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How to use d_exp method in fMBT

Best Python code snippet using fMBT_python

view_results.py

Source:view_results.py

1#! /usr/bin/python32#-*-coding: utf-8-*-3from init_fba import go, iplot, sleep, cl, pd, np, operator, ply4def create_scatter_plot_rxn_c3(D_fba, L_r, title, xaxis_title, save_fig = False):5    data = []6    for r_id in L_r:7        trace = go.Scatter(y = [D_fba[exp][r_id] for exp in sorted(D_fba.keys())],8                           x = sorted(D_fba.keys()),9                           name = r_id,10                           mode = 'lines+markers',11                          )12        data.append(trace)13    layout = go.Layout(title = title,14                       yaxis = dict(title = 'Flux [Âµmol/s/m2]'),15                       xaxis = dict(title = xaxis_title),16                       width = 500,17                      )18    fig = go.Figure(data=data, layout=layout)19    20    if save_fig:21        iplot(fig,filename=title,image='svg',image_width=500,image_height=500)22        sleep(5)23    else:24        iplot(fig)25        26def create_scatter_plot_met_c3(model, D_fba, L_r, m_id, title, xaxis_title, save_fig = False):27    data = []28    for r_id in L_r:29        r_obj = model.reactions.get_by_id(r_id)30        m_v = r_obj.get_coefficient(m_id)31        trace = go.Scatter(y = [abs(m_v)*D_fba[exp][r_id] for exp in sorted(D_fba.keys())],32                           x = sorted(D_fba.keys()),33                           name = r_id,34                           mode = 'lines+markers',35                          )36        data.append(trace)37    layout = go.Layout(title = title,38                       yaxis = dict(title = 'Flux [Âµmol/s/m2]'),39                       xaxis = dict(title = xaxis_title),40                       width = 500,41                      )42    fig = go.Figure(data=data, layout=layout)43    44    if save_fig:45        iplot(fig,filename=title,image='svg',image_width=500,image_height=500)46        sleep(5)47    else:48        iplot(fig)49        50def create_bar_plot_met_c3(model, D_fba, L_r, m_id, title, xaxis_title, save_fig = False):51    data = []52    for r_id in L_r:53        r_obj = model.reactions.get_by_id(r_id)54        m_v = r_obj.get_coefficient(m_id)55        trace = go.Bar(y = [abs(m_v)*D_fba[exp][r_id] for exp in sorted(D_fba.keys())],56                           x = sorted(D_fba.keys()),57                           name = r_id,58                          )59        data.append(trace)60    layout = go.Layout(title = title,61                       yaxis = dict(title = 'Flux [Âµmol/s/m2]'),62                       xaxis = dict(title = xaxis_title),63                       width = 500,64                        barmode='stack',65                      )66    fig = go.Figure(data=data, layout=layout)67    68    if save_fig:69        iplot(fig,filename=title,image='svg',image_width=500,image_height=500)70        sleep(5)71    else:72        iplot(fig)73        74def create_bar_plot_rxn(D_fba, D_exp, D_rxn, title, xaxis_title, stacked = False, y_max = None, c = False, save_fig = False, absolute = True):75    76    #Coloring of bars77    L_colM = cl.scales['5']['seq']['Oranges']78    L_colM = L_colM[::-1]79    L_colB = cl.scales['5']['seq']['Blues']80    L_colB = L_colB[::-1]81    82    83    if len(D_rxn) >= 5 or c:84        L_colM = cl.scales['11']['qual']['Paired']85        L_colB = cl.scales['11']['qual']['Paired']86        87    if isinstance(D_rxn, list):88        D_rxn = {r_id: r_id for r_id in D_rxn}89    90    D_rid_colM = {r_id2: L_colM[i] for i, r_id2 in enumerate([r_id1 for r_id1 in D_rxn if r_id1[1] == 'M'])}91    D_rid_colB = {r_id2: L_colB[i] for i, r_id2 in enumerate([r_id1 for r_id1 in D_rxn if