diff --git a/docs/sphinx-docs/source/user/tools.rst b/docs/sphinx-docs/source/user/tools.rst index 5559a8e37b..27dac8a98c 100644 --- a/docs/sphinx-docs/source/user/tools.rst +++ b/docs/sphinx-docs/source/user/tools.rst @@ -27,3 +27,6 @@ Tools & Utilities Image Viewer File Converter + + MuMag Tool + diff --git a/src/sas/qtgui/MainWindow/GuiManager.py b/src/sas/qtgui/MainWindow/GuiManager.py index fe3c14ca81..126e0464c9 100644 --- a/src/sas/qtgui/MainWindow/GuiManager.py +++ b/src/sas/qtgui/MainWindow/GuiManager.py @@ -34,6 +34,8 @@ from sas.qtgui.Utilities.ResultPanel import ResultPanel from sas.qtgui.Utilities.OrientationViewer.OrientationViewer import show_orientation_viewer from sas.qtgui.Utilities.HidableDialog import hidable_dialog + +from sas.qtgui.Utilities.MuMag.MuMag import MuMag from sas.qtgui.Utilities.DocViewWidget import DocViewWindow from sas.qtgui.Utilities.DocRegenInProgess import DocRegenProgress from sas.qtgui.Utilities.Reports.ReportDialog import ReportDialog @@ -204,6 +206,7 @@ def addWidgets(self): self.SLDCalculator = SldPanel(self) self.DVCalculator = DensityPanel(self) self.KIESSIGCalculator = KiessigPanel(self) + self.MuMag_Fitter = MuMag(self) self.SlitSizeCalculator = SlitSizeCalculator(self) self.ResolutionCalculator = ResolutionCalculatorPanel(self) self.GENSASCalculator = None @@ -736,6 +739,7 @@ def addTriggers(self): self._workspace.actionSLD_Calculator.triggered.connect(self.actionSLD_Calculator) self._workspace.actionDensity_Volume_Calculator.triggered.connect(self.actionDensity_Volume_Calculator) self._workspace.actionKeissig_Calculator.triggered.connect(self.actionKiessig_Calculator) + self._workspace.actionMuMag_Fitter.triggered.connect(self.actionMuMag_Fitter) #self._workspace.actionKIESSING_Calculator.triggered.connect(self.actionKIESSING_Calculator) self._workspace.actionSlit_Size_Calculator.triggered.connect(self.actionSlit_Size_Calculator) self._workspace.actionSAS_Resolution_Estimator.triggered.connect(self.actionSAS_Resolution_Estimator) @@ -1022,6 +1026,11 @@ def actionKiessig_Calculator(self): """ self.KIESSIGCalculator.show() + def actionMuMag_Fitter(self): + """ + """ + self.MuMag_Fitter.show() + def actionSlit_Size_Calculator(self): """ """ diff --git a/src/sas/qtgui/MainWindow/UI/MainWindowUI.ui b/src/sas/qtgui/MainWindow/UI/MainWindowUI.ui index 5d0ac847ce..7af0efede0 100755 --- a/src/sas/qtgui/MainWindow/UI/MainWindowUI.ui +++ b/src/sas/qtgui/MainWindow/UI/MainWindowUI.ui @@ -91,6 +91,7 @@ + @@ -620,6 +621,11 @@ Preferences... + + + MuMag Fitter + + What's New diff --git a/src/sas/qtgui/Utilities/MuMag/MuMag.py b/src/sas/qtgui/Utilities/MuMag/MuMag.py new file mode 100644 index 0000000000..199ba9d7c3 --- /dev/null +++ b/src/sas/qtgui/Utilities/MuMag/MuMag.py @@ -0,0 +1,336 @@ +import webbrowser + +from sas.qtgui.Utilities.MuMag.UI.MuMagUI import Ui_MuMagTool +from PySide6.QtWidgets import QVBoxLayout +from PySide6 import QtWidgets +from sas.qtgui.Utilities.MuMag import MuMagLib + +from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas +import matplotlib.pyplot as plt + +import matplotlib.pylab as pl +import numpy as np + +from sas.qtgui.Utilities.MuMag.datastructures import ExperimentalData, LoadFailure, FitFailure, ExperimentGeometry, \ + FitParameters, FitResults, LeastSquaresOutputPerpendicular +from sas.qtgui.Utilities.MuMag.MuMagLib import MuMagLib + +from logging import getLogger + +log = getLogger("MuMag") + +class MuMag(QtWidgets.QMainWindow, Ui_MuMagTool): + """ Main widget for the MuMag tool """ + + def __init__(self, parent=None): + super().__init__() + + self.setupUi(self) + + # Callbacks + self.ImportDataButton.clicked.connect(self.importData) + self.SimpleFitButton.clicked.connect(self.onFit) + self.SaveResultsButton.clicked.connect(self.onSave) + self.helpButton.clicked.connect(self.onHelp) + + # + # Data + # + + self.data: list[ExperimentalData] | None = None + self.fit_data: FitResults | None = None + + # + # Plotting + # + + # Data + data_plot_layout = QVBoxLayout() + self.data_tab.setLayout(data_plot_layout) + self.data_figure = plt.figure() #Figure(figsize=(width, height), dpi=dpi) + self.figure_canvas = FigureCanvas(self.data_figure) + self.data_axes = self.data_figure.add_subplot(1, 1, 1) + self.data_axes.set_visible(False) + data_plot_layout.addWidget(self.figure_canvas) + + # Fit results + fit_results_layout = QVBoxLayout() + self.fit_results_tab.setLayout(fit_results_layout) + self.fit_results_figure = plt.figure() + self.fit_results_canvas = FigureCanvas(self.fit_results_figure) + + self.chi_squared_axes = self.fit_results_figure.add_subplot(2, 2, 1) + self.residual_axes = self.fit_results_figure.add_subplot(2, 2, 2) + self.s_h_axes = self.fit_results_figure.add_subplot(2, 2, 3) + self.longitudinal_scattering_axes = self.fit_results_figure.add_subplot(2, 2, 4) + + fit_results_layout.addWidget(self.fit_results_canvas) + + # Comparison + comparison_layout = QVBoxLayout() + self.comparison_tab.setLayout(comparison_layout) + self.comparison_figure = plt.figure() + self.comparison_canvas = FigureCanvas(self.comparison_figure) + + self.comparison_axes = self.comparison_figure.add_subplot(1, 1, 1) + + comparison_layout.addWidget(self.comparison_canvas) + + # Set visibility + self.hide_everything() + + def importData(self): + """ Callback for the import data button """ + + # Get the directory from the user + directory = MuMagLib.directory_popup() + + if directory is None: + log.info("No directory selected") + return + + try: + self.data = MuMagLib.import_data(directory) + except LoadFailure as lf: + log.error(repr(lf)) + return + + log.info(f"Loaded {len(self.data)} datasets") + + self.hide_everything() + self.plot_tabs.setTabEnabled(0, True) + self.show_input_data() + + def hide_everything(self): + """ Hide all plots, disable tabs""" + + self.data_axes.cla() + self.chi_squared_axes.cla() + self.residual_axes.cla() + self.s_h_axes.cla() + self.longitudinal_scattering_axes.cla() + + self.plot_tabs.setTabEnabled(1, False) + self.plot_tabs.setTabEnabled(2, False) + # weird order because of how the widget behaves when all are not enabled + self.plot_tabs.setTabEnabled(0, False) + + + def show_input_data(self): + """ Plot Experimental Data: Generate Figure """ + + colors = pl.cm.jet(np.linspace(0, 1, len(self.data))) + + for i, datum in enumerate(self.data): + + self.data_axes.loglog(datum.scattering_curve.x, + datum.scattering_curve.y, + linestyle='-', color=colors[i], linewidth=0.5, + label=r'$B_0 = ' + str(datum.applied_field) + '$ T') + + self.data_axes.loglog(datum.scattering_curve.x, + datum.scattering_curve.y, '.', + color=colors[i], linewidth=0.3, markersize=1) + + # Plot limits + qlim = MuMagLib.nice_log_plot_bounds([datum.scattering_curve.x for datum in self.data]) + ilim = MuMagLib.nice_log_plot_bounds([datum.scattering_curve.y for datum in self.data]) + + self.data_axes.set_xlabel(r'$q$ [1/nm]') + self.data_axes.set_ylabel(r'$I_{\mathrm{exp}}$') + self.data_axes.set_xlim(qlim) + self.data_axes.set_ylim(ilim) + self.data_figure.tight_layout() + + self.data_axes.set_visible(True) + self.data_figure.canvas.draw() + + + def get_fit_parameters(self) -> FitParameters: + """ Get an object containing all the parameters needed for doing the fitting """ + + a_min = self.aMinSpinBox.value() + a_max = self.aMaxSpinBox.value() + + if a_max <= a_min: + raise ValueError(f"minimum A must be less than maximum A") + + match self.ScatteringGeometrySelect.currentText().lower(): + case "parallel": + geometry = ExperimentGeometry.PARALLEL + case "perpendicular": + geometry = ExperimentGeometry.PERPENDICULAR + case _: + raise ValueError(f"Unknown experiment geometry: {self.ScatteringGeometrySelect.currentText()}") + + return FitParameters( + q_max=self.qMaxSpinBox.value(), + min_applied_field=self.hMinSpinBox.value(), + exchange_A_n=self.aSamplesSpinBox.value(), + exchange_A_min=a_min, + exchange_A_max=a_max, + experiment_geometry=geometry) + + def onFit(self): + + if self.data is None: + log.error("No data loaded") + return None + + parameters = self.get_fit_parameters() + + match parameters.experiment_geometry: + case ExperimentGeometry.PERPENDICULAR: + self.longitudinal_scattering_axes.set_visible(True) + case ExperimentGeometry.PARALLEL: + self.longitudinal_scattering_axes.set_visible(False) + case _: + raise log.error(f"Unknown geometry: {parameters.experiment_geometry}") + + try: + self.fit_data = MuMagLib.simple_fit(self.data, parameters) + + except FitFailure as ff: + log.error("Fitting failed - are the parameters correct? "+repr(ff)) + return + + + self.show_fit_results() + + + def show_fit_results(self): + """ Show the results of the fit in the widget """ + + # Check for data + if self.fit_data is None: + log.error("No fit data to show") + return + + # Some dereferencing to make things more readable + refined = self.fit_data.refined_fit_data + sweep_data = self.fit_data.sweep_data + + q = refined.q * 1e-9 + + # Update text boxes + + self.exchange_a_display.setText(f"{self.fit_data.refined_fit_data.exchange_A * 1e12 : .5g} pJ/m") + self.exchange_a_std_display.setText(f"{self.fit_data.optimal_exchange_A_uncertainty : .5g} pJ/m") + + + + # Clear plots + self.chi_squared_axes.cla() + self.residual_axes.cla() + self.s_h_axes.cla() + self.longitudinal_scattering_axes.cla() + + # Plot A search data + self.chi_squared_axes.plot(sweep_data.exchange_A_checked * 1e12, sweep_data.exchange_A_chi_sq) + self.chi_squared_axes.plot(sweep_data.optimal.exchange_A * 1e12, sweep_data.optimal.exchange_A_chi_sq, 'o') + + self.chi_squared_axes.set_xlim([min(sweep_data.exchange_A_checked * 1e12), max(sweep_data.exchange_A_checked * 1e12)]) + self.chi_squared_axes.set_xlabel('$A$ [pJ/m]') + self.chi_squared_axes.set_ylabel('$\chi^2$') + + # Residual intensity plot + self.residual_axes.plot(q, refined.I_residual, label='fit') + self.residual_axes.set_yscale('log') + self.residual_axes.set_xscale('log') + self.residual_axes.set_xlim([min(q), max(q)]) + self.residual_axes.set_xlabel('$q$ [1/nm]') + self.residual_axes.set_ylabel('$I_{\mathrm{res}}$') + + # S_H parameter + self.s_h_axes.plot(q, refined.S_H, label='fit') + self.s_h_axes.set_yscale('log') + self.s_h_axes.set_xscale('log') + self.s_h_axes.set_xlim([min(q), max(q)]) + self.s_h_axes.set_xlabel('$q$ [1/nm]') + self.s_h_axes.set_ylabel('$S_H$') + + # S_M parameter + if isinstance(refined, LeastSquaresOutputPerpendicular): + self.longitudinal_scattering_axes.plot(q, refined.S_M, label='fit') + self.longitudinal_scattering_axes.set_yscale('log') + self.longitudinal_scattering_axes.set_xscale('log') + self.longitudinal_scattering_axes.set_xlim([min(q), max(q)]) + self.longitudinal_scattering_axes.set_xlabel('$q$ [1/nm]') + self.longitudinal_scattering_axes.set_ylabel('$S_M$') + + self.fit_results_figure.tight_layout() + + self.chi_squared_axes.set_visible(True) + self.residual_axes.set_visible(True) + self.s_h_axes.set_visible(True) + self.longitudinal_scattering_axes.set_visible(True) + + # + # Comparison Tab + # + + # Plot limits + qlim = MuMagLib.nice_log_plot_bounds([datum.scattering_curve.x for datum in self.data]) + ilim = MuMagLib.nice_log_plot_bounds([datum.scattering_curve.y for datum in self.data]) + + # Show the experimental data + colors = pl.cm.jet(np.linspace(0, 1, len(self.fit_data.input_data))) + for k, datum in enumerate(self.fit_data.input_data): + self.comparison_axes.loglog( + datum.scattering_curve.x, + datum.scattering_curve.y, + linestyle='None', color=colors[k], marker='x') + + # Show the fitted curves + n_sim = self.fit_data.refined_fit_data.I_simulated.shape[0] + colors = pl.cm.jet(np.linspace(0, 1, n_sim)) + for k in range(n_sim): + self.comparison_axes.loglog( + self.fit_data.refined_fit_data.q * 1e-9, + self.fit_data.refined_fit_data.I_simulated[k, :], + linestyle='solid', color=colors[k], + label='B_0 = ' + str(self.fit_data.input_data[k].applied_field) + ' T') + + self.comparison_axes.set_xlabel(r'$q$ [1/nm]') + self.comparison_axes.set_ylabel(r'$I_{\mathrm{exp}}$') + self.comparison_axes.set_xlim(qlim) + self.comparison_axes.set_ylim(ilim) + self.comparison_figure.tight_layout() + self.comparison_figure.canvas.draw() + + + # + # Set up tabs + # + + self.plot_tabs.setTabEnabled(1, True) + self.plot_tabs.setTabEnabled(2, True) + + self.plot_tabs.setCurrentIndex(1) + + def onSave(self): + """ Save button pressed """ + + if self.fit_data is None: + log.error("Nothing to save!") + return + + directory = MuMagLib.directory_popup() + + if directory is not None: + + MuMagLib.save_data(self.fit_data, directory) + + def onHelp(self): + webbrowser.open("https://www.sasview.org/docs/user/qtgui/Utilities/MuMag/mumag_help.html") + +def main(): + """ Show a demo of the slider """ + app = QtWidgets.QApplication([]) + form = MuMag() + form.show() + app.exec_() + + +if __name__ == "__main__": + main() \ No newline at end of file diff --git a/src/sas/qtgui/Utilities/MuMag/MuMagLib.py b/src/sas/qtgui/Utilities/MuMag/MuMagLib.py new file mode 100644 index 0000000000..662e620278 --- /dev/null +++ b/src/sas/qtgui/Utilities/MuMag/MuMagLib.py @@ -0,0 +1,558 @@ +import numpy as np +import matplotlib.pylab as pl +import os +import os.path +from datetime import datetime + +import scipy.optimize + +from PySide6 import QtWidgets +from PySide6.QtWidgets import QFileDialog + +from sas.qtgui.Utilities.MuMag.datastructures import ExperimentalData, LoadFailure, FitFailure, ExperimentGeometry, \ + FitParameters, FitResults, LeastSquaresOutputParallel, LeastSquaresOutputPerpendicular, SweepOutput + +from sasdata.dataloader.loader import Loader + + +class MuMagLib: + """ Library for methods supporting MuMag""" + + mu_0 = 4 * np.pi * 1e-7 + + @staticmethod + def directory_popup(): + directory = QFileDialog.getExistingDirectory() + + if directory.strip() == "": + return None + else: + return directory + + + @staticmethod + def import_data(directory): + """Import experimental data and get information from filenames""" + + try: + # Load the data + loader = Loader() + input_names = [name for name in os.listdir(directory) if name.lower().endswith(".csv")] + input_paths = [os.path.join(directory, filename) for filename in input_names] + + input_data = loader.load(input_paths) + + data = [] + for filename, data1d in zip(input_names, input_data): + + # Extract the metadata from the filename + filename_parts = filename.split(".") + filename = ".".join(filename_parts[:-1]) + + parts = filename.split("_") + + applied_field = float(parts[1]) # mT + saturation_magnetisation = float(parts[2]) # mT + demagnetising_field = float(parts[3]) # mT + + # Create input data object + data.append(ExperimentalData( + scattering_curve=data1d, + applied_field=applied_field, + saturation_magnetisation=saturation_magnetisation, + demagnetising_field=demagnetising_field)) + + return sorted(data, key=lambda x: x.applied_field) + + except Exception as e: + raise LoadFailure(f"Failed to load from {directory}: " + repr(e)) + + @staticmethod + def nice_log_plot_bounds(data: list[np.ndarray]): + """ Get nice bounds for the loglog plots + + :return: (lower, upper) bounds appropriate to pass to plt.xlim/ylim + """ + + upper = np.amax(np.array(data)) + lower = np.amin(np.array(data)) + + return ( + 10 ** (np.floor(np.log10(lower))) * np.floor(lower / 10 ** (np.floor(np.log10(lower)))), + 10 ** (np.floor(np.log10(upper))) * np.ceil(upper / 10 ** (np.floor(np.log10(upper)))) + ) + + + @staticmethod + def simple_fit(data: list[ExperimentalData], parameters: FitParameters): + """ Main fitting ("simple fit") """ + + geometry = parameters.experiment_geometry + + # Use an index for data upto qmax based on first data set + # Not ideal, would be preferable make sure the data was + # compatible, using something like interpolation TODO + square_distance_from_qmax = (data[0].scattering_curve.x - parameters.q_max) ** 2 + max_q_index = int(np.argmin(square_distance_from_qmax)) + + filtered_inputs = [datum.restrict_by_index(max_q_index) + for datum in data + if datum.applied_field >= parameters.min_applied_field] + + # Brute force check for something near the minimum + sweep_data = MuMagLib.sweep_exchange_A(parameters, filtered_inputs) + + # Refine this result + crude_A = sweep_data.optimal.exchange_A + refined = MuMagLib.refine_exchange_A(filtered_inputs, crude_A, geometry) + + # Get uncertainty estimate TODO: Check units + uncertainty = MuMagLib.uncertainty(filtered_inputs, refined.exchange_A, geometry) * 1e12 + + return FitResults( + parameters=parameters, + input_data=filtered_inputs, + sweep_data=sweep_data, + refined_fit_data=refined, + optimal_exchange_A_uncertainty=uncertainty) + + @staticmethod + def sweep_exchange_A(parameters: FitParameters, data: list[ExperimentalData]) -> SweepOutput: + """ Sweep over Exchange Stiffness A for perpendicular SANS geometry to + get an initial estimate which can then be