hands-on-tutorial.bkr 219 KB
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                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/P4yGX8shyBMvC1NNZEtDcz7qkYo7w.json',",
                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/PS8-Qv7N2kCKONdZmesS1w_Tausnz.json',",
                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/PcbZStKVRBBwjdBQsmIjYkXoiFcdT.json',",
                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/PPNfqOn3-H1S-OkwjTCUA3-2xOE6J.json',",
                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/P5kIJZn1GeEgprRouYLEkIN-fg3C2.json',",
                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/PIpmcuIBHiIJC4Lqs2R0sv9qyvL-u.json',",
                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/Pdcr6Adm1jZz-oisSZdbBH1Qwq7nF.json',",
                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/PY7l7lhAx7h9mjAMHhGVBrlNfHUXL.json',",
                    "'/parsed/prod-022/FhiAimsParser2.0.0-2-gf9335c4/RtWXnFiiVtrVb-3TOz9-k-ogZr2-t/PhVVJJOydBaE8d2tVngRXEYiX0520.json'",
                    "]",
                    "",
                    "json_lists = {'RS': json_list_RS, 'ZB': json_list_ZB, 'CsCl': json_list_CsCl, 'NiAs': json_list_NiAs, 'CrB':json_list_CrB}"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "selectedType": "Hidden",
                "pluginName": "IPython",
                "shellId": "C4475869101842A09C3FED6220F6253E",
                "elapsedTime": 524
            },
            "evaluatorReader": true,
            "lineCount": 428
        },
        {
            "id": "codeQIGx6m",
            "type": "code",
            "evaluator": "TeX",
            "input": {
                "body": [
                    "\\text{Introduce octet binary systems... } (r_s(\\text{A}), r_p(\\text{A}), r_d(\\text{A}), r_s(\\text{B}), r_s(\\text{B}), r_d(\\text{B})) \\text{. Get the data from the nomad repository.}"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Latex",
                    "object": "\\text{Introduce octet binary systems... } (r_s(\\text{A}), r_p(\\text{A}), r_d(\\text{A}), r_s(\\text{B}), r_s(\\text{B}), r_d(\\text{B})) \\text{. Get the data from the nomad repository.}"
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 73,
                "height": 57
            },
            "evaluatorReader": true,
            "lineCount": 1
        },
        {
            "id": "codewqXgZa",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "from nomad_sim.wrappers import get_json_list, plot, calc_descriptor ",
                    "from nomad_sim.gen_similarity_matrix import load_sim_matrix",
                    "from nomad_sim.convert import build_sim_matrix",
                    "from nomad_sim.utils_crystals import convert_energy_substance",
                    "from pint import UnitRegistry",
                    "from nomadcore.local_meta_info import loadJsonFile, InfoKindEl",
                    "from nomad_sim.l1_l0 import  combine_features",
                    "import hashlib",
                    "import sys, os",
                    "import pandas as pd",
                    "import numpy as np",
                    "import json",
                    "import __builtin__",
                    "__builtin__.isBeaker = True",
                    "",
                    "",
                    "def get_data_from_nomad_sim(calc_desc=True, allowed_operations=None, **kwargs):",
                    "    __file__ = '/usr/lib/python2.7/nomad_sim/wrappers.py'",
                    "    __metainfopath__ = '../../../../nomad-meta-info/meta_info/nomad_meta_info/atomic_data.nomadmetainfo.json'",
                    "    desc_folder = kwargs['tmp_folder']",
                    "    desc_type = kwargs['desc_type']",
                    "    energy_unit = kwargs['energy_unit']",
                    "    length_unit = kwargs['length_unit']",
                    "    ureg = UnitRegistry(os.path.normpath(\"/usr/lib/python2.7/nomadcore/unit_conversion/units.txt\"))",
                    "    ",
                    "    if calc_desc:",
                    "        descriptor = calc_descriptor(**kwargs)",
                    "    ",
                    "    matrix_file = os.path.abspath(",
                    "        os.path.normpath(",
                    "            os.path.join(",
                    "                desc_folder,",
                    "                'data.npz')))",
                    "    build_sim_matrix(",
                    "        desc_folder=desc_folder,",
                    "        matrix_file=matrix_file,",
                    "        f_count_max=1000,",
                    "        desc_type=desc_type)",
                    "",
                    "    # load similarity matrix",
                    "    X, X_labels, target, lookup = load_sim_matrix(matrix_file=matrix_file, desc_type=desc_type)",
                    "",
                    "    # target is a list of tuples ",
                    "    # converter works for either float or lists",
                    "    # convert target (always in Joule if energy) in energy_unit",
                    "    target = [convert_energy_substance('J', list(item),",
                    "                                       ureg=ureg, energy_unit=energy_unit,",
                    "                                       length_unit=length_unit) for item in target]",
                    "",
                    "    # build dataframe with data to combine features",
                    "    json_file_path = lookup[:, 1]",
                    "    frame_number = lookup[:, 2]",
                    "    chemical_formula = lookup[:, 4]",
                    "    energy = lookup[:, 5]",
                    "",
                    "    json_file_path = np.asarray(json_file_path).reshape(-1, 1)",
                    "    frame_number = np.asarray(frame_number).reshape(-1, 1)",
                    "    chemical_formula = np.asarray(chemical_formula).reshape(-1, 1)",
                    "    energy = np.asarray(energy).reshape(-1, 1)",
                    "    data = np.concatenate((X, json_file_path, frame_number, chemical_formula, energy, target), axis=1)",
                    "    X_labels.append('json_file_path')",
                    "    X_labels.append('frame_number')",
                    "    X_labels.append('chemical_formula')",
                    "    X_labels.append('energy')",
                    "    X_labels.append('target')",
                    "",
                    "    df = pd.DataFrame(data=data, columns=X_labels)",
                    "    df['energy'] = df['energy'].apply(pd.to_numeric)",
                    "    # find rows that correspond to lowest energy structures",
                    "    df = df.sort_values(by='energy').groupby(['chemical_formula'], as_index=False).first()",
                    "",
                    "    # copy dataframe with features only to give to l1-l0 minimization",
                    "    df_features = df.copy(deep=True)",
                    "",
                    "    #for item in df_features['json_file_path'].tolist():",
                    "    #    print item",
                    "",
                    "    target = np.asarray(df['target'].values.astype(float))",
                    "",
                    "    # drop columns that are not features",
                    "    df_col_list = df_features.columns.tolist()",
                    "",
                    "    if 'json_file_path' in df_col_list:",
                    "        df_features.drop('json_file_path', axis=1, inplace=True)",
                    "    if 'frame_number' in df_col_list:",
                    "        df_features.drop('frame_number', axis=1, inplace=True)",
                    "    if 'energy' in df_col_list:",
                    "        df_features.drop('energy', axis=1, inplace=True)",
                    "    if 'chemical_formula' in df_col_list:",
                    "        df_features.drop('chemical_formula', axis=1, inplace=True)",
                    "    if 'target' in df_col_list:",
                    "        df_features.drop('target', axis=1, inplace=True)",
                    "    if 'index' in df_col_list:",
                    "        df_features.drop('index', axis=1, inplace=True)",
                    "",
                    "    # load the file containing the atomic metadata",
                    "    metadata_info_path = os.path.normpath(os.path.join(os.path.dirname(os.path.abspath(__file__)), __metainfopath__))",
                    "    metadata_info, warns = loadJsonFile(filePath=metadata_info_path, dependencyLoader=None,",
                    "        extraArgsHandling=InfoKindEl.ADD_EXTRA_ARGS,uri=None)",
                    "",
                    "    # convert numerical columns in float",
                    "    for col in df_features.columns.tolist():",
                    "        df_features[str(col)] = df_features[str(col)].astype(float)",
                    "",
                    "    # make dict with metadata name: shorname",
                    "    features = df_features.columns.tolist()",
                    "    features = [feature.split('(', 1)[0] for feature in features]",
                    "",
                    "    shortname = []",
                    "    # in foor loop to allow exception",
                    "    for feature in features:",
                    "        try:",
                    "            shortname.append(metadata_info[str(feature)]['shortname'])",
                    "        except:",
                    "            shortname.append(feature)",
                    "",
                    "    features_shortnames = dict(zip(features, shortname))",
                    "    ",
                    "    df_combined = combine_features(",
                    "        df=df_features,",
                    "        energy_unit=energy_unit,",
                    "        length_unit=length_unit,",
                    "        metadata_info=metadata_info,",
                    "        allowed_operations=allowed_operations)",
                    "       ",
                    "    feature_list = df_combined.columns.tolist()",
                    "    for fullname, shortname in features_shortnames.items():",
                    "        feature_list = [item.replace(fullname.lower(), shortname) for item in feature_list]",
                    "",
                    "    return target, np.array(df_combined), feature_list",
                    ""
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "selectedType": "Results",
                "pluginName": "IPython",
                "shellId": "C4475869101842A09C3FED6220F6253E",
                "elapsedTime": 16572,
                "height": 222,
                "result": {
                    "type": "Results",
                    "outputdata": [
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Redefining 'footHTwoO' (<class 'pint.definitions.UnitDefinition'>)\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve count: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve julianYear: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve waterSixtyF: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve countsPerSecond: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve inchHTwoOSixtyF: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve cps: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve ly: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve lightyear: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING:pint.util:Could not resolve lightYear: UndefinedUnitError()\n"
                        },
                        {
                            "type": "err",
                            "value": "Using TensorFlow backend.\n"
                        }
                    ]
                }
            },
            "evaluatorReader": true,
            "lineCount": 131
        },
        {
            "id": "codeMVPG8k",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "from nomad_sim.utils_crystals import create_supercell",
                    "",
                    "# define parameters",
                    "json_list = json_list_RS + json_list_ZB",
                    "op_list = np.zeros(len(json_list))",
                    "selected_feature_list = ['atomic_rs_max', 'atomic_rp_max', 'atomic_rd_max']",
                    "",
                    "kwargs = {'allowed_operations':[], ",
                    "          'selected_feature_list':selected_feature_list,",
                    "          'json_list':json_list, ",
                    "          'op_list':op_list,",
                    "          'desc_type':'atomic_features',",
                    "          'spacegroup_tuples':[(225, 221), (216, 227)], # RS vs. ZB structure",
                    "          'operations_on_structure':[(create_supercell, {'replicas': [3, 3, 3]})],",
                    "          'tmp_folder':'/home/beaker/.beaker/v1/web/tmp/',  ",
                    "          'path_to_collection': '/home/beaker/test/nomad_sim/data_zcrs/ExtendedBinaries_Dimers_Atoms_new.json',",
                    "          'feature_order_by': 'atomic_mulliken_electronegativity',",
                    "          'energy_unit': 'eV',",
                    "          'length_unit': 'angstrom'      ",
                    "         }",
                    "",
                    "P, D, feature_list = get_data_from_nomad_sim(**kwargs)",
                    "# Seperate"
                ]
            },
            "output": {
                "state": {},
                "result": {
                    "type": "Results",
                    "outputdata": [
                        {
                            "type": "err",
                            "value": "INFO: Calculating descriptor: atomic_features\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Writing descriptor to file.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Writing descriptor information to file.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Descriptor calculation: done.\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING: No allowed operations selected.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Number of total features generated: 6\n"
                        }
                    ]
                },
                "selectedType": "Results",
                "pluginName": "IPython",
                "shellId": "C4475869101842A09C3FED6220F6253E",
                "elapsedTime": 19655,