r_id1[1] == 'B'])}92    D_rid_col = D_rid_colM.copy()93    D_rid_col.update(D_rid_colB)94    95    #Create bar plot96    data = []97    for r_id, r_name in sorted(D_rxn.items()):98        trace = go.Bar(name = r_name,99                       y = [abs(D_fba[x][r_id]) for x in sorted(D_fba.keys())] if absolute else [D_fba[x][r_id] for x in sorted(D_fba.keys())],100                       x = [D_exp[exp]  for exp in sorted(D_fba.keys())],101                       marker = {'color': D_rid_col[r_id] if D_rid_col else '#1f77b4'} 102                      )103        data.append(trace)104    layout = go.Layout(height = 400,105                       width = 600,106                       margin = dict(b  = 100),107                       barmode='stack' if stacked else 'group',108                       xaxis= {'title': xaxis_title, 'tickangle':45 if len(D_exp) >= 8 else 0},109                       title = title,110                       yaxis = { 'title': 'Flux [Âµmol/s/m2]','range': [0, y_max] if y_max else None,'autorange': False if  y_max else True}111                       )112    fig = go.Figure(data=data, layout=layout)113    114    if save_fig:115        iplot(fig,image='svg', filename=title,image_width=600, image_height=400)116        sleep(5)117    else:118        iplot(fig)119        120        121def create_bar_plot_met(D_fba, D_exp, D_rxn, m_id, title, xaxis_title, c3_model, stacked = False, y_max = None, c = False, save_fig = False):122    123    #Coloring of bars124    L_colM = cl.scales['5']['seq']['Oranges']125    L_colM = L_colM[::-1]126    L_colB = cl.scales['5']['seq']['Blues']127    L_colB = L_colB[::-1]128    129    130    if len(D_rxn) >= 5 or c:131        L_colM = cl.scales['11']['qual']['Paired']132        L_colB = cl.scales['11']['qual']['Paired']133        134    if isinstance(D_rxn, list):135        D_rxn = {r_id: r_id for r_id in D_rxn}136    137    D_rid_colM = {r_id2: L_colM[i] for i, r_id2 in enumerate([r_id1 for r_id1 in D_rxn if r_id1[1] == 'M'])}138    D_rid_colB = {r_id2: L_colB[i] for i, r_id2 in enumerate([r_id1 for r_id1 in D_rxn if r_id1[1] == 'B'])}139    D_rid_col = D_rid_colM.copy()140    D_rid_col.update(D_rid_colB)141    142    #Create bar plot143    data = []144    for r_id, r_name in sorted(D_rxn.items()):145        r_obj = c3_model.reactions.get_by_id(r_id[4:])146        m_v = r_obj.get_coefficient(m_id)147        trace = go.Bar(name = r_name,148                       y = [abs(m_v*D_fba[x][r_id]) for x in sorted(D_fba.keys())],149                       x = [D_exp[exp]  for exp in sorted(D_fba.keys())],150                       marker = {'color': D_rid_col[r_id] if D_rid_col else '#1f77b4'} 151                      )152        data.append(trace)153    layout = go.Layout(height = 400,154                       width = 600,155                       margin = dict(b  = 100),156                       barmode='stack' if stacked else 'group',157                       xaxis= {'title': xaxis_title, 'tickangle':45 if len(D_exp) >= 8 else 0},158                       title = title,159                       yaxis = {'title': 'Flux [Âµmol/s/m2]','range': [0, y_max] if y_max else None,'autorange': False if  y_max else True})160    fig = go.Figure(data=data, layout=layout)161    162    if save_fig:163        iplot(fig,image='svg', filename=title,image_width=500,image_height=500)164        sleep(5)165    else:166        iplot(fig)167        168def plot_transport_MB(D_fba, D_exp, L_r, xaxis_title, save_fig, cut_off):169    170    df = pd.DataFrame(index = [], columns= [D_exp[exp]  for exp in sorted(D_fba.keys())])171    172    yTickNames_MB = []173    174    D_rid_meanFlux_MB = {r_id:abs(np.mean([0]+[D_fba[x][r_id] for x in D_exp if D_fba[x][r_id] > 0])) for r_id in L_r if abs(np.mean([0]+[D_fba[x][r_id] for