Modify the code to loop over another dataset - python

I am using haversine_distance function to calculate distance between coordinates in a dataset to a specific coordinate. [start_lat, start_lon = 40.6976637, -74.1197643]
def haversine_distance(lat1, lon1, lat2, lon2):
r = 6371
phi1 = np.radians(lat1)
phi2 = np.radians(lat2)
delta_phi = np.radians(lat2-lat1)
delta_lambda = np.radians(lon2-lon1)
a = np.sin(delta_phi / 2)**2 + np.cos(phi1) * np.cos(phi2) * np.sin(delta_lambda / 2)**2
res = r * (2 * np.arctan2(np.sqrt(a), np.sqrt(1-a)))
return np.round(res, 2)
start_lat, start_lon = 40.6976637, -74.1197643
distances_km = []
for row in pandas_df.itertuples(index=False):
distances_km.append(
haversine_distance(start_lat, start_lon, row.lat, row.lon)
)
pandas_df['Distance'] = distances_km
pandas_df
This successfully creates a column in my data set measuring the distance from given point like this:
Now I want to modify this code so that instead of using [start_lat, start_lon = 40.6976637, -74.1197643] I want to use another dataset containing cities.
How can I modify this existing code such that I create column for every city using its coordinates instead.
So desired output shows different columns with each city name and distance as calculated above.
Any Help is appreciated, new to python!
Cities array as requested in comments
[['Nanaimo' -123.9364 49.1642]
['Prince Rupert' -130.3271 54.3122]
['Vancouver' -123.1386 49.2636]
['Victoria' -123.3673 48.4275]
['Edmonton' -113.4909 53.5445]
['Winnipeg' -97.1392 49.8994]
['Sarnia' -82.4065 42.9746]
['Sarnia' -82.4065 42.9746]
['North York' -79.4112 43.7598]
['Kingston' -76.4812 44.2305]
['St. Catharines' -79.2333 43.1833]
['Thunder Bay' -89.2461 48.3822]
['Gaspé' -64.4833 48.8333]
['Cap-aux-Meules' -61.8607 47.3801]
['Kangiqsujuaq' -71.9667 61.6]
['Montreal' -73.5534 45.5091]
['Quebec City' -71.2074 46.8142]
['Rimouski' -68.524 48.4489]
['Sept-Îles' -66.3833 50.2167]
['Bathurst' -65.6497 47.6186]
['Charlottetown' -63.1399 46.24]
['Corner Brook' -57.9711 48.9411]
['Dartmouth' -63.5714 44.6715]
['Lewisporte' -55.0667 49.2333]
['Port Hawkesbury' -61.3642 45.6153]
['Saint John' -66.0628 45.2796]
["St. John's" -52.7072 47.5675]
['Sydney' -60.1947 46.1381]
['Yarmouth' -66.1175 43.8361]]