                "height": 139
            },
            "evaluatorReader": true,
            "lineCount": 23
        },
        {
            "id": "codeCBYp2q",
            "type": "code",
            "evaluator": "TeX",
            "input": {
                "body": [
                    "\\text{Target: Find the best low-dimensional descriptors for a linear model. The following equation provides exatly what we want: }\\text{argmin}_{\\mathbf{c} \\in \\mathbb{R}^{m}} \\{\\|\\mathbf{P} - \\mathbf{D}\\mathbf{c}\\|^2_2 +\\lambda \\|\\mathbf{c}\\|_0\\}\\text{. It is solved combinatorial.}"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Latex",
                    "object": "\\text{Target: Find the best low-dimensional descriptors for a linear model. The following equation provides exatly what we want: }\\text{argmin}_{\\mathbf{c} \\in \\mathbb{R}^{m}} \\{\\|\\mathbf{P} - \\mathbf{D}\\mathbf{c}\\|^2_2 +\\lambda \\|\\mathbf{c}\\|_0\\}\\text{. It is solved combinatorial.}"
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 31,
                "height": 57
            },
            "evaluatorReader": true,
            "lineCount": 1
        },
        {
            "id": "code5rtN3R",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "from itertools import combinations",
                    "",
                    "def L0(P,D,dimension):",
                    "    n_rows, n_columns = D.shape",
                    "    D = np.column_stack((D,np.ones(n_rows)))",
                    "    MSEdic={}",
                    "    for permu in combinations(range(n_columns),dimension):",
                    "        D_ls = D[:,permu+(-1,)]",
                    "        x = np.linalg.lstsq(D_ls,P)",
                    "        if not len(x[1]) == 0: ",
                    "            MSE = x[1][0]/n_rows",
                    "            MSEdic.update({MSE:[x[0],permu]})",
                    "    MSE = min(MSEdic)",
                    "    coefficients, permu_selected = MSEdic[MSE]",
                    "    RMSE = np.sqrt(MSE)",
                    "    return RMSE, coefficients, permu_selected",
                    "",
                    "for dim in range(1,7):",
                    "    RMSE, coefficients, selected_indices = L0(P,D,dim)",
                    "    print RMSE, [feature_list[i] for i in selected_indices]"
                ]
            },
            "output": {
                "state": {},
                "result": {
                    "type": "Results",
                    "outputdata": [
                        {
                            "type": "out",
                            "value": "0.31333947491 [u'r_p(A)']\n0.29493770298 [u'r_p(A)', u'r_d(B)']\n0.280145383704 [u'r_p(B)', u'r_p(A)', u'r_s(B)']\n0.276359790086 [u'r_p(B)', u'r_p(A)', u'r_s(B)', u'r_s(A)']\n0.272705955462 [u'r_p(B)', u'r_p(A)', u'r_s(B)', u'r_s(A)', u'r_d(B)']\n0.272444482677 [u'r_p(B)', u'r_p(A)', u'r_s(B)', u'r_d(A)', u'r_s(A)', u'r_d(B)']\n"
                        }
                    ]
                },
                "selectedType": "Results",
                "pluginName": "IPython",
                "shellId": "C4475869101842A09C3FED6220F6253E",
                "elapsedTime": 311,
                "height": 139
            },
            "evaluatorReader": true,
            "lineCount": 20
        },
        {
            "id": "codegBQKBa",
            "type": "code",
            "evaluator": "HTML",
            "input": {
                "body": [
                    "However, the l0-method comes up with one crucial drawback: a rapidly increasing computational cost, when the features space is becoming larger. Consider randomly created P, D with different feature space sizes."
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Html",
                    "object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\nHowever, the l0-method comes up with one crucial drawback: a rapidly increasing computational cost, when the features space is becoming larger. Consider randomly created P, D with different feature space sizes."
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 0,
                "height": 55
            },
            "evaluatorReader": true,
            "lineCount": 1
        },
        {
            "id": "codem84yx2",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "from time import time",
                    "from nomad_sim.sis import ncr",
                    "",
                    "fig = plt.figure()",
                    "",
                    "rows = 100",
                    "dimensions = [2,3]",
                    "numbers_of_features = [",
                    "    [10,100,400,600][:4],",
                    "    [10,30,80,100][:4]",
                    "    ]",
                    "",
                    "P_random = np.random.rand(rows,)",
                    "for n_dim, dim in enumerate(dimensions):",
                    "    time_list = []",
                    "    for n_o_f in numbers_of_features[n_dim]:",
                    "        D_random = np.random.rand(rows,n_o_f)",
                    "        n = ncr(n_o_f,dim)",
                    "        ",
                    "        t1 = time()",
                    "        L0(P_random,D_random,dim)",
                    "        t2 = time()-t1",
                    "        time_list.append(t2)",
                    "    plt.plot(numbers_of_features[n_dim], time_list, label='%s-dimensional' %dim)",
                    "    plt.plot(numbers_of_features[n_dim], time_list, 'rs') ",
                    "",
                    "plt.legend(loc='best')",
                    "plt.xlabel('Number of features')",
                    "plt.ylabel('Time [s]')",
                    "plt.show()",
                    "",
                    ""
                ]
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Error",
                    "object": [
                        "Interrupted"
                    ]
                },
                "selectedType": "BeakerDisplay",
                "pluginName": "IPython",
                "shellId": "C4475869101842A09C3FED6220F6253E",
                "elapsedTime": 3605,
                "height": 78
            },
            "evaluatorReader": true,
            "lineCount": 32
        },
        {
            "id": "codehLXC3s",
            "type": "code",
            "evaluator": "TeX",
            "input": {
                "body": [
                    "\\text{Use instead approximations, i.e. LASSO: }\\text{argmin}_{\\mathbf{c} \\in \\mathbb{R}^{m}} \\{\\|\\mathbf{P} - \\mathbf{D}\\mathbf{c}\\|^2_2 +\\lambda \\|\\mathbf{c}\\|_1\\}\\text{. } \\lambda\\text{ regulates the sparsity. Try different lambdas for the example of octed binaries. How good does LASSO approximate L0?}"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Latex",
                    "object": "\\text{Use instead approximations, i.e. LASSO: }\\text{argmin}_{\\mathbf{c} \\in \\mathbb{R}^{m}} \\{\\|\\mathbf{P} - \\mathbf{D}\\mathbf{c}\\|^2_2 +\\lambda \\|\\mathbf{c}\\|_1\\}\\text{. } \\lambda\\text{ regulates the sparsity. Try different lambdas for the example of octed binaries. How good does LASSO approximate L0?}"
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 48,
                "height": 57
            },
            "evaluatorReader": true,
            "lineCount": 1
        },
        {
            "id": "coded2PoWQ",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "from sklearn.linear_model import Lasso",
                    "import scipy.stats as ss",
                    "",
                    "D_standardized = ss.zscore(D)",
                    "lam =0.5",
                    "",
                    "lasso =  Lasso(alpha=lam)",
                    "lasso.fit(D_standardized, P)",
                    "coef =  lasso.coef_",
                    "",
                    "print lam, coef, [feature_list[i] for i in np.nonzero(coef)[0]]"
                ]
            },
            "output": {
                "state": {},
                "result": {
                    "type": "Results",
                    "outputdata": [
                        {
                            "type": "out",
                            "value": "0.5 [-0. -0. -0. -0. -0. -0.] []\n"
                        }
                    ]
                },
                "selectedType": "Results",
                "pluginName": "IPython",
                "shellId": "CF239072B98E4D2890C4EF3EAF36FD99",
                "elapsedTime": 294,
                "height": 56
            },
            "evaluatorReader": true,
            "lineCount": 11
        },
        {
            "id": "codevI3556",
            "type": "code",
            "evaluator": "HTML",
            "input": {
                "body": [
                    "Methods as LASSO+L0 or SIS+L0 shown to give better approximations to L0. We will focus, now, on LASSO+L0. With LASSO+L0 we can scan large feature spaces efficiently.  ",
                    "-to improve the model, consider more complex features by applying arithmetic operations: feature space becomes larger"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Html",
                    "object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\nMethods as LASSO+L0 or SIS+L0 shown to give better approximations to L0. We will focus, now, on LASSO+L0. With LASSO+L0 we can scan large feature spaces efficiently.  \n-to improve the model, consider more complex features by applying arithmetic operations: feature space becomes larger"
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 0,
                "height": 55
            },
            "evaluatorReader": true,
            "lineCount": 2
        },
        {
            "id": "code1xeZvT",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "def iter_LASSO(P ,D, lambda_grid, lasso_number=30, print_lasso=False):",
                    "    collection=[]",
                    "    if print_lasso:",
                    "        print 'lamda      #collected   Indices'",
                    "    for lam in lambda_grid:",
                    "        lasso = Lasso(alpha=lam)",
                    "        lasso.fit(D, P)",
                    "        coef = lasso.coef_ ",
                    "        collection = collection + list(set(np.nonzero(coef)[0]) - set(collection))",
                    "        if print_lasso:",
                    "            print '%.10f   %s   %s'%(lam,len(collection), np.nonzero(coef)[0])",
                    "        if len(collection) > lasso_number - 1:",
                    "            break",
                    "    collection=collection[:lasso_number]",
                    "    collection.sort()",
                    "    return collection   ",
                    "",
                    "def evaluate_lambda_grid(P, D, lambda_grid_points=150, lambda_max_factor=1.0, lambda_min_factor=0.001):",
                    "    correlations = abs(np.dot(P,D))",
                    "    lam_max = max(correlations)/(len(P)) ",
                    "    lam_min = lam_max*lambda_min_factor",
                    "    lam_max = lambda_max_factor * lam_max",
                    "    log_max,log_min = np.log10(lam_max),np.log10(lam_min)",
                    "    lambda_grid = [pow(10,i) for i in np.linspace(log_min,log_max,lambda_grid_points)]",
                    "    lambda_grid.sort(reverse=True)",
                    "    return lambda_grid",
                    "",
                    "def get_string(RMSE, selected_features, coefficients):",
                    "    dimension = len(selected_features)",
                    "    string = '%sD:\\t%8f\\t' %(dimension, RMSE)",
                    "    for i in range(dimension+1):",
                    "        if coefficients[i]>0:",
                    "            sign = '+' ",
                    "            c = coefficients[i]",
                    "        else:",
                    "            sign = '-'",
                    "            c = abs(coefficients[i]) ",
                    "        if i < dimension:",
                    "            string += '%s %.3f %s ' %(sign,c,selected_features[i])",
                    "        else:",
                    "            string += '%s %.3f\\n' %(sign,c)",
                    "    return string",
                    "    ",
                    "    ",
                    "def LILO(P,D,features, dimrange=range(1,1+3),lasso_number=30,lambda_grid_points=150,lambda_max_factor=1.0,lambda_min_factor=0.001,print_lasso=False,lambda_grid=None, print_model=False):    ",
                    "    Dstan=np.array(ss.zscore(D))",
                    "    lambda_grid = evaluate_lambda_grid(P, Dstan)",
                    "    collection = iter_LASSO(P ,Dstan, lambda_grid, lasso_number=lasso_number, print_lasso=print_lasso)    ",
                    "    if len(collection) < lasso_number:",
                    "        print \"Only %s features are collected\" %len(collection)      ",
                    "    D_collection = D[:,collection]",
                    "    D_collection = np.column_stack( (D_collection,np.ones(len(P))) ) ",
                    "    out = []",
                    "    string = ''",
                    "    for dimension in dimrange:",
                    "        RMSE, coefficients, good_permu = L0(P, D_collection, dimension)",
                    "        indices_for_D = [collection[gp] for gp in good_permu]",
                    "        selected_features = [features[collection[gp]] for gp in good_permu]",
                    "        string += get_string(RMSE, selected_features, coefficients)",
                    "        out.append((indices_for_D,coefficients,RMSE))",
                    "    if print_model:",
                    "        print string",
                    "    return out",
                    ""
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "selectedType": "Hidden",
                "pluginName": "IPython",
                "shellId": "CF239072B98E4D2890C4EF3EAF36FD99",
                "elapsedTime": 422,
                "height": 1074
            },
            "evaluatorReader": true,
            "lineCount": 64
        },
        {
            "id": "codeSa0aqN",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "op_lists = [[], ['+','|-|'], ['+','|-|','exp'], ['+','|-|','exp', '^2'] ,['+','|-|','exp', '/'], ['+','|-|','exp', '/', '^2']]",
                    "X, Y = [], np.empty([3,len(op_lists)])",
                    "for n_op, op_list in enumerate(op_lists):",