x in D_exp if D_fba[x][r_id] > 0])) > cut_off}175    D_rid_meanFlux_MB = sorted(D_rid_meanFlux_MB.items(), key=operator.itemgetter(1))176    177    for entry in D_rid_meanFlux_MB:178        r_id = entry[0]179        for x in D_exp:180            if D_fba[x][r_id] > 0:181                df.loc[r_id, D_exp[x]] = abs(D_fba[x][r_id]) if not abs(D_fba[x][r_id]) < cut_off else float('nan')182                # .loc[] to locate a specific value in a dataframe183                # always takes the index AND the column => 2 elements184                # if we want to assign this value, once we located it, we assign it185                186                if not r_id[5:-2] in yTickNames_MB:187                    yTickNames_MB.append(r_id[5:-2])188                        189    scl = cl.scales['9']['seq']['Reds']190    colorscale = [ [ float(i)/float(len(scl)-1), scl[i] ] for i in range(len(scl))]191    192    trace_MB = go.Heatmap(z=df.values.tolist(),193                          x=df.columns,194                          y=yTickNames_MB,195                          colorbar= {'title':'Flux [Âµmol/s/m2]', 'titleside':'right'},196                          colorscale = colorscale)197    198    layout_MB = go.Layout(width = 500,199                          margin = {'b':100},200                          yaxis = {'tickmode': 'array', 'tickvals': list(range(0,len(yTickNames_MB))), 'ticktext': yTickNames_MB, 'title': 'Transport Metabolites'},201                          xaxis= {'title':xaxis_title,'tickangle':45 if len(D_exp) >= 8 else 0},202                          title = 'Mesophyll ==> Bundlesheat Transport')203    data_MB=[trace_MB]204    205    fig_MB = go.Figure(data=data_MB, layout=layout_MB)206    if save_fig:207        iplot(fig_MB,image='svg', filename='transport_MB',image_width=500,image_height=500)208        sleep(5)209    else:210        iplot(fig_MB)211        212        213def plot_transport_BM(D_fba, D_exp, L_r, xaxis_title, save_fig, cut_off):214    215    df = pd.DataFrame(index = [], columns= [D_exp[exp]  for exp in sorted(D_fba.keys())])216    217    yTickNames_BM = []218        219    D_rid_meanFlux_BM = {r_id:abs(np.mean([0]+[D_fba[x][r_id] for x in D_exp if D_fba[x][r_id] < 0])) for r_id in L_r if abs(np.mean([0]+[D_fba[x][r_id] for x in D_exp if D_fba[x][r_id] < 0])) > cut_off}220    D_rid_meanFlux_BM = sorted(D_rid_meanFlux_BM.items(), key=operator.itemgetter(1))221    222    for entry in D_rid_meanFlux_BM:223        r_id = entry[0]224        for x in D_exp:225            if D_fba[x][r_id] < 0:226                df.loc[r_id, D_exp[x]] = abs(D_fba[x][r_id]) if not abs(D_fba[x][r_id]) < cut_off else float('nan')227                if not r_id[5:-2] in yTickNames_BM:228                    yTickNames_BM.append(r_id[5:-2])229    230    scl = cl.scales['9']['seq']['Blues']231    colorscale = [ [ float(i)/float(len(scl)-1), scl[i] ] for i in range(len(scl)) ]232    233    trace_BM = go.Heatmap(z=df.values.tolist(),234                          x=df.columns,235                          y=yTickNames_BM,236                          colorbar= {'title':'Flux [Âµmol/s/m2]', 'titleside':'right'},237                          colorscale = colorscale)238    239    layout_BM = go.Layout(width = 500,240                          margin = {'b':100},241                          yaxis = {'tickmode': 'array', 'tickvals': list(range(0,len(yTickNames_BM))), 'ticktext': yTickNames_BM, 'title': 'Transport Metabolites'},242                          xaxis= {'title':xaxis_title,'tickangle':45 if len(D_exp) >= 8 else 0},243                          title = 'Bundlesheat ==> Mesophyll Transport')244    data_BM=[trace_BM]245    246    fig_BM = go.Figure(data=data_BM, layout=layout_BM,)247    248    if save_fig:249        