refined""" + + a_values = np.linspace( + parameters.exchange_A_min, + parameters.exchange_A_max, + parameters.exchange_A_n) * 1e-12 # From pJ/m to J/m + + if parameters.experiment_geometry == ExperimentGeometry.PERPENDICULAR: + least_squared_fits = [MuMagLib.least_squares_perpendicular(data, a) for a in a_values] + + elif parameters.experiment_geometry == ExperimentGeometry.PARALLEL: + least_squared_fits = [MuMagLib.least_squares_parallel(data, a) for a in a_values] + + else: + raise ValueError(f"Unknown ExperimentGeometry value: {parameters.experiment_geometry}") + + optimal_fit = min(least_squared_fits, key=lambda x: x.exchange_A_chi_sq) + + chi_sq = np.array([fit.exchange_A_chi_sq for fit in least_squared_fits]) + + return SweepOutput( + exchange_A_checked=a_values, + exchange_A_chi_sq=chi_sq, + optimal=optimal_fit) + + @staticmethod + def least_squares_perpendicular(data: list[ExperimentalData], A) -> LeastSquaresOutputPerpendicular: + """ Least squares fitting for a given exchange stiffness, A, perpendicular case + + We are fitting the equation: + + I_sim = I_res + response_H * S_H + response_M * S_M + = (I_res, S_H, S_M) . (1, response_H, response_M) + = (I_res, S_H, S_M) . least_squares_x + + finding I_res, S_H, and S_M for each q value + + + """ + + # Get matrices from the input data + n_data = len(data) + + # Factor of (1e-3 / mu_0) converts from mT to A/m + applied_field = np.array([datum.applied_field for datum in data]) * (1e-3 / MuMagLib.mu_0) + demagnetising_field = np.array([datum.demagnetising_field for datum in data]) * (1e-3 / MuMagLib.mu_0) + saturation_magnetisation = np.array([datum.saturation_magnetisation for datum in data]) * (1e-3 / MuMagLib.mu_0) + + # TODO: The following is how things should be done in the future, rather than hard-coding + # a scaling factor... + # def data_nanometers(data: Data1D): + # raw_data = data.x + # units = data.x_unit + # converter = Converter(units) + # return converter.scale("1/m", raw_data) + # + # q = np.array([data_nanometers(datum.scattering_curve) for datum in data]) + + q = np.array([datum.scattering_curve.x for datum in data]) * 1e9 + I = np.array([datum.scattering_curve.y for datum in data]) + I_stdev = np.array([datum.scattering_curve.dy for datum in data]) + + n_q = q.shape[1] + + # Micromagnetic Model + internal_field = (applied_field - demagnetising_field).reshape(-1, 1) + magnetic_scattering_length = np.sqrt( + (2 * A) / (MuMagLib.mu_0 * saturation_magnetisation.reshape(-1, 1) * internal_field)) + effective_field = internal_field * (1 + (magnetic_scattering_length ** 2) * (q ** 2)) + + # Calculate the response functions + p = saturation_magnetisation.reshape(-1, 1) / effective_field + response_H = (p ** 2) / 4 * (2 + 1 / np.sqrt(1 + p)) + response_M = (np.sqrt(1 + p) - 1) / 2 + + # print("Input", q.shape, q[0,10]) + # sys.exit() + + # Lists for output of calculation + I_residual = [] + S_H = [] + S_M = [] + + I_residual_error_weight = [] + S_M_error_weight = [] + S_H_error_weight = [] + + for nu in range(n_q): + + # non-negative linear least squares + least_squares_x = (np.array([np.ones((n_data,)), response_H[:, nu], response_M[:, nu]]) / I_stdev[:, nu]).T + least_squares_y = I[:, nu] / I_stdev[:, nu] + + least_squares_x_squared = np.dot(least_squares_x.T, least_squares_x) + + # Non-negative least squares + try: + fit_result = scipy.optimize.nnls( + least_squares_x_squared, + np.matmul(least_squares_x.T, least_squares_y)) + + except ValueError as ve: + raise FitFailure(f"A = {A} ({repr(ve)})") + + I_residual.append(fit_result[0][0]) + S_H.append(fit_result[0][1]) + S_M.append(fit_result[0][2]) + + errors = np.linalg.inv(np.dot(least_squares_x_squared.T, least_squares_x_squared)) + + I_residual_error_weight.append(errors[0, 0]) + S_H_error_weight.append(errors[1, 1]) + S_M_error_weight.append(errors[2, 2]) + + # Arrayise + S_H = np.array(S_H) + S_M = np.array(S_M) + I_residual = np.array(I_residual) + + I_sim = I_residual + response_H * S_H + response_M * S_M + + s_q = np.mean(((I - I_sim) / I_stdev) ** 2, axis=0) + + sigma_I_res = np.sqrt(np.abs(np.array(I_residual_error_weight) * s_q)) + sigma_S_H = np.sqrt(np.abs(np.array(S_H_error_weight) * s_q)) + sigma_S_M = np.sqrt(np.abs(np.array(S_M_error_weight) * s_q)) + + chi_sq = float(np.mean(s_q)) + + output_q_values = np.mean(q, axis=0) + + return LeastSquaresOutputPerpendicular( + exchange_A=A, + exchange_A_chi_sq=chi_sq, + q=output_q_values, + I_residual=I_residual, + I_simulated=I_sim, + S_H=S_H, + S_M=S_M, + I_residual_stdev=sigma_I_res, + S_H_stdev=sigma_S_H, + S_M_stdev=sigma_S_M) + + + @staticmethod + def least_squares_parallel(data: list[ExperimentalData], A): + + """ Least squares fitting for a given exchange stiffness, A, parallel case + + We are fitting the equation: + + I_sim = I_res + response_H * S_H + = (I_res, S_H) . (1, response_H) + = (I_res, S_H) . least_squares_x + + finding I_res and S_H for each q value + + + """ + + # Get matrices from the input data + n_data = len(data) + + # Factor of (1e-3 / mu_0) converts from mT to A/m + applied_field = np.array([datum.applied_field for datum in data]) * (1e-3 / MuMagLib.mu_0) + demagnetising_field = np.array([datum.demagnetising_field for datum in data]) * (1e-3 / MuMagLib.mu_0) + saturation_magnetisation = np.array([datum.saturation_magnetisation for datum in data]) * (1e-3 / MuMagLib.mu_0) + + # TODO: The following is how things should be done in the future, rather than hard-coding + # a scaling factor... + # def data_nanometers(data: Data1D): + # raw_data = data.x + # units = data.x_unit + # converter = Converter(units) + # return