{ "cells": [ { "cell_type": "code", "execution_count": 141, "metadata": {}, "outputs": [], "source": [ "# use numpy number of threads one\n", "# print(threadpool_info())\n", "# from threadpoolctl import threadpool_info, threadpool_limits\n", "# user_api = threadpool_info()[0][\"user_api\"]\n", "# threadpool_limits(limits=1, user_api=user_api)\n", "# print(threadpool_info())" ] }, { "cell_type": "code", "execution_count": 142, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.14.3\n", "1.24.4\n" ] } ], "source": [ "from sys import getsizeof\n", "from timeit import default_timer as timer\n", "\n", "import sisl\n", "from src.grogupy import *\n", "from mpi4py import MPI\n", "import warnings\n", "\n", "# runtime information\n", "times = dict()\n", "times[\"start_time\"] = timer()\n", "########################\n", "# it works if data is in downloads folder\n", "########################\n", "sisl.__version__\n", "\n", "try:\n", " print(sisl.__version__)\n", "except:\n", " print(\"sisl version unknown.\")\n", "\n", "try:\n", " print(np.__version__)\n", "except:\n", " print(\"numpy version unknown.\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(array([[-8.20799665e+01, 1.42696825e-04, -8.30905002e-04],\n", " [ 1.41821186e-04, -8.20626555e+01, -1.88623702e-01],\n", " [ 6.97129733e-04, 1.88607418e-01, -8.92465137e+01]]), -84.46304519743876, array([[ 2.38307873e+00, 1.42259005e-04, -6.68876347e-05],\n", " [ 1.42259005e-04, 2.40038974e+00, -8.14185600e-06],\n", " [-6.68876347e-05, -8.14185600e-06, -4.78346847e+00]]), array([[ 0.00000000e+00, 4.37819604e-07, -7.64017368e-04],\n", " [-4.37819604e-07, 0.00000000e+00, -1.88615560e-01],\n", " [ 7.64017368e-04, 1.88615560e-01, 0.00000000e+00]]))\n", "[[-8.20799665e+01 1.42259005e-04 -6.68876347e-05]\n", " [ 1.42259005e-04 -8.20626555e+01 -8.14185600e-06]\n", " [-6.68876347e-05 -8.14185600e-06 -8.92465137e+01]] -84.46304519743875 [ 2.38307873e+00 2.40038974e+00 1.42259005e-04 -6.68876347e-05\n", " -8.14185600e-06] [ 1.88615560e-01 -7.64017368e-04 -4.37819604e-07]\n" ] }, { "ename": "LinAlgError", "evalue": "Singular matrix", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mLinAlgError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[187], line 60\u001b[0m\n\u001b[1;32m 57\u001b[0m M \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mouter(ekkprime, ekprimek)\n\u001b[1;32m 58\u001b[0m V \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m E[j] \u001b[38;5;241m*\u001b[39m ekkprime\u001b[38;5;241m.\u001b[39mflatten()\n\u001b[0;32m---> 60\u001b[0m K \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlinalg\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msolve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mM\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mV\u001b[49m\u001b[43m)\u001b[49m\n", "File \u001b[0;32m<__array_function__ internals>:200\u001b[0m, in \u001b[0;36msolve\u001b[0;34m(*args, **kwargs)\u001b[0m\n", "File \u001b[0;32m~/Documents/oktatás/elte/phd/grogu_project/.venv/lib/python3.9/site-packages/numpy/linalg/linalg.py:386\u001b[0m, in \u001b[0;36msolve\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m 384\u001b[0m signature \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mDD->D\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m isComplexType(t) \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mdd->d\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m 385\u001b[0m extobj \u001b[38;5;241m=\u001b[39m get_linalg_error_extobj(_raise_linalgerror_singular)\n\u001b[0;32m--> 386\u001b[0m r \u001b[38;5;241m=\u001b[39m \u001b[43mgufunc\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mb\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msignature\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43msignature\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mextobj\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mextobj\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 388\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m wrap(r\u001b[38;5;241m.\u001b[39mastype(result_t, copy\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m))\n", "File \u001b[0;32m~/Documents/oktatás/elte/phd/grogu_project/.venv/lib/python3.9/site-packages/numpy/linalg/linalg.py:89\u001b[0m, in \u001b[0;36m_raise_linalgerror_singular\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m 88\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_raise_linalgerror_singular\u001b[39m(err, flag):\n\u001b[0;32m---> 89\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m LinAlgError(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mSingular matrix\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n", "\u001b[0;31mLinAlgError\u001b[0m: Singular matrix" ] } ], "source": [ "import pickle\n", "import numpy as np\n", "\n", "with open(\"./Fe3GeTe2_fdf_test.pickle\", \"rb\") as file:\n", " out = pickle.load(file)\n", "\n", "ref_xcf = out[\"parameters\"][\"ref_xcf_orientations\"]\n", "energies = out[\"pairs\"][0][\"energies\"]\n", "\n", "\n", "def fit_energies(energies, ref_xcf):\n", " M = np.zeros((9, 9))\n", " V = np.zeros(9)\n", "\n", " for i in range(len(ref_xcf)):\n", " E = energies[i]\n", " vw = ref_xcf[i][\"vw\"][:2]\n", " o = ref_xcf[i][\"o\"]\n", "\n", " vw = np.array([[vw[0], vw[0]], [vw[0], vw[1]], [vw[1], vw[0]], [vw[1], vw[1]]])\n", "\n", " for j in range(len(vw)):\n", " aa = np.cross(vw[j, 0], o)\n", " bb = np.cross(vw[j, 1], o)\n", " ekkprime = np.outer(aa, bb)\n", " ekprimek = np.outer(bb, aa)\n", " M += np.outer(ekkprime, ekprimek)\n", " V += E[j] * ekkprime.flatten()\n", "\n", " J = np.linalg.solve(M, V)\n", " J = J.reshape(3, 3) * sisl.unit_convert(\"eV\", \"meV\")\n", " J_s = 0.5 * (J + J.T)\n", " D = 0.5 * (J - J.T)\n", " J_iso = np.trace(J_s) / 3\n", " J_S = J_s - np.eye(3) * J_iso\n", "\n", " return J, J_iso, J_S, D\n", "\n", "\n", "print(fit_energies(energies, ref_xcf))\n", "print(\n", " out[\"pairs\"][0][\"J\"],\n", " out[\"pairs\"][0][\"J_iso\"],\n", " out[\"pairs\"][0][\"J_S\"],\n", " out[\"pairs\"][0][\"D\"],\n", ")\n", "\n", "\n", "energies = out[\"magnetic_entities\"][0][\"energies\"]\n", "M = np.zeros((9, 9))\n", "V = np.zeros(9)\n", "\n", "for i in range(len(ref_xcf)):\n", " E = energies[i]\n", " vw = ref_xcf[i][\"vw\"]\n", " o = ref_xcf[i][\"o\"]\n", "\n", " vw = np.array([[vw[0], vw[0]], [vw[1], vw[1]], [vw[2], vw[2]]])\n", "\n", " for j in range(len(vw)):\n", " aa = np.cross(vw[j, 0], o)\n", " bb = np.cross(vw[j, 1], o)\n", " ekkprime = np.outer(aa, bb)\n", " ekprimek = np.outer(bb, aa)\n", " M += np.outer(ekkprime, ekprimek)\n", " V += E[j] * ekkprime.flatten()\n", "\n", "K = np.linalg.solve(M, V)" ] }, { "cell_type": "code", "execution_count": 144, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matrix([[a1], [a2], [a3]])\n", "Matrix([[b1], [b2], [b3]])\n", "Matrix([[J11, J12, J13], [J21, J22, J23], [J31, J32, J33]])\n", "J11*a1*b1 + J12*a1*b2 + J13*a1*b3 + J21*a2*b1 + J22*a2*b2 + J23*a2*b3 + J31*a3*b1 + J32*a3*b2 + J33*a3*b3\n", "J11*a1*b1 + J12*a1*b2 + J13*a1*b3 + J21*a2*b1 + J22*a2*b2 + J23*a2*b3 + J31*a3*b1 + J32*a3*b2 + J33*a3*b3\n", "Matrix([[J11], [J12], [J13], [J21], [J22], [J23], [J31], [J32], [J33]])\n", "Matrix([[J11*a1*b1 + J12*a1*b2 + J13*a1*b3 + J21*a2*b1 + J22*a2*b2 + J23*a2*b3 + J31*a3*b1 + J32*a3*b2 + J33*a3*b3]])\n", "Matrix([[a1*b1], [a1*b2], [a1*b3], [a2*b1], [a2*b2], [a2*b3], [a3*b1], [a3*b2], [a3*b3]])\n" ] } ], "source": [ "import sympy as sy\n", "\n", "a = sy.symbols(\"a1:4\")\n", "b = sy.symbols(\"b1:4\")\n", "J = sy.symbols(\"J(1:4)(1:4)\")\n", "\n", "\n", "aa = sy.Matrix(a)\n", "bb = sy.Matrix(b)\n", "\n", "print(aa)\n", "print(bb)\n", "\n", "JJ = sy.Matrix(J).reshape(3, 3)\n", "\n", "print(JJ)\n", "\n", "print((aa.T @ JJ @ bb)[0].expand())\n", "print(sy.trace(JJ @ (bb @ aa.T)))\n", "print(JJ.reshape(9, 1))\n", "print(JJ.reshape(1, 9) @ (aa @ bb.T).reshape(9, 1))\n", "print((aa @ bb.T).reshape(9, 1))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 151, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'parameters': {'infile': '/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf',\n", " 'outfile': './Fe3GeTe2_fdf_test.pickle',\n", " 'scf_xcf_orientation': array([0., 0., 1.]),\n", " 'ref_xcf_orientations': [{'o': array([1., 0., 0.]),\n", " 'vw': array([[0. , 1. , 0. ],\n", " [0. , 0. , 1. ],\n", " [0. , 0.70710678, 0.70710678]])},\n", " {'o': array([0., 1., 0.]),\n", " 'vw': array([[1. , 0. , 0. ],\n", " [0. , 0. , 1. ],\n", " [0.70710678, 0. , 0.70710678]])},\n", " {'o': array([0., 0., 1.]),\n", " 'vw': array([[1. , 0. , 0. ],\n", " [0. , 1. , 0. ],\n", " [0.70710678, 0.70710678, 0. ]])}],\n", " 'kset': 10,\n", " 'kdirs': 'xy',\n", " 'ebot': -12.906878959999998,\n", " 'eset': 600,\n", " 'esetp': 1000.0,\n", " 'parallel_solver_for_Gk': False,\n", " 'padawan_mode': True,\n", " 'parallel_size': 1,\n", " 'automatic_ebot': True,\n", " 'cell': array([[ 3.79100000e+00, 0.00000000e+00, 0.00000000e+00],\n", " [-1.89550000e+00, 3.28310231e+00, 0.00000000e+00],\n", " [ 1.25954923e-15, 2.18160327e-15, 2.05700000e+01]])},\n", " 'magnetic_entities': [{'atom': 3,\n", " 'l': [2],\n", " 'orbital_indices': array([41, 42, 43, 44, 45, 46, 47, 48, 49, 50], dtype=int32),\n", " 'spin_box_indices': array([ 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94,\n", " 95, 96, 97, 98, 99, 100, 101]),\n", " 'tags': ['[3]Fe([2])'],\n", " 'xyz': [array([-7.33915874e-06, 4.14927851e-06, 1.16575858e+01])],\n", " 'energies': array([[1.17772527, 1.17771974, 1.17772812],\n", " [1.17764184, 1.177567 , 1.17761357],\n", " [1.17892446, 1.17892335, 1.17892284]]),\n", " 'K': array([[-0.07483657, 0.00106563, -0.0091485 ],\n", " [ 0.00106563, -0.00553059, -0.00561574],\n", " [-0.0091485 , -0.00561574, 0. ]]),\n", " 'K_consistency': 6.819575556149537e-05},\n", " {'atom': 4,\n", " 'l': [2],\n", " 'orbital_indices': array([56, 57, 58, 59, 60, 61, 62, 63, 64, 65], dtype=int32),\n", " 'spin_box_indices': array([112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124,\n", " 125, 126, 127, 128, 129, 130, 131]),\n", " 'tags': ['[4]Fe([2])'],\n", " 'xyz': [array([-7.32698766e-06, 4.15827452e-06, 8.91242254e+00])],\n", " 'energies': array([[1.17774 , 1.17766249, 1.17769662],\n", " [1.1776063 , 1.17760676, 1.17759665],\n", " [1.17893438, 1.17893546, 1.17893594]]),\n", " 'K': array([[ 0.00045681, -0.00101949, 0.00987698],\n", " [-0.00101949, -0.07750577, 0.00462617],\n", " [ 0.00987698, 0.00462617, 0. ]]),\n", " 'K_consistency': 7.687732837413641e-05},\n", " {'atom': 5,\n", " 'l': [2],\n", " 'orbital_indices': array([71, 72, 73, 74, 75, 76, 77, 78, 79, 80], dtype=int32),\n", " 'spin_box_indices': array([142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154,\n", " 155, 156, 157, 158, 159, 160, 161]),\n", " 'tags': ['[5]Fe([2])'],\n", " 'xyz': [array([ 1.89546671, 1.09439132, 10.2850027 ])],\n", " 'energies': array([[0.82604465, 0.82600318, 0.82602942],\n", " [0.82596082, 0.82597202, 0.82596098],\n", " [0.83074663, 0.83074663, 0.83074663]]),\n", " 'K': array([[ 1.12053382e-02, -4.12902668e-06, 5.44290076e-03],\n", " [-4.12902668e-06, -4.14783466e-02, -5.50288071e-03],\n", " [ 5.44290076e-03, -5.50288071e-03, 0.00000000e+00]]),\n", " 'K_consistency': 5.2686617336705766e-05}],\n", " 'pairs': [{'ai': 0,\n", " 'aj': 1,\n", " 'Ruc': array([0, 0, 0]),\n", " 'dist': 2.745163300331324,\n", " 'tags': ['[3]Fe([2])', '[4]Fe([2])'],\n", " 