iplot(fig_BM,image='svg', filename='transport_BM',image_width=500,image_height=500)250        sleep(5)251    else:252        iplot(fig_BM)  253    254    255def plot_transport(D_fba, D_exp, L_r, xaxis_title, save_fig = False):256    257    cut_off = 0.1258    259    plot_transport_MB(D_fba, D_exp, L_r, xaxis_title, save_fig, cut_off)260    plot_transport_BM(D_fba, D_exp, L_r, xaxis_title, save_fig, cut_off)261        262def plot_transport_fva(c4_model, D_exp, D_pfva, D_pfba, L_r_org, flux_max, title, save_fig=False, L_r_index=None):263    264    L_colors = ply.colors.DEFAULT_PLOTLY_COLORS265    266    if len(D_exp) > len(L_colors):267        print('Too many experiments.')268    else:269        p_value = 0.1 #p value270        271        #prepare data for plotting272        D_r_flux_range = {}273        D_exp_r_FVA ={}274        data = []275        276        for exp in D_exp:277            D_exp_r_FVA[exp] = {}278            for r_id in L_r_org:279                D_FVA = {}280                r_obj = c4_model.reactions.get_by_id(r_id)281                D_FVA['max'] = D_pfva[exp].loc[r_id,'maximum']282                D_FVA['min'] = D_pfva[exp].loc[r_id,'minimum']283                D_FVA['flux'] = D_pfba[exp][r_id]284                285                #filter flux ranges of particular size (p_value % of maximum C transport rate)286                if abs(D_FVA['max']) > p_value * flux_max or abs(D_FVA['min']) > p_value * flux_max:287                     #determine maximum flux range over all exp for each reaction288                    if not r_id in D_r_flux_range: 289                        D_r_flux_range[r_id] = D_FVA['max'] - D_FVA['min']290                    else:291                        if D_r_flux_range[r_id] < (D_FVA['max'] - D_FVA['min']):292                            D_r_flux_range[r_id] = D_FVA['max'] - D_FVA['min']293                            294                D_exp_r_FVA[exp][r_id] = D_FVA295        296        #sort reactions by size of flux range297        L_r = [r_flux_range[0] for r_flux_range in sorted(D_r_flux_range.items(), key=operator.itemgetter(1), reverse= True)]298        299        create_plot = True300        301        if L_r_index:302            L_r_ex1 = list(set(L_r_index)-set(L_r))303            L_r_ex2 = list(set(L_r)-set(L_r_index))304            L_r_ex = L_r_ex1 + L_r_ex2305            if not L_r_ex:306                L_r = L_r_index307            else:308                print('Warning: L_r and L_r_index are not matching: %s' %L_r_ex)309                create_plot = False310                311        if create_plot:312                #set up x-values for each experiment313                L_x_axis = np.arange(1,len(L_r)*2+1,2)314                D_exp_x_axis = {exp: [] for exp in D_exp}315                for x in L_x_axis:316                    L_x_exp = np.linspace(x-0.3,x+0.3,len(D_exp))317                    for i_exp, exp in enumerate(D_exp.keys()):318                        D_exp_x_axis[exp].append(L_x_exp[i_exp]) 319                        #prepare trace for each experiment320                for i_exp, (exp,exp_name) in enumerate(D_exp.items()):321                    L_r_flux = [D_exp_r_FVA[exp][r_id]['flux'] for r_id in L_r]322                    L_r_min= [D_exp_r_FVA[exp][r_id]['flux'] - D_exp_r_FVA[exp][r_id]['min'] for r_id in L_r]323                    L_r_max = [D_exp_r_FVA[exp][r_id]['max'] - D_exp_r_FVA[exp][r_id]['flux'] for r_id in L_r]324                    325                    trace = go.Scatter(326                        x = D_exp_x_axis[exp],327                        y = L_r_flux,328                        error_y={'type':'data', 'symmetric':False, 'array':L_r_max, 'arrayminus':L_r_min},329                        marker = {'color' : L_colors[i_exp]},330                        