converter.scale("1/m", raw_data) + # + # q = np.array([data_nanometers(datum.scattering_curve) for datum in data]) + + q = np.array([datum.scattering_curve.x for datum in data]) * 1e9 + I = np.array([datum.scattering_curve.y for datum in data]) + I_stdev = np.array([datum.scattering_curve.dy for datum in data]) + + n_q = q.shape[1] + + # Micromagnetic Model + internal_field = (applied_field - demagnetising_field).reshape(-1, 1) + magnetic_scattering_length = np.sqrt( + (2 * A) / (MuMagLib.mu_0 * saturation_magnetisation.reshape(-1, 1) * internal_field)) + effective_field = internal_field * (1 + (magnetic_scattering_length ** 2) * (q ** 2)) + + # Calculate the response functions + p = saturation_magnetisation.reshape(-1, 1) / effective_field + response_H = (p ** 2) / 2 + + # Lists for output of calculation + I_residual = [] + S_H = [] + + I_residual_error_weight = [] + S_H_error_weight = [] + + for nu in range(n_q): + + # non-negative linear least squares + least_squares_x = (np.array([np.ones((n_data,)), response_H[:, nu]]) / I_stdev[:, nu]).T + least_squares_y = I[:, nu] / I_stdev[:, nu] + + least_squares_x_squared = np.dot(least_squares_x.T, least_squares_x) + + # Non-negative least squares + try: + fit_result = scipy.optimize.nnls( + least_squares_x_squared, + np.matmul(least_squares_x.T, least_squares_y)) + + except ValueError as ve: + raise FitFailure(f"A = {A} ({repr(ve)})") + + I_residual.append(fit_result[0][0]) + S_H.append(fit_result[0][1]) + + errors = np.linalg.inv(np.dot(least_squares_x_squared.T, least_squares_x_squared)) + + I_residual_error_weight.append(errors[0, 0]) + S_H_error_weight.append(errors[1, 1]) + + # Arrayise + S_H = np.array(S_H) + I_residual = np.array(I_residual) + + I_sim = I_residual + response_H * S_H + + s_q = np.mean(((I - I_sim) / I_stdev) ** 2, axis=0) + + sigma_I_res = np.sqrt(np.abs(np.array(I_residual_error_weight) * s_q)) + sigma_S_H = np.sqrt(np.abs(np.array(S_H_error_weight) * s_q)) + + chi_sq = float(np.mean(s_q)) + + output_q_values = np.mean(q, axis=0) + + return LeastSquaresOutputParallel( + exchange_A=A, + exchange_A_chi_sq=chi_sq, + q=output_q_values, + I_residual=I_residual, + I_simulated=I_sim, + S_H=S_H, + I_residual_stdev=sigma_I_res, + S_H_stdev=sigma_S_H) + + @staticmethod + def refine_exchange_A( + data: list[ExperimentalData], + exchange_A_initial: float, + geometry: ExperimentGeometry, + epsilon: float = 0.0001) -> LeastSquaresOutputPerpendicular | LeastSquaresOutputParallel: + + """ Refines the A parameter using Jarratt's method of successive parabolic interpolation""" + + match geometry: + case ExperimentGeometry.PARALLEL: + least_squares_function = MuMagLib.least_squares_parallel + case ExperimentGeometry.PERPENDICULAR: + least_squares_function = MuMagLib.least_squares_perpendicular + case _: + raise ValueError(f"Unknown experimental geometry: {geometry}") + + delta = exchange_A_initial * 0.1 + + x_1 = exchange_A_initial - delta + x_2 = exchange_A_initial + x_3 = exchange_A_initial + delta + + # We want all the least squares fitting data around the final value, so keep that in a variable + refined_least_squared_data = least_squares_function(data, x_3) + + y_1 = least_squares_function(data, x_1).exchange_A_chi_sq + y_2 = least_squares_function(data, x_2).exchange_A_chi_sq + y_3 = refined_least_squared_data.exchange_A_chi_sq + + x_4 = x_3 + 0.5 * ((x_2 - x_3) ** 2 * (y_3 - y_1) + (x_1 - x_3) ** 2 * (y_2 - y_3)) \ + / ((x_2 - x_3) * (y_3 - y_1) + (x_1 - x_3) * (y_2 - y_3)) + + for i in range(200): + if np.abs(2 * (x_4 - x_3) / (x_4 + x_3)) < epsilon: + break + + refined_least_squared_data = least_squares_function(data, x_3) + + x_1, x_2, x_3 = x_2, x_3, x_4 + y_1, y_2, y_3 = y_2, y_3, refined_least_squared_data.exchange_A_chi_sq + + x_4 = x_3 + 0.5 * ((x_2 - x_3) ** 2 * (y_3 - y_1) + (x_1 - x_3) ** 2 * (y_2 - y_3)) \ + / ((x_2 - x_3) * (y_3 - y_1) + (x_1 - x_3) * (y_2 - y_3)) + + return refined_least_squared_data + + @staticmethod + def uncertainty( + data: list[ExperimentalData], + A_opt: float, + geometry: ExperimentGeometry) -> float: + """Calculate the uncertainty for the optimal exchange stiffness A""" + + # Estimate variance from second order derivative of chi-square function via Finite Differences + + match geometry: + case ExperimentGeometry.PARALLEL: + least_squares_function = MuMagLib.least_squares_parallel + case ExperimentGeometry.PERPENDICULAR: + least_squares_function = MuMagLib.least_squares_perpendicular + case _: + raise ValueError(f"Unknown experimental geometry: {geometry}") + + p = 0.001 # fractional gap size for finite differences + dA = A_opt * p + A1 = A_opt - 2 * dA + A2 = A_opt - 1 * dA + A3 = A_opt + A4 = A_opt + 1 * dA + A5 = A_opt + 2 * dA + + chi1 = least_squares_function(data, A1).exchange_A_chi_sq + chi2 = least_squares_function(data, A2).exchange_A_chi_sq + chi3 = least_squares_function(data, A3).exchange_A_chi_sq + chi4 = least_squares_function(data, A4).exchange_A_chi_sq + chi5 = least_squares_function(data, A5).exchange_A_chi_sq + + d2chi_dA2 = (-chi1 + 16 * chi2 - 30 * chi3 + 16 * chi4 - chi5) / (12 * dA ** 2) + + # Scale variance by number of samples and return reciprocal square root + + n_field_strengths = len(data) # Number of fields + n_q = len(data[0].scattering_curve.x) # Number of q points + + return np.sqrt(2 / (n_field_strengths * n_q * d2chi_dA2)) + + @staticmethod + def _filename_string(datum: ExperimentalData): + """ Get the filename string associated with a bit of experimental data """ + + return f"{datum.applied_field}_{datum.saturation_magnetisation}_{datum.demagnetising_field}" + + @staticmethod + def save_data(data: FitResults, directory: str): + """ Save the data """ + + now = datetime.now() + timestamp = now.strftime("%d-%m-%Y_%H-%M-%S") + output_folder = f"mumag_fit_{timestamp}" + path = os.path.join(directory, output_folder) + + if not os.path.exists(path): + os.mkdir(path) + + with open(os.path.join(path, "fit_info.txt"), "w") as fid: + fid.write(f"FitMagneticSANS Toolbox - SimpleFit Results Info File \n\n") + fid.write(f"Timestamp: {timestamp}\n") + fid.write(f"SANS geometry: {data.parameters.experiment_geometry.name}\n\n") + fid.write(f"Maximal Scattering Vector: q_max = {np.max(data.refined_fit_data.q)} /nm\n") + fid.write(f"Minimal Applied Field: mu_0*H_min = {data.input_data[0].applied_field}\n mT \n") + fid.write(f"Result for the exchange stiffness constant: " + f"A = {data.refined_fit_data.exchange_A} +- {data.optimal_exchange_A_uncertainty} pJ/m \n") + + # + # Save fitted data + # + + subpath = os.path.join(path, "intensity_fit") + + if not os.path.exists(subpath): + os.mkdir(subpath) + + for k, datum in enumerate(data.input_data): + + filename = f"{k}_" + MuMagLib._filename_string(datum) + ".csv" + + q = data.refined_fit_data.q + I = data.refined_fit_data.I_simulated[k, :] + + np.savetxt(os.path.join(subpath, filename), np.array([q, I]).T, delimiter=",") + + # + # Save original data (but truncated) + # + + subpath = os.path.join(path, "input_intensity") + + if not os.path.exists(subpath): + os.mkdir(subpath) + + for k, datum in enumerate(data.input_data): + filename = f"{k}_" + MuMagLib._filename_string(datum) + ".csv" + + q = datum.scattering_curve.x + I = datum.scattering_curve.y + dI = datum.scattering_curve.dy + + np.savetxt(os.path.join(subpath, filename), np.array([q, I, dI]).T, delimiter=",") + + # + # Optimised results + # + + np.savetxt(os.path.join(path, "chi.csv"), + np.array([ + data.sweep_data.exchange_A_checked, + data.sweep_data.exchange_A_chi_sq]).T, + delimiter=",") + + np.savetxt(os.path.join(path, "S_H.csv"), + np.array([ + data.refined_fit_data.q, + data.refined_fit_data.S_H, + data.refined_fit_data.S_H_stdev]).T, + delimiter=",") + + np.savetxt(os.path.join(path, "I_res.csv"), + np.array([ + data.refined_fit_data.q, + data.refined_fit_data.I_residual, + data.refined_fit_data.I_residual_stdev]).T, + delimiter=",") + + if data.parameters.experiment_geometry == ExperimentGeometry.PERPENDICULAR: + np.savetxt(os.path.join(path, "S_M.csv"), + np.array([ + data.refined_fit_data.q, + data.refined_fit_data.S_M, + data.refined_fit_data.S_M_stdev]).T, + delimiter=",") + + + + + diff --git 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0000000000..03d157c583 --- /dev/null +++ b/src/sas/qtgui/Utilities/MuMag/SANSData/NdFeB_parallel_Bick_et_al/5_16000_1600_1070.csv @@ -0,0 +1,53 @@ +0.02466 8403.24 95.8365 +0.02779 5866.26 69.5434 +0.03118 4356.78 53.6923 +0.03472 3299.25 42.8649 +0.03798 2597.38 38.2386 +0.04103 2129.79 33.557 +0.04439 1878.69 25.9888 +0.04789 1624.61 24.3861 +0.05145 1439.52 20.6737 +0.05487 1263.65 20.5759 +0.05809 1171.99 18.386 +0.06147 1079.56 16.577 +0.06487 1041.15 16.3129 +0.06823 1001.7 14.8847 +0.07159 961.645 14.563 +0.07491 923.442 13.6706 +0.07817 896.915 13.3973 +0.08149 883.652 12.6286 +0.08492 862.753 12.0581 +0.08832 824.722 11.795 +0.09171 784.35 11.1756 +0.09497 769.294 11.1579 +0.09818 755.349 10.8901 +0.10176 749.016 9.48228 +0.10537 742.393 10.4072 +0.10864 731.812 9.80011 +0.11191 725.902 9.97489 +0.11529 687.755 9.06119 +0.11874 695.826 9.13917 +0.12204 706.826 9.47552 +0.1253 686.062 8.69528 +0.12868 672.907 8.67583 +0.13213 693.14 8.48682 +0.13557 670.728 8.38538 +0.13878 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GroupBox + + + + + + Import Data + + + + + + + Fit + + + + + + + Save Result + + + + + + + + + + Parameters + + + + + + + Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter + + + 7 + + + + + Analysis Method: + + + + + + + + 0 + + + + + Perpendicular + + + + Perpendicular + + + + + Parallel + + + + + + + + Qt::Horizontal + + + + 40 + 20 + + + + + + + + + + + Maximum q: + + + + + + + + 0 + + + + + 5 + + + 0.000010000000000 + + + 0.010000000000000 + + + 0.600000000000000 + + + + + + + nm<sup>-1</sup> + + + + + + + + + + Applied Field (μ<sub>0</sub> H<sub>min</sub>): + + + + + + + + 0 + + + + + 5 + + + 10000.000000000000000 + + + 75.000000000000000 + + + + + + + mT + + + + + + + + + + Scan Range for A: + + + + + + + + 0 + + + 0 + + + + + 100000.000000000000000 + + + 5.000000000000000 + + + + + + + to + + + + + + + 100000.000000000000000 + + + 20.000000000000000 + + + + + + + pJ/m + + + + + + + Qt::Horizontal + + + + 40 + 20 + + + + + + + + + + + + 7 + + + 0 + + + 0 + + + 0 + + + + + 10000 + + + 200 + + + + + + + steps + + + + + + + Qt::Horizontal + + + + 40 + 20 + + + + + + + + + + + + + + + + + Results + + + + Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter + + + + + A value: + + + + + + + A uncertainty: + + + + + + + + + + + + + + + + + + + + + + + + Qt::Vertical + + + + 20 + 40 + + + + + + + + + + + Qt::Horizontal + + + + 40 + 20 + + + + + + + + Help + + + + + + + + + + + + + + + + 0 + + + + Data + + + + + Fit Results + + + + + Comparison + + + + + + + + + + 0 + 0 + 819 + 20 + + + + + + + + diff --git a/src/sas/qtgui/Utilities/MuMag/UI/__init__.py b/src/sas/qtgui/Utilities/MuMag/UI/__init__.py new file mode 100644 index 0000000000..e69de29bb2 diff --git a/src/sas/qtgui/Utilities/MuMag/__init__.py b/src/sas/qtgui/Utilities/MuMag/__init__.py new file mode 100644 index 0000000000..e69de29bb2 diff --git a/src/sas/qtgui/Utilities/MuMag/datastructures.py b/src/sas/qtgui/Utilities/MuMag/datastructures.py new file mode 100644 index 