The beauty of Python is that you can use the same code to do different things.
To consider different [start_lat, start_lon] values for every column in your data, you can use the same code that you have now. All you need to do is to define start_lat and start_lon as arrays:
# --------------------- Array Initialization ---------------------
import pandas as pd
import numpy as np
np.random.seed(0)
pandas_df = pd.DataFrame(data = {'lat': np.random.rand(100),
'lon': np.random.rand(100)})
start_cities = pd.DataFrame([['Nanaimo' , -123.9364 , 49.1642], ['Prince Rupert' , -130.3271 , 54.3122],
['Vancouver' , -123.1386 , 49.2636], ['Victoria' , -123.3673 , 48.4275],
['Edmonton' , -113.4909 , 53.5445], ['Winnipeg' , -97.1392 , 49.8994],
['Sarnia' , -82.4065 , 42.9746], ['Sarnia' , -82.4065 , 42.9746],
['North York' , -79.4112 , 43.7598], ['Kingston' , -76.4812 , 44.2305],
['St. Catharines' , -79.2333 , 43.1833], ['Thunder Bay' , -89.2461 , 48.3822],
['Gaspé' , -64.4833 , 48.8333], ['Cap-aux-Meules' , -61.8607 , 47.3801],
['Kangiqsujuaq' , -71.9667 , 61.6 ], ['Montreal' , -73.5534 , 45.5091],
['Quebec City' , -71.2074 , 46.8142], ['Rimouski' , -68.524 , 48.4489],
['Sept-Îles' , -66.3833 , 50.2167], ['Bathurst' , -65.6497 , 47.6186],
['Charlottetown' , -63.1399 , 46.24 ], ['Corner Brook' , -57.9711 , 48.9411],
['Dartmouth' , -63.5714 , 44.6715], ['Lewisporte' , -55.0667 , 49.2333],
['Port Hawkesbury' , -61.3642 , 45.6153], ['Saint John' , -66.0628 , 45.2796],
["St. John's" , -52.7072 , 47.5675], ['Sydney' , -60.1947 , 46.1381],
['Yarmouth' , -66.1175 , 43.8361]])
start_cities.columns = 'names', 'start_lat', 'start_lon'
start_lat = start_cities.start_lat
start_lon = start_cities.start_lon
# --------------------- Same code as before (as promised) ---------------------
def haversine_distance(lat1, lon1, lat2, lon2):
r = 6371
phi1 = np.radians(lat1)
phi2 = np.radians(lat2)
delta_phi = np.radians(lat2-lat1)
delta_lambda = np.radians(lon2-lon1)
a = np.sin(delta_phi / 2)**2 + np.cos(phi1) * np.cos(phi2) * np.sin(delta_lambda / 2)**2
res = r * (2 * np.arctan2(np.sqrt(a), np.sqrt(1-a)))
return np.round(res, 2)
distances_km = []
for row in pandas_df.itertuples(index=False):
distances_km.append(
haversine_distance(start_lat, start_lon, row.lat, row.lon))
# --------------------- Store data ---------------------
distances_km = np.array(distances_km)
for ind, name in enumerate(start_cities.names):
pandas_df['distance_km_' + name] = distances_km[:,ind]
# print(pandas_df.keys())
# ["lat" , "lon" ,
# "distance_km_Nanaimo" , "distance_km_Prince Rupert" ,
# "distance_km_Vancouver" , "distance_km_Victoria" ,
# "distance_km_Edmonton" , "distance_km_Winnipeg" ,
# "distance_km_Sarnia" , "distance_km_North York" ,
# "distance_km_Kingston" , "distance_km_St. Catharines" ,
# "distance_km_Thunder Bay" , "distance_km_Gaspé" ,
# "distance_km_Cap-aux-Meules" , "distance_km_Kangiqsujuaq" ,
# "distance_km_Montreal" , "distance_km_Quebec City" ,
# "distance_km_Rimouski" , "distance_km_Sept-Îles" ,
# "distance_km_Bathurst" , "distance_km_Charlottetown" ,
# "distance_km_Corner Brook" , "distance_km_Dartmouth" ,
# "distance_km_Lewisporte" , "distance_km_Port Hawkesbury",
# "distance_km_Saint John" , "distance_km_St. John's" ,
# "distance_km_Sydney" , "distance_km_Yarmouth" ]

Related

curve fitting with scipy

I am trying to fit a curve with curve_fit from SciPy. But it doesn't work as intended, and I don't know why. Here is my code:
xdata = np.asarray(std_ex_90degree[5050:5150,0])
ydata = np.asarray(std_ex_90degree[5050:5150,1])
print(xdata,ydata)
def Gauss(x, A, B):
y = A*np.exp(-1*B*x**2)
return y
popt, covariance = curve_fit(Gauss, xdata, ydata)
fit_A, fit_B = popt
fit_y = Gauss(xdata, fit_A, fit_B)
plt.scatter(xdata, ydata, label='data',s=5)
plt.plot(xdata, fit_y, '-', label='fit')
plt.legend()
As you can see the Gaussian Fit didn't work and I only got a straight line.
Here is the data:
[2834.486 2834.968 2835.45 2835.932 2836.414 2836.896 2837.378 2837.861
2838.343 2838.825 2839.307 2839.789 2840.271 2840.753 2841.235 2841.718
2842.2 2842.682 2843.164 2843.646 2844.128 2844.61 2845.093 2845.575
2846.057 2846.539 2847.021 2847.503 2847.985 2848.468 2848.95 2849.432
2849.914 2850.396 2850.878 2851.36 2851.843 2852.325 2852.807 2853.289
2853.771 2854.253 2854.735 2855.218 2855.699 2856.182 2856.664 2857.146
2857.628 2858.11 2858.592 2859.074 2859.557 2860.039 2860.521 2861.003
2861.485 2861.967 2862.449 2862.932 2863.414 2863.896 2864.378 2864.86
2865.342 2865.824 2866.307 2866.789 2867.271 2867.753 2868.235 2868.717
2869.199 2869.682 2870.164 2870.646 2871.128 2871.61 2872.092 2872.574
2873.056 2873.539 2874.021 2874.503 2874.985 2875.467 2875.949 2876.431
2876.914 2877.396 2877.878 2878.36 2878.842 2879.324 2879.806 2880.289
2880.771 2881.253 2881.735 2882.217]
[0.5027119 0.5155925 0.5296563 0.5450429 0.5619112 0.5804411 0.6008373
0.6233361 0.6482099 0.67577 0.7063611 0.7403504 0.7781109 0.8200049
0.8663718 0.9175249 0.9737514 1.035319 1.102472 1.175419 1.254304
1.339163 1.429889 1.526202 1.627649 1.733603 1.84322 1.955248
2.067605 2.176702 2.276757 2.359875 2.417753 2.445059 2.441798
2.41245 2.362954 2.298523 2.223243 2.14052 2.05336 1.964326
1.87539 1.787885 1.702644 1.620191 1.540921 1.465193 1.393333
1.325607 1.262171 1.203057 1.148185 1.097403 1.050529 1.007382
0.9678 0.9316369 0.8987471 0.8689752 0.8421496 0.8180863 0.7965991
0.7775094 0.76065 0.7458642 0.732995 0.7218768 0.7123291 0.7041584
0.6971676 0.6911709 0.6860058 0.6815417 0.6776828 0.674363 0.6715436
0.6692089 0.6673671 0.6660498 0.6653103 0.6652156 0.6658351 0.6672268
0.6694273 0.6724483 0.676279 0.6808962 0.686272 0.6923797 0.699192
0.7066767 0.7147906 0.7234787 0.7326793 0.7423348 0.7524015 0.7628553
0.7736901 0.7849081]