name = exp_name,331                        mode = 'markers'332                    )333            334                    data.append(trace)335                #prepare layout336                layout = go.Layout(337                    xaxis = {'tickvals':L_x_axis, 'ticktext':[r_id[5:-2] for r_id in L_r], 'title':'Exchange Metabolites'},338                    #margin = {'b': 300},339                    title = title,340                    yaxis = {'title':'Flux [Âµmol/s/m2]'},341                    legend = {'orientation':'h', 'x':0, 'y':-0.15},342                    shapes = [343                            {344                                'type': 'rect',345                                'x0': -0.1,346                                'y0': -0.5,347                                'x1': -1.5,348                                'y1': -50,349                                'line': {350                                    'color': 'rgba(255, 255, 255, 1)',351                                    'width': 1,352                                },353                                'fillcolor': 'rgba(255, 255, 255, 1)',354                            },355                            {356                                'type': 'rect',357                                'x0': -0.1,358                                'y0': 0.5,359                                'x1': -1.5,360                                'y1': 50,361                                'line': {362                                    'color': 'rgba(255, 255, 255, 1)',363                                    'width': 1,364                                },365                                'fillcolor': 'rgba(255, 255, 255, 1)',366                            },367                    ],368                    annotations=[369                        dict(370                            x=-0.5,371                            y=25,372                            xref='x',373                            yref='y',374                            text='Mesophyll -> Bundle Sheath',375                            textangle= -90,376                            showarrow=False,377                            font=dict(378                                size=10,379                                color='#000000'380                            ),381                            align='center',382                        ),383                        dict(384                        x=-0.5,385                        y=-25,386                        xref='x',387                        yref='y',388                        text='Bundle Sheath -> Mesophyll',389                        textangle= -90,390                        showarrow=False,391                        font=dict(392                            size=10,393                            color='#000000'394                        ),395                        align='center',396        397                    )398                ]399                )400                401                #create figure402                fig = go.Figure(data=data, layout=layout)403                if save_fig:404                    iplot(fig,image='svg', filename='FVA')405                    sleep(5)406                else:407                    iplot(fig) 408    409def get_fluxes_by_metabolite(D_exp, D_fba, model, m_id, cell):410    if cell in ['M','B']:411        df = pd.DataFrame(columns=['rxn']+[D_exp[exp] for exp in D_exp])412        m_obj = model.metabolites.get_by_id('['+cell+']_'+m_id)413        for r_obj in m_obj.reactions:414            if not r_obj.id in df.index:415                df.loc[r_obj.id] = [r_obj.reaction] + [round(D_fba[exp][r_obj.id],3) for exp in D_exp]416        return df417    else:418        return 'Choose either M or B as cell type'...