                    "    kwargs['allowed_operations'] = op_list",
                    "    P, D, feature_list = get_data_from_nomad_sim(calc_desc=False, **kwargs)",
                    "    out = LILO(P, D, feature_list, print_lasso=False, lasso_number=50, print_model=True)",
                    "    number_of_features = len(feature_list)",
                    "    X.append(number_of_features)",
                    "    for i in range(3):",
                    "        Y[i][n_op] = out[i][2] #RMSE",
                    "",
                    "for i in range(3):",
                    "    print Y[i]",
                    "    plt.plot(X,Y[i],label='%s-dimensional' %(i+1))",
                    "    ",
                    "    ",
                    "#plt.xscale('log', nonposy='clip')",
                    "plt.xlabel('Number of features')",
                    "plt.ylabel('RMSE [eV]')",
                    "plt.legend(loc='best')",
                    "plt.show()"
                ]
            },
            "output": {
                "state": {},
                "result": {
                    "type": "Results",
                    "outputdata": [
                        {
                            "type": "err",
                            "value": "WARNING: No allowed operations selected.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Number of total features generated: 6\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Selected operations:\n ['+', '|-|']\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Number of total features generated: 36\n"
                        },
                        {
                            "type": "out",
                            "value": "Only 6 features are collected\n1D:\t0.313339\t- 0.477 r_p(A) + 1.014\n2D:\t0.294938\t- 0.498 r_p(A) - 0.379 r_d(B) + 1.771\n3D:\t0.280145\t- 5.845 r_p(B) - 0.439 r_p(A) + 8.426 r_s(B) - 0.348\n\nOnly 23 features are collected"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.296668\t- 0.484 r_p(A)+r_d(B) + 1.944\n2D:\t0.265921\t- 0.527 r_p(A)+r_d(B) + 0.315 |r_p(A)-r_d(B)| + 1.911\n3D:\t0.230570\t- 0.601 |r_p(B)-r_p(A)| - 3.919 |r_p(B)-r_s(B)| + 0.460 |r_p(A)-r_d(B)| + 0.943\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Selected operations:\n ['+', '|-|', 'exp']\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Number of total features generated: 57\n"
                        },
                        {
                            "type": "out",
                            "value": "\nOnly 42 features are collected"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.296668\t- 0.484 r_p(A)+r_d(B) + 1.944\n2D:\t0.227539\t- 1.371 r_p(A)+r_s(B) + 0.047 exp(r_p(A)+r_s(B)) + 2.898\n3D:\t0.200506\t- 4.621 |r_p(B)-r_s(B)| - 1.346 |r_p(A)-r_s(B)| + 0.098 exp(r_p(A)) + 1.412\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Selected operations:\n ['+', '|-|', 'exp', '^2']\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Number of total features generated: 99\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.296668\t- 0.484 r_p(A)+r_d(B) + 1.944\n2D:\t0.210940\t- 2.497 r_p(A) + 0.499 r_p(A)^2 + 2.826\n3D:\t0.185127\t- 2.487 r_p(A) - 1.459 |r_p(B)-r_s(B)| + 0.491 r_p(A)^2 + 3.016\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Selected operations:\n ['+', '|-|', 'exp', '/']\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Number of total features generated: 813\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.192323\t+ 21.112 |r_s(B)-r_d(B)|/exp(r_p(A)+r_d(B)) - 0.543\n2D:\t0.129760\t- 20.783 |r_p(B)-r_s(B)|/exp(r_p(A)+r_s(A)) + 26.784 |r_s(A)-r_d(B)|/exp(r_p(A)+r_d(B)) - 0.284\n3D:\t0.112322\t- 19.562 |r_p(B)-r_s(B)|/exp(r_p(A)+r_s(A)) + 2.299 |r_p(A)-r_d(A)|/exp(r_p(A)+r_d(B)) + 25.103 |r_s(A)-r_d(B)|/exp(r_p(A)+r_d(B)) - 0.342\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Selected operations:\n ['+', '|-|', 'exp', '/', '^2']\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Number of total features generated: 2367\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.159652\t+ 10.095 r_p(B)+r_p(A)/exp((r_p(A)+r_s(B))^2) - 0.102\n2D:\t0.107856\t+ 16.302 r_s(B)/exp((r_p(A)+r_s(B))^2) + 4.448 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.412\n3D:\t0.077499\t+ 9.331 r_p(B)+r_p(A)/exp((r_p(A)+r_s(B))^2) - 12.329 |r_p(B)-r_s(B)|/exp(r_s(B)+r_d(A)) - 1.898 |r_p(B)-r_s(A)|/exp(r_s(A)) + 0.235\n"
                        },
                        {
                            "type": "out",
                            "value": "\n[ 0.31333947  0.29666785  0.29666785  0.29666785  0.19232315  0.15965235]\n[ 0.2949377   0.26592148  0.22753931  0.21094036  0.1297597   0.10785618]\n[ 0.28014538  0.23056963  0.20050649  0.1851272   0.11232199  0.07749948]\n"
                        }
                    ],
                    "payload": "<div class=\"output_subarea output_png\"><img 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Ee5vJX2YgLL7TXo8yZ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                "selectedType": "Results",
                "pluginName": "IPython",
                "shellId": "9F533114F51B41D4A9DB4EF14E0B36FC",
                "elapsedTime": 29259,
                "height": 1124
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            "evaluatorReader": true,
            "lineCount": 21
        },
        {
            "id": "codeN23KOq",
            "type": "code",
            "evaluator": "HTML",
            "input": {
                "body": [
                    "<script>",
                    "var run_lasso = function() {",
                    "  $(\"#lasso_result_button\").removeClass(\"active\").addClass(\"disabled\");",
                    "  getFeatures();",
                    "  getOperators();",
                    "  beaker.max_dim = $(\"#lasso_max_dim_selector\").val();",
                    "  beaker.structures_diff = $(\"#lasso_structures_diff\").val();",
                    "  beaker.n_comb = $(\"#n_comb\").val();",
                    "  beaker.n_sis = $(\"#n_sis\").val();",
                    "  beaker.units = $(\"#units_select\").val();",
                    "  beaker.evaluate(\"calc_cell\"); // evaluate cells with tag \"lasso_cell\"",
                    " // view_result()",
                    "};",
                    "var reset_lasso = function(){",
                    "  beaker.evaluate(\"lasso-settings-cell\");",
                    "  var e = document.getElementById('lasso-hidden-settings-div');",
                    "  var b = document.getElementById('lasso-hidden-settings-button');",
                    "  e.style.display = 'block';",
                    "  b.style.display = 'inline';",
                    "};",
                    "var getFeatures = function() {",
                    "    beaker.selected_feature_list = [];",
                    "    $('#lasso_features_select input:checkbox').each(function () {",
                    "        if(this.checked )",
                    "          beaker.selected_feature_list.push(this.value);",
                    "    });",
                    "};",
                    "var getOperators = function() {",
                    "    beaker.allowed_operations = [];",
                    "    $('#lasso_operators_select input:checkbox').each(function () {",
                    "        if(this.checked )",
                    "          beaker.allowed_operations.push(this.value);",
                    "    });",
                    "};  ",
                    "",
                    "var toggle_settings = function(){",
                    "  var e = document.getElementById('lasso-hidden-settings-div');",
                    "  var b = document.getElementById('lasso-hidden-settings-button');",
                    "  if(e.style.display == 'block'){",
                    "    e.style.display = 'none';",
                    "    b.style.display = 'none';",
                    "  }",
                    "  else{",
                    "    e.style.display = 'block';",
                    "    b.style.display = 'inline';",
                    "  }",
                    "};",
                    "beaker.view_result = function(result_link) {",
                    "//   beaker.evaluate(\"lasso_viewer_result\").then(function(x) {",
                    "    $(\"#lasso_result_button\").attr(\"href\", result_link);",
                    "//   }); ",
                    "  $(\"#lasso_result_button\").removeClass(\"disabled\").addClass(\"active\");",
                    "}",
                    "",
                    "",
                    "",
                    "",
                    "",
                    "",
                    "",
                    "</script>",
                    "<style type=\"text/css\">",
                    " .lasso_instructions{",
                    "    font-size: 15px;",
                    "  } ",
                    "</style>",
                    "<!-- Button trigger modal -->",
                    "<button type=\"button\" class=\"btn btn-default\" data-toggle=\"modal\" data-target=\"#lasso-motivation-modal\">",
                    " Background",
                    "</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;",
                    "",
                    "<!-- Modal -->",
                    "<div class=\"modal fade\" id=\"lasso-motivation-modal\" tabindex=\"-1\" role=\"dialog\" aria-labelledby=\"lasso-motivation-modal-label\">",
                    "  <div class=\"modal-dialog modal-lg\" role=\"document\">",
                    "    <div class=\"modal-content\">",
                    "      <div class=\"modal-header\">",
                    "        <button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\"><span aria-hidden=\"true\">×</span></button>",
                    "        <h4 class=\"modal-title\" id=\"lasso-motivation-modal-label\">Background</h4>",
                    "      </div>",
                    "      <div class=\"modal-body lasso_instructions\">",
                    "        <p>We present a tool for predicting the crystal structure of octet binary compounds, by using a set of descriptive parameters (a descriptor) based on free-atom data of the atomic species constituting the binary material. This task is similar to the one presented in the tutorial <a href=\"http://analytics-toolkit.nomad-coe.eu/tutorial-LASSO_L0\">\"[Predicting energy differences between different crystal structures I: large feature space]\"</a>\". In contrast to that tutorial, here we apply a newly developed method: Sure Independence Screening - Sparse Approximation (SIS-SA), that allows to find an optimal descriptor in a huge feature space containing billions of features.",
                    "The method is described in:",
                    "<div style=\"padding: 1ex; margin-top: 1ex; margin-bottom: 1ex; border-style: dotted; border-width: 1pt; border-color: blue; border-radius: 3px;\">",
                    "R. Ouyang, E. Ahmetcik, L. M. Ghiringhelli, and M. Scheffler: <span style=\"font-style: italic;\">Descriptor identification for material properties via compressed sensing</span>, in preparation.",
                    "</div>",
                    "</p>",
                    " ",
                    "<p>SIS-SA works iteratively. In the first iteration, a number k of features is collected as those that have the largest correlation (scalar product) with the property vector. The feature with the largest correlation is simply the 1D descriptor. Next, a residual is constructed as the error made at the first iteration. A new set of k features is now selected as those having the largest  correlation with the residual. The 2D descriptor is the pair of features that yield the smallest fitting error upon least square regression, among all possible pairs contained in the union of the sets selected in this and the first iteration. In each next iteration a new residual is constructed as the error made in the previous iteration, then a new set of k features is extracted as those that have largest correlation with each new residual. The nD descriptor is the n-tuple of features that yield the smallest fitting error upon least square regression, among all possible n-tuples contained in the union of the sets obtained in each new iteration and all the previous iterations. If k=1 the method collapses to the so-called orthogonal matching pursuit.",
                    "</p>",
                    "",
                    "        <p>The prediction of the ground-state structure for binary compounds from a simple descriptor has a notable history in materials science [1-7], where descriptors were designed by chemically/physically-inspired intuition. The tool presented here allows for the machine-learning-aided automatic discovery of a descriptor and a model for the prediction of the difference in energy between a selected pair of structures for 82 octet binary materials.</p>",
                    "",
                    "",
                    "        <p> By running the tutorial with the default setting, the (RS vs. ZB) results of the <a href=\"http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.105503\" target=\"_blank\">PRL 2015</a> identified by the LASSO+L0 method can be recovered.</p>",
                    "        ",
                    "",
                    "        <p>References:</p>",
                    "        <ol>",
                    "          <li>J. A. van Vechten, Phys. Rev. 182, 891 (1969).</li>",
                    "          <li>J. C. Phillips, Rev. Mod. Phys. 42, 317 (1970).</li>",
                    "          <li>J. St. John and A.N. Bloch, Phys. Rev. Lett. 33, 1095 (1974).</li>",
                    "          <li>J. R. Chelikowsky and J. C. Phillips, Phys. Rev. B 17, 2453 (1978).</li>",
                    "          <li>A. Zunger, Phys. Rev. B 22, 5839 (1980).</li>",
                    "          <li>D. G. Pettifor, Solid State Commun. 51, 31 (1984).</li>",
                    "          <li>Y. Saad, D. Gao, T. Ngo, S. Bobbitt, J. R. Chelikowsky, and W. Andreoni, Phys. Rev. B 85, 104104 (2012).</li>",
                    "        </ol>",
                    "      </div>",
                    "      <div class=\"modal-footer\">",
                    "        <button type=\"button\" class=\"btn btn-default\" data-dismiss=\"modal\">Close</button>",
                    "<!--         <button type=\"button\" class=\"btn btn-primary\">Save changes</button> -->",
                    "      </div>",
                    "    </div>",
                    "  </div>",
                    "</div>",
                    "",