Inappropriate model. Minor adjustments to model yield a rough fit:
import numpy as np
from matplotlib import pyplot as plt
from scipy.optimize import curve_fit
xdata = np.array((
2834.486, 2834.968, 2835.45 , 2835.932, 2836.414, 2836.896, 2837.378, 2837.861,
2838.343, 2838.825, 2839.307, 2839.789, 2840.271, 2840.753, 2841.235, 2841.718,
2842.2 , 2842.682, 2843.164, 2843.646, 2844.128, 2844.61 , 2845.093, 2845.575,
2846.057, 2846.539, 2847.021, 2847.503, 2847.985, 2848.468, 2848.95 , 2849.432,
2849.914, 2850.396, 2850.878, 2851.36 , 2851.843, 2852.325, 2852.807, 2853.289,
2853.771, 2854.253, 2854.735, 2855.218, 2855.699, 2856.182, 2856.664, 2857.146,
2857.628, 2858.11 , 2858.592, 2859.074, 2859.557, 2860.039, 2860.521, 2861.003,
2861.485, 2861.967, 2862.449, 2862.932, 2863.414, 2863.896, 2864.378, 2864.86 ,
2865.342, 2865.824, 2866.307, 2866.789, 2867.271, 2867.753, 2868.235, 2868.717,
2869.199, 2869.682, 2870.164, 2870.646, 2871.128, 2871.61 , 2872.092, 2872.574,
2873.056, 2873.539, 2874.021, 2874.503, 2874.985, 2875.467, 2875.949, 2876.431,
2876.914, 2877.396, 2877.878, 2878.36 , 2878.842, 2879.324, 2879.806, 2880.289,
2880.771, 2881.253, 2881.735, 2882.217,
))
ydata = np.array((
0.5027119, 0.5155925, 0.5296563, 0.5450429, 0.5619112, 0.5804411, 0.6008373,
0.6233361, 0.6482099, 0.67577 , 0.7063611, 0.7403504, 0.7781109, 0.8200049,
0.8663718, 0.9175249, 0.9737514, 1.035319 , 1.102472 , 1.175419 , 1.254304 ,
1.339163 , 1.429889 , 1.526202 , 1.627649 , 1.733603 , 1.84322 , 1.955248 ,
2.067605 , 2.176702 , 2.276757 , 2.359875 , 2.417753 , 2.445059 , 2.441798 ,
2.41245 , 2.362954 , 2.298523 , 2.223243 , 2.14052 , 2.05336 , 1.964326 ,
1.87539 , 1.787885 , 1.702644 , 1.620191 , 1.540921 , 1.465193 , 1.393333 ,
1.325607 , 1.262171 , 1.203057 , 1.148185 , 1.097403 , 1.050529 , 1.007382 ,
0.9678 , 0.9316369, 0.8987471, 0.8689752, 0.8421496, 0.8180863, 0.7965991,
0.7775094, 0.76065 , 0.7458642, 0.732995 , 0.7218768, 0.7123291, 0.7041584,
0.6971676, 0.6911709, 0.6860058, 0.6815417, 0.6776828, 0.674363 , 0.6715436,
0.6692089, 0.6673671, 0.6660498, 0.6653103, 0.6652156, 0.6658351, 0.6672268,
0.6694273, 0.6724483, 0.676279 , 0.6808962, 0.686272 , 0.6923797, 0.699192 ,
0.7066767, 0.7147906, 0.7234787, 0.7326793, 0.7423348, 0.7524015, 0.7628553,
0.7736901, 0.7849081,
))
def gauss(x: np.ndarray, *args: float) -> np.ndarray:
a, b, c, d = args
return a*np.exp(-b*(x - c)**2) + d
popt, _ = curve_fit(
gauss, xdata, ydata,
p0=(1.7, 0.02, 2851, 0.7),
maxfev=100_000,
)
print(popt)
fit_y = gauss(xdata, *popt)
plt.scatter(xdata, ydata, label='data', s=5)
plt.plot(xdata, fit_y, '-', label='fit')
plt.legend()
plt.show()
[1.68927347e+00 2.10977276e-02 2.85117456e+03 6.81806648e-01]
To do any better, your model needs to change more.