init_nuisance.py

Source:init_nuisance.py

1#!/usr/bin/env python32from scipy.optimize import minimize3import numpy as np4from scipy.optimize import fmin_slsqp5from scipy.optimize import fsolve6# from scipy.optimize import minimize7from scipy.optimize import leastsq8from instagraal.leastsqbound import *9d0 = 1.0  # distance bias Hi-C10d_exp = -10.011import matplotlib.pyplot as plt12def log_residuals_4_min(param, y, x):13    d_init, alpha_0, alpha_1, A = param14    hic_c = np.zeros(x.shape)15    log_val_lim_0 = (16        np.log(A)17        + (alpha_0 - alpha_1) * np.log(d_init)18        + ((d_exp - 2) / (np.power(d_init, 2) + d_exp))19    )20    for i in range(0, len(hic_c)):21        if x[i] < d_init and x[i] > 0:22            hic_c[i] = (23                np.log(A)24                + np.log(x[i]) * alpha_025                + ((d_exp - 2) / (np.power(x[i], 2) + d_exp))26            )27        else:28            hic_c[i] = log_val_lim_0 + np.log(x[i]) * alpha_129    err = np.sqrt(np.power(y - hic_c, 2).sum())30    return err31def log_residuals(param, y, x):32    alpha_0, alpha_1, A = param33    hic_c = np.zeros(x.shape)34    log_val_lim_0 = (35        np.log(A)36        + (alpha_0 - alpha_1) * np.log(d0)37        + ((d_exp - 2) / (np.power(d0, 2) + d_exp))38    )39    for i in range(0, len(hic_c)):40        if x[i] <= 0:41            hic_c[i] = 042        elif x[i] < d0 and x[i] > 0:43            hic_c[i] = (44                np.log(A)45                + np.log(x[i]) * alpha_046                + ((d_exp - 2) / (np.power(x[i], 2) + d_exp))47            )48        else:49            hic_c[i] = log_val_lim_0 + np.log(x[i]) * alpha_150    err = y - hic_c51    return err52def residuals(param, y, x):53    alpha_0, alpha_1, A = param54    hic_c = np.zeros(x.shape)55    val_lim_0 = A * np.power(d0, alpha_0 - alpha_1)56    for i in range(0, len(hic_c)):57        if x[i] < d0:58            hic_c[i] = A * np.power(x[i], alpha_0)59        else:60            hic_c[i] = val_lim_0 * np.power(x[i], alpha_1)61    err = y - hic_c62    return err63def peval(x, param):64    d_init, alpha_0, alpha_1, A = param65    hic_c = np.zeros(x.shape)66    val_lim_0 = (67        A68        * np.power(d_init, alpha_0 - alpha_1)69        * np.exp((d_exp - 2) / (np.power(d_init, 2) + d_exp))70    )71    for i in range(0, len(hic_c)):72        if x[i] < d_init:73            hic_c[i] = (74                A75                * np.power(x[i], alpha_0)76                * np.exp((d_exp - 2) / (np.power(x[i], 2) + d_exp))77            )78        else:79            hic_c[i] = val_lim_0 * np.power(x[i], alpha_1)80    return hic_c81def estimate_param_hic(y_meas, x_bins):82    alpha_0 = -1083    alpha_1 = -1.584    x0 = x_bins.min()85    print("x0 = ", x0)86    A = (87        y_meas.max()88        * (x0 ** (-alpha_0))89        / np.exp((d_exp - 2) / (x0 ** 2 + d_exp))90    )91    print("A = ", A)92    p0 = [alpha_0, alpha_1, A]93    args = (np.log(y_meas), x_bins)94    plsq = leastsq(log_residuals, p0, args=args)95    plsq[0]96    print(plsq)97    bnds = ((0, 3), (-10, -0.2), (-2, -0.2), (0, None))98    alpha_0, alpha_1, A = plsq[0]99    p0 = [d0, alpha_0, alpha_1, A]100    # cns = ({'type': 'ineq', 'fun': lambda x:  x[0] - x[1]})101    # alpha_0 > alpha_1102    cns = {"type": "ineq", "fun": lambda x: x[1] - x[0]}103    res = minimize(104        log_residuals_4_min,105        p0,106        args=args,107        method="L-BFGS-B",108        bounds=bnds,109        constraints=cns,110        options={"disp": True},111    )112    print("res = ", res)113    y_estim_sls = peval(x_bins, res.x)114    plt.loglog(x_bins, y_estim_sls)115    plt.loglog(x_bins, y_meas)116    plt.show()117    return res, y_estim_sls118def residual_4_max_dist(x, p):119    d_init, alpha_0, alpha_1, A, y = p120    hic_c = np.zeros(x.shape)121    val_lim_0 = (122        A123        * np.power(d_init, alpha_0 - alpha_1)124        * np.exp((d_exp - 2) / (np.power(d_init, 2) + d_exp))125    )126    for i in range(0, len(hic_c)):127        if x[i] < d_init:128            hic_c[i] = (129                A130                * np.power(x[i], alpha_0)131                * np.exp((d_exp - 2) / (np.power(x[i], 2) + d_exp))132            )133        else:134            hic_c[i] = val_lim_0 * np.power(x[i], alpha_1)135    err = y - hic_c136    return err137def estimate_max_dist_intra(p, val_inter):138    print("val_inter = ", val_inter)139    d_init, alpha_0, alpha_1, A = p140    p0 = [d_init, alpha_0, alpha_1, A, val_inter]141    s0 = 500142    x = fsolve(residual_4_max_dist, s0, args=(p0))143    print("limit inter/intra distance = ", x)144    print("val model @ dist inter = ", peval(x, p))...

