In [1]:

    

#Purpose: import from other notebook...
#Ref: http://jupyter-notebook.readthedocs.io/en/latest/examples/Notebook/Importing%20Notebooks.html
import io, os, sys, types
from IPython import get_ipython
from nbformat import read
from IPython.core.interactiveshell import InteractiveShell
#--------------------------------------------------------------------------------
def find_notebook(fullname, path=None):
    """find a notebook, given its fully qualified name and an optional path
    
    This turns "foo.bar" into "foo/bar.ipynb"
    and tries turning "Foo_Bar" into "Foo Bar" if Foo_Bar
    does not exist.
    """
    name = fullname.rsplit('.', 1)[-1]
    if not path:
        path = ['']
    for d in path:
        nb_path = os.path.join(d, name + ".ipynb")
        if os.path.isfile(nb_path):
            return nb_path
        # let import Notebook_Name find "Notebook Name.ipynb"
        nb_path = nb_path.replace("_", " ")
        if os.path.isfile(nb_path):
            return nb_path
#--------------------------------------------------------------------------------
class NotebookLoader(object):
    """Module Loader for Jupyter Notebooks"""
    def __init__(self, path=None):
        self.shell = InteractiveShell.instance()
        self.path = path
    
    def load_module(self, fullname):
        """import a notebook as a module"""
        path = find_notebook(fullname, self.path)
        
        print ("importing Jupyter notebook from %s" % path)
                                       
        # load the notebook object
        with io.open(path, 'r', encoding='utf-8') as f:
            nb = read(f, 4)
        
        
        # create the module and add it to sys.modules
        # if name in sys.modules:
        #    return sys.modules[name]
        mod = types.ModuleType(fullname)
        mod.__file__ = path
        mod.__loader__ = self
        mod.__dict__['get_ipython'] = get_ipython
        sys.modules[fullname] = mod
        
        # extra work to ensure that magics that would affect the user_ns
        # actually affect the notebook module's ns
        save_user_ns = self.shell.user_ns
        self.shell.user_ns = mod.__dict__
        
        try:
          for cell in nb.cells:
            if cell.cell_type == 'code':
                # transform the input to executable Python
                code = self.shell.input_transformer_manager.transform_cell(cell.source)
                # run the code in themodule
                exec(code, mod.__dict__)
        finally:
            self.shell.user_ns = save_user_ns
        return mod
#--------------------------------------------------------------------------------
class NotebookFinder(object):
    """Module finder that locates Jupyter Notebooks"""
    def __init__(self):
        self.loaders = {}
    
    def find_module(self, fullname, path=None):
        nb_path = find_notebook(fullname, path)
        if not nb_path:
            return
        
        key = path
        if path:
            # lists aren't hashable
            key = os.path.sep.join(path)
        
        if key not in self.loaders:
            self.loaders[key] = NotebookLoader(path)
        return self.loaders[key]
#--------------------------------------------------------------------------------
sys.meta_path.append(NotebookFinder())


    

In [2]:

    

ls


    

    




gradient_descent.ipynb          LICENSE               statistics.ipynb
hypothesis_and_inference.ipynb  linear_algebra.ipynb  visualizing_data.ipynb
Importing Notebooks.ipynb       probability.ipynb
__init__.py                     README.md

In [3]:

    

from collections import Counter
from linear_algebra import distance, vector_subtract, scalar_multiply
import math, random
#--------------------------------------------------------------------------------
def sum_of_squares(v):
    """computes the sum of squared elements in v"""
    return sum(v_i ** 2 for v_i in v)
#--------------------------------------------------------------------------------
def difference_quotient(f, x, h):
    return (f(x + h) - f(x)) / h
#--------------------------------------------------------------------------------
def plot_estimated_derivative():

    def square(x):
        return x * x

    def derivative(x):
        return 2 * x

    derivative_estimate = lambda x: difference_quotient(square, x, h=0.00001)

    # plot to show they're basically the same
    import matplotlib.pyplot as plt
    x = range(-10,10)
    plt.plot(x, map(derivative, x), 'rx')           # red  x
    plt.plot(x, map(derivative_estimate, x), 'b+')  # blue +
    plt.show()                                      # purple *, hopefully
#--------------------------------------------------------------------------------
def partial_difference_quotient(f, v, i, h):