Getting "TypeError: string indices must be integers" while printing in python; dictionary of lists with quantities and units

I have file test.txt (given below)
When I tried to print I get this error.
>>> print(content['mass'])
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: string indices must be integers
But when
>>> print(content)
works ok, and show whole content (test.txt)
I need to print each list from the dict (like mass, temperature, etc.) and plot any 2 of them.
The content of the file is as follows:
{'mass': <Quantity [0.01066337, 0.05677534, 0.01377424, 0.06982872, 0.02665362] solar_mass>, 'temperature': <[values ... ] unit>}
full content file:
{'mass': <Quantity [0.01066337, 0.05677534, 0.01377424, 0.06982872, 0.02665362,
0.05278109, 0.01705602, 0.01321568, 0.08957726, 0.01409967,
0.02680093, 0.04329349, 0.04019967, 0.01633035, 0.09329267,
0.09963128, 0.04351358, 0.07735598, 0.02380135, 0.02242677,
0.03210654, 0.08636837, 0.02273623, 0.08528297, 0.07963256,
0.01457712, 0.07067075, 0.03672347, 0.08830624, 0.0152433 ,
0.02692899, 0.06610553, 0.09237312, 0.01470838, 0.06389854,
0.0367586 , 0.01463151, 0.05156612, 0.09061456, 0.02097923,
0.09724939, 0.01442857, 0.04258596, 0.09389821, 0.04595303,
0.01288873, 0.09977905, 0.08107244, 0.07191315, 0.01770304,
0.080393 , 0.02020766, 0.07458504, 0.01695185, 0.07393091,
0.03053152, 0.06589851, 0.02035323, 0.07618899, 0.03820138,
0.02377403, 0.07995724, 0.04570385, 0.02277475, 0.01927913,
0.02415907, 0.01820019, 0.04897082, 0.05023911, 0.02736103,
0.05118501, 0.05433449, 0.05497384, 0.0278658 , 0.0109119 ,
0.04103063, 0.05278137, 0.08110729, 0.02117512, 0.02299667,
0.02712591, 0.09289156, 0.07933846, 0.07723336, 0.07550681,
0.09140791, 0.05044324, 0.04048182, 0.0540212 , 0.06348042,
0.09851312, 0.06866901, 0.04383336, 0.06000141, 0.06026228,
0.09245798, 0.06652555, 0.08638328, 0.02669351, 0.03291363,
0.09498578, 0.07123481, 0.01734788, 0.06394011, 0.09080883,
0.0100093 , 0.05614301, 0.08463198, 0.08348169, 0.0695272 ,
0.012756 , 0.08004025, 0.042433 , 0.04228984, 0.05852984,
0.09786057, 0.09222483, 0.05554798, 0.02833528, 0.05775946,
0.04866883, 0.08642554, 0.05625195, 0.04145988, 0.03118205,
0.06150846, 0.03043129, 0.08140125, 0.0371213 , 0.08422178,
0.04447278, 0.05010288, 0.03013005, 0.07293837, 0.04287462,
0.07925233, 0.03597007, 0.06064241, 0.01506324, 0.01661757,
0.09065556, 0.01877721, 0.06181287, 0.01797611, 0.08751541,
0.06245063, 0.05643477, 0.09667603, 0.02816646, 0.05963242,
0.09114687, 0.08555436, 0.03389574, 0.03619514, 0.09107117,
0.08513269, 0.02986811, 0.06354284, 0.03119169, 0.02294978,
0.08086929, 0.07718417, 0.03123856, 0.03509633, 0.05837078,
0.02374362, 0.06490901, 0.05722849, 0.05868046, 0.01302157,
0.01879107, 0.07831512, 0.04077195, 0.02944109, 0.06633705,
0.09150163, 0.03014493, 0.07650354, 0.05166767, 0.0630273 ,
0.04772543, 0.0354305 , 0.02018854, 0.09507716, 0.02150221,
0.01615494, 0.06707219, 0.06575294, 0.05319418, 0.06806339,
0.084564 , 0.06717039, 0.07972018, 0.06372022, 0.03449891,
0.01062518, 0.0362224 , 0.06631852, 0.06794747, 0.07164968] solMass>,