'energies': array([[-8.92392323e-02, 1.88623702e-04, -1.88607418e-04,\n", " -8.91422199e-02],\n", " [-8.92537950e-02, 8.30905002e-07, -6.97129733e-07,\n", " -8.91766857e-02],\n", " [-7.49830910e-02, -1.42696825e-07, -1.41821186e-07,\n", " -7.49832472e-02]]),\n", " 'J_iso': -84.46304519743875,\n", " 'J_S': array([ 2.38307873e+00, 2.40038974e+00, 1.42259005e-04, -6.68876347e-05,\n", " -8.14185600e-06]),\n", " 'D': array([ 1.88615560e-01, -7.64017368e-04, -4.37819604e-07]),\n", " 'J': array([[-8.20799665e+01, 1.42259005e-04, -6.68876347e-05],\n", " [ 1.42259005e-04, -8.20626555e+01, -8.14185600e-06],\n", " [-6.68876347e-05, -8.14185600e-06, -8.92465137e+01]])},\n", " {'ai': 0,\n", " 'aj': 2,\n", " 'Ruc': array([0, 0, 0]),\n", " 'dist': 2.5835033632437767,\n", " 'tags': ['[3]Fe([2])', '[5]Fe([2])'],\n", " 'energies': array([[-0.04075836, 0.00119288, -0.00112921, -0.04080086],\n", " [-0.04056911, 0.00207638, -0.00198342, -0.04056736],\n", " [-0.04367583, -0.00022997, -0.00023025, -0.04340975]]),\n", " 'J_iso': -41.630212919435856,\n", " 'J_S': array([-0.35834154, -0.60813515, 0.23011103, -0.046484 , -0.03183377]),\n", " 'D': array([ 1.16104682e+00, -2.02989980e+00, 1.42005544e-04]),\n", " 'J': array([[-4.19885545e+01, 2.30111030e-01, -4.64839962e-02],\n", " [ 2.30111030e-01, -4.22383481e+01, -3.18337650e-02],\n", " [-4.64839962e-02, -3.18337650e-02, -4.06637362e+01]])},\n", " {'ai': 1,\n", " 'aj': 2,\n", " 'Ruc': array([0, 0, 0]),\n", " 'dist': 2.583501767937866,\n", " 'tags': ['[4]Fe([2])', '[5]Fe([2])'],\n", " 'energies': array([[-0.04077002, -0.00117329, 0.00113811, -0.04082399],\n", " [-0.04057372, -0.00204387, 0.00197878, -0.0405759 ],\n", " [-0.04367653, -0.00022997, -0.00023026, -0.04341045]]),\n", " 'J_iso': -41.63843353643032,\n", " 'J_S': array([-0.35473711, -0.61182503, 0.23011277, 0.03254538, 0.01758745]),\n", " 'D': array([-1.15570028e+00, 2.01132360e+00, 1.42811452e-04]),\n", " 'J': array([[-4.19931707e+01, 2.30112766e-01, 3.25453781e-02],\n", " [ 2.30112766e-01, -4.22502586e+01, 1.75874450e-02],\n", " [ 3.25453781e-02, 1.75874450e-02, -4.06718714e+01]])},\n", " {'ai': 0,\n", " 'aj': 2,\n", " 'Ruc': array([-1, -1, 0]),\n", " 'dist': 2.5834973202859075,\n", " 'tags': ['[3]Fe([2])', '[5]Fe([2])'],\n", " 'energies': array([[-4.05164545e-02, -2.37526408e-03, 2.29370374e-03,\n", " -4.04788963e-02],\n", " [-4.09074301e-02, -2.05208851e-07, -8.74099273e-08,\n", " -4.09801092e-02],\n", " [-4.32782877e-02, 1.10167960e-07, 1.95301791e-07,\n", " -4.38099217e-02]]),\n", " 'J_iso': -41.66184991462266,\n", " 'J_S': array([-7.33165557e-01, -2.16742080e-01, -1.52734875e-04, 1.46309389e-04,\n", " 4.07801676e-02]),\n", " 'D': array([-2.33448391e+00, 5.88994618e-05, -4.25669156e-05]),\n", " 'J': array([[-4.23950155e+01, -1.52734875e-04, 1.46309389e-04],\n", " [-1.52734875e-04, -4.18785920e+01, 4.07801676e-02],\n", " [ 1.46309389e-04, 4.07801676e-02, -4.07119423e+01]])},\n", " {'ai': 1,\n", " 'aj': 2,\n", " 'Ruc': array([-1, -1, 0]),\n", " 'dist': 2.583495745338251,\n", " 'tags': ['[4]Fe([2])', '[5]Fe([2])'],\n", " 'energies': array([[-4.05171468e-02, 2.37529161e-03, -2.29373272e-03,\n", " -4.04795842e-02],\n", " [-4.08811902e-02, 1.57284973e-07, -4.45157439e-07,\n", " -4.09421171e-02],\n", " [-4.32789799e-02, 1.09351818e-07, 1.96420584e-07,\n", " -4.38106181e-02]]),\n", " 'J_iso': -41.651606039885934,\n", " 'J_S': array([-7.24761554e-01, -2.27675997e-01, -1.52886201e-04, 1.43936233e-04,\n", " -4.07794409e-02]),\n", " 'D': array([ 2.33451216e+00, -3.01221206e-04, -4.35343826e-05]),\n", " 'J': array([[-4.23763676e+01, -1.52886201e-04, 1.43936233e-04],\n", " [-1.52886201e-04, -4.18792820e+01, -4.07794409e-02],\n", " [ 1.43936233e-04, -4.07794409e-02, -4.06991685e+01]])},\n", " {'ai': 0,\n", " 'aj': 2,\n", " 'Ruc': array([-1, 0, 0]),\n", " 'dist': 2.583541444641373,\n", " 'tags': ['[3]Fe([2])', '[5]Fe([2])'],\n", " 'energies': array([[-0.04075762, 0.00117311, -0.00113797, -0.04081104],\n", " [-0.04055754, -0.00207635, 0.00198375, -0.04055565],\n", " [-0.04366146, 0.00022983, 0.00023003, -0.04339595]]),\n", " 'J_iso': -41.62320943278901,\n", " 'J_S': array([-0.35258884, -0.61303902, -0.22992743, 0.04629825, -0.01757271]),\n", " 'D': array([ 1.15553939e+00, 2.03005138e+00, -1.00670740e-04]),\n", " 'J': array([[-4.19757983e+01, -2.29927428e-01, 4.62982483e-02],\n", " [-2.29927428e-01, -4.22362485e+01, -1.75727100e-02],\n", " [ 4.62982483e-02, -1.75727100e-02, -4.06575816e+01]])},\n", " {'ai': 1,\n", " 'aj': 2,\n", " 'Ruc': array([-1, 0, 0]),\n", " 'dist': 2.5835398672184064,\n", " 'tags': ['[4]Fe([2])', '[5]Fe([2])'],\n", " 'energies': array([[-0.04074738, -0.00119276, 0.00112911, -0.04078932],\n", " [-0.04056216, 0.00204384, -0.00197854, -0.04056432],\n", " [-0.04366217, 0.00022983, 0.00023003, -0.04339665]]),\n", " 'J_iso': -41.62033567430795,\n", " 'J_S': array([-0.36015198, -0.6054113 , -0.22992935, -0.03265044, 0.03182307]),\n", " 'D': array([-1.16093344e+00, -2.01119076e+00, -9.97127859e-05]),\n", " 'J': array([[-4.19804877e+01, -2.29929354e-01, -3.26504440e-02],\n", " [-2.29929354e-01, -4.22257470e+01, 3.18230690e-02],\n", " [-3.26504440e-02, 3.18230690e-02, -4.06547724e+01]])},\n", " {'ai': 1,\n", " 'aj': 2,\n", " 'Ruc': array([-2, 0, 0]),\n", " 'dist': 5.951322298958084,\n", " 'tags': ['[4]Fe([2])', '[5]Fe([2])'],\n", " 'energies': array([[-1.72611605e-03, -4.36527901e-05, 1.26576311e-04,\n", " -1.82722454e-03],\n", " [-1.80427815e-03, -2.63038710e-04, 2.20144926e-04,\n", " -1.73941292e-03],\n", " [-1.75263911e-03, 1.36519152e-03, -1.52871309e-03,\n", " -1.52707483e-03]]),\n", " 'J_iso': -1.7294575999129687,\n", " 'J_S': array([ 0.09621372, -0.06047422, 0.08176078, 0.02144689, -0.04146176]),\n", " 