What is the correct way handle with multidimensional array?

[kapkirl]

Trying to use sample with nonlinear regression

import pandas
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt

# # measurements
xm = np.array([[80435, 33576, 3930495], [63320, 21365, 2515052],
[131294, 46680, 10339497], [64470, 29271, 3272846],
[23966, 7973, 3450144], [19863, 11429, 3427307],
[32139, 13114, 2462822], [78976, 26973, 5619715],
[32857, 10455, 3192817], [29400, 12808, 3665615],
[4667, 2876, 2556650], [21477, 10349, 6005812],
[9168, 4617, 2878631], [385112, 127609, 4063576],
[55522, 29954, 3632023], [155, 197, 507],
[160, 106, 336], [25, 23, 669], [86, 96, 751], [199, 235, 515],
[60, 83, 511], [8, 25, 187], [32, 59, 679], [11, 22, 365],
[322, 244, 2001], [172, 229, 1110], [41, 48, 447], [109, 144, 2386],
[23, 27, 319], [105, 204, 672], [77, 77, 2]])

ym = np.array([90,85,91,90,90,82,81,85,83,83,72,78,
74,92,90,28,26,13,12,22,25,5,10,15,50,54,4,28,10,7,6])

# GEKKO model
m = GEKKO()

# parameters
x = m.Param(value=xm, name='X')
y = m.CV(value=ym)
y.FSTATUS = 1

a1 = m.FV()
a1.STATUS=1

a2 = m.FV()
a2.STATUS=1

a3 = m.FV()
a3.STATUS=1

# regression equation
for i in range(len(x)):
    m.Equation(
        y[i] == np.log10(x[i][0]) * a1 +
                np.log10(x[i][1]) * a2 +
                np.log10(x[i][2]) * a3)

# regression mode
m.options.IMODE = 2

# optimize
m.solve(disp=False, GUI=False)

# print parameters
print('Optimized, a = ', str(a1), str(a2), str(a3))

plt.plot(y.value, ym, 'bo')
# plt.plot(xm, y.value, 'r-')
plt.show()

gives error

File "/usr/local/lib/python3.6/dist-packages/gekko/gekko.py", line 1830, in solve self._write_csv() File "/usr/local/lib/python3.6/dist-packages/gekko/gk_write_files.py", line 184, in _write_csv raise Exception('Data arrays must have the same length, and match time discretization in dynamic problems') Exception: Data arrays must have the same length, and match time discretization in dynamic problems

How can I handle this case?

[APMonitor]

Here is a summary of the modifications:

• Use m.log10 instead of np.log10
• Define x as an Array and load each column (e.g. xm[:,0]) into the x[0].value separately
• Define the equation only once, not multiple times for each data row. IMODE=2 is efficient for large data sets this way because the equation is only defined one and the data points are all evaluated with that same expression.
• Added red line to plot
• Print a[i].value[0] to display the numeric solution

import pandas
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt

# # measurements
xm = np.array([[80435, 33576, 3930495], [63320, 21365, 2515052],
[131294, 46680, 10339497], [64470, 29271, 3272846],
[23966, 7973, 3450144], [19863, 11429, 3427307],
[32139, 13114, 2462822], [78976, 26973, 5619715],
[32857, 10455, 3192817], [29400, 12808, 3665615],
[4667, 2876, 2556650], [21477, 10349, 6005812],
[9168, 4617, 2878631], [385112, 127609, 4063576],
[55522, 29954, 3632023], [155, 197, 507],
[160, 106, 336], [25, 23, 669], [86, 96, 751], [199, 235, 515],
[60, 83, 511], [8, 25, 187], [32, 59, 679], [11, 22, 365],
[322, 244, 2001], [172, 229, 1110], [41, 48, 447], [109, 144, 2386],
[23, 27, 319], [105, 204, 672], [77, 77, 2]])

ym = np.array([90,85,91,90,90,82,81,85,83,83,72,78,
74,92,90,28,26,13,12,22,25,5,10,15,50,54,4,28,10,7,6])

# GEKKO model
m = GEKKO(remote=False)

# parameters
n = np.size(xm,1)
x = m.Array(m.Param,n)
for i in range(n):
    x[i].value = xm[:,i]
y = m.CV(value=ym)
y.FSTATUS = 1

a1 = m.FV()
a1.STATUS=1

a2 = m.FV()
a2.STATUS=1

a3 = m.FV()
a3.STATUS=1

# regression equation
m.Equation(y == m.log10(x[0]) * a1 + \
                m.log10(x[1]) * a2 + \
                m.log10(x[2]) * a3)

# regression mode
m.options.IMODE = 2

# optimize
m.solve(disp=True, GUI=False)

# print parameters
print('Optimized, a = ', str(a1.value.value[0]), str(a2.value[0]), str(a3.value[0]))

plt.plot(y.value, ym, 'bo')
plt.plot([0,max(ym)],[0,max(ym)],'r-')
plt.show()

[APMonitor]

This is a good question for StackOverflow. Could you post it there with tag [gekko]?

https://stackoverflow.com/questions/tagged/gekko

[kapkirl]

Thank you! Done https://stackoverflow.com/questions/57726954/what-is-the-correct-way-handle-with-multidimensional-array-in-gekko-nonlinear-re/57727056#57727056

[jpatria]

@APMonitor , I'd like to perform a linear regression with the same dataset as above, but when I do so, my adapted code gives me all 0s for my coefficients. i.e. i want to solve y==b + b1x1 + b2x2 + b3*x3 ...

Would you be able to clarify the correct way of formulating the equation and setting up the FV?

[APMonitor]

Here are a few example problems for regression: https://apmonitor.com/che263/index.php/Main/PythonDataRegression If you don't have constraints on the coefficients then there are many options in Python besides Gekko: https://github.com/APMonitor/data_science/blob/master/06.%20Regression.ipynb Here are a few more examples in Gekko: http://apmonitor.com/do/index.php/Main/DynamicEstimation (see examples 3 and 4).