'age': <Quantity [2.1892995 , 0.17371445, 6.37350567, 3.65552583, 0.26690645,
9.01274312, 9.5712514 , 4.12433204, 1.46197905, 6.69672667,
2.60662951, 0.07088385, 5.68504611, 2.14170039, 8.25031197,
1.05353222, 6.38848764, 4.91127832, 4.83363973, 1.06507071,
8.91887495, 9.04766237, 6.77889849, 9.2907544 , 9.85479148,
2.02304717, 3.2270554 , 9.36069897, 8.1881205 , 8.26326698,
4.24937976, 5.43265177, 1.23439319, 0.66178519, 7.30850369,
8.53579481, 0.58917658, 9.52785688, 8.78128074, 7.49955993,
6.07008997, 2.43334746, 9.15192905, 5.34271923, 1.03902797,
7.85382611, 9.07929136, 2.34516092, 4.0336831 , 6.9754011 ,
1.65513417, 5.78941649, 6.28545569, 7.14168201, 4.5552691 ,
6.21132475, 6.81369173, 1.74626285, 9.87199907, 3.68096459,
5.70725541, 8.50758903, 4.5958371 , 9.26271041, 9.21219332,
1.12404491, 8.46718892, 2.41106556, 9.5383536 , 2.845751 ,
5.48186263, 3.75960932, 9.46408245, 3.070541 , 5.14349759,
6.72742338, 2.056287 , 8.26982877, 3.23218309, 4.17451665,
5.77088167, 0.44298759, 9.65296989, 2.61752721, 9.13504304,
7.98373538, 5.71220366, 1.56916865, 1.97688569, 1.91507324,
9.17263502, 1.77701376, 4.55412645, 3.2627102 , 7.35668915,
2.50479129, 2.61109961, 6.37928278, 4.95950159, 3.05026315,
4.05514457, 0.08672433, 2.86609243, 1.35325359, 3.42583719,
4.26484596, 5.1162449 , 4.85971091, 4.44955176, 2.23475404,
3.31668938, 8.43803181, 0.72360653, 4.15507274, 0.87411426,
7.75213716, 4.6793922 , 7.48000041, 5.72125433, 1.31397429,
5.95206492, 8.58636847, 5.89774647, 3.26018283, 8.27834433,
4.00586172, 5.53028026, 4.79525327, 3.29217389, 4.87280459,
3.7335077 , 3.30432489, 3.60355157, 9.34549498, 6.49931121,
0.02732216, 6.94381144, 5.90679801, 3.16357294, 7.82961274,
0.0888311 , 7.9029332 , 4.33901607, 5.51927395, 6.53654137,
7.64875188, 3.09088845, 6.17206639, 4.5635939 , 1.12640628,
6.55772591, 0.8635738 , 8.86321633, 6.58032887, 0.57264661,
9.99113685, 0.83339148, 6.32905049, 9.21722392, 1.65153675,
4.29805491, 4.29669901, 5.58498365, 9.08169993, 6.42132207,
2.0412622 , 4.7042499 , 8.45610063, 5.53653754, 4.27634556,
0.98283569, 4.70564712, 4.85030912, 4.43987977, 2.20253426,
5.61759252, 7.5305766 , 9.28187195, 0.06004595, 0.8131256 ,
0.9932211 , 1.47332778, 1.44624897, 9.23842621, 5.34899458,
8.43612797, 9.4825792 , 5.94245213, 6.74007551, 6.20404917,
9.53766677, 4.60019672, 1.59700463, 5.52334977, 0.48772997,
0.59965089, 1.75955369, 9.56138032, 1.04756037, 3.91171088] Gyr>, 'temperature': <Quantity [ 416.26187575, 2386.00147856, 356.96775964, 1611.48635911,
1386.90459789, 843.45377056, 359.56621029, 397.98698621,
2615.60719944, 356.35902942, 696.73157636, 2452.07321025,
738.22537858, 532.80565595, 2677.89432543, 2778.16848831,
769.31944774, 2151.4339527 , 533.16952309, 812.50564763,
548.1938236 , 2513.85620097, 471.13610308, 2481.15025828,
2297.11805108, 508.33419459, 1725.63923115, 602.54069179,
2572.14755174, 351.02698579, 599.78662322, 1332.30425907,
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Try this:
import json
json_data = json.loads(content)
print(json_data["mass"])