'D': array([-0.08511455, 0.24159182, 1.4469523 ]),\n", " 'J': array([[-1.63324388, 0.08176078, 0.02144689],\n", " [ 0.08176078, -1.78993182, -0.04146176],\n", " [ 0.02144689, -0.04146176, -1.7651971 ]])},\n", " {'ai': 1,\n", " 'aj': 2,\n", " 'Ruc': array([-3, 0, 0]),\n", " 'dist': 9.638732176310562,\n", " 'tags': ['[4]Fe([2])', '[5]Fe([2])'],\n", " 'energies': array([[-7.80160843e-04, 3.56600605e-05, -6.10780433e-05,\n", " -7.42312414e-04],\n", " [-7.94983595e-04, -5.77431729e-05, 5.08380963e-05,\n", " -8.34625148e-04],\n", " [ 2.17237059e-04, -1.43586609e-04, 1.74512092e-04,\n", " 2.13496975e-04]]),\n", " 'J_iso': -0.45355799416161025,\n", " 'J_S': array([ 0.14299391, 0.19102032, -0.01546274, 0.00345254, 0.01270899]),\n", " 'D': array([ 0.04836905, 0.05429063, -0.15904935]),\n", " 'J': array([[-0.31056409, -0.01546274, 0.00345254],\n", " [-0.01546274, -0.26253768, 0.01270899],\n", " [ 0.00345254, 0.01270899, -0.78757222]])}],\n", " 'runtime': {'start_time': 0.881972083,\n", " 'setup_time': 0.979693,\n", " 'H_and_XCF_time': 1.361691666,\n", " 'site_and_pair_dictionaries_time': 1.40248525,\n", " 'k_set_time': 1.432338791,\n", " 'reference_rotations_time': 1.68477325,\n", " 'green_function_inversion_time': 281.406242666,\n", " 'end_time': 281.949395875}}" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "out" ] }, { "cell_type": "code", "execution_count": 171, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([0., 0., 1.]), array([0., 1., 0.]))" ] }, "execution_count": 171, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scf_xcf_orientation = out[\"parameters\"][\"scf_xcf_orientation\"]\n", "\n", "ref_xcf_orientations = out[\"parameters\"][\"ref_xcf_orientations\"]\n", "\n", "scf_xcf_orientation\n", "\n", "from grogupy import *\n", "from grogupy.utilities import *\n", "\n", "\n", "def generate_perpendicular(orientation, reference):\n", " x = np.array([1, 0, 0])\n", " y = np.array([0, 1, 0])\n", " z = np.array([0, 0, 1])\n", "\n", " R_to_reference = RotMa2b(z, reference)\n", " x = R_to_reference @ x\n", " y = R_to_reference @ y\n", " z = R_to_reference @ z\n", "\n", " R_to_orientation = RotMa2b(z, orientation)\n", " x = R_to_orientation @ x\n", " y = R_to_orientation @ y\n", "\n", " return x, y\n", "\n", "\n", "generate_perpendicular(ref_xcf_orientations[0][\"o\"], scf_xcf_orientation)" ] }, { "cell_type": "code", "execution_count": 172, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1. 0. 0.]\n", "[[0. 1. 0. ]\n", " [0. 0. 1. ]\n", " [0. 0.70710678 0.70710678]]\n", "(array([0., 0., 1.]), array([0., 1., 0.]))\n", "[0. 1. 0.]\n", "[[1. 0. 0. ]\n", " [0. 0. 1. ]\n", " [0.70710678 0. 0.70710678]]\n", "(array([-1., 0., 0.]), array([ 0., 0., -1.]))\n", "[0. 0. 1.]\n", "[[1. 0. 0. ]\n", " [0. 1. 0. ]\n", " [0.70710678 0.70710678 0. ]]\n", "(array([-1., 0., 0.]), array([0., 1., 0.]))\n" ] } ], "source": [ "for ref in ref_xcf_orientations:\n", " print(ref[\"o\"])\n", " print(ref[\"vw\"])\n", " print(generate_perpendicular(ref[\"o\"], scf_xcf_orientation))" ] }, { "cell_type": "code", "execution_count": 182, "metadata": {}, "outputs": [ { "ename": "LinAlgError", "evalue": "Singular matrix", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mLinAlgError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[182], line 25\u001b[0m\n\u001b[1;32m 22\u001b[0m M \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mouter(ekkprime, ekprimek)\n\u001b[1;32m 23\u001b[0m V \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m E[j] \u001b[38;5;241m*\u001b[39m ekkprime\u001b[38;5;241m.\u001b[39mflatten()\n\u001b[0;32m---> 25\u001b[0m K \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlinalg\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msolve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mM\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mV\u001b[49m\u001b[43m)\u001b[49m\n", "File \u001b[0;32m<__array_function__ internals>:200\u001b[0m, in \u001b[0;36msolve\u001b[0;34m(*args, **kwargs)\u001b[0m\n", "File \u001b[0;32m~/Documents/oktatás/elte/phd/grogu_project/.venv/lib/python3.9/site-packages/numpy/linalg/linalg.py:386\u001b[0m, in \u001b[0;36msolve\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m 384\u001b[0m signature \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mDD->D\u001b[39m\u001b[38;5;124m'\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m isComplexType(t) \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mdd->d\u001b[39m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m 385\u001b[0m extobj \u001b[38;5;241m=\u001b[39m get_linalg_error_extobj(_raise_linalgerror_singular)\n\u001b[0;32m--> 386\u001b[0m r \u001b[38;5;241m=\u001b[39m \u001b[43mgufunc\u001b[49m\u001b[43m(\u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mb\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msignature\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43msignature\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mextobj\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mextobj\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 388\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m wrap(r\u001b[38;5;241m.