    # add h to just the i-th element of v
    w = [v_j + (h if j == i else 0)
         for j, v_j in enumerate(v)]
         
    return (f(w) - f(v)) / h
#--------------------------------------------------------------------------------
def estimate_gradient(f, v, h=0.00001):
    return [partial_difference_quotient(f, v, i, h)
            for i, _ in enumerate(v)] 
#--------------------------------------------------------------------------------
def step(v, direction, step_size):
    """move step_size in the direction from v"""
    return [v_i + step_size * direction_i
            for v_i, direction_i in zip(v, direction)]
#--------------------------------------------------------------------------------
def sum_of_squares_gradient(v): 
    return [2 * v_i for v_i in v]
#--------------------------------------------------------------------------------
def safe(f):
    """define a new function that wraps f and return it"""
    def safe_f(*args, **kwargs):
        try:
            return f(*args, **kwargs)
        except:
            return float('inf')         # this means "infinity" in Python
    return safe_f
#--------------------------------------------------------------------------------

#
# 
# minimize / maximize batch
#
#

def minimize_batch(target_fn, gradient_fn, theta_0, tolerance=0.000001):
    """use gradient descent to find theta that minimizes target function"""
    
    step_sizes = [100, 10, 1, 0.1, 0.01, 0.001, 0.0001, 0.00001]
    
    theta = theta_0                           # set theta to initial value
    target_fn = safe(target_fn)               # safe version of target_fn
    value = target_fn(theta)                  # value we're minimizing
    
    while True:
        gradient = gradient_fn(theta)  
        next_thetas = [step(theta, gradient, -step_size)
                       for step_size in step_sizes]
                   
        # choose the one that minimizes the error function        
        next_theta = min(next_thetas, key=target_fn)
        next_value = target_fn(next_theta)
        
        # stop if we're "converging"
        if abs(value - next_value) < tolerance:
            return theta
        else:
            theta, value = next_theta, next_value
#--------------------------------------------------------------------------------
def negate(f):
    """return a function that for any input x returns -f(x)"""
    return lambda *args, **kwargs: -f(*args, **kwargs)
#--------------------------------------------------------------------------------    
def negate_all(f):
    """the same when f returns a list of numbers"""
    return lambda *args, **kwargs: [-y for y in f(*args, **kwargs)]
#--------------------------------------------------------------------------------
def maximize_batch(target_fn, gradient_fn, theta_0, tolerance=0.000001):
    return minimize_batch(negate(target_fn),
                          negate_all(gradient_fn),
                          theta_0, 
                          tolerance)
#--------------------------------------------------------------------------------
#
# minimize / maximize stochastic
#

def in_random_order(data):
    """generator that returns the elements of data in random order"""
    indexes = [i for i, _ in enumerate(data)]  # create a list of indexes
    random.shuffle(indexes)                    # shuffle them
    for i in indexes:                          # return the data in that order
        yield data[i]
#--------------------------------------------------------------------------------
def minimize_stochastic(target_fn, gradient_fn, x, y, theta_0, alpha_0=0.01):

    data = zip(x, y)
    theta = theta_0                             # initial guess
    alpha = alpha_0                             # initial step size
    min_theta, min_value = None, float("inf")   # the minimum so far
    iterations_with_no_improvement = 0
    
    # if we ever go 100 iterations with no improvement, stop
    while iterations_with_no_improvement < 100:
        value = sum( target_fn(x_i, y_i, theta) for x_i, y_i in data )

        if value < min_value:
            # if we've found a new minimum, remember it
            # and go back to the original step size
            min_theta, min_value = theta, value
            iterations_with_no_improvement = 0
            alpha = alpha_0
        else:
            # otherwise we're not improving, so try shrinking the step size
            iterations_with_no_improvement += 1
            alpha *= 0.9

        # and take a gradient step for each of the data points        
        for x_i, y_i in in_random_order(data):
            gradient_i = gradient_fn(x_i, y_i, theta)
            theta = vector_subtract(theta, scalar_multiply(alpha, gradient_i))
            
    return min_theta
#--------------------------------------------------------------------------------
def maximize_stochastic(target_fn, gradient_fn, x, y, theta_0, alpha_0=0.01):
    return minimize_stochastic(negate(target_fn), negate_all(gradient_fn), x, y, theta_0, alpha_0)


