# cfisher: Auto-constructing Fisher Information matrix In LDOD: Finding Locally D-optimal optimal designs for some nonlinear and generalized linear models.

## Description

Auto-constructs Fisher information matrix for nonlinear and generalized linear models as two R functions.

## Usage

 `1` ```cfisher(ymean, yvar, ndpoints, prec = 53) ```

## Arguments

 `ymean` a character string, formula of E(y) with specific satndard: characters `b1`, `b2`, `b3`, ... symbolize model parameters and `x1`, `x2`, `x3`, ... symbolize explanatory variables. See 'Examples'. `yvar` a character string, formula of Var(y) with specific standard as `ymean`. See 'Details' and 'Examples'. `ndpoints` number of design points. `prec` (optional) a number, the maximal precision to be used for D-efficiency calculation, in bite. Must be at least 2 (default 53).

## Details

If response variables have the same constant variance, for example σ^2, then `yvar` must be 1.

## Value

a list containing two closures:

 `fim` a function in which its arguments are vector of design points (x), vector of corresponding weights (w) and vector of parameters (β) and its output is Fisher information matrix. `fim.mpfr` a function in which its arguments are vector of design points (x), vector of corresponding weights (w) and vector of parameters (β) and its output is Fisher information matrix of class 'mpfrMatrix'.

For more details, see 'Note'.

## Note

This function is applicable for models that can be written as E(Y_i)=f(x_i,β) where y_i is the ith response variable, x_i is the observation vector of the ith explanatory variables, β is the vector of parameters and f is a continuous and differentiable function with respect to β. In addition, response variables must be independent with distributions that belong to the Natural exponential family. Logistic,Poisson, Negative Binomial, Exponential, Richards, Weibull, Log-linear, Inverse Quadratic and Michaelis-Menten are examples of these models.

Consider a p-parameter model and a design ξ that contains n m-dimensional points. Then

x = (x_1, x_2, …, x_i, …, x_n),

w = (w_1, w_2,…, w_n),

β = (β_1, β_2, …, β_p),

where x_i = (x_{i1}, x_{i2}, …, x_{im}) is the ith design point.

## Author(s)

Ehsan Masoudi, Majid Sarmad and Hooshang Talebi

## References

Masoudi, E., Sarmad, M. and Talebi, H. 2012, An Almost General Code in R to Find Optimal Design, In Proceedings of the 1st ISM International Statistical Conference 2012, 292-297.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97``` ```## Logistic dose response model ymean <- "(1/(exp(-b2 * (x1 - b1)) + 1))" yvar <- "(1/(exp(-b2 * (x1 - b1)) + 1)) * (1 - (1/(exp(-b2 * (x1 - b1)) + 1)))" res <- cfisher(ymean, yvar, ndpoints = 2, prec = 54) # res\$fim is Fisher information matrix for a two-points design res\$fim(x = c(x11 = 2, x21 = 3), w = c(w1 = .5, w2 = .5), b = c(b1 = .9, b2 = .8)) # res\$fim is Fisher information matrix for a two-points design with 54 precision res\$fim.mpfr(x = c(x11 = 2, x21 = 3), w = c(w1 = .5, w2 = .5), b = c(b1 = .9, b2 = .8)) # Fisher information matrix for model: fim<- cfisher(ymean, yvar, ndpoints = 1, prec = 54) res\$fim(x = c(x11 = 2), w = c(w1 = 1), b = c(b1 = .9, b2 = .8)) ## posison with E(y) = exp(b1 + b2 * x1 + b3 * x1^2 + b4 * x2 +b5 * x2^2 + b6 * x1 * x2) ymean <- yvar <- "exp(b1 + b2 * x1 + b3 * x1^2 + b4 * x2 +b5 * x2^2 + b6 * x1 * x2)" fim <- cfisher(ymean, yvar, ndpoints = 6, prec = 54) # res\$fim is Fisher information matrix for a six-points design res\$fim(x = c(1:12), w = rep(1/6, 6), b = c(1:6)) ## NAN # res\$fim.mpfr is Fisher information matrix for a six-points design with 53 precision res\$fim.mpfr(x = c(1:12), w = rep(1/6, 6), b = c(1:6)) ## Linear regression with two indeoendent varibales (the design points are two-dimensional) ymean <- "b1 + b2 * x1 + b3 * x2" yvar = "1" res <- cfisher(ymean, yvar, ndpoints = 3, prec = 54) res\$fim(x = c(1:6), w = c(.3, .3, .3)) res\$fim.mpfr(x = c(1:6), w = c(.3, .3, .3)) ## Logistic model: ymean <- "1/(exp(-b1 - b2 * x1) + 1)" yvar <- "(1/(exp(-b1 - b2 * x1) + 1)) * (1 - (1/(exp(-b1 - b2 * x1) + 1)))" cfisher(ymean, yvar, ndpoints = 2, prec = 54) ## Poisson model: ymean <- yvar <- "exp(b1 + b2 * x1)" cfisher(ymean, yvar, ndpoints = 2, prec = 54) ## Poisson dose response model: ymean <- yvar <- "b1 * exp(-b2 * x1)" cfisher(ymean, yvar, ndpoints = 2, prec = 54) ## Inverse Quadratic model: ymean <- "(b1 * x1)/(b2 + x1 + b3 * (x1)^2)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 3, prec = 54) # ymean <- "x1/(b1 + b2 * x1 + b3 * (x1)^2)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 3, prec = 54) ## Weibull model: ymean <- "b1 - b2 * exp(-b3 * x1^b4)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 4, prec = 54) ## Richards model: ymean <- "b1/(1 + b2 * exp(-b3 * x1))^b4" yvar <- "1" cfisher(ymean, yvar, ndpoints = 4, prec = 54) ## Michaelis-Menten model: ymean <- "(b1 * x1)/(1 + b2 * x1)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 2, prec = 54) # ymean <- "(b1 * x1)/(b2 + x1)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 2, prec = 54) # ymean <- "x1/(b1 + b2 * x1)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 2, prec = 54) ## log-linear model ymean <- "b1 + b2 * log(x1 + b3)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 3, prec = 54) ## Exponential model: ymean <- "b1 + b2 * exp(x1/b3)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 3, prec = 54) ## Emax model: ymean <- "b1 + (b2 * x1)/(x1 + b3)" yvar <- "1" cfisher(ymean, yvar, ndpoints = 3, prec = 54) ## Negative binomial model Y ~ NB(E(Y), theta) where E(Y) = b1*exp(-b2*x1): theta = 5 ymean <- "b1 * exp(-b2 * x1)" yvar <- paste("b1 * exp(-b2 * x1) * (1 + (1/", theta, ") * b1 * exp(-b2 * x1))", sep = "") cfisher(ymean, yvar, ndpoints = 3, prec = 54) ```