\u001b[39mastype(result_t, copy\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m))\n", "File \u001b[0;32m~/Documents/oktatás/elte/phd/grogu_project/.venv/lib/python3.9/site-packages/numpy/linalg/linalg.py:89\u001b[0m, in \u001b[0;36m_raise_linalgerror_singular\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m 88\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_raise_linalgerror_singular\u001b[39m(err, flag):\n\u001b[0;32m---> 89\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m LinAlgError(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mSingular matrix\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n", "\u001b[0;31mLinAlgError\u001b[0m: Singular matrix" ] } ], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "################################################################################\n", "#################################### INPUT #####################################\n", "################################################################################\n", "path = (\n", " \"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf\"\n", ")\n", "outfile = \"./Fe3GeTe2_notebook\"\n", "\n", "# this information needs to be given at the input!!\n", "scf_xcf_orientation = np.array([0, 0, 1]) # z\n", "# list of reference directions for around which we calculate the derivatives\n", "# o is the quantization axis, v and w are two axes perpendicular to it\n", "# at this moment the user has to supply o,v,w on the input.\n", "# we can have some default for this\n", "ref_xcf_orientations = [\n", " dict(o=np.array([1, 0, 0]), vw=[np.array([0, 1, 0]), np.array([0, 0, 1])]),\n", " dict(o=np.array([0, 1, 0]), vw=[np.array([1, 0, 0]), np.array([0, 0, 1])]),\n", " dict(o=np.array([0, 0, 1]), vw=[np.array([1, 0, 0]), np.array([0, 1, 0])]),\n", "]\n", "magnetic_entities = [\n", " dict(atom=3, l=2),\n", " dict(atom=4, l=2),\n", " dict(atom=5, l=2),\n", "]\n", "pairs = [\n", " dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),\n", " dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),\n", " dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),\n", " dict(ai=0, aj=2, Ruc=np.array([-1, -1, 0])),\n", " dict(ai=1, aj=2, Ruc=np.array([-1, -1, 0])),\n", " dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),\n", " dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),\n", " dict(ai=1, aj=2, Ruc=np.array([-2, 0, 0])),\n", " dict(ai=1, aj=2, Ruc=np.array([-3, 0, 0])),\n", "]\n", "\n", "# Brilloun zone sampling and Green function contour integral\n", "kset = 100\n", "kdirs = \"xy\"\n", "ebot = -13\n", "eset = 300\n", "esetp = 1000\n", "################################################################################\n", "#################################### INPUT #####################################\n", "################################################################################" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "300\n", "100\n", "3\n" ] } ], "source": [ "eset_space = np.linspace(0, eset - 1, eset, dtype=int)\n", "kset_space = np.linspace(0, kset - 1, kset, dtype=int)\n", "orient_space = np.linspace(\n", " 0, len(ref_xcf_orientations) - 1, len(ref_xcf_orientations), dtype=int\n", ")\n", "print(len(kset_space))\n", "print(len(orient_space))\n", "print(len(eset_space))" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [], "source": [ "from itertools import product\n", "\n", "combinations = product(eset_space, eset_space, eset_space)\n", "asd = np.array_split(np.array(list(combinations)), 128)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "================================================================================================================================================================\n", "SLURM job ID not found.\n", "Input file: \n", "/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf\n", "Output file: \n", "./Fe3GeTe2_notebook.pickle\n", "Number of nodes in the parallel cluster: 1\n", "================================================================================================================================================================\n", "Cell [Ang]: \n", "[[ 3.79100000e+00 0.00000000e+00 0.00000000e+00]\n", " [-1.89550000e+00 3.28310231e+00 0.00000000e+00]\n", " [ 1.25954923e-15 2.18160327e-15 2.05700000e+01]]\n", "================================================================================================================================================================\n", "DFT axis: \n", "[0 0 1]\n", "Quantization axis and perpendicular rotation directions:\n", "[1 0 0] --» [array([0, 1, 0]), array([0, 0, 1])]\n", "[0 1 0] --» [array([1, 0, 0]), array([0, 0, 1])]\n", "[0 0 1] --» [array([1, 0, 0]), array([0, 1, 0])]\n", "================================================================================================================================================================\n", "Parameters for the contour integral:\n", "Number of k points: 3\n", "k point directions: xy\n", "Ebot: -13\n", "Eset: 300\n", "Esetp: 1000\n", "================================================================================================================================================================\n", "Setup done. Elapsed time: 3.275603625 s\n", "================================================================================================================================================================\n" ] } ], "source": [ "# MPI parameters\n", "comm = MPI.COMM_WORLD\n", "size = comm.Get_size()\n", "rank = comm.Get_rank()\n", "root_node = 0\n", "\n", "# rename outfile\n", "if not outfile.endswith(\".pickle\"):\n", " outfile += \".pickle\"\n", "\n", "simulation_parameters = dict(\n", " infile=path,\n", " outfile=outfile,\n", " scf_xcf_orientation=scf_xcf_orientation,\n", " ref_xcf_orientations=ref_xcf_orientations,\n", " kset=kset,\n", " kdirs=kdirs,\n", " ebot=ebot,\n", " eset=eset,\n", " esetp=esetp,\n", " parallel_size=size,\n", ")\n", "\n", "# if ebot is not given put it 0.1 eV under the smallest energy\n", "if simulation_parameters[\"ebot\"] is None:\n", " try:\n", " eigfile = simulation_parameters[\"infile\"][:-3] + \"EIG\"\n", " simulation_parameters[\"ebot\"] = read_siesta_emin(eigfile) - 0.1\n", " except:\n", " print(\"Could not determine ebot.