                    "<!-- Button trigger modal -->",
                    "<button type=\"button\" class=\"btn btn-default\" data-toggle=\"modal\" data-target=\"#lasso-instructions-modal\">",
                    " Instructions",
                    "</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;",
                    "",
                    "<!-- Modal -->",
                    "<div class=\"modal fade\" id=\"lasso-instructions-modal\" tabindex=\"-1\" role=\"dialog\" aria-labelledby=\"lasso-instructions-modal-label\">",
                    "  <div class=\"modal-dialog\" role=\"document\">",
                    "    <div class=\"modal-content\">",
                    "      <div class=\"modal-header\">",
                    "        <button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\"><span aria-hidden=\"true\">×</span></button>",
                    "        <h4 class=\"modal-title\" id=\"lasso-instructions-modal-label\">Instructions</h4>",
                    "      </div>",
                    "      <div class=\"modal-body lasso_instructions\">",
                    "<p>In this example, you can run a compressed-sensing based algorithm for finding the optimal descriptor and model that predicts the difference in energy between crystal structures (here, rocksalt vs. zincblende vs. CsCl structure). </p>",
                    "",
                    "<p>The descriptor is selected out of a large number of candidates constructed as functions of basic input features, the primary features. </p>",
                    "",
                    "<p>By clicking <b>Settings</b> you can select the structure pair of interest (either RS/ZB, CsCl/ZB, NiAs/ZB or CrB/ZB), the primary features as well as which kind of unary and binary operations are allowed from the checklist below. Moreover the dimension of the output energies (kcal/mol or eV) and the following three parameters of the SIS+L0 algorithm can be specified: ",
                    "        <ul>",
                    "          <li>Number of iterations for the construction for the feature space: How often the selected operations are applied to build the feature space. At each step the opreations are applied on all features created untill the current step. </li>",
                    "          <li>Optimal descriptor maximum dimension: Number of SIS+SA iterations.</li>",
                    "          <li>Number of collected features per SIS iteration.</li>",
                    "        </ul>    ",
                    "        ",
                    "</p>",
                    "    ",
                    "  ",
                    "<p>        After the preferred settings have been adjusted, click <b>RUN</b> for performing the calculations (loading the values of the primary features, creation of the feature space, and optimization via SIS+L0). </p>",
                    "",
                    "During the run, a brief summary is printed out below the <b>RUN</b> button. At the end of the run: ",
                    "  <ul>",
                    "  <li> the solution (machine-learned descriptor, model, and its performance in terms of training error) is printed out underneath starting from the one-dimensional solution to the selected maximum dimensionality and</li>",
                    "<li> the “View interactive 2D scatter plot” button unlocks; by clicking, the scatter plot with the two-dimensional descriptor appears in a separate tab. In case a dimensionality higher than 2 was selected for the descriptor, the plot displays the two-dimensional descriptor.</li>",
                    "</ul>",
                    "<p>Note: the plot stays active also after another run is performed, so that the output of several sets of input parameters can be compared in the viewer tabs.</p>",
                    "      </div>",
                    "      <div class=\"modal-footer\">",
                    "        <button type=\"button\" class=\"btn btn-default\" data-dismiss=\"modal\">Close</button>",
                    "<!--         <button type=\"button\" class=\"btn btn-primary\">Save changes</button> -->",
                    "      </div>",
                    "    </div>",
                    "  </div>",
                    "</div>",
                    "",
                    "<!-- Button trigger modal -->",
                    "<button type=\"button\" class=\"btn btn-default\" onclick='toggle_settings()'>",
                    " Settings",
                    "</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;",
                    "",
                    "<a target=\"_blank\" href=\"http://forum.analytics-toolkit.nomad-coe.eu/\" class=\"btn btn-primary\"> Tell us what you think</a>",
                    "",
                    ""
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Html",
                    "object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\n<script>\nvar run_lasso = function() {\n  $(\"#lasso_result_button\").removeClass(\"active\").addClass(\"disabled\");\n  getFeatures();\n  getOperators();\n  beaker.max_dim = $(\"#lasso_max_dim_selector\").val();\n  beaker.structures_diff = $(\"#lasso_structures_diff\").val();\n  beaker.n_comb = $(\"#n_comb\").val();\n  beaker.n_sis = $(\"#n_sis\").val();\n  beaker.units = $(\"#units_select\").val();\n  beaker.evaluate(\"calc_cell\"); // evaluate cells with tag \"lasso_cell\"\n // view_result()\n};\nvar reset_lasso = function(){\n  beaker.evaluate(\"lasso-settings-cell\");\n  var e = document.getElementById('lasso-hidden-settings-div');\n  var b = document.getElementById('lasso-hidden-settings-button');\n  e.style.display = 'block';\n  b.style.display = 'inline';\n};\nvar getFeatures = function() {\n    beaker.selected_feature_list = [];\n    $('#lasso_features_select input:checkbox').each(function () {\n        if(this.checked )\n          beaker.selected_feature_list.push(this.value);\n    });\n};\nvar getOperators = function() {\n    beaker.allowed_operations = [];\n    $('#lasso_operators_select input:checkbox').each(function () {\n        if(this.checked )\n          beaker.allowed_operations.push(this.value);\n    });\n};  \n\nvar toggle_settings = function(){\n  var e = document.getElementById('lasso-hidden-settings-div');\n  var b = document.getElementById('lasso-hidden-settings-button');\n  if(e.style.display == 'block'){\n    e.style.display = 'none';\n    b.style.display = 'none';\n  }\n  else{\n    e.style.display = 'block';\n    b.style.display = 'inline';\n  }\n};\nbeaker.view_result = function(result_link) {\n//   beaker.evaluate(\"lasso_viewer_result\").then(function(x) {\n    $(\"#lasso_result_button\").attr(\"href\", result_link);\n//   }); \n  $(\"#lasso_result_button\").removeClass(\"disabled\").addClass(\"active\");\n}\n\n\n\n\n\n\n\n</script>\n<style type=\"text/css\">\n .lasso_instructions{\n    font-size: 15px;\n  } \n</style>\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" data-toggle=\"modal\" data-target=\"#lasso-motivation-modal\">\n Background\n</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n\n<!-- Modal -->\n<div class=\"modal fade\" id=\"lasso-motivation-modal\" tabindex=\"-1\" role=\"dialog\" aria-labelledby=\"lasso-motivation-modal-label\">\n  <div class=\"modal-dialog modal-lg\" role=\"document\">\n    <div class=\"modal-content\">\n      <div class=\"modal-header\">\n        <button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\"><span aria-hidden=\"true\">×</span></button>\n        <h4 class=\"modal-title\" id=\"lasso-motivation-modal-label\">Background</h4>\n      </div>\n      <div class=\"modal-body lasso_instructions\">\n        <p>We present a tool for predicting the crystal structure of octet binary compounds, by using a set of descriptive parameters (a descriptor) based on free-atom data of the atomic species constituting the binary material. This task is similar to the one presented in the tutorial <a href=\"http://analytics-toolkit.nomad-coe.eu/tutorial-LASSO_L0\">\"[Predicting energy differences between different crystal structures I: large feature space]\"</a>\". In contrast to that tutorial, here we apply a newly developed method: Sure Independence Screening - Sparse Approximation (SIS-SA), that allows to find an optimal descriptor in a huge feature space containing billions of features.\nThe method is described in:\n</p><div style=\"padding: 1ex; margin-top: 1ex; margin-bottom: 1ex; border-style: dotted; border-width: 1pt; border-color: blue; border-radius: 3px;\">\nR. Ouyang, E. Ahmetcik, L. M. Ghiringhelli, and M. Scheffler: <span style=\"font-style: italic;\">Descriptor identification for material properties via compressed sensing</span>, in preparation.\n</div>\n<p></p>\n \n<p>SIS-SA works iteratively. In the first iteration, a number k of features is collected as those that have the largest correlation (scalar product) with the property vector. The feature with the largest correlation is simply the 1D descriptor. Next, a residual is constructed as the error made at the first iteration. A new set of k features is now selected as those having the largest  correlation with the residual. The 2D descriptor is the pair of features that yield the smallest fitting error upon least square regression, among all possible pairs contained in the union of the sets selected in this and the first iteration. In each next iteration a new residual is constructed as the error made in the previous iteration, then a new set of k features is extracted as those that have largest correlation with each new residual. The nD descriptor is the n-tuple of features that yield the smallest fitting error upon least square regression, among all possible n-tuples contained in the union of the sets obtained in each new iteration and all the previous iterations. If k=1 the method collapses to the so-called orthogonal matching pursuit.\n</p>\n\n        <p>The prediction of the ground-state structure for binary compounds from a simple descriptor has a notable history in materials science [1-7], where descriptors were designed by chemically/physically-inspired intuition. The tool presented here allows for the machine-learning-aided automatic discovery of a descriptor and a model for the prediction of the difference in energy between a selected pair of structures for 82 octet binary materials.</p>\n\n\n        <p> By running the tutorial with the default setting, the (RS vs. ZB) results of the <a href=\"http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.105503\" target=\"_blank\">PRL 2015</a> identified by the LASSO+L0 method can be recovered.</p>\n        \n\n        <p>References:</p>\n        <ol>\n          <li>J. A. van Vechten, Phys. Rev. 182, 891 (1969).</li>\n          <li>J. C. Phillips, Rev. Mod. Phys. 42, 317 (1970).</li>\n          <li>J. St. John and A.N. Bloch, Phys. Rev. Lett. 33, 1095 (1974).</li>\n          <li>J. R. Chelikowsky and J. C. Phillips, Phys. Rev. B 17, 2453 (1978).</li>\n          <li>A. Zunger, Phys. Rev. B 22, 5839 (1980).</li>\n          <li>D. G. Pettifor, Solid State Commun. 51, 31 (1984).</li>\n          <li>Y. Saad, D. Gao, T. Ngo, S. Bobbitt, J. R. Chelikowsky, and W. Andreoni, Phys. Rev. B 85, 104104 (2012).</li>\n        </ol>\n      </div>\n      <div class=\"modal-footer\">\n        <button type=\"button\" class=\"btn btn-default\" data-dismiss=\"modal\">Close</button>\n<!--         <button type=\"button\" class=\"btn btn-primary\">Save changes</button> -->\n      </div>\n    </div>\n  </div>\n</div>\n\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" data-toggle=\"modal\" data-target=\"#lasso-instructions-modal\">\n Instructions\n</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n\n<!-- Modal -->\n<div class=\"modal fade\" id=\"lasso-instructions-modal\" tabindex=\"-1\" role=\"dialog\" aria-labelledby=\"lasso-instructions-modal-label\">\n  <div class=\"modal-dialog\" role=\"document\">\n    <div class=\"modal-content\">\n      <div class=\"modal-header\">\n        <button type=\"button\" class=\"close\" data-dismiss=\"modal\" aria-label=\"Close\"><span aria-hidden=\"true\">×</span></button>\n        <h4 class=\"modal-title\" id=\"lasso-instructions-modal-label\">Instructions</h4>\n      </div>\n      <div class=\"modal-body lasso_instructions\">\n<p>In this example, you can run a compressed-sensing based algorithm for finding the optimal descriptor and model that predicts the difference in energy between crystal structures (here, rocksalt vs. zincblende vs. CsCl structure). </p>\n\n<p>The descriptor is selected out of a large number of candidates constructed as functions of basic input features, the primary features. </p>\n\n<p>By clicking <b>Settings</b> you can select the structure pair of interest (either RS/ZB, CsCl/ZB, NiAs/ZB or CrB/ZB), the primary features as well as which kind of unary and binary operations are allowed from the checklist below. Moreover the dimension of the output energies (kcal/mol or eV) and the following three parameters of the SIS+L0 algorithm can be specified: \n        </p><ul>\n          <li>Number of iterations for the construction for the feature space: How often the selected operations are applied to build the feature space. At each step the opreations are applied on all features created untill the current step. </li>\n          <li>Optimal descriptor maximum dimension: Number of SIS+SA iterations.</li>\n          <li>Number of collected features per SIS iteration.</li>\n        </ul>    \n        \n<p></p>\n    \n  \n<p>        After the preferred settings have been adjusted, click <b>RUN</b> for performing the calculations (loading the values of the primary features, creation of the feature space, and optimization via SIS+L0). </p>\n\nDuring the run, a brief summary is printed out below the <b>RUN</b> button. At the end of the run: \n  <ul>\n  <li> the solution (machine-learned descriptor, model, and its performance in terms of training error) is printed out underneath starting from the one-dimensional solution to the selected maximum dimensionality and</li>\n<li> the “View interactive 2D scatter plot” button unlocks; by clicking, the scatter plot with the two-dimensional descriptor appears in a separate tab. In case a dimensionality higher than 2 was selected for the descriptor, the plot displays the two-dimensional descriptor.</li>\n</ul>\n<p>Note: the plot stays active also after another run is performed, so that the output of several sets of input parameters can be compared in the viewer tabs.</p>\n      </div>\n      <div class=\"modal-footer\">\n        <button type=\"button\" class=\"btn btn-default\" data-dismiss=\"modal\">Close</button>\n<!--         <button type=\"button\" class=\"btn btn-primary\">Save changes</button> -->\n      </div>\n    </div>\n  </div>\n</div>\n\n<!-- Button trigger modal -->\n<button type=\"button\" class=\"btn btn-default\" onclick=\"toggle_settings()\">\n Settings\n</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n\n<a target=\"_blank\" href=\"http://forum.analytics-toolkit.nomad-coe.eu/\" class=\"btn btn-primary\"> Tell us what you think</a>\n\n"