    

    




importing Jupyter notebook from linear_algebra.ipynb






    

In [4]:

    

if __name__ == "__main__":

    print("using the gradient")

    v = [random.randint(-10,10) for i in range(3)]

    tolerance = 0.0000001

    while True:
        print(v, sum_of_squares(v))
        gradient = sum_of_squares_gradient(v)   # compute the gradient at v
        next_v = step(v, gradient, -0.01)       # take a negative gradient step
        if distance(next_v, v) < tolerance:     # stop if we're converging
            break
        v = next_v                              # continue if we're not

    print("minimum v", v)
    print("minimum value", sum_of_squares(v))
    print()


    print("using minimize_batch")

    v = [random.randint(-10,10) for i in range(3)]

    v = minimize_batch(sum_of_squares, sum_of_squares_gradient, v)

    print("minimum v", v)
    print("minimum value", sum_of_squares(v))


    

    




using the gradient
[-7, -2, 9] 134
[-6.86, -1.96, 8.82] 128.6936
[-6.7228, -1.9208, 8.643600000000001] 123.59733344000001
[-6.588344, -1.882384, 8.470728000000001] 118.70287903577602
[-6.45657712, -1.84473632, 8.301313440000001] 114.0022450259593
[-6.327445577600001, -1.8078415936, 8.135287171200002] 109.48775612293132
[-6.200896666048001, -1.771684761728, 7.972581427776001] 105.15204098046323
[-6.076878732727041, -1.73625106649344, 7.813129799220481] 100.98802015763688
[-5.9553411580725, -1.7015260451635712, 7.656867203236072] 96.98889455939447
[-5.83623433491105, -1.6674955242602998, 7.50372985917135] 93.14813433484244
[-5.71950964821283, -1.6341456137750938, 7.353655261987923] 89.45946821518268
[-5.605119455248573, -1.601462701499592, 7.206582156748165] 85.91687327386146
[-5.493017066143602, -1.5694334474696001, 7.062450513613202] 82.51456509221656
[-5.383156724820729, -1.538044778520208, 6.921201503340938] 79.24698831456477
[-5.275493590324315, -1.5072838829498039, 6.782777473274119] 76.108807577308
[-5.169983718517829, -1.4771382052908077, 6.647121923808636] 73.0948987972466
[-5.066584044147472, -1.4475954411849916, 6.5141794853324635] 70.20034080487564
[-4.965252363264523, -1.4186435323612918, 6.383895895625814] 67.42040730900257
[-4.865947315999232, -1.3902706617140659, 6.256217977713298] 64.75055917956607
[-4.768628369679248, -1.3624652484797846, 6.131093618159032] 62.18643703605525
[-4.673255802285663, -1.335215943510189, 6.008471745795852] 59.72385412942747
[-4.579790686239949, -1.308511624639985, 5.888302310879935] 57.35878950590214
[-4.48819487251515, -1.2823413921471853, 5.7705362646623355] 55.08738144146841
[-4.398430975064847, -1.2566945643042415, 5.655125539369089] 52.905921136386254
[-4.31046235556355, -1.2315606730181567, 5.542023028581707] 50.81084665938536
[-4.224253108452279, -1.2069294595577935, 5.431182568010073] 48.798737131673704
[-4.139768046283233, -1.1827908703666377, 5.3225589166498715] 46.86630714125942
[-4.056972685357569, -1.159135052959305, 5.216107738316874] 45.01040137846555
[-3.9758332316504177, -1.135952351900119, 5.111785583550537] 43.22798948387832
[-3.896316567017409, -1.1132333048621166, 5.009549871879527] 41.51616110031674
[-3.818390235677061, -1.0909686387648743, 4.909358874441936] 39.8721211207442
[-3.7420224309635195, -1.0691492659895767, 4.811171696953097] 38.29318512436272
