs":[{"execution_count":9,"output_type":"execute_result","data":{"text/plain":"(-25.0, 25.0)"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 864x360 with 1 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