### Example output

```Loading required package: Rsolnp

Attaching package: 'gmp'

The following objects are masked from 'package:base':

%*%, apply, crossprod, matrix, tcrossprod

C code of R package 'Rmpfr': GMP using 64 bits per limb

Attaching package: 'Rmpfr'

The following objects are masked from 'package:stats':

dbinom, dnorm, dpois, pnorm

The following objects are masked from 'package:base':

cbind, pmax, pmin, rbind

[,1]       [,2]
[1,]  0.1086851 -0.2024087
[2,] -0.2024087  0.4173492
'mpfrMatrix' of dim(.) =  (2, 2) of precision  54   bits
[,1]                  [,2]
[1,]  0.108685136448971514 -0.202408655633780798
[2,] -0.202408655633780798  0.417349208164616625
[,1] [,2]
[1,]   NA   NA
[2,]   NA   NA
[,1]        [,2]
[1,]  0.23666239 -0.03499786
[2,] -0.03499786  0.01749893
'mpfrMatrix' of dim(.) =  (2, 2) of precision  54   bits
[,1]                   [,2]
[1,]   0.236662390269004305 -0.0349978618011688274
[2,] -0.0349978618011688239  0.0174989309005844137
[,1] [,2] [,3]
[1,]  0.9  2.7  3.6
[2,]  2.7 10.5 13.2
[3,]  3.6 13.2 16.8
'mpfrMatrix' of dim(.) =  (3, 3) of precision  54   bits
[,1]                 [,2]                [,3]
[1,] 0.899999999999999967 2.69999999999999996 3.59999999999999987
[2,]  2.69999999999999996 10.5000000000000000 13.1999999999999993
[3,]  3.59999999999999987 13.1999999999999993 16.8000000000000007
\$fim
function (x = c(x11, x21), w = c(w1, w2), b = c(b1, b2))
{
Mat = matrix(c(+w[1] * 1/((1/(exp(-b[1] - b[2] * x[1]) +
1)) * (1 - (1/(exp(-b[1] - b[2] * x[1]) + 1)))) * exp(-b[1] -
b[2] * x[1])/(exp(-b[1] - b[2] * x[1]) + 1)^2 * exp(-b[1] -
b[2] * x[1])/(exp(-b[1] - b[2] * x[1]) + 1)^2 + w[2] *
1/((1/(exp(-b[1] - b[2] * x[2]) + 1)) * (1 - (1/(exp(-b[1] -
b[2] * x[2]) + 1)))) * exp(-b[1] - b[2] * x[2])/(exp(-b[1] -
b[2] * x[2]) + 1)^2 * exp(-b[1] - b[2] * x[2])/(exp(-b[1] -
b[2] * x[2]) + 1)^2, +w[1] * 1/((1/(exp(-b[1] - b[2] *
x[1]) + 1)) * (1 - (1/(exp(-b[1] - b[2] * x[1]) + 1)))) *
exp(-b[1] - b[2] * x[1]) * x[1]/(exp(-b[1] - b[2] * x[1]) +
1)^2 * exp(-b[1] - b[2] * x[1])/(exp(-b[1] - b[2] * x[1]) +
1)^2 + w[2] * 1/((1/(exp(-b[1] - b[2] * x[2]) + 1)) *
(1 - (1/(exp(-b[1] - b[2] * x[2]) + 1)))) * exp(-b[1] -
b[2] * x[2]) * x[2]/(exp(-b[1] - b[2] * x[2]) + 1)^2 *
exp(-b[1] - b[2] * x[2])/(exp(-b[1] - b[2] * x[2]) +
1)^2, +w[1] * 1/((1/(exp(-b[1] - b[2] * x[1]) + 1)) *
(1 - (1/(exp(-b[1] - b[2] * x[1]) + 1)))) * exp(-b[1] -
b[2] * x[1])/(exp(-b[1] - b[2] * x[1]) + 1)^2 * exp(-b[1] -
b[2] * x[1]) * x[1]/(exp(-b[1] - b[2] * x[1]) + 1)^2 +
w[2] * 1/((1/(exp(-b[1] - b[2] * x[2]) + 1)) * (1 - (1/(exp(-b[1] -
b[2] * x[2]) + 1)))) * exp(-b[1] - b[2] * x[2])/(exp(-b[1] -
b[2] * x[2]) + 1)^2 * exp(-b[1] - b[2] * x[2]) *
x[2]/(exp(-b[1] - b[2] * x[2]) + 1)^2, +w[1] * 1/((1/(exp(-b[1] -
b[2] * x[1]) + 1)) * (1 - (1/(exp(-b[1] - b[2] * x[1]) +
1)))) * exp(-b[1] - b[2] * x[1]) * x[1]/(exp(-b[1] -
b[2] * x[1]) + 1)^2 * exp(-b[1] - b[2] * x[1]) * x[1]/(exp(-b[1] -
b[2] * x[1]) + 1)^2 + w[2] * 1/((1/(exp(-b[1] - b[2] *
x[2]) + 1)) * (1 - (1/(exp(-b[1] - b[2] * x[2]) + 1)))) *
exp(-b[1] - b[2] * x[2]) * x[2]/(exp(-b[1] - b[2] * x[2]) +
1)^2 * exp(-b[1] - b[2] * x[2]) * x[2]/(exp(-b[1] - b[2] *
x[2]) + 1)^2), 2, 2)
d = Mat
return(d)
}
<environment: 0x52b78f8>

\$fim.mpfr
function (x = c(x11, x21), w = c(w1, w2), b = c(b1, b2))
{
Mat = new("mpfrMatrix", c(+mpfr(w[1], precBits = 54) * 1/((1/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + 1)) * (1 - (1/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) +