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 0,
                "height": 73
            },
            "evaluatorReader": true,
            "lineCount": 168
        },
        {
            "id": "codeLLo3xr",
            "type": "code",
            "evaluator": "HTML",
            "input": {
                "body": [
                    "<style type=\"text/css\">",
                    "  .lasso_control{",
                    "    margin-left: 10px;",
                    "  }",
                    "</style>",
                    "<div class=\"lasso_control\" id=\"lasso-hidden-settings-div\">",
                    "  <div class=\"row\">",
                    "    <p class=\"lasso_selection_description\"><b>Primary features </b>",
                    "  (hover the mouse",
                    "pointer over the feature names to see a full description):</p>",
                    "    <form id=\"lasso_features_select\">",
                    "      <div class=\"lasso_form_group\">",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_ionization_potential\" CHECKED > <span title=\"Atomic ionization potential\"><i>IP</i> </span></label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_electron_affinity\" CHECKED > <span title=\"Atomic electron affinity\"> <i>EA</i></span></label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_homo\" CHECKED> <span title=\"Energy of highest occupied molecular orbital\"><i>E</i> <sub>HOMO</sub></span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_lumo\" CHECKED> <span title=\"Energy of lowest unoccupied molecular orbital\"> <i>E</i> <sub>LUMO</sub>  </span> </label>",
                    "        ",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_rs_max\" CHECKED > <span title=\"Radius at which the radial probability density of the valence s orbital is maximum\"> <i>r</i><sub>s</sub>  </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_rp_max\" CHECKED > <span title=\"Radius at which the radial probability density of the valence p orbital is maximum\"> <i>r</i><sub>p</sub>  </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_rd_max\" CHECKED > <span title=\"Radius at which the radial probability density of the valence d orbital is maximum\"> <i>r</i><sub>d</sub>  </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_number\" > <span title=\"Atomic number\"> <i>Z</i>  </span> </label>",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_number_valence_electrons\" > <span title=\"Number of valence electrons\"> <i>Z</i><sub>val</sub>  </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"period\" > <span title=\"Period (in the periodic table)\"> <i>n</i> <sub>period</sub>  </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_r_by_2_dimer\" > <span title=\"Bond length of the dimer\"> <i>d</i> <sub>dimer</sub> </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_electronic_binding_energy_dimer\" > <span title=\"Binding energy of the dimer\"> <i>E</i> <sub>b</sub> </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"atomic_homo_lumo_diff\" > <span title=\"HOMO-LUMO gap of the dimer\"> Δ<i>E</i><sub>HL</sub>  </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"r_sigma\" > <span title=\"John-Bloch's indicator1: |rp(A) + rs(A) - rp(B) -rs(B)| ",
                    "           [Phys. Rev. Lett. 33. 1095 (1974)]\"> r<sub>σ</sub>  </span> </label>",
                    "         <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"r_pi\" > <span title=\"John-Bloch's indicator2: |rp(A) - rs(A)| +| rp(B) -rs(B)| ",
                    "          [Phys. Rev. Lett. 33. 1095 (1974)]\">  r<sub>π</sub>  </span> </label>",
                    "      </div>",
                    "    </form>",
                    "  </div>  <!-- End of row-->",
                    "  <div class=\"row\"> <!-- Start of second row-->",
                    "    <p class=\"lasso_selection_description\"><b>Allowed operations:</b> <br>",
                    "  Given features x and y, apply these operations:</p>",
                    "    <form id=\"lasso_operators_select\">",
                    "      <div class=\"lasso_form_group\">",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-1\"> <input type=\"checkbox\" value=\"+\" CHECKED > x+y  </label>",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-1\"> <input type=\"checkbox\" value=\"-\" > x-y  </label>",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-1\"> <input type=\"checkbox\" value=\"|-|\" CHECKED > |x-y|  </label>",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-1\"> <input type=\"checkbox\" value=\"*\" > x &middot y  </label>",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-1\"> <input type=\"checkbox\" value=\"/\" CHECKED > x/y  </label>",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-1\"> <input type=\"checkbox\" value=\"^2\" CHECKED > x^2  </label>",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"^3\" > x^3  </label>",
                    "        <label class =\"col-xs-4 col-md-4 col-lg-3\"> <input type=\"checkbox\" value=\"exp\" CHECKED > exp(x)  </label>",
                    "      </div>",
                    "    </form>",
                    "  </div>  <!-- End of row-->",
                    "  <div class=\"row\"> <!-- Start of third row-->",
                    "  <p class=\"lasso_selection_description\"><b>Optimal descriptor maximum dimension: </b> ",
                    "  <select id='lasso_max_dim_selector'>",
                    "    <option value=\"2\" > 2D</option>",
                    "    <option value=\"3\" > 3D</option>",
                    "    <option value=\"4\" > 4D</option>",
                    "    <option value=\"5\" > 5D</option>",
                    "  </select> </p>",
                    "  </div><!-- End of row-->",
                    "  <div class=\"row\"> <!-- Start of forth row-->",
                    "  <p class=\"lasso_selection_description\"><b>Units of measurement: </b> ",
                    "  <select id='units_select'>",
                    "    <option value=\"eV_angstrom\" > [energy]=eV;&nbsp;&nbsp;[length]=angstrom</option>",
                    "    <option value=\"J_m\" > [energy]=J;&nbsp;&nbsp;[length]=m</option>",
                    "    <option value=\"kcal/mol_angstrom\" > [energy]=kcal/mol;&nbsp;&nbsp;[length]=angstrom</option>",
                    "  </select> </p>",
                    "  </div><!-- End of row-->",
                    " ",
                    "</div>"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Html",
                    "object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\n<style type=\"text/css\">\n  .lasso_control{\n    margin-left: 10px;\n  }\n</style>\n<div class=\"lasso_control\" id=\"lasso-hidden-settings-div\">\n  <div class=\"row\">\n    <p class=\"lasso_selection_description\"><b>Primary features </b>\n  (hover the mouse\npointer over the feature names to see a full description):</p>\n    <form id=\"lasso_features_select\">\n      <div class=\"lasso_form_group\">\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_ionization_potential\" checked=\"\" type=\"checkbox\"> <span title=\"Atomic ionization potential\"><i>IP</i> </span></label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_electron_affinity\" checked=\"\" type=\"checkbox\"> <span title=\"Atomic electron affinity\"> <i>EA</i></span></label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_homo\" checked=\"\" type=\"checkbox\"> <span title=\"Energy of highest occupied molecular orbital\"><i>E</i> <sub>HOMO</sub></span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_lumo\" checked=\"\" type=\"checkbox\"> <span title=\"Energy of lowest unoccupied molecular orbital\"> <i>E</i> <sub>LUMO</sub>  </span> </label>\n        \n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_rs_max\" checked=\"\" type=\"checkbox\"> <span title=\"Radius at which the radial probability density of the valence s orbital is maximum\"> <i>r</i><sub>s</sub>  </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_rp_max\" checked=\"\" type=\"checkbox\"> <span title=\"Radius at which the radial probability density of the valence p orbital is maximum\"> <i>r</i><sub>p</sub>  </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_rd_max\" checked=\"\" type=\"checkbox\"> <span title=\"Radius at which the radial probability density of the valence d orbital is maximum\"> <i>r</i><sub>d</sub>  </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_number\" type=\"checkbox\"> <span title=\"Atomic number\"> <i>Z</i>  </span> </label>\n        <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_number_valence_electrons\" type=\"checkbox\"> <span title=\"Number of valence electrons\"> <i>Z</i><sub>val</sub>  </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"period\" type=\"checkbox\"> <span title=\"Period (in the periodic table)\"> <i>n</i> <sub>period</sub>  </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_r_by_2_dimer\" type=\"checkbox\"> <span title=\"Bond length of the dimer\"> <i>d</i> <sub>dimer</sub> </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_electronic_binding_energy_dimer\" type=\"checkbox\"> <span title=\"Binding energy of the dimer\"> <i>E</i> <sub>b</sub> </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"atomic_homo_lumo_diff\" type=\"checkbox\"> <span title=\"HOMO-LUMO gap of the dimer\"> Δ<i>E</i><sub>HL</sub>  </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"r_sigma\" type=\"checkbox\"> <span title=\"John-Bloch's indicator1: |rp(A) + rs(A) - rp(B) -rs(B)| \n           [Phys. Rev. Lett. 33. 1095 (1974)]\"> r<sub>σ</sub>  </span> </label>\n         <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"r_pi\" type=\"checkbox\"> <span title=\"John-Bloch's indicator2: |rp(A) - rs(A)| +| rp(B) -rs(B)| \n          [Phys. Rev. Lett. 33. 1095 (1974)]\">  r<sub>π</sub>  </span> </label>\n      </div>\n    </form>\n  </div>  <!-- End of row-->\n  <div class=\"row\"> <!-- Start of second row-->\n    <p class=\"lasso_selection_description\"><b>Allowed operations:</b> <br>\n  Given features x and y, apply these operations:</p>\n    <form id=\"lasso_operators_select\">\n      <div class=\"lasso_form_group\">\n        <label class=\"col-xs-4 col-md-4 col-lg-1\"> <input value=\"+\" checked=\"\" type=\"checkbox\"> x+y  </label>\n        <label class=\"col-xs-4 col-md-4 col-lg-1\"> <input value=\"-\" type=\"checkbox\"> x-y  </label>\n        <label class=\"col-xs-4 col-md-4 col-lg-1\"> <input value=\"|-|\" checked=\"\" type=\"checkbox\"> |x-y|  </label>\n        <label class=\"col-xs-4 col-md-4 col-lg-1\"> <input value=\"*\" type=\"checkbox\"> x · y  </label>\n        <label class=\"col-xs-4 col-md-4 col-lg-1\"> <input value=\"/\" checked=\"\" type=\"checkbox\"> x/y  </label>\n        <label class=\"col-xs-4 col-md-4 col-lg-1\"> <input value=\"^2\" checked=\"\" type=\"checkbox\"> x^2  </label>\n        <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"^3\" type=\"checkbox\"> x^3  </label>\n        <label class=\"col-xs-4 col-md-4 col-lg-3\"> <input value=\"exp\" checked=\"\" type=\"checkbox\"> exp(x)  </label>\n      </div>\n    </form>\n  </div>  <!-- End of row-->\n  <div class=\"row\"> <!-- Start of third row-->\n  <p class=\"lasso_selection_description\"><b>Optimal descriptor maximum dimension: </b> \n  <select id=\"lasso_max_dim_selector\">\n    <option value=\"2\"> 2D</option>\n    <option value=\"3\"> 3D</option>\n    <option value=\"4\"> 4D</option>\n    <option value=\"5\"> 5D</option>\n  </select> </p>\n  </div><!-- End of row-->\n  <div class=\"row\"> <!-- Start of forth row-->\n  <p class=\"lasso_selection_description\"><b>Units of measurement: </b> \n  <select id=\"units_select\">\n    <option value=\"eV_angstrom\"> [energy]=eV;&nbsp;&nbsp;[length]=angstrom</option>\n    <option value=\"J_m\"> [energy]=J;&nbsp;&nbsp;[length]=m</option>\n    <option value=\"kcal/mol_angstrom\"> [energy]=kcal/mol;&nbsp;&nbsp;[length]=angstrom</option>\n  </select> </p>\n  </div><!-- End of row-->\n \n</div>"
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 0,
                "height": 379
            },
            "evaluatorReader": true,
            "lineCount": 68
        },
        {
            "id": "code8GyXFv",
            "type": "code",
            "evaluator": "HTML",
            "input": {
                "body": [
                    "<div class=\"lasso_control\">",
                    "",
                    "  <p style=\"margin-top: 1ex;\"></p>",
                    "  <button class=\"btn btn-default\" onclick='run_lasso()' style=\"font-weight: bold;\">RUN</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;",
                    "  <div id=\"lasso-hidden-settings-button\"><button class=\"btn btn-default\" onclick='reset_lasso()'>RESET</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</div>",
                    "  <label title=\"This button becomes active when the",
                    "run is finished. By clicking it, an interactive plot of the first 2",
                    "dimensions of the optimized descriptor will be opened\"> ",
                    "  <a href=\"#\" target=\"_blank\" class=\"btn btn-primary disabled\" id=\"lasso_result_button\" >View interactive 2D scatter plot</a> </label>",
                    "</div>"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Html",
                    "object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\n<div class=\"lasso_control\">\n\n  <p style=\"margin-top: 1ex;\"></p>\n  <button class=\"btn btn-default\" onclick=\"run_lasso()\" style=\"font-weight: bold;\">RUN</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n  <div id=\"lasso-hidden-settings-button\"><button class=\"btn btn-default\" onclick=\"reset_lasso()\">RESET</button>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</div>\n  <label title=\"This button becomes active when the\nrun is finished. By clicking it, an interactive plot of the first 2\ndimensions of the optimized descriptor will be opened\"> \n  <a href=\"/user/tmp/7719891784df6878.html\" target=\"_blank\" class=\"btn btn-primary active\" id=\"lasso_result_button\">View interactive 2D scatter plot</a> </label>\n</div>"