Differential evolution in SciPy

I am trying to use differential_evolution from SciPy. I have three matrices: x, y and P - all of size (14,6). I have to use the following formula:
z= np.log10(g)+ np.log10(c)*np.log10(P)
to find the value of c (real number from 0 to 2) which minimize:
numpy.median(z**2)
this expression. What I try is this (I provide the data for the convenience):
import numpy as np
from scipy.optimize import differential_evolution
def func(c, args):
z = args[0] + np.log10(c)*np.log10(args[1])
return np.median(z**2)
if __name__ == '__main__':
bounds = [(0, 2)]
x = np.array([[126581.94951205, 97601.85624482, 59659.00330833,
27646.48551627, 9202.50377458, 4840.25789068],
[213571.84886437, 148750.52154776, 85979.81139937,
38757.37831212, 11775.99906427, 4619.32027948],
[195684.50299021, 131818.78542437, 74376.55189913,
32793.21715377, 10288.70838873, 4042.58093119],
[177598.13865746, 120942.50439911, 68866.09898276,
30819.5354775 , 10588.08746517, 5011.71808947],
[126433.18311483, 85863.57788065, 48923.64502157,
21828.60950911, 7907.37639781, 4410.61819399],
[103431.88029629, 67452.94418262, 37608.36861047,
16456.97701443, 6027.98704858, 3550.06927169],
[100689.06813945, 64380.21348052, 34764.02910376,
14849.85472635, 5607.19256065, 3605.5709208 ],
[ 96509.22946744, 63832.74512518, 36041.69174706,
15802.87650901, 6473.33232805, 4664.07058733],
[113078.63455882, 73227.02362359, 40861.09037499,
17385.89127848, 7074.98444924, 5136.84232454],
[121241.93118924, 78537.13681709, 44257.97654994,
18584.94999742, 7733.39219718, 5869.49536788],
[115948.06368262, 73995.07204278, 41536.21315507,
16851.59724901, 6736.25125909, 4851.5738275 ],
[115024.20359423, 72108.15245783, 40341.98473413,
15900.55422399, 6243.63777265, 4411.24859372],
[108754.83802899, 66210.25952459, 36485.42905112,
14577.73925124, 5553.23702141, 3736.5217322 ],
[ 95340.59125024, 58458.97552915, 32364.19705748,
13236.30114676, 4929.04023171, 3202.21731277]])
y = y=np.array([[118166.08 , 95784.692 , 68134.878 , 37119.959 , 17924.157 ,
7445.3083],
[ 99265.027 , 70679.135 , 43297.559 , 19822.017 , 8527.8497,
3404.7113],
[ 80227.797 , 50972.879 , 26648.604 , 11190.488 , 4836.6514,
2249.9172],
[ 68510.582 , 39288.19 , 19938.938 , 9312.6881, 4907.6661,
2681.2709],
[ 65193.15 , 36610.107 , 18612.181 , 9211.144 , 5416.1685,
3372.1282],
[ 67188.918 , 37227.699 , 20132.92 , 11663.275 , 7315.3472,
4648.1669],
[ 64802.06 , 38885.622 , 22008.537 , 13100.638 , 8043.0185,
5049.2097],
[ 68104.867 , 41212.89 , 23247.898 , 14134.707 , 8805.2547,
5526.1014],
[ 74180.595 , 41268.904 , 22868.016 , 13841.437 , 8660.1413,
5401.245 ],
[ 78920.685 , 42743.389 , 23932.305 , 13910.089 , 8439.3342,
5141.7051],
[ 91329.012 , 45733.772 , 25430.818 , 14144.185 , 8273.7953,
5016.5839],
[ 92217.594 , 44984.3 , 23353.596 , 13467.631 , 8099.728 ,
4948.26 ],
[ 94508.441 , 48114.879 , 24735.311 , 13358.097 , 7821.8587,
4806.7923],
[108211.73 , 53987.095 , 25872.772 , 13189.61 , 7552.7164,
4497.2611]])
P=10000*np.array([[0.6011,0.6011,0.6011,0.6011,0.6011,0.6011],
[0.9007,0.9007,0.9007,0.9007,0.9007,0.9007],
[1.1968,1.1968,1.1968,1.1968,1.1968,1.1968],
[1.4178,1.4178,1.4178,1.4178,1.4178,1.4178],
[1.5015,1.5015,1.5015,1.5015,1.5015,1.5015],
[1.439,1.439,1.439,1.439,1.439,1.439],
[1.2721,1.2721,1.2721,1.2721,1.2721,1.2721],
[1.0616,1.0616,1.0616,1.0616,1.0616,1.0616],
[0.8543,0.8543,0.8543,0.8543,0.8543,0.8543],
[0.6723,0.6723,0.6723,0.6723,0.6723,0.6723],
[0.5204,0.5204,0.5204,0.5204,0.5204,0.5204],
[0.3963,0.3963,0.3963,0.3963,0.3963,0.3963],
[0.2990,0.2990,0.2990,0.2990,0.2990,0.2990],
[0.2211,0.2211,0.2211,0.2211,0.2211,0.2211]])
g=np.log10(y) - np.log10(x)
args = (g,P)
result = differential_evolution(func, bounds, args=args)
print(func(bounds, args))
I get this error: TypeError: func() takes exactly 2 arguments (3 given) . Is there any way to fix this?

def func(c, g, P):
z = g + np.log10(c)*np.log10(P)
return np.median(z**2)
if __name__ == '__main__':
# Your arrays go here
g = np.log10(y) - np.log10(x)
args = (g, P)
result = differential_evolution(func, bounds, args=(g, P))
# will print the value of c and value of the optimized function
print (result.x, result.fun)