[-3.6671819823442493, -1.0477662806697852, 4.714948263014035] 36.77677499343796
[-3.593838342697364, -1.0268109550563895, 4.620649297753754] 35.320414703697814
[-3.5219615758434166, -1.0062747359552617, 4.528236311798679] 33.921726281431376
[-3.4515223443265484, -0.9861492412361565, 4.437671585562706] 32.5784259206867
[-3.3824918974400173, -0.9664262564114334, 4.348918153851452] 31.288320254227507
[-3.314842059491217, -0.9470977312832047, 4.261939790774423] 30.049302772160097
[-3.2485452183013925, -0.9281557766575407, 4.176700994958934] 28.85935038238256
[-3.1835743139353645, -0.9095926611243899, 4.093166975059756] 27.716520107240207
[-3.119902827656657, -0.891400807901902, 4.01130363555856] 26.618945910993492
[-3.057504771103524, -0.8735727917438639, 3.9310775628473893] 25.56483565291815
[-2.9963546756814536, -0.8561013359089866, 3.8524560115904416] 24.552468161062592
[-2.9364275821678247, -0.8389793091908069, 3.775406891358633] 23.580190421884517
[-2.877699030524468, -0.8221997230069907, 3.6998987535314605] 22.64641488117789
[-2.820145049913979, -0.805755728546851, 3.6259007784608315] 21.749616851883246
[-2.7637421489156995, -0.7896406139759139, 3.553382762891615] 20.888332024548674
[-2.7084673059373854, -0.7738478016963957, 3.4823151076337826] 20.061154076376546
[-2.6542979598186376, -0.7583708456624677, 3.4126688054811067] 19.26673237495203
[-2.6012120006222648, -0.7432034287492184, 3.3444154293714847] 18.503769772903933
[-2.5491877606098194, -0.7283393601742341, 3.277527120784055] 17.771020489896934
[-2.498204005397623, -0.7137725729707494, 3.2119765783683736] 17.067288078497015
[-2.4482399252896707, -0.6994971215113344, 3.147737046801006] 16.39142347058853
[-2.3992751267838774, -0.6855071790811077, 3.084782305864986] 15.742323101153229
[-2.3512896242481998, -0.6717970354994856, 3.023086659747686] 15.11892710634756
[-2.304263831763236, -0.6583610947894959, 2.9626249265527322] 14.520217592936195
[-2.258178555127971, -0.645193872893706, 2.9033724280216777] 13.945216976255923
[-2.2130149840254116, -0.6322899954358319, 2.845304979461244] 13.392986383996188
[-2.1687546843449033, -0.6196441955271152, 2.788398879872019] 12.862624123189939
[-2.1253795906580053, -0.607251311616573, 2.732630902274579] 12.353264207911618
[-2.082871998844845, -0.5951062853842415, 2.6779782842290873] 11.864074945278318
[-2.041214558867948, -0.5832041596765567, 2.6244187185445056] 11.394257577445295
[-2.000390267690589, -0.5715400764830255, 2.5719303441736154] 10.943044977378461
[-1.9603824623367774, -0.560109274953365, 2.520491737290143] 10.509700396274273
[-1.921174813090042, -0.5489070894542978, 2.47008190254434] 10.093516260581813
[-1.882751316828241, -0.5379289476652118, 2.4206802644934533] 9.693813016662773
[-1.8450962904916761, -0.5271703687119076, 2.3722666592035844] 9.309938021202928
[-1.8081943646818426, -0.5166269613376694, 2.3248213260195127] 8.941264475563292
[-1.7720304773882056, -0.506294422110916, 2.2783248994991223] 8.587190402330984
[-1.7365898678404414, -0.4961685336686977, 2.2327584015091397] 8.247137662398677
[-1.7018580704836326, -0.4862451629953237, 2.188103233478957] 7.920551010967689
[-1.66782090907396, -0.47652025973541723, 2.144341168809378] 7.606897190933369
[-1.6344644908924808, -0.4669898545407089, 2.1014543454331904] 7.305664062172408