0000000000..0cf59de57b --- /dev/null +++ b/src/sas/qtgui/Utilities/MuMag/datastructures.py @@ -0,0 +1,124 @@ +from dataclasses import dataclass +from enum import Enum +from typing import Generic + +import numpy as np + +from sas.qtgui.Plotting.PlotterData import Data1D + +from typing import TypeVar + +""" Data structures used in MuMag""" + +# +# Errors +# + + +class LoadFailure(Exception): + """ File loading failed """ + pass + + +class FitFailure(Exception): + """ Fit failed """ + pass + +# +# Enums +# + + +class ExperimentGeometry(Enum): + """ Type of experiment """ + PARALLEL = 1 + PERPENDICULAR = 2 + +# +# Data classes +# + + +@dataclass +class ExperimentalData: + """ Datapoint used as input for the MuMag tool""" + + scattering_curve: Data1D + + applied_field: float + saturation_magnetisation: float + demagnetising_field: float + + def restrict_by_index(self, max_index: int): + """ Remove all points from data up to given index""" + + x = self.scattering_curve.x[:max_index] + y = self.scattering_curve.y[:max_index] + dy = self.scattering_curve.dy[:max_index] + + return ExperimentalData( + scattering_curve=Data1D(x=x, y=y, dy=dy), + applied_field=self.applied_field, + saturation_magnetisation=self.saturation_magnetisation, + demagnetising_field=self.demagnetising_field) + + +@dataclass +class FitParameters: + """ Input parameters for the fit""" + q_max: float + min_applied_field: float + exchange_A_min: float + exchange_A_max: float + exchange_A_n: int + experiment_geometry: ExperimentGeometry + + +@dataclass +class LeastSquaresOutput: + """ Output from least squares method""" + exchange_A: float + exchange_A_chi_sq: float + q: np.ndarray + I_simulated: np.ndarray + I_residual: np.ndarray + S_H: np.ndarray + I_residual_stdev: np.ndarray + S_H_stdev: np.ndarray + + +@dataclass +class LeastSquaresOutputParallel(LeastSquaresOutput): + """ Output from least squares method for parallel case""" + pass + + +@dataclass +class LeastSquaresOutputPerpendicular(LeastSquaresOutput): + """ Output from least squares method for perpendicular case""" + S_M: np.ndarray + S_M_stdev: np.ndarray + + +T = TypeVar("T", bound=LeastSquaresOutput) + + +@dataclass +class SweepOutput(Generic[T]): + """ + Results from brute force optimisiation of the chi squared for the exchange A parameter + """ + + exchange_A_checked: np.ndarray + exchange_A_chi_sq: np.ndarray + optimal: T + + +@dataclass +class FitResults: + """ Output the MuMag fit """ + parameters: FitParameters + input_data: list[ExperimentalData] + sweep_data: SweepOutput + refined_fit_data: LeastSquaresOutputParallel | LeastSquaresOutputPerpendicular + optimal_exchange_A_uncertainty: float diff --git a/src/sas/qtgui/Utilities/MuMag/media/mumag_help.rst b/src/sas/qtgui/Utilities/MuMag/media/mumag_help.rst new file mode 100644 index 0000000000..0ff884eb75 --- /dev/null +++ b/src/sas/qtgui/Utilities/MuMag/media/mumag_help.rst @@ -0,0 +1,95 @@ +.. mumag_help.rst + +MuMag Tool +========== + +Introduction +------------ + +MuMag is an analysis tool for calculating exchange stiffness constants, residual scattering, anisotropy field +and longitudinal magnetization based on unpolarized 1D SANS experiments with applied magnetic fields. The theory +behind this has been published `here `_. + +Given some scattering curve recorded at different applied field intensities, :math:`I(q, H)`, MuMag will break +down these curves into two (in the case of parallel magnetic fields) and three, components ( +for perpendicular fields relative to the beam). In the perpendicular case, the resulting linear +decomposition has the following form: + +:math:`I(q, H) = I_res(q) + S_H(q) R_H(q, H) + S_M(q) R_M(q, H)` + +Where :math:`R_H` and :math:`R_M` are known magnetic response functions (see the paper above), and :math:`I_res`, +:math:`S_H` and :math:`S_M` are non-field dependent terms: the residual scattering function, +the anisotropy field scattering function and the longitudinal magnetisation scattering function respectively. + +In the parallel case :math:`S_M` and :math:`R_M` are zero. + + +Loading data +------------ + +To load data click on the `Import Data` button. This will give you a file chooser that allows you to select a +**directory**. This directory should contain multiple files for measurements take with different applied magnetic fields. + +Currently, *the magnetic field and other information is expected to be in filename with a format as described below* + +Form of Data Files +.................. + +The experimental magnetic SANS data for a given analysis is expected to be stored as CSV files in a single folder. +Information about each SANS scattering curve must be given through the file names, like in the following example: + +Example filenames: + +- 1_0_1340_10.csv +- 2_20_1340_10.csv +- 3_35_1340_10.csv +- 4_50_1340_10.csv +- ... + +The fields separated by underscores have the following meaning + +1. Index of the files (e.g. 1, 2, 3, 4, ...) - (not used by SasView's MuMag, but is used by the MATLAB version) +2. Externally applied magnetic field :math:`μ_0 H_0` in mT (e.g. 0, 20, 25, 50, ...) +3. Saturation magnetization :math:`μ_0 M_s` in mT (e.g. 1340, 1340, 1340, 1340, ...) +4. Demagnetization field :math:`μ_0 H_d` in mT (e.g. 10, 10, 10, 10, 10, ...) + +(All these values could also be written as float number with dot separator e.g. 10.4345) + +The CSV files are expected have three columns: momentum transfer :math:`q` in nm :math:`^{-1}`, +scattering intensity :math:`I(q)`, and the standard error corresponding to `I(q)`. + +Each of the files must have the same length and got to be sorted from the lowest to the