py-optim | Gradient-based optimization algorithms in Python | Computer Vision library

I am dealing with multivariate regression problems. My dataset is something like X = (nsample, nx) and Y = (nsample, ny). nx and ny may vary based on different dataset of different case to study, so they should be general in the code.

I would like to determine the coefficients for the multivariate polynomial regression minimizing the root mean square error. I thought to split the problem in ny different regressions, so for each of them my dataset is X = (nsample, nx) and Y = (nsample, 1). So, for each depended variable (Uj) the second order polynomial has the following form:

I coded the function in python as:

I'm trying to fit a function using SciPy's optimize.curve_fit to some scattered data, but I need the area under the fitted curve to be the same as that calculated based on the scattered data, and also that the curve passes through the initial and end points of the data. In order to do that, I am using the area (integral) defined by the scattered data in a penalization formulation as in this answer, while weighing the fit with the parameter sigma as proposed here.

Unfortunately, I can't get my fit to pass through the initial and end points when including the integral constraint. If I disregard the integral constraint, the fit works fine and passes through the point. Is it not possible to satisfy both the integral and points constraint? I am using Python 3.7.10 on Windows 10.

I am learning how to use GEKKO for kinetic parameter estimation based on laboratory batch reactor data, which essentially consists of the concentration profiles of three species A, C, and P. For the purposes of my question, I am using a model that I previously featured in a question related to parameter estimation from a single data set.

My ultimate goal is to be able to use multiple experimental runs for parameter estimation, leveraging data that may be collected at different temperatures, species concentrations, etc. Due to the independent nature of individual batch reactor experiments, each data set features samples collected at different time points. These different time points (and in the future, different temperatures for instance) are difficult for me to implement into a GEKKO model, as I previosly used the experimental data collection time points as the m.time parameter for the GEKKO model. (See end of post for code) I have solved problems like this in the past with gPROMS and Athena Visual Studio.

To illustrate my problem, I generated an artificial data set of 'experimental' data from my original model by introducing noise to the species concentration profiles, and shifting the experimental time points slightly. I then combined all data sets of the same experimental species into new arrays featuring multiple columns. My thought process here was that GEKKO would carry out the parameter estimation by using the experimental data of each corresponding column of the arrays, so that times_comb[:,0] would be related to A_comb[:,0] while times_comb[:,1] would be related to A_comb[:,1].

When I attempt to run the GEKKO model, the system does obtain a solution for the parameter estimation, but it is unclear to me if the problem solution is reasonable, as I notice that the GEKKO Variables A, B, C, and P are 34 element vectors, which is double the elements in each of the experimental data sets. I presume GEKKO is somehow combining both columns of the time and Parameter vectors during model setup that leads to those 34 element variables? I am also concerned that during this combination of the columns of each input parameter, that the relationship between a certain time point and the collected species information is lost.

How could I improve the use of multiple data sets that GEKKO can simultaneously use for parameter estimation, with the consideration that the time points of each data set may be different? I looked on the GEKKO documentation examples as well as the APMonitor website, but I could not find examples featuring multiple data sets that I could use for guidance, as I am fairly new to the GEKKO package.

Thank you for your time reading my question and for any help/ideas you may have.

Code below:

I am trying to fit a 2D Gaussian with an offset to a 2D array. The code is based on this thread here (which was written for Python2 while I am using Python3, therefore some changes were necessary to make it run somewhat):

So I have a problem and I'm a little bit lost at this point. So any input would be greatly appreciated, as I'm really struggeling right now ^^!

I have a model I want to check / optimise using some experimental data I got.

Generally speaking, my model takes two inputs (let's call say: time and temperature) and has 8 variables (x0-x7). The model generates two outputs (out1 and out2).

Each set of my experimental data gives me 4 sets of information I can use for my optimisation: 2 inputs (time and temperature) and 2 experimental results (result1 and result2).

Ultimately I want to minimize the difference between result1 & out1 and result2 & out2. So basically minimizing two residuals with several sets of data which are affected by 8 parameters which they all have in common (x0-x7).

I have some bounds for the parameters x0-x7 which can help, but besides that no real constraints.

So far I have tried using scipy.minimize with an iteration through my experimental result datasets like so (very schematic):

I asked similar questions in January and April that @Miłosz Wieczór and @Joe were kind enough to show interest in. Now, I am facing a similar but different problem because I need to do a joint-fit with multiple equations and inputs in order to get the universal solutions for two parameters fc and alpha. My code (which is based on the answers from the previous questions) is as follows:

When using Scipy's fmin function, I keep encountering the error message: ValueError: setting an array element with a sequence I have seen that this question has been asked already some times, and I have read interesting posts such as:

• ValueError: setting an array element with a sequence
• Scipy optimize fmin ValueError: setting an array element with a sequence
• Scipy minimize fmin - problems with syntax

..and have tried implementing the suggested solutions, such as adding '*args' to the cost function, appending the variables in the cost function to a list and vectorizing the variables. But nothing has worked for me so far.

I am quite new to programming in Python, so it is possible that I have read the solution and not known how to apply it.

A simplified version of the code, which I used to try to find the problem, is as follows:

I am interesting in knowing the phase shift between two sine-waves type. For that I am trying to fit each wave with scipy.cuve_fit. I have been following this post. However I obtain negative amplitudes and the phase shift looks like forwarded pi radians sometimes.

The code that I am using is that one below:

I'm looking for a Python algorithm to find the root of a function f(x) using bisection, equivalent to scipy.optimize.bisect, but allowing for discontinuities (jumps) in f. The function f is weakly monotonous.

It would be nice but not necessary for the algorithm to flag if the crossing (root) is directly 'at' a jump, and in this case to return the exact value x at which the relevant jump occurs (i.e. say the x for which sign(f(x-e)) != sign(f(x+e)) and abs(f(x-e)-f(x+e)>a for infinitesimal e>0 and non-infinitesimal a>0). It is also okay if instead the algorithm, for example, simply returns an x within a certain tolerance in this case.

As the function is only weakly monotonous, it can have flat areas, and theoretically these can occur 'at' the root, i.e. where f=0: f(x)=0 for an entire range, x in [x_0,x_1]. In this case again, nice but not necessary for the algo to flag this particularity, and to, say, ensure an x from the range [x_0,x_1] is returned.