[-1.6017752010746311, -0.45765005744989473, 2.0594252585245267] 7.01635976531038
[-1.5697396970531385, -0.4484970563008968, 2.0182367533540364] 6.7385119186040905
[-1.5383449031120757, -0.43952711517487886, 1.9778720182869556] 6.471666846627368
[-1.5075780050498342, -0.4307365728713813, 1.9383145779212165] 6.215388839500925
[-1.4774264449488375, -0.42212184141395365, 1.8995482863627922] 5.969259441456687
[-1.4478779160498607, -0.4136794045856746, 1.8615573206355363] 5.732876767575003
[-1.4189203577288636, -0.4054058164939611, 1.8243261742228256] 5.505854847579034
[-1.3905419505742864, -0.3972977001640819, 1.7878396507383691] 5.287822995614904
[-1.3627311115628007, -0.38935174616080026, 1.7520828577236018] 5.078425204988553
[-1.3354764893315447, -0.38156471123758423, 1.7170412005691298] 4.877319566871007
[-1.3087669595449138, -0.37393341701283256, 1.6827003765577473] 4.684177712022915
[-1.2825916203540155, -0.3664547486725759, 1.6490463690265924] 4.498684274626808
[-1.2569397879469353, -0.35912565369912436, 1.6160654416460605] 4.320536377351586
[-1.2318009921879967, -0.35194314062514187, 1.5837441328131392] 4.149443136808464
[-1.2071649723442368, -0.34490427781263905, 1.5520692501568765] 3.9851251885908487
[-1.1830216728973522, -0.3380061922563863, 1.521027865153739] 3.827314231122652
[-1.159361239439405, -0.33124606841125853, 1.4906073078506643] 3.675752587570195
[-1.136174014650617, -0.32462114704303335, 1.460795161693651] 3.5301927851024146
[-1.1134505343576047, -0.3181287241021727, 1.431579258459778] 3.390397150812359
[-1.0911815236704525, -0.3117661496201292, 1.4029476732905823] 3.2561374236401894
[-1.0693578931970436, -0.3055308266277266, 1.3748887198247708] 3.1271943816640384
[-1.0479707353331027, -0.2994202100951721, 1.3473909454282753] 3.0033574841501425
[-1.0270113206264406, -0.29343180589326867, 1.3204431265197099] 2.8844245277777967
[-1.006471094213912, -0.2875631697754033, 1.2940342639893156] 2.770201316477796
[-0.9863416723296337, -0.2818119063798952, 1.2681535787095293] 2.6605013443452754
[-0.966614838883041, -0.27617566825229733, 1.2427905071353387] 2.5551454911092026
[-0.9472825421053802, -0.27065215488725136, 1.217934696992632] 2.453961729661278
[-0.9283368912632726, -0.2652391117895063, 1.1935760030527793] 2.3567848451666915
[-0.9097701534380072, -0.2599343295537162, 1.1697044829917238] 2.263456165298091
[-0.891574750369247, -0.2547356429626419, 1.1463103933318892] 2.1738233011522863
[-0.8737432553618621, -0.24964093010338906, 1.1233841854652515] 2.087739898426656
[-0.8562683902546249, -0.24464811150132126, 1.1009165017559466] 2.0050653984489606
[-0.8391430224495323, -0.23975514927129485, 1.0788981717208277] 1.9256648086703818
[-0.8223601620005416, -0.23496004628586895, 1.057320208286411] 1.8494084822470345
[-0.8059129587605308, -0.23026084536015157, 1.0361738041206827] 1.7761719063500516
[-0.7897946995853202, -0.22565562845294854, 1.015450328038269] 1.7058354988585895
[-0.7739988055936138, -0.22114251588388956, 0.9951413214775036] 1.6382844131037892
[-0.7585188294817415, -0.21671966556621178, 0.9752384950479535] 1.573408350344879
[-0.7433484528921067, -0.21238527225488754, 0.9557337251469944] 1.511101379671222
[-0.7284814838342646, -0.2081375668097898, 0.9366190506440545] 1.4512617650362416
