{
    "cells": [
        {
            "attachments": {},
            "cell_type": "markdown",
            "id": "c48993ec-314c-432a-827e-ff6e35502cb7",
            "metadata": {},
            "source": [
                "# Spin-weighted spherical harmonics"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "id": "122d31c5",
            "metadata": {},
            "outputs": [],
            "source": [
                "import numpy as np\n",
                "\n",
                "import few\n",
                "\n",
                "# tune few configuration\n",
                "cfg_set = few.get_config_setter(reset=True)\n",
                "cfg_set.enable_backends(\"cpu\")  # This tutorial only uses CPU\n",
                "cfg_set.set_log_level(\"info\")\n",
                "cfg_set.finalize()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "id": "06e4ccab-0329-4cdd-b4b2-bf8154137063",
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "[ 2.17261840e-17+3.54815511e-01j -1.28533838e-17-2.09911687e-01j\n",
                        "  1.24292687e-16-1.24292687e-16j -2.46692086e-01+2.46692086e-01j]\n"
                    ]
                }
            ],
            "source": [
                "from few.utils.ylm import GetYlms\n",
                "\n",
                "ylm_gen = GetYlms(assume_positive_m=False)\n",
                "\n",
                "ls = np.array([2, 3, 4, 5])\n",
                "ms = np.array([2, 2, 3, 3])\n",
                "\n",
                "# viewing angles\n",
                "theta = np.pi / 3\n",
                "phi = np.pi / 4\n",
                "\n",
                "print(ylm_gen(ls, ms, theta, phi))"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "id": "95fd7bdc-1dc6-45ca-84df-54e04e718b63",
            "metadata": {},
            "source": [
                "If we assume positive m, it will return -m entries for all +m. The last 5 below are for -m. The final shape will be twice the initial length and will duplicate m=0 so be careful."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "id": "4fed355a-2b1b-4218-a5b4-32a30cd6c748",
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "(2,2): (2.1726183986132197e-17+0.3548155109090852j)\n",
                        "(3,2): (-1.285338378442592e-17-0.20991168708193983j)\n",
                        "(4,3): (1.242926870060164e-16-1.2429268700601641e-16j)\n",
                        "(5,3): (-0.24669208642519014+0.2466920864251902j)\n",
                        "(2,0): (0.2897056515173922+0j)\n",
                        "(2,-2): (2.4140204429035754e-18-0.039423945656564985j)\n",
                        "(3,-2): (-9.997076276775717e-18+0.16326464550817543j)\n",
                        "(4,-3): (-0.12119256904280647-0.12119256904280648j)\n",
                        "(5,-3): (0.235727993695182+0.23572799369518202j)\n",
                        "(2,-0): (0.2897056515173922+0j)\n"
                    ]
                }
            ],
            "source": [
                "ylm_gen = GetYlms(assume_positive_m=True)\n",
                "\n",
                "ls = np.array([2, 3, 4, 5, 2])\n",
                "ms = np.array([2, 2, 3, 3, 0])\n",
                "\n",
                "# viewing angles\n",
                "theta = np.pi / 3\n",
                "phi = np.pi / 4\n",
                "\n",
                "ylms = ylm_gen(ls, ms, theta, phi)\n",
                "\n",
                "for l, m, ylm in zip(ls, ms, ylms[:5]):\n",
                "    print(\"({},{}):\".format(l, m), ylm)\n",
                "\n",
                "for l, m, ylm in zip(ls, ms, ylms[5:]):\n",
                "    print(\"({},-{}):\".format(l, m), ylm)"
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "few-venv",
            "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": "3.12.3"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 5
}