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 0,
                "height": 196
            },
            "evaluatorReader": true,
            "lineCount": 10
        },
        {
            "id": "codeo0JBr5",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "",
                    "if beaker.units == 'eV_angstrom':",
                    "    energy_unit = 'eV'",
                    "    length_unit = 'angstrom'",
                    "elif beaker.units == 'J_m':",
                    "    energy_unit = 'J'",
                    "    length_unit = 'm'",
                    "elif beaker.units == 'kcal/mol_angstrom':",
                    "    energy_unit = 'kcal/mol'",
                    "    length_unit = 'angstrom'",
                    "",
                    "kwargs['energy_unit'] = energy_unit",
                    "kwargs['length_unit'] = length_unit",
                    "kwargs['selected_feature_list'] = beaker.selected_feature_list",
                    "print beaker.selected_feature_list",
                    "print beaker.allowed_operations",
                    "",
                    "P, D, feature_list = get_data_from_nomad_sim(beaker.allowed_operations, **kwargs)",
                    "out = LILO(P, D, feature_list, print_lasso=False, lasso_number=30, print_model=True)"
                ]
            },
            "output": {
                "state": {},
                "result": {
                    "type": "Results",
                    "outputdata": [
                        {
                            "type": "err",
                            "value": "INFO: Calculating descriptor: atomic_features\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Writing descriptor to file.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Writing descriptor information to file.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Descriptor calculation: done.\n"
                        },
                        {
                            "type": "err",
                            "value": "WARNING: No allowed operations selected.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Number of total features generated: 8\n"
                        },
                        {
                            "type": "out",
                            "value": "['atomic_ionization_potential', 'atomic_electron_affinity', 'atomic_rs_max', 'atomic_rp_max']\n['+', '|-|', '/', '^2', 'exp']\nOnly 8 features are collected"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.313339\t- 0.477 r_p(A) + 1.014\n2D:\t0.304003\t- 0.285 r_p(B) - 0.498 r_p(A) + 1.294\n3D:\t0.280145\t- 5.845 r_p(B) - 0.439 r_p(A) + 8.426 r_s(B) - 0.348\n\n"
                        }
                    ]
                },
                "selectedType": "Results",
                "pluginName": "IPython",
                "shellId": "CF239072B98E4D2890C4EF3EAF36FD99",
                "elapsedTime": 15202,
                "height": 309
            },
            "evaluatorReader": true,
            "lineCount": 19,
            "tags": "calc_cell"
        },
        {
            "id": "codekH7ZWC",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "parameter_list = beaker.selected_feature_list",
                    "parameter_list.append(beaker.allowed_operations)",
                    "name_html_page = hashlib.sha224(str(parameter_list)).hexdigest()[:16]",
                    "",
                    "data_folder='/parsed/prod-017/FhiAimsParser2.0.0/RdUzye8EKmv-z4LGNHGTSk8S3S1WY'",
                    "lookup_file = '/home/beaker/.beaker/v1/web/tmp/lookup.dat'",
                    "control_file = '/home/beaker/.beaker/v1/web/tmp/control.json'",
                    "legend_title='Reference E(RS)-E(ZB)'",
                    "target_name='E(RS)-E(ZB)'",
                    "",
                    "json_list, frame_list, x_list, y_list, target_list, target_pred_list = get_json_list(method='file', data_folder=data_folder,",
                    "    path_to_file=lookup_file, drop_duplicates=False, displace_duplicates=True, predicted_value=True)",
                    "beaker.viewer_result = name_html_page",
                    "",
                    "",
                    "plot_result = plot(name=name_html_page, json_list=json_list, frames='list', frame_list=frame_list, ",
                    "    file_format='NOMAD', clustering_x_list=x_list, clustering_y_list=y_list, target_list=target_list,",
                    "    target_unit=energy_unit, legend_title=legend_title, target_name=target_name,",
                    "    target_pred_list=target_pred_list,",
                    "    plot_title='SIS+L0 structure map',",
                    "    clustering_point_size=12, tmp_folder=kwargs['tmp_folder'], control_file=control_file,",
                    "    op_list=kwargs['op_list'], operations_on_structure=kwargs['operations_on_structure'])"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "Results",
                    "outputdata": [
                        {
                            "type": "err",
                            "value": "INFO: Generating figures and geometry files.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Generating figures and geometry files: done.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: The color in the plot is given by the target value.\n"
                        },
                        {
                            "type": "err",
                            "value": "INFO: Click on the button 'View interactive 2D scatter plot' to see the plot.\n"
                        }
                    ]
                },
                "selectedType": "Results",
                "pluginName": "IPython",
                "shellId": "CF239072B98E4D2890C4EF3EAF36FD99",
                "elapsedTime": 5043,
                "height": 142
            },
            "evaluatorReader": true,
            "lineCount": 22,
            "tags": "calc_cell"
        },
        {
            "id": "codepqAHnM",
            "type": "code",
            "evaluator": "JavaScript",
            "input": {
                "body": [
                    "var result_link = '/user/tmp/' + beaker.viewer_result + '.html';",
                    "beaker.view_result(result_link);"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "selectedType": "BeakerDisplay",
                "pluginName": "JavaScript",
                "elapsedTime": 92
            },
            "evaluatorReader": true,
            "lineCount": 2,
            "tags": "calc_cell"
        },
        {
            "id": "codebAh66z",
            "type": "code",
            "evaluator": "HTML",
            "input": {
                "body": [
                    "We obtain good fits. But what about predicting Ediff of a new material? We test the prediction performance via leave one out CV. How often is the same descriptor selected?"
                ],
                "hidden": true
            },
            "output": {
                "state": {},
                "result": {
                    "type": "BeakerDisplay",
                    "innertype": "Html",
                    "object": "<script>\nvar beaker = bkHelper.getBeakerObject().beakerObj;\n</script>\nWe obtain good fits. But what about predicting Ediff of a new material? We test the prediction performance via leave one out CV. How often is the same descriptor selected?"
                },
                "selectedType": "BeakerDisplay",
                "elapsedTime": 0,
                "height": 92
            },
            "evaluatorReader": true,
            "lineCount": 1
        },
        {
            "id": "codel2Xara",
            "type": "code",
            "evaluator": "IPython",
            "input": {
                "body": [
                    "def split_data(P, D, cv_i):",
                    "    P_1, P_test, P_2 = np.split(P, [cv_i, cv_i+1])",
                    "    P_train = np.concatenate((P_1,P_2))",
                    "    D_1, D_test, D_2 = np.split(D, [cv_i, cv_i+1])",
                    "    D_train = np.concatenate((D_1,D_2))",
                    "    D_test = np.column_stack( (D_test, np.ones(1)) )  ",
                    "    return P_train, P_test, D_train, D_test",
                    "",
                    "# Leave-one-out cross-validation",
                    "compounds = len(P)",
                    "dimensions = range(1,4)",
                    "",
                    "",
                    "P_predict = np.empty([len(dimensions),compounds])",
                    "for cv_i in range(compounds):",
                    "    P_train, P_test, D_train, D_test = split_data(P, D, cv_i)",
                    "    out = LILO(P_train, D_train, feature_list, print_lasso=False, lasso_number=20, print_model=True)",
                    "    for dim in dimensions:",
                    "        indices_for_D, coef,RMSE = out[dim-1]",
                    "        P_predict[dim-1,cv_i] = np.dot(D_test[:, indices_for_D+[-1]], coef)",
                    "print np.linalg.norm(P-P_predict, axis=1)/np.sqrt(compounds)",
                    "",
                    "",
                    "",
                    "# plot",
                    "for dim in dimensions:",
                    "    predict = P_predict[dim-1]",
                    "    if dim == 1:",
                    "        maxi = max(max(P), max(predict))",
                    "        mini = min(min(P), min(predict))",
                    "        plt.plot([maxi,mini], [maxi,mini], 'k')",
                    "    plt.scatter(P, predict, color=['b','r', 'g'][dim-1], label='%s-dimensional' %dim)",
                    "plt.legend(loc='best')",
                    "plt.show()",
                    "",
                    ""
                ]
            },
            "output": {
                "state": {},
                "result": {
                    "type": "Results",
                    "outputdata": [
                        {
                            "type": "out",
                            "value": "1D:\t0.138036\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100832\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.482 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.083799\t+ 16.030 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.519 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n\n1D:\t0.137927\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100832\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.483 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.081872\t+ 16.058 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.084 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.117 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.247\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.135085\t- 0.101 EA(A)+IP(B)/r_p(A)^2 - 0.378\n2D:\t0.104454\t+ 16.080 r_s(B)/exp((r_s(B)+r_p(A))^2) + 4.572 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.418\n3D:\t0.094990\t+ 13.047 r_p(B)/exp((r_p(B)+r_p(A))^2) + 3.209 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 + 6.377 |r_s(A)-r_d(B)|/exp(r_p(A)+r_d(B)) - 0.388\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137849\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100774\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.477 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084110\t+ 16.054 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.268 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.504 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.236\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137448\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100631\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.500 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.142\n3D:\t0.084212\t+ 16.063 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.266 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.504 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136161\t+ 0.340 |EA(B)-IP(B)|/exp(r_p(A)^2) - 0.190\n2D:\t0.098612\t+ 0.115 |EA(B)-IP(B)|/r_p(A)^2 - 1.440 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.150\n3D:\t0.079913\t+ 15.994 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.199 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.632 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.253\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137532\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100733\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.492 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.084231\t+ 16.070 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.502 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137751\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100807\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.487 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.081838\t+ 16.105 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.076 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.102 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.248\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136271\t- 0.056 IP(A)+IP(B)/r_p(A)^2 - 0.336\n2D:\t0.106724\t+ 16.583 r_s(B)/exp((r_s(B)+r_p(A))^2) + 4.441 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.411\n3D:\t0.079819\t+ 16.363 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.086 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.095 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.246\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137217\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100763\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.493 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.084225\t+ 16.065 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.264 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.504 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137573\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100639\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.498 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.142\n3D:\t0.083509\t+ 16.002 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.286 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.530 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.235\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.133112\t- 0.211 IP(A)+IP(B)/(r_p(A)+r_s(A))^2 - 0.408\n2D:\t0.111514\t+ 11.570 r_p(B)/exp((r_p(B)+r_p(A))^2) + 3.926 r_s(B)/(r_p(B)+r_p(A))^2 - 0.424\n3D:\t0.083829\t+ 16.337 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.250 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.495 