[-0.7139118541575793, -0.203974815473594, 0.9178866696311734] 1.3937917991408064
[-0.6996336170744277, -0.19989531916412212, 0.8995289362385499] 1.3385976438948304
[-0.6856409447329391, -0.1958974127808397, 0.881538357513779] 1.285589177196595
[-0.6719281258382803, -0.1919794645252229, 0.8639075903635034] 1.23467984577961
[-0.6584895633215148, -0.18813987523471845, 0.8466294385562333] 1.1857865238867373
[-0.6453197720550845, -0.18437707773002407, 0.8296968497851086] 1.1388293775408227
[-0.6324133766139828, -0.18068953617542358, 0.8131029127894064] 1.093731734190206
[-0.6197651090817031, -0.1770757454519151, 0.7968408545336183] 1.0504199575162738
[-0.607369806900069, -0.17353423054287678, 0.7809040374429459] 1.0088233271986293
[-0.5952224107620676, -0.17006354593201925, 0.7652859566940869] 0.9688739234415635
[-0.5833179625468262, -0.16666227501337885, 0.7499802375602052] 0.9305065160732775
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[-1.8402726869746255e-05, -5.2579219627846404e-06, 2.3660648832530903e-05] 9.261324027855598e-10
[-1.803467233235133e-05, -5.1527635235289475e-06, 2.3187435855880284e-05] 8.894575596352516e-10
[-1.76739788857043e-05, -5.0497082530583685e-06, 2.2723687138762677e-05] 8.542350402736956e-10
[-1.7320499307990214e-05, -4.948714087997201e-06, 2.2269213395987424e-05] 8.204073326788571e-10
[-1.697408932183041e-05, -4.849739806237257e-06, 2.1823829128067677e-05] 7.879192023047744e-10
[-1.6634607535393802e-05, -4.752745010112512e-06, 2.1387352545506325e-05] 7.567176018935055e-10
[-1.6301915384685927e-05, -4.657690109910262e-06, 2.0959605494596198e-05] 7.267515848585227e-10
[-1.597587707699221e-05, -4.564536307712057e-06, 2.0540413384704275e-05] 6.979722220981253e-10
[-1.5656359535452365e-05, -4.473245581557816e-06, 2.012960511701019e-05] 6.703325221030396e-10
[-1.5343232344743317e-05, -4.3837806699266595e-06, 1.9727013014669985e-05] 6.437873542277591e-10
[-1.5036367697848451e-05, -4.296105056528127e-06, 1.9332472754376584e-05] 6.182933750003398e-10
[-1.4735640343891483e-05, -4.210182955397564e-06, 1.8945823299289053e-05] 5.938089573503264e-10
[-1.4440927537013654e-05, -4.125979296289613e-06, 1.856690683330327e-05] 5.702941226392534e-10
[-1.4152108986273381e-05, -4.04345971036382e-06, 1.8195568696637207e-05] 5.477104753827391e-10
[-1.3869066806547914e-05, -3.962590516156543e-06, 1.7831657322704462e-05] 5.260211405575825e-10
[-1.3591685470416955e-05, -3.8833387058334125e-06, 1.7475024176250372e-05] 5.051907033915022e-10
[-1.3319851761008617e-05, -3.8056719317167442e-06, 1.7125523692725364e-05] 4.851851515371988e-10
[-1.3053454725788445e-05, -3.7295584930824095e-06, 1.6783013218870858e-05] 4.659718195363258e-10
[-1.2792385631272677e-05, -3.6549673232207612e-06, 1.6447352954493442e-05] 4.4751933548268735e-10
[-1.2536537918647224e-05, -3.581867976756346e-06, 1.6118405895403572e-05] 4.297975697975729e-10
[-1.228580716027428e-05, -3.510230617221219e-06, 1.57960377774955e-05] 4.12777586033589e-10
[-1.2040091017068794e-05, -3.4400260048767947e-06, 1.548011702194559e-05] 3.9643159362665893e-10
[-1.1799289196727418e-05, -3.371225484779259e-06, 1.517051468150668e-05] 3.807329025190432e-10
[-1.1563303412792869e-05, -3.303800975083674e-06, 1.4867104387876546e-05] 3.6565587957928907e-10