\")\n", " print(\"Parameter was not given and .EIG file was not found.\")\n", "# digestion of the input\n", "# read sile\n", "fdf = sisl.get_sile(simulation_parameters[\"infile\"])\n", "# read in hamiltonian\n", "dh = fdf.read_hamiltonian()\n", "simulation_parameters[\"cell\"] = fdf.read_geometry().cell\n", "\n", "# unit cell index\n", "uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])\n", "\n", "if rank == root_node:\n", " print_parameters(simulation_parameters)\n", " times[\"setup_time\"] = timer()\n", " print(f\"Setup done. Elapsed time: {times['setup_time']} s\")\n", " print(\n", " \"================================================================================================================================================================\"\n", " )" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hamiltonian and exchange field rotated. Elapsed time: 3.976168875 s\n", "================================================================================================================================================================\n" ] } ], "source": [ "hh, ss = build_hh_ss(dh)\n", "NO = dh.no\n", "\n", "# symmetrizing Hamiltonian and overlap matrix to make them hermitian\n", "for i in range(dh.lattice.sc_off.shape[0]):\n", " j = dh.lattice.sc_index(-dh.lattice.sc_off[i])\n", " h1, h1d = hh[i], hh[j]\n", " hh[i], hh[j] = (h1 + h1d.T.conj()) / 2, (h1d + h1.T.conj()) / 2\n", " s1, s1d = ss[i], ss[j]\n", " ss[i], ss[j] = (s1 + s1d.T.conj()) / 2, (s1d + s1.T.conj()) / 2\n", "\n", "\n", "# identifying TRS and TRB parts of the Hamiltonian\n", "TAUY = np.kron(np.eye(NO), TAU_Y)\n", "hTR = np.array([TAUY @ hh[i].conj() @ TAUY for i in range(dh.lattice.nsc.prod())])\n", "hTRS = (hh + hTR) / 2\n", "hTRB = (hh - hTR) / 2\n", "\n", "# extracting the exchange field\n", "traced = [spin_tracer(hTRB[i]) for i in range(dh.lattice.nsc.prod())] # equation 77\n", "XCF = np.array(\n", " [\n", " np.array([f[\"x\"] / 2 for f in traced]),\n", " np.array([f[\"y\"] / 2 for f in traced]),\n", " np.array([f[\"z\"] / 2 for f in traced]),\n", " ]\n", ") # equation 77\n", "\n", "\n", "# Check if exchange field has scalar part\n", "max_xcfs = abs(np.array(np.array([f[\"c\"] / 2 for f in traced]))).max()\n", "if max_xcfs > 1e-12:\n", " warnings.warn(\n", " f\"Exchange field has non negligible scalar part. Largest value is {max_xcfs}\"\n", " )\n", "\n", "if rank == root_node:\n", " times[\"H_and_XCF_time\"] = timer()\n", " print(\n", " f\"Hamiltonian and exchange field rotated. Elapsed time: {times['H_and_XCF_time']} s\"\n", " )\n", " print(\n", " \"================================================================================================================================================================\"\n", " )" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Site and pair dictionaries created. Elapsed time: 4.091688166 s\n", "================================================================================================================================================================\n" ] } ], "source": [ "pairs, magnetic_entities = setup_pairs_and_magnetic_entities(\n", " magnetic_entities, pairs, dh, simulation_parameters\n", ")\n", "\n", "if rank == root_node:\n", " times[\"site_and_pair_dictionaries_time\"] = timer()\n", " print(\n", " f\"Site and pair dictionaries created. Elapsed time: {times['site_and_pair_dictionaries_time']} s\"\n", " )\n", " print(\n", " \"================================================================================================================================================================\"\n", " )" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k set created. Elapsed time: 22.801980041 s\n", "================================================================================================================================================================\n" ] } ], "source": [ "kset = make_kset(\n", " dirs=simulation_parameters[\"kdirs\"], NUMK=simulation_parameters[\"kset\"]\n", ") # generate k space sampling\n", "wkset = np.ones(len(kset)) / len(kset) # generate weights for k points\n", "kpcs = np.array_split(kset, size) # split the k points based on MPI size\n", "\n", "\n", "if rank == root_node:\n", " times[\"k_set_time\"] = timer()\n", " print(f\"k set created. Elapsed time: {times['k_set_time']} s\")\n", " print(\n", " \"================================================================================================================================================================\"\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "9" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# make energy contour\n", "# we are working in eV now !\n", "# and sisl shifts E_F to 0 !\n", "cont = make_contour(\n", " emin=simulation_parameters[\"ebot\"],\n", " enum=simulation_parameters[\"eset\"],\n", " p=simulation_parameters[\"esetp\"],\n", ")\n", "eran = cont.ze" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# this will contain the three hamiltonians in the reference directions needed to calculate the energy variations upon rotation\n", "hamiltonians = []\n", "\n", "# iterate over the reference directions (quantization axes)\n", "for i, orient in enumerate(simulation_parameters[\"ref_xcf_orientations\"]):\n", " # obtain rotated exchange field\n", " R = RotMa2b(simulation_parameters[\"scf_xcf_orientation\"], orient[\"o\"])\n", " rot_XCF = np.einsum(\"ij,jklm->iklm\", R, XCF)\n", " rot_H_XCF = sum(\n", " [np.kron(rot_XCF[i], tau) for i, tau in enumerate([tau_x, tau_y, tau_z])]\n", " )\n", " rot_H_XCF_uc = rot_H_XCF[uc_in_sc_idx]\n", "\n", " # obtain total Hamiltonian with the rotated exchange field\n", " rot_H = hTRS + rot_H_XCF # equation 