softmax.py

Source:softmax.py

1import numpy as np2from random import shuffle3def softmax_loss_naive(W, X, y, reg):4  """5  Softmax loss function, naive implementation (with loops)6  Inputs have dimension D, there are C classes, and we operate on minibatches7  of N examples.8  Inputs:9  - W: A numpy array of shape (D, C) containing weights.10  - X: A numpy array of shape (N, D) containing a minibatch of data.11  - y: A numpy array of shape (N,) containing training labels; y[i] = c means12    that X[i] has label c, where 0 <= c < C.13  - reg: (float) regularization strength14  Returns a tuple of:15  - loss as single float16  - gradient with respect to weights W; an array of same shape as W17  """18  # Initialize the loss and gradient to zero.19  loss = 0.020  dW = np.zeros_like(W)21  num_train = X.shape[0]22  #############################################################################23  # TODO: Compute the softmax loss and its gradient using explicit loops.     #24  # Store the loss in loss and the gradient in dW. If you are not careful     #25  # here, it is easy to run into numeric instability. Don't forget the        #26  # regularization!                                                           #27  #############################################################################28  # Loss29  d = X.dot(W) # NumInstances x Classes30  d -= np.max(d, axis=1).reshape(-1, 1) # For numeric stability31  d_exp = np.exp(d) # Raise all of them to Exp32  d_exp_sums = np.sum(d_exp, axis=1).reshape(-1, 1) # Calculate the denominators33  d_exp_reg = d_exp / d_exp_sums # Normalize34  Li = -np.log(d_exp_reg[np.arange(len(d_exp_reg)), y])35  loss = np.sum(Li) / num_train # Data loss36  loss += 0.5 * reg * np.sum(W * W) # Add the regularization loss37    38  # Gradient39  # https://eli.thegreenplace.net/2016/the-softmax-function-and-its-derivative/40  # for derivation41  probs = d_exp_reg42  probs[np.arange(num_train),y] -= 143  dW = X.T.dot(probs)44  dW /= num_train45  dW += reg * W46  #############################################################################47  #                          END OF YOUR CODE                                 #48  #############################################################################49  return loss, dW50def softmax_loss_vectorized(W, X, y, reg):51  """52  Softmax loss function, vectorized version.53  Inputs and outputs are the same as softmax_loss_naive.54  """55  # Initialize the loss and gradient to zero.56  loss = 0.057  dW = np.zeros_like(W)58  num_train = X.shape[0]59  #############################################################################60  # TODO: Compute the softmax loss and its gradient using no explicit loops.  #61  # Store the loss in loss and the gradient in dW. If you are not careful     #62  # here, it is easy to run into numeric instability. Don't forget the        #63  # regularization!                                                           #64  #############################################################################65  # Loss66  d = X.dot(W) # NumInstances x Classes67  d -= np.max(d, axis=1).reshape(-1, 1) # For numeric stability68  d_exp = np.exp(d) # Raise all of them to Exp69  d_exp_sums = np.sum(d_exp, axis=1).reshape(-1, 1) # Calculate the denominators70  d_exp_reg = d_exp / d_exp_sums # Normalize71  Li = -np.log(d_exp_reg[np.arange(len(d_exp_reg)), y])72  loss = np.sum(Li) / num_train # Data loss73  loss += 0.5 * reg * np.sum(W * W) # Add the regularization loss74    75  # Gradient76  probs = d_exp_reg77  probs[np.arange(num_train),y] -= 178  dW = X.T.dot(probs)79  dW /= num_train80  dW += reg * W81  #############################################################################82  #                          END OF YOUR CODE                                 #83  #############################################################################...

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