highest q-value. +In the files only the numerical data is stored, no headers. + +Running MuMag +------------- + +To run MuMag, load the data, set the parameters below, and click `Fit`. + +Parameters +.......... + +* **Analysis method** - This chooses one of two experiment types. Perpendicular is where the applied field is perpendicular to the beam (e.g. beam in x direction and field in z), and parallel where the applied field is parallel. +* **Maximum q** - MuMag has the ability to exclude q values beyond a given value, specified here +* **Applied field** - MuMag will use only data with applied field strengths above this value. MuMag requires the sample to be at (or close to) saturation, use this field to specify where this is. +* **Scan range** - When calculating the exchange stiffness constant A, MuMag's minimisation step has two components. (1) A brute for search, then (2) a refinement. These three values that describe the values for which the brute force search will take place (start, stop and step), as well as the values used for related plots. + +Results +....... + +* **A value** - The estimated exchange stiffness constant (A) +* **A uncertainty** - An estimate of the uncertainty associated with it + +Plots +..... + + +When you load data the `data` plot will be populated. When you click `fit` the rest will be. + +* **Data** - A plot of all the loaded data +* **Fit Results** + * :math:`\chi^2` - figure of merit used by MuMag to calculate the best A value, across different values of A (currently mean squared). This plot is useful to checking your problem is well conditioned. + * :math:`I_res` - The *residual intensity* - the part of the scattering that doesn't respond to applied field changes, inferred from the data (see above for details) + * :math:`S_H` - Anisotropy field scattering function + * :math:`S_M` - Scattering function of the longitudinal magnetization +* **Comparison** - Crosses show original data, lines show scattering curves reconstructed based on :math:`I_res`, :math:`S_H` and :math:`S_M` diff --git a/src/sas/qtgui/Utilities/MuMag/models.py b/src/sas/qtgui/Utilities/MuMag/models.py new file mode 100644 index 0000000000..2bd6579064 --- /dev/null +++ b/src/sas/qtgui/Utilities/MuMag/models.py @@ -0,0 +1,123 @@ +import numpy as np + +""" Models that are useful for verifying results of MuMag """ + +def LorentzianNoisyModelPERP(q, A, M_s, H_0, H_dem, a_H, a_M, l_c, beta): + """ Lorentzian Model for the generation of noisy synthetic test data for perpendicular SANS geometry """ + # All inputs in SI-units + + # Micromagnetic Model + mu_0 = 4 * np.pi * 1e-7 + H_i = H_0 - H_dem + l_H = np.sqrt((2*A)/(mu_0 * M_s * H_i)) + H_eff = H_i * (1 + l_H**2 * q**2) + p = M_s/H_eff + R_H = p**2 / 4 * (2 + 1/np.sqrt(1 + p)) + R_M = (np.sqrt(1 + p) - 1)/2 + + # Lorentzian functions for S_H, S_M + S_H = a_H**2/(1 + q**2 * l_c**2)**2 + S_M = a_M**2/(1 + q**2 * l_c**2)**2 + + # Magnetic SANS cross sections + I_M = R_H * S_H + R_M * S_M + + # Model of I_res + idx = np.argmax(H_0[:, 1]) + I_res = 0.9 * I_M[idx, :] + + # Model of standard deviation + sigma = beta * (I_res + I_M) + + # Total SANS cross section + I_sim = I_res + I_M + sigma * np.random.randn(len(sigma[:, 1]), len(sigma[1, :])) + + return I_sim, sigma, S_H, S_M, I_res + + +def LorentzianModelPAR(q, A, M_s, H_0, H_dem, a_H, l_c): + """ Lorentzian Model for the generation of clean synthetic test data for parallel SANS geometry""" + + # All inputs in SI-units + # Micromagnetic Model + mu_0 = 4 * np.pi * 1e-7 + H_i = H_0 - H_dem + l_H = np.sqrt((2 * A) / (mu_0 * M_s * H_i)) + H_eff = H_i * (1 + (l_H ** 2) * (q ** 2)) + p = M_s / H_eff + R_H = (p ** 2) / 2 + + # Lorentzian functions for S_H, S_M + S_H = a_H**2/(1 + q**2 * l_c**2)**2 + + # Magnetic SANS cross sections + I_M = R_H * S_H + + # Model of I_res + idx = np.argmax(H_0[:, 1]) + I_res = 0.9 * I_M[idx, :] + + # Total SANS cross section + I_sim = I_res + I_M + sigma = 0 * I_sim + 1 + + return I_sim, sigma, S_H, I_res + + +def LorentzianModelPERP(q, A, M_s, H_0, H_dem, a_H, a_M, l_c): + """ Lorentzian Model for the generation of clean synthetic test data for perpendicular SANS geometry""" + + # All inputs in SI-units + # Micromagnetic Model + mu_0 = 4 * np.pi * 1e-7 + H_i = H_0 - H_dem + l_H = np.sqrt((2*A)/(mu_0 * M_s * H_i)) + H_eff = H_i * (1 + l_H**2 * q**2) + p = M_s/H_eff + R_H = p**2 / 4 * (2 + 1/np.sqrt(1 + p)) + R_M = (np.sqrt(1 + p) - 1)/2 + + # Lorentzian functions for S_H, S_M + S_H = a_H**2/(1 + q**2 * l_c**2)**2 + S_M = a_M**2/(1 + q**2 * l_c**2)**2 + + # Magnetic SANS cross sections + I_M = R_H * S_H + R_M * S_M + + # Model of I_res + idx = np.argmax(H_0[:, 1]) + print(H_0[idx, 1]*mu_0*1e3) + I_res = 0.9 * I_M[idx, :] + + # Total SANS cross section + I_sim = I_res + I_M + sigma = 0 * I_sim + 1 + + return I_sim, sigma, S_H, S_M, I_res + +def SANS_Model_PERP(q, S_H, S_M, I_res, M_s, H_0, H_dem, A): + """ 1D-Cross-Section of the perendicular model """ + + # Micromagnetic Model + mu_0 = 4 * np.pi * 1e-7 + H_i = H_0 - H_dem + l_H = np.sqrt((2 * A) / (mu_0 * M_s * H_i)) + H_eff = H_i * (1 + (l_H ** 2) * (q ** 2)) + p = M_s / H_eff + R_H = (p ** 2) / 4 * (2 + 1 / np.sqrt(1 + p)) + R_M = (np.sqrt(1 + p) - 1) / 2 + + return I_res + R_H * S_H + R_M * S_M + +def SANS_Model_PAR(q, S_H, I_res, M_s, H_0, H_dem, A): + """ 1D-Cross-Section of the parallel model""" + + # Micromagnetic Model + mu_0 = 4 * np.pi * 1e-7 + H_i = H_0 - H_dem + l_H = np.sqrt((2 * A) / (mu_0 * M_s * H_i)) + H_eff = H_i * (1 + (l_H ** 2) * (q ** 2)) + p = M_s / H_eff + R_H = (p ** 2) / 2 + + return I_res + R_H * S_H \ No newline at end of file