76\n", "\n", " hamiltonians.append(\n", " dict(\n", " orient=orient[\"o\"],\n", " H=rot_H,\n", " GS=np.zeros(\n", " (simulation_parameters[\"eset\"], rot_H.shape[1], rot_H.shape[2]),\n", " dtype=\"complex128\",\n", " ),\n", " GS_tmp=np.zeros(\n", " (simulation_parameters[\"eset\"], rot_H.shape[1], rot_H.shape[2]),\n", " dtype=\"complex128\",\n", " ),\n", " )\n", " ) # store orientation and rotated Hamiltonian\n", "\n", " # these are the rotations (for now) perpendicular to the quantization axis\n", " for u in orient[\"vw\"]:\n", " Tu = np.kron(np.eye(NO, dtype=int), tau_u(u)) # section 2.H\n", "\n", " Vu1, Vu2 = calc_Vu(rot_H_XCF_uc, Tu)\n", "\n", " for mag_ent in magnetic_entities:\n", " idx = mag_ent[\"spin_box_indeces\"]\n", " # fill up the perturbed potentials (for now) based on the on-site projections\n", " mag_ent[\"Vu1\"][i].append(Vu1[:, idx][idx, :])\n", " mag_ent[\"Vu2\"][i].append(Vu2[:, idx][idx, :])\n", "\n", "if rank == root_node:\n", " times[\"reference_rotations_time\"] = timer()\n", " print(\n", " f\"Rotations done perpendicular to quantization axis. Elapsed time: {times['reference_rotations_time']} s\"\n", " )\n", " print(\n", " \"================================================================================================================================================================\"\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "if rank == root_node:\n", " print(\"Starting matrix inversions.\")\n", " print(f\"Total number of k points: {kset.shape[0]}\")\n", " print(f\"Number of energy samples per k point: {simulation_parameters['eset']}\")\n", " print(f\"Total number of directions: {len(hamiltonians)}\")\n", " print(\n", " f\"Total number of matrix inversions: {kset.shape[0] * len(hamiltonians) * simulation_parameters['eset']}\"\n", " )\n", " print(f\"The shape of the Hamiltonian and the Greens function is {NO}x{NO}={NO*NO}\")\n", " # https://stackoverflow.com/questions/70746660/how-to-predict-memory-requirement-for-np-linalg-inv\n", " # memory is O(64 n**2) for complex matrices\n", " memory_size = getsizeof(hamiltonians[0][\"H\"].base) / 1024\n", " print(\n", " f\"Memory taken by a single Hamiltonian is: {getsizeof(hamiltonians[0]['H'].base) / 1024} KB\"\n", " )\n", " print(f\"Expected memory usage per matrix inversion: {memory_size * 32} KB\")\n", " print(\n", " f\"Expected memory usage per k point for parallel inversion: {memory_size * len(hamiltonians) * simulation_parameters['eset'] * 32} KB\"\n", " )\n", " print(\n", " f\"Expected memory usage on root node: {len(np.array_split(kset, size)[0]) * memory_size * len(hamiltonians) * simulation_parameters['eset'] * 32 / 1024} MB\"\n", " )\n", " print(\n", " \"================================================================================================================================================================\"\n", " )\n", "\n", "comm.Barrier()\n", "# ----------------------------------------------------------------------\n", "\n", "# make energy contour\n", "# we are working in eV now !\n", "# and sisl shifts E_F to 0 !\n", "cont = make_contour(\n", " emin=simulation_parameters[\"ebot\"],\n", " enum=simulation_parameters[\"eset\"],\n", " p=simulation_parameters[\"esetp\"],\n", ")\n", "eran = cont.ze\n", "\n", "# ----------------------------------------------------------------------\n", "# sampling the integrand on the contour and the BZ\n", "for k in kpcs[rank]:\n", " wk = wkset[rank] # weight of k point in BZ integral\n", " # iterate over reference directions\n", " for i, hamiltonian_orientation in enumerate(hamiltonians):\n", " # calculate Greens function\n", " H = hamiltonian_orientation[\"H\"]\n", " HK, SK = hsk(H, ss, dh.sc_off, k)\n", "\n", " # solve Greens function sequentially for the energies, because of memory bound\n", " Gk = sequential_GK(HK, SK, eran, simulation_parameters[\"eset\"])\n", "\n", " # saving this for total charge\n", " hamiltonian_orientation[\"GS_tmp\"] += Gk @ SK * wk\n", "\n", " # store the Greens function slice of the magnetic entities (for now) based on the on-site projections\n", " for mag_ent in magnetic_entities:\n", " mag_ent[\"Gii_tmp\"][i] += (\n", " Gk[:, mag_ent[\"spin_box_indeces\"], :][:, :, mag_ent[\"spin_box_indeces\"]]\n", " * wk\n", " )\n", "\n", " for pair in pairs:\n", " # add phase shift based on the cell difference\n", " phase = np.exp(1j * 2 * np.pi * k @ pair[\"Ruc\"].T)\n", "\n", " # get the pair orbital sizes from the magnetic entities\n", " ai = magnetic_entities[pair[\"ai\"]][\"spin_box_indeces\"]\n", " aj = magnetic_entities[pair[\"aj\"]][\"spin_box_indeces\"]\n", "\n", " # store the Greens function slice of the magnetic entities (for now) based on the on-site projections\n", " pair[\"Gij_tmp\"][i] += Gk[:, ai][..., aj] * phase * wk\n", " pair[\"Gji_tmp\"][i] += Gk[:, aj][..., ai] / phase * wk\n", "\n", "# summ reduce partial results of mpi nodes\n", "for i in range(len(hamiltonians)):\n", " # for total charge\n", " comm.Reduce(hamiltonians[i][\"GS_tmp\"], hamiltonians[i][\"GS\"], root=root_node)\n", "\n", " for mag_ent in magnetic_entities:\n", " comm.Reduce(mag_ent[\"Gii_tmp\"][i], mag_ent[\"Gii\"][i], root=root_node)\n", "\n", " for pair in pairs:\n", " comm.Reduce(pair[\"Gij_tmp\"][i], pair[\"Gij\"][i], root=root_node)\n", " comm.Reduce(pair[\"Gji_tmp\"][i], pair[\"Gji\"][i], root=root_node)\n", "\n", "if rank == root_node:\n", " times[\"green_function_inversion_time\"] = timer()\n", " print(\n", " f\"Calculated Greens functions. Elapsed time: {times['green_function_inversion_time']} s\"\n", " )\n", " print(\n", " \"================================================================================================================================================================\"\n", " )" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "if rank == root_node:\n", " # Calculate total charge\n", " for hamiltonian in hamiltonians:\n", " GS = hamiltonian[\"GS\"]\n", " traced = np.trace((GS), axis1=1, axis2=2)\n", " print(\"Total charge: \", int_de_ke(traced, cont.we))\n", "\n", " # iterate over the magnetic entities\n", " for tracker, mag_ent in enumerate(magnetic_entities):\n", " # iterate over the quantization axes\n", " for i, Gii in enumerate(mag_ent[\"Gii\"]):\n", " storage = []\n", " # iterate over the first and second order local perturbations\n", " for Vu1, Vu2 in zip(mag_ent[\"Vu1\"][i], mag_ent[\"Vu2\"][i]):\n", " # The Szunyogh-Lichtenstein formula\n", " traced = np.trace((Vu2 @ Gii + 0.5 * Gii @ Vu1 @ Gii), axis1=1, axis2=2)\n", " # evaluation of the contour integral\n", " storage.append(int_de_ke(traced, cont.we))\n", "\n", " # fill up the magnetic entities dictionary with the energies\n", " magnetic_entities[tracker][\"energies\"].append(storage)\n", " # convert to np array\n", " magnetic_entities[tracker][\"energies\"] = np.array(\n", " magnetic_entities[tracker][\"energies\"]\n", " )\n", " print(\"Magnetic entities integrated.\")\n", "\n", " # iterate over the pairs\n", " for tracker, pair in enumerate(pairs):\n", " # iterate over the quantization axes\n", " for i, (Gij, Gji) in enumerate(zip(pair[\"Gij\"], pair[\"Gji\"])):\n", " site_i = magnetic_entities[pair[\"ai\"]]\n", " site_j = magnetic_entities[pair[\"aj\"]]\n", "\n", " storage = []\n", " # iterate over the first order local perturbations in all possible orientations for the two sites\n", " for Vui in site_i[\"Vu1\"][i]:\n", " for Vuj in site_j[\"Vu1\"][i]:\n", " # The Szunyogh-Lichtenstein formula\n", " traced = np.trace((Vui @ Gij @ Vuj @ Gji), axis1=1, axis2=2)\n", " # evaluation of the contour integral\n", " storage.append(int_de_ke(traced, cont.we))\n", " # fill up the pairs dictionary with the energies\n", " pairs[tracker][\"energies\"].append(storage)\n", " # convert to np array\n", " pairs[tracker][\"energies\"] = np.array(pairs[tracker][\"energies\"])\n", "\n", " print(\"Pairs integrated.\")\n", "\n", " # calculate magnetic parameters\n", " for mag_ent in magnetic_entities:\n", " Kxx, Kyy, Kzz, consistency = calculate_anisotropy_tensor(mag_ent)\n", " mag_ent[\"K\"] = np.array([Kxx, Kyy, Kzz]) * sisl.unit_convert(\"eV\", \"meV\")\n", " mag_ent[\"K_consistency\"] = consistency\n", "\n", " for pair in pairs:\n", " J_iso, J_S, D, J = calculate_exchange_tensor(pair)\n", " pair[\"J_iso\"] = J_iso * sisl.unit_convert(\"eV\", \"meV\")\n", " pair[\"J_S\"] = J_S * sisl.unit_convert(\"eV\", \"meV\")\n", " pair[\"D\"] = D * sisl.unit_convert(\"eV\", \"meV\")\n", " pair[\"J\"] = J * sisl.unit_convert(\"eV\", \"meV\")\n", "\n", " print(\"Magnetic parameters calculated.\")\n", "\n", " times[\"end_time\"] = timer()\n", " print(\n", " \"##################################################################### GROGU OUTPUT #############################################################################\"\n", " )\n", "\n", " print_parameters(simulation_parameters)\n", " print_atoms_and_pairs(magnetic_entities, pairs)\n", " print_runtime_information(times)\n", "\n", " pairs, magnetic_entities = remove_clutter_for_save(pairs, magnetic_entities)\n", " # create output dictionary with all the relevant data\n", " results = dict(\n", " parameters=simulation_parameters,\n", " magnetic_entities=magnetic_entities,\n", " pairs=pairs,\n", " runtime=times,\n", " )\n", "\n", " save_pickle(simulation_parameters[\"outfile\"], results)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "========================================\n", " \n", "Atom Angstrom\n", "# Label, x y z Sx Sy Sz #Q Lx Ly Lz Jx Jy Jz\n", "--------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n", "Te1 1.8955 1.0943 13.1698 -0.0000 0.0000 -0.1543 # 5.9345 -0.0000 0.0000 -0.0537 -0.0000 0.0000 -0.2080 \n", "Te2 1.8955 1.0943 7.4002 0.0000 -0.0000 -0.1543 # 5.9345 0.0000 -0.0000 -0.0537 0.0000 -0.0000 -0.2080 \n", "Ge3 -0.0000 2.1887 10.2850 0.0000 0.0000 -0.1605 # 3.1927 -0.0000 0.0000 0.0012 0.0000 0.0000 -0.1593 \n", "Fe4 -0.0000 0.0000 11.6576 0.0001 -0.0001 2.0466 # 8.3044 0.0000 -0.0000 0.1606 0.0001 -0.0001 2.2072 \n", "Fe5 -0.0000 0.0000 8.9124 -0.0001 0.0001 2.0466 # 8.3044 -0.0000 0.0000 0.1606 -0.0001 0.0001 2.2072 \n", "Fe6 1.8955 1.0944 10.2850 0.0000 0.0000 1.5824 # 8.3296 -0.0000 -0.0000 0.0520 -0.0000 0.0000 1.6344 \n", "==================================================================================================================================\n", " \n", "Exchange meV\n", "--------------------------------------------------------------------------------\n", "# at1 at2 i j k # d (Ang)\n", "--------------------------------------------------------------------------------\n", "Fe4 Fe5 0 0 0 # 2.7452\n", "Isotropic -82.0854\n", "DMI 0.12557 -0.00082199 6.9668e-08\n", "Symmetric-anisotropy -0.60237 -0.83842 -0.00032278 -1.2166e-05 -3.3923e-05\n", "--------------------------------------------------------------------------------\n", "Fe4 Fe6 0 0 0 # 2.5835\n", "Isotropic -41.9627\n", "DMI 1.1205 -1.9532 0.0018386\n", "Symmetric-anisotropy 0.26007 -0.00013243 0.12977 -0.069979 -0.042066\n", "--------------------------------------------------------------------------------\n", "\n", "\n", "On-site meV\n", "----------------------------------------\n", "Fe4\n", "0.16339\t0.16068\t0\t0\t0\t0\n", "========================================\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": ".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": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 2 }