[-1.1332037344537011e-05, -3.2377249555820005e-06, 1.4569762300119015e-05] 3.5117590674794924e-10
[-1.110539659764627e-05, -3.1729704564703603e-06, 1.4278367054116635e-05] 3.372693408407304e-10
[-1.0883288665693346e-05, -3.109511047340953e-06, 1.3992799713034303e-05] 3.2391347494343754e-10
[-1.066562289237948e-05, -3.047320826394134e-06, 1.3712943718773617e-05] 3.110865013356774e-10
[-1.045231043453189e-05, -2.9863744098662514e-06, 1.3438684844398145e-05] 2.9876747588278464e-10
[-1.0243264225841253e-05, -2.9266469216689264e-06, 1.3169911147510182e-05] 2.869362838378264e-10
[-1.0038398941324428e-05, -2.8681139832355477e-06, 1.290651292455998e-05] 2.755736069978485e-10
[-9.837630962497938e-06, -2.8107517035708368e-06, 1.264838266606878e-05] 2.646608921607336e-10
[-9.64087834324798e-06, -2.75453666949942e-06, 1.2395415012747403e-05] 2.541803208311686e-10
[-9.448060776383021e-06, -2.6994459361094317e-06, 1.2147506712492455e-05] 2.4411478012625427e-10
[-9.259099560855361e-06, -2.645457017387243e-06, 1.1904556578242606e-05] 2.3444783483325463e-10
[-9.073917569638254e-06, -2.592547877039498e-06, 1.1666465446677753e-05] 2.2516370057385773e-10
[-8.892439218245489e-06, -2.540696919498708e-06, 1.1433136137744197e-05] 2.1624721803113297e-10
[-8.71459043388058e-06, -2.4898829811087337e-06, 1.1204473414989314e-05] 2.0768382819710012e-10
[-8.540298625202968e-06, -2.440085321486559e-06, 1.0980383946689527e-05] 1.9945954860049494e-10
[-8.369492652698908e-06, -2.391283615056828e-06, 1.0760776267755737e-05] 1.9156095047591537e-10
[-8.20210279964493e-06, -2.3434579427556917e-06, 1.0545560742400622e-05] 1.839751368370691e-10
[-8.038060743652031e-06, -2.296588783900578e-06, 1.033464952755261e-05] 1.7668972141832113e-10
[-7.87729952877899e-06, -2.2506570082225666e-06, 1.0127956537001556e-05] 1.696928084501556e-10
[-7.71975353820341e-06, -2.2056438680581154e-06, 9.925397406261525e-06] 1.6297297323552943e-10
[-7.565358467439341e-06, -2.161530990696953e-06, 9.726889458136294e-06] 1.5651924349540245e-10
[-7.414051298090555e-06, -2.118300370883014e-06, 9.532351668973569e-06] 1.5032108145298453e-10
[-7.265770272128744e-06, -2.0759343634653537e-06, 9.341704635594098e-06] 1.4436836662744637e-10
[-7.120454866686169e-06, -2.0344156761960467e-06, 9.154870542882216e-06] 1.3865137930899948e-10
[-6.978045769352446e-06, -1.9937273626721257e-06, 8.971773132024571e-06] 1.331607846883631e-10
[-6.838484853965396e-06, -1.9538528154186834e-06, 8.79233766938408e-06] 1.2788761761470392e-10
[-6.701715156886088e-06, -1.9147757591103096e-06, 8.616490915996399e-06] 1.2282326795716166e-10
[-6.567680853748366e-06, -1.8764802439281035e-06, 8.444161097676471e-06] 1.1795946654605805e-10
[-6.436327236673399e-06, -1.8389506390495413e-06, 8.275277875722941e-06] 1.1328827167083414e-10
[-6.307600691939931e-06, -1.8021716262685506e-06, 8.109772318208482e-06] 1.0880205611266911e-10
[-6.181448678101132e-06, -1.7661281937431795e-06, 7.947576871844314e-06] 1.0449349469060741e-10
[-6.0578197045391095e-06, -1.730805629868316e-06, 7.788625334407427e-06] 1.0035555230085936e-10
[-5.936663310448327e-06, -1.6961895172709497e-06, 7.632852827719278e-06] 9.638147242974533e-11
[-5.8179300442393605e-06, -1.6622657269255306e-06, 7.480195771164892e-06] 9.25647661215274e-11
[-5.7015714433545735e-06, -1.62902041238702e-06, 7.330591855741594e-06] 8.889920138311493e-11
