polynomials

I'm using R to create a linear regression model having orthogonal polynomial. My model is: fit=lm(log(UFB2_BITRATE_REF3) ~ poly(QPB2_REF3,2) + B2DBSA_REF3,data=UFB) UFB2_FPS_REF1= 29.98 27.65 26.30 25.69 24.68 23.07 22.96 22.16 21.51 20.75 20.75 26.15 24.59 22.91 21.02 19.59 18.80 18.21 17.07 16.74 15.98 15.80 QPB2_REF1 = 36 34 32 30 28 26 24 22 20 18 16 36 34 32 30 28 26 24 22 20 18 16 B2DBSA_REF1 = DOFFSOFF DOFFSOFF DOFFSOFF DOFFSOFF DOFFSOFF DOFFSOFF DOFFSOFF DOFFSOFF DOFFSOFF DOFFSOFF DOFFSOFF DONSON DONSON DONSON DONSON DONSON DONSON DONSON DONSON DONSON DONSON DONSON Levels: DOFFSOFF

I'm trying to implement the idea I have suggested here , for Cauchy product of multivariate finite power series (i.e. polynomials) represented as NumPy ndarrays. numpy.convolve does the job for 1D arrays, respectively. But to my best knowledge there is no implementations of convolution for arbitrary dimensional arrays. In the above link, I have suggested the equation: for convolution of two n dimensional arrays Phi of shape P=[p1,...,pn] and Psi of the shape Q=[q1,...,qn] , where: omega s are the elements of n dimensional array Omega of the shape O=P+Q-1 <A,B>_F is the generalization of

For instance 3x^4 - 17x^2 - 3x + 5. Each term of the polynomial can be represented as a pair of integers (coefficient,exponent). The polynomial itself is then a list of such pairs like [(3,4), (-17,2), (-3,1), (5,0)] for the polynomial as shown. Zero polynomial, 0, is represented as the empty list [] , since it has no terms with nonzero coefficients. I want to write two functions to add and multiply two input polynomials with the same representation of tuple (coefficient, exponent): addpoly(p1, p2) multpoly(p1, p2) Test Cases: addpoly([(4,3),(3,0)], [(-4,3),(2,1)]) should give [(2, 1),(3, 0)]

I have some data that doesn't fit a linear regression, In fact should fit 'exactly' a quadratic function: P = R*I**2 I'm miking this: model = sklearn.linear_model.LinearRegression() X = alambres[alambre]['mediciones'][x].reshape(-1, 1) Y = alambres[alambre]['mediciones'][y].reshape(-1, 1) model.fit(X,Y) Is there any chance to solve it by doing something like: model.fit([X,X**2],Y) ? You can use numpy's polyfit . import numpy as np from matplotlib import pyplot as plt X = np.linspace(0, 100, 50) Y = 23.24 + 2.2*X + 0.24*(X**2) + 10*np.random.randn(50) #added some noise coefs = np.polyfit(X, Y,

I've found polynomial coefficients from my data: R <- c(0.256,0.512,0.768,1.024,1.28,1.437,1.594,1.72,1.846,1.972,2.098,2.4029) Ic <- c(1.78,1.71,1.57,1.44,1.25,1.02,0.87,0.68,0.54,0.38,0.26,0.17) NN <- 3 ft <- lm(Ic ~ poly(R, NN, raw = TRUE)) pc <- coef(ft) So I can create a polynomial function: f1 <- function(x) pc[1] + pc[2] * x + pc[3] * x ^ 2 + pc[4] * x ^ 3 And for example, take a derivative: g1 <- Deriv(f1) How to create a universal function so that it doesn't have to be rewritten for every new polynomial degree NN ? My original answer may not be what you really want, as it was

I'm trying to get my head around the use of the tilde operator, and associated functions. My 1st question is why does I() need to be used to specify arithmetic operators? For example, these 2 plots generate different results (the former having a straight line, and the latter the expected curve) x <- c(1:100) y <- seq(0.1,10,0.1) plot(y~x^3) plot(y~I(x^3)) further, both of the following plots also generate the expected result plot(x^3, y) plot(I(x^3), y) My second question is, perhaps the examples I've been using are too simple, but I don't understand where ~ should actually be used. The issue

I haven't been able to find an answer to this question, largely because googling anything with a standalone letter (like "I") causes issues. What does the "I" do in a model like this? data(rock) lm(area~I(peri - mean(peri)), data = rock) Considering that the following does NOT work: lm(area ~ (peri - mean(peri)), data = rock) and that this does work: rock$peri - mean(rock$peri) Any key words on how to research this myself would also be very helpful. I isolates or insulates the contents of I( ... ) from the gaze of R's formula parsing code. It allows the standard R operators to work as they