Solving a first order BVP with two boundary conditions with scipy's solve_bvp

I am using scipy's BVP solver:
http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_bvp.html
The problem I am running into is that you can only have as many boundary conditions as you have equations. I only have one equation but I have two boundary conditions. How can this be fixed?
MWE
>>> import numpy as np
>>> from scipy.integrate import solve_bvp
>>>
>>> x = np.linspace(0, 1, 100)
>>> dydx = lambda x,y: y*np.sin(x)
>>>
>>> result = solve_bvp(dydx,
... lambda ya,yb: np.array([ (ya[0]-1)**2 + (yb[0]-1)**2 ]),
... x, [np.ones(len(x))], max_nodes=100000, tol=1e-9)
>>>
>>> result
message: 'The algorithm converged to the desired accuracy.'
niter: 2
p: None
rms_residuals: array([ 3.48054730e-10, 3.47134800e-10, 3.46220750e-10,
3.45304147e-10, 3.44446495e-10, 3.43708535e-10,
3.42834209e-10, 3.41730399e-10, 3.40902853e-10,
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0.43520202, 0.43856597, 0.44193917, 0.44532166, 0.4487135 ,
0.45211476, 0.45552551, 0.45894578, 0.46237566, 0.4658152 ,
0.46926446, 0.47272349, 0.47619237, 0.47967114, 0.48315988,
0.48665863, 0.49016747, 0.49368644, 0.49721562, 0.50075505,
0.5043048 , 0.50786493, 0.5114355 , 0.51501656, 0.51860818,
0.52221041, 0.52582331, 0.52944695, 0.53308138, 0.53672666,
0.54038285, 0.54405001, 0.54772819, 0.55141745, 0.55511786,
0.55882946, 0.56255232, 0.5662865 , 0.57003205, 0.57378903,
0.5775575 , 0.58133751, 0.58512912, 0.58893239, 0.59274738,
0.59657414, 0.60041272, 0.60426319, 0.6081256 , 0.61200001,
0.61588646, 0.61978503, 0.62369576, 0.6276187 , 0.63155392,
0.63550147, 0.6394614 , 0.64343376, 0.64741862, 0.65141602,
0.65542602, 0.65944867, 0.66348403, 0.66753215, 0.67159308,
0.67566687, 0.67975358, 0.68385327, 0.68796597, 0.69209174,
0.69623064, 0.70038272, 0.70454802, 0.7087266 , 0.7129185 ,
0.71712379, 0.7213425 , 0.72557469, 0.72982041, 0.7340797 ,
0.73835262, 0.74263921, 0.74693953, 0.75125361, 0.75558151,
0.75992327, 0.76427895, 0.76864858, 0.77303222, 0.7774299 ,
0.78184168, 0.7862676 , 0.79070771, 0.79516204, 0.79963065,
0.80411358, 0.80861086, 0.81312256, 0.81764869, 0.82218932,
0.82674447, 0.8313142 , 0.83589854, 0.84049753, 0.84511122,
0.84973964, 0.85438283, 0.85904083, 0.86371368, 0.86840142,
0.87310408, 0.8778217 , 0.88255432, 0.88730198, 0.89206471,
0.89684254, 0.90163551, 0.90644365, 0.911267 , 0.91610559,
0.92095945, 0.92582862, 0.93071312, 0.93561298, 0.94052825,
0.94545894, 0.95040508, 0.95536671, 0.96034386, 0.96533654,
0.97034479, 0.97536863, 0.98040809, 0.98546319, 0.99053396,
0.99562042, 1.0007226 , 1.00584051, 1.01097418, 1.01612363,
1.02128888, 1.02646995, 1.03166686, 1.03687962, 1.04210827,
1.0473528 , 1.05261324, 1.0578896 ]])
As you can see, y is very far from the boundary conditions of y(x=0) = y(x=1) = 1.

If you specify two boundary conditions y(0)=1 and y(1)=1 for a first order ODE, then in general the problem is overdetermined and there is no solution. If you specify just the initial condition y(0)=y0, you have a first order initial value problem. In fact, in this case, you can derive the exact solution: y(x) = y0*exp(-cos(x)).

Can JModelica print results directly to file?

I am running the following JModelica script:
#!/usr/local/jmodelica/bin/jm_python.sh
import pyjmi
op = pyjmi.transfer_optimization_problem("BatchReactor", "model.mop")
opt_opts = op.optimize_options()
opt_opts['n_e'] = 40 # Number of elements
opt_opts['IPOPT_options']['tol'] = 1e-10
opt_opts['IPOPT_options']['print_level'] = 8
opt_opts['IPOPT_options']['output_file'] = '/z/out'
res = op.optimize(options=opt_opts)
I had hoped that the results (e.g. time, x1, x2, &c.) would be printed to the file /z/out. But the file only contains IPOPT verbose debugging/status info.
Is there a way to print the information that would be stored in res directly to a file? Either by somehow writing res itself or, preferably, having IPOPT/JModelica write the results without having to go through Python?