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.239\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137692\t- 0.056 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100776\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.485 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.081220\t+ 16.266 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.096 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.093 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.244\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.129244\t- 0.057 IP(A)+IP(B)/r_p(A)^2 - 0.339\n2D:\t0.110603\t+ 11.242 r_p(B)/exp((r_p(B)+r_p(A))^2) + 4.036 r_s(B)/(r_p(B)+r_p(A))^2 - 0.433\n3D:\t0.080562\t+ 16.071 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.311 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.412 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.226\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137869\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.099810\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.509 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.082653\t+ 16.043 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.289 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.540 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.239\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137337\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.330\n2D:\t0.100226\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.476 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.083912\t+ 16.107 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.259 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.462 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.234\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137129\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.329\n2D:\t0.099823\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.479 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.142\n3D:\t0.081447\t+ 16.147 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.089 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.039 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.240\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136799\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.329\n2D:\t0.098896\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.489 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.140\n3D:\t0.081126\t+ 16.180 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.097 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.005 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.236\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137952\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.099938\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.522 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.139\n3D:\t0.080669\t+ 16.071 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.137 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.018 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.234\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137994\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.108145\t+ 16.328 r_s(B)/exp((r_s(B)+r_p(A))^2) + 4.410 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.410\n3D:\t0.093789\t- 1.313 EA(A)/exp(r_d(A)^2) + 11.839 r_p(B)/exp((r_p(B)+r_p(A))^2) + 3.528 r_s(B)/(r_p(B)+r_p(A))^2 - 0.367\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137905\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100560\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.468 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.147\n3D:\t0.083683\t+ 16.121 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.244 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.464 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137820\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100406\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.459 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.149\n3D:\t0.081052\t+ 16.158 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.056 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.061 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.248\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137730\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100358\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.484 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.147\n3D:\t0.084091\t+ 16.054 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.260 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.523 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.240\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137813\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100440\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.476 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.147\n3D:\t0.084127\t+ 16.094 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.259 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.491 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138054\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100784\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.484 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.084231\t+ 16.071 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.501 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137936\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100466\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.487 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084120\t+ 16.079 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.263 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.502 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137892\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100323\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.488 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084222\t+ 16.070 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.260 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.500 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137783\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100253\t+ 0.115 |EA(B)-IP(B)|/r_p(A)^2 - 1.486 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084030\t+ 16.049 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.262 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.528 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.240\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.119515\t- 0.254 IP(B)/exp(r_p(A)^2) - 0.178\n2D:\t0.099153\t+ 0.288 |EA(B)-IP(B)|/exp(r_p(A)^2) - 0.306 r_p(B)+r_d(A)/exp(r_d(A)^2) - 0.123\n3D:\t0.073519\t+ 0.281 |EA(B)-IP(B)|/exp(r_p(A)^2) - 11.139 |r_p(B)-r_s(B)|/exp(r_s(B)+r_d(A)) - 1.092 |r_p(B)-r_s(A)|/exp(r_s(A)) + 0.063\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.131019\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.095780\t+ 0.113 |EA(B)-IP(B)|/r_p(A)^2 - 1.484 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.082295\t+ 16.038 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.267 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.436 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.233\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136280\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100196\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.485 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.084215\t+ 16.077 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.260 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.507 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.135518\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.335\n2D:\t0.098696\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.499 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.083156\t+ 16.105 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.275 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.448 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.233\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136780\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.329\n2D:\t0.100551\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.463 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.082495\t+ 15.940 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.298 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.616 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.244\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.135764\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.328\n2D:\t0.098737\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.468 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.084132\t+ 16.026 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.543 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.241\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136102\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.328\n2D:\t0.098713\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.477 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.142\n3D:\t0.084227\t+ 16.080 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.493 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136488\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.329\n2D:\t0.098292\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.496 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.139\n3D:\t0.081134\t+ 16.172 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.100 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.010 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.236\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.135465\t- 0.219 IP(A)+IP(B)/(r_p(A)+r_s(A))^2 - 0.419\n2D:\t0.100194\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.449 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.148\n3D:\t0.082983\t+ 15.976 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.214 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.579 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.248\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138046\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100710\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.481 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084223\t+ 16.064 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.505 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137978\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100731\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.477 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084211\t+ 16.062 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.263 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.505 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137670\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100787\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.475 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084212\t+ 16.064 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.266 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.502 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137741\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100254\t+ 0.115 |EA(B)-IP(B)|/r_p(A)^2 - 1.487 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084046\t+ 16.054 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.262 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.524 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.240\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137931\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100266\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.485 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.083981\t+ 16.108 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.264 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.480 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.236\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138056\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100772\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.486 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.084232\t+ 16.071 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.501 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138019\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100470\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.492 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.083999\t+ 16.084 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.268 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.499 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137971\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100221\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.495 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.084230\t+ 16.071 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.262 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.502 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137807\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100113\t+ 0.115 |EA(B)-IP(B)|/r_p(A)^2 - 1.491 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.083967\t+ 16.049 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.264 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.528 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.240\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137647\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.335\n2D:\t0.099798\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.501 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.083654\t+ 16.059 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.272 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.523 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.239\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137721\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100527\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.480 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.147\n3D:\t0.084099\t+ 16.049 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.258 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.527 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.240\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.134586\t- 0.101 EA(A)+IP(B)/r_p(A)^2 - 0.380\n2D:\t0.099977\t+ 0.115 |EA(B)-IP(B)|/r_p(A)^2 - 1.437 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.150\n3D:\t0.083558\t+ 15.999 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.220 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.567 