[-5.587540014487482e-06, -1.5964400041392797e-06, 7.183980018626762e-06] 8.537879300834358e-11
[-5.4757892141977324e-06, -1.5645112040564941e-06, 7.040300418254227e-06] 8.199779280521317e-11
[-5.366273429913778e-06, -1.5332209799753643e-06, 6.8994944098891425e-06] 7.875068021012672e-11
[-5.258947961315502e-06, -1.502556560375857e-06, 6.7615045216913595e-06] 7.56321532738057e-11
[-5.153769002089192e-06, -1.47250542916834e-06, 6.626274431257532e-06] 7.263712000416299e-11
[-5.050693622047408e-06, -1.4430553205849732e-06, 6.493748942632382e-06] 6.976069005199815e-11
[-4.94967974960646e-06, -1.4141942141732736e-06, 6.363873963779734e-06] 6.699816672593902e-11
[-4.8506861546143305e-06, -1.3859103298898081e-06, 6.23659648450414e-06] 6.434503932359183e-11
[-4.753672431522044e-06, -1.358192123292012e-06, 6.111864554814057e-06] 6.179697576637759e-11
[-4.658598982891603e-06, -1.3310282808261717e-06, 5.989627263717775e-06] 5.934981552602903e-11
[-4.56542700323377e-06, -1.3044077152096484e-06, 5.86983471844342e-06] 5.699956283119829e-11
[-4.474118463169095e-06, -1.2783195609054555e-06, 5.752438024074552e-06] 5.474238014308283e-11
[-4.384636093905713e-06, -1.2527531696873464e-06, 5.63738926359306e-06] 5.2574581889416745e-11
[-4.2969433720275985e-06, -1.2276981062935994e-06, 5.5246414783211995e-06] 5.049262844659585e-11
[-4.211004504587047e-06, -1.2031441441677274e-06, 5.414148648754776e-06] 4.849312036011065e-11
[-4.1267844144953055e-06, -1.1790812612843729e-06, 5.30586567577968e-06] 4.657279279385027e-11
[-4.0442487262054e-06, -1.1554996360586853e-06, 5.1997483622640865e-06] 4.47285101992138e-11
[-3.963363751681292e-06, -1.1323896433375117e-06, 5.095753395018805e-06] 4.295726119532494e-11
[-3.884096476647666e-06, -1.1097418504707613e-06, 4.993838327118429e-06] 4.1256153651990076e-11
[-3.806414547114713e-06, -1.0875470134613462e-06, 4.893961560576061e-06] 3.9622409967371276e-11
[-3.7302862561724184e-06, -1.0657960731921192e-06, 4.7960823293645396e-06] 3.805336253266337e-11
[-3.65568053104897e-06, -1.0444801517282768e-06, 4.700160682777249e-06] 3.6546449376369904e-11
[-3.5825669204279906e-06, -1.0235905486937114e-06, 4.606157469121704e-06] 3.509920998106565e-11
[-3.5109155820194306e-06, -1.003118737719837e-06, 4.51403431973927e-06] 3.370928126581545e-11
[-3.440697270379042e-06, -9.830563629654404e-07, 4.423753633344485e-06] 3.237439372768916e-11
[-3.371883324971461e-06, -9.633952357061315e-07, 4.335278560677595e-06] 3.109236773607267e-11
[-3.304445658472032e-06, -9.441273309920089e-07, 4.248572989464043e-06] 2.986110997372419e-11
[-3.2383567453025914e-06, -9.252447843721687e-07, 4.163601529674763e-06] 2.867861001876472e-11
[-3.1735896103965395e-06, -9.067398886847253e-07, 4.080329499081268e-06] 2.754293706202164e-11
[-3.1101178181886085e-06, -8.886050909110308e-07, 3.998722909099643e-06] 2.6452236754365585e-11
[-3.047915461824836e-06, -8.708329890928103e-07, 3.91874845091765e-06] 2.5404728178892703e-11
[-2.9869571525883393e-06, -8.53416329310954e-07, 3.840373481899297e-06] 2.4398700943008556e-11
minimum v [-2.9869571525883393e-06, -8.53416329310954e-07, 3.840373481899297e-06]
minimum value 2.4398700943008556e-11

using minimize_batch
minimum v [0.001063382396627933, 0.0, 0.001063382396627933]
minimum value 2.2615642429163335e-06