There is a way to print the information directly to a file. The following accomplishes this. Note that result_file_name is the key to making this happen.
#!/usr/local/jmodelica/bin/jm_python.sh
import pyjmi
op = pyjmi.transfer_optimization_problem("BatchReactor", "model.mop")
opt_opts = op.optimize_options()
opt_opts['n_e'] = 40 # Number of elements
opt_opts['result_file_name'] = '/z/out'
opt_opts['IPOPT_options']['tol'] = 1e-10
opt_opts['IPOPT_options']['print_level'] = 0
res = op.optimize(options=opt_opts)
Unfortunately, the contents of the file are somewhat mysterious.

You may find that using result_file_name per another answer here results in an output file which is difficult to understand.
The following produces a nicer format:
import StringIO
import numpy as np
def PrintResToFile(filename,result):
def StripMX(x):
return str(x).replace('MX(','').replace(')','')
varstr = '#Variable Name={name: <10}, Unit={unit: <7}, Val={val: <10}, Col={col:< 5}, Comment="{comment}"\n'
with open(filename,'w') as fout:
#Print all variables at the top of the file, along with relevant information
#about them.
for var in result.model.getAllVariables():
if not result.is_variable(var.getName()):
val = result.initial(var.getName())
col = -1
else:
val = "Varies"
col = result.get_column(var.getName())
unit = StripMX(var.getUnit())
if not unit:
unit = "X"
fout.write(varstr.format(
name = var.getName(),
unit = unit,
val = val,
col = col,
comment = StripMX(var.getAttribute('comment'))
))
#Ensure that time variable is printed
fout.write(varstr.format(
name = 'time',
unit = 's',
val = 'Varies',
col = 0,
comment = 'None'
))
#The data matrix contains only time-varying variables. So fetch all of
#these, couple them in tuples with their column number, sort by column
#number, and then extract the name of the variable again. This results in a
#list of variable names which are guaranteed to be in the same order as the
#data matrix.
vkeys_in_order = map(lambda x: x[1], sorted([(result.get_column(x),x) for x in result.keys() if result.is_variable(x)]))
for vk in vkeys_in_order:
fout.write("{0:>13},".format(vk))
fout.write("\n")
sio = StringIO.StringIO()
np.savetxt(sio, result.data_matrix, delimiter=',', fmt='%13.5f')
fout.write(sio.getvalue())
which looks like this:
#Variable Name=S0 , Unit=kg , Val=2.0 , Col=-1 , Comment="Solid Mass"
#Variable Name=F0 , Unit=kg , Val=0.0 , Col=-1 , Comment="Fluid Mass"
#Variable Name=a , Unit=Hz , Val=0.2 , Col=-1 , Comment="None"
#Variable Name=b , Unit=kg/s , Val=1.0 , Col=-1 , Comment="None"
#Variable Name=f , Unit=kg/s , Val=0.05 , Col=-1 , Comment="None"
#Variable Name=h , Unit=1/g , Val=0.05 , Col=-1 , Comment="None"
#Variable Name=der(F) , Unit=X , Val=Varies , Col= 1 , Comment="None"
#Variable Name=F , Unit=kg , Val=Varies , Col= 3 , Comment="None"
#Variable Name=der(S) , Unit=X , Val=Varies , Col= 2 , Comment="None"
#Variable Name=S , Unit=kg , Val=Varies , Col= 4 , Comment="None"
#Variable Name=u , Unit=X , Val=Varies , Col= 5 , Comment="None"
#Variable Name=startTime , Unit=X , Val=0.0 , Col=-1 , Comment="None"
#Variable Name=finalTime , Unit=X , Val=100.0 , Col=-1 , Comment="None"
#Variable Name=time , Unit=s , Val=Varies , Col= 0 , Comment="None"
time, der(F), der(S), F, S, u,
0.00000, 0.97097, -0.97097, 0.00000, 2.00000, 0.97097
0.38763, 1.07704, -1.05814, 0.38519, 1.61698, 1.00000
1.61237, 0.88350, -0.80485, 1.70714, 0.35885, 0.65862
2.50000, 0.00000, 0.09688, 2.14545, 0.00000, 0.00000
2.88763, 0.09842, -0.00000, 2.18330, 0.00000, 0.06851
4.11237, 0.10342, 0.00000, 2.30688, 0.00000, 0.07077
5.00000, 0.10716, 0.00000, 2.40033, 0.00000, 0.07240
5.38763, 0.10882, -0.00000, 2.44219, 0.00000, 0.07311
6.61237, 0.11421, 0.00000, 2.57875, 0.00000, 0.07535

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