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.247\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136996\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.335\n2D:\t0.100271\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.459 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.149\n3D:\t0.083902\t+ 16.103 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.245 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.495 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.240\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138001\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100812\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.487 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.084230\t+ 16.072 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.262 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.501 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137844\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.331\n2D:\t0.100812\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.489 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.083479\t+ 16.096 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.297 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.485 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.233\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138047\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100152\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.518 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.142\n3D:\t0.083888\t+ 16.081 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.284 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.498 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.235\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137839\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.099667\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.510 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.083605\t+ 16.057 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.278 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.523 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136889\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100367\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.498 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.084202\t+ 16.075 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.265 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.490 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.236\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136322\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.335\n2D:\t0.100832\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.483 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.084182\t+ 16.085 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.253 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.495 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137980\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100831\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.482 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.084062\t+ 16.093 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.257 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.493 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137706\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100486\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.488 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.084039\t+ 16.037 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.263 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.524 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138006\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100720\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.487 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.084229\t+ 16.067 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.504 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138000\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.099521\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.520 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.138\n3D:\t0.083198\t+ 0.111 |EA(B)-IP(B)|/r_p(A)^2 - 2.799 |r_p(B)-r_s(B)|/exp(r_d(A)^2) - 1.510 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.107\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138038\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100817\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.482 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.084230\t+ 16.069 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.261 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.504 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137752\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100552\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.479 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.146\n3D:\t0.084216\t+ 16.073 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.260 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.503 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137742\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100521\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.480 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.147\n3D:\t0.084141\t+ 16.070 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.262 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.495 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.236\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137753\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100473\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.481 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.147\n3D:\t0.084055\t+ 16.045 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.258 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.531 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.241\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138044\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100832\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.483 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.082042\t+ 16.081 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.085 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.109 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.247\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137211\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100832\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.482 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.145\n3D:\t0.084133\t+ 16.046 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.268 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.513 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137854\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100559\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.500 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.141\n3D:\t0.083432\t+ 16.007 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.287 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.522 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.234\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.134610\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.329\n2D:\t0.099178\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.428 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.150\n3D:\t0.079162\t+ 15.947 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.019 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.207 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.260\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137906\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100747\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.482 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.081263\t+ 16.027 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.087 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.129 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.247\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138048\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100805\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.484 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.083314\t+ 16.015 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.268 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.521 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137924\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.100821\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.486 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.083532\t+ 16.032 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.282 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.505 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.234\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137775\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.331\n2D:\t0.100821\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.486 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.144\n3D:\t0.083994\t+ 16.056 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.275 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.519 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.135541\t- 0.220 IP(A)+IP(B)/(r_p(A)+r_s(A))^2 - 0.421\n2D:\t0.100592\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.464 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.147\n3D:\t0.083796\t+ 16.022 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.234 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.552 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.244\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136449\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.329\n2D:\t0.099449\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.471 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.083734\t+ 16.126 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.258 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.445 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.232\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137564\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.099958\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.469 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.148\n3D:\t0.080928\t+ 16.169 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.076 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.061 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.246\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136468\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.329\n2D:\t0.099160\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.477 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.142\n3D:\t0.081401\t+ 16.162 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.089 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.027 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.239\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137497\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100296\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.463 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.149\n3D:\t0.081273\t+ 16.154 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.067 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.076 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.248\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137896\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.332\n2D:\t0.100514\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.492 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.084158\t+ 16.081 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.257 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.495 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.238\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.138049\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.333\n2D:\t0.099991\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.516 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.139\n3D:\t0.083761\t+ 0.111 |EA(B)-IP(B)|/r_p(A)^2 - 2.799 |r_p(B)-r_s(B)|/exp(r_d(A)^2) - 1.507 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.108\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137738\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.331\n2D:\t0.100468\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.488 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.143\n3D:\t0.084189\t+ 16.063 r_p(B)/exp((r_p(B)+r_p(A))^2) - 1.263 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.503 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.136542\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.329\n2D:\t0.098501\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.491 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.139\n3D:\t0.081466\t+ 16.177 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.097 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.013 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.237\n"
                        },
                        {
                            "type": "out",
                            "value": "\n1D:\t0.137428\t- 0.055 IP(A)+IP(B)/r_p(A)^2 - 0.334\n2D:\t0.100543\t+ 0.114 |EA(B)-IP(B)|/r_p(A)^2 - 1.460 |r_p(B)-r_s(A)|/exp(r_s(A)) - 0.149\n3D:\t0.081218\t+ 16.146 r_s(B)/exp((r_s(B)+r_p(A))^2) - 1.054 |r_p(B)-r_s(A)|/exp(r_s(A)) + 4.092 |r_s(B)-r_d(A)|/(r_p(A)+r_d(A))^2 - 0.251\n"
                        },
                        {
                            "type": "out",
                            "value": "\n[ 0.19000064  0.1441343   0.12024634]\n"
                        }
                    ],
                    "payload": "<div class=\"output_subarea output_png\"><img 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                },
                "selectedType": "Results",
                "pluginName": "IPython",
                "shellId": "9F533114F51B41D4A9DB4EF14E0B36FC",
                "elapsedTime": 465205,
                "height": 5799
            },
            "evaluatorReader": true,
            "lineCount": 36
        }
    ],
    "namespace": {
        "selected_feature_list": [
            "atomic_ionization_potential",
            "atomic_electron_affinity",
            "atomic_rs_max",
            "atomic_rp_max"
        ],
        "allowed_operations": [
            "+",
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            "/",
            "^2",
            "exp"
        ],
        "max_dim": "2",
        "structures_diff": null,
        "n_comb": null,
        "n_sis": null,
        "units": "eV_angstrom",
        "viewer_result": "7719891784df6878"
    }
}