1)))) * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54))/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) +
1)^2 * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54))/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) +
1)^2 + mpfr(w[2], precBits = 54) * 1/((1/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) + 1)) * (1 - (1/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) +
1)))) * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54))/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) +
1)^2 * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54))/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) +
1)^2, +mpfr(w[1], precBits = 54) * 1/((1/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + 1)) * (1 - (1/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) +
1)))) * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54)) * mpfr(x[1], precBits = 54)/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + 1)^2 * exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54))/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + 1)^2 + mpfr(w[2], precBits = 54) *
1/((1/(exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54)) + 1)) * (1 - (1/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) + 1)))) * exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) *
mpfr(x[2], precBits = 54)/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) +
1)^2 * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54))/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) +
1)^2, +mpfr(w[1], precBits = 54) * 1/((1/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + 1)) * (1 - (1/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) +
1)))) * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54))/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) +
1)^2 * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54)) * mpfr(x[1], precBits = 54)/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + 1)^2 + mpfr(w[2], precBits = 54) *
1/((1/(exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54)) + 1)) * (1 - (1/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) + 1)))) * exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54))/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) + 1)^2 * exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) *
mpfr(x[2], precBits = 54)/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) +
1)^2, +mpfr(w[1], precBits = 54) * 1/((1/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + 1)) * (1 - (1/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) +
1)))) * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54)) * mpfr(x[1], precBits = 54)/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + 1)^2 * exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) *
mpfr(x[1], precBits = 54)/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54)) +
1)^2 + mpfr(w[2], precBits = 54) * 1/((1/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) + 1)) * (1 - (1/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) +
1)))) * exp(-mpfr(b[1], precBits = 54) - mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54)) * mpfr(x[2], precBits = 54)/(exp(-mpfr(b[1],
precBits = 54) - mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) + 1)^2 * exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) *
mpfr(x[2], precBits = 54)/(exp(-mpfr(b[1], precBits = 54) -
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54)) +
1)^2), Dim = c(2L, 2L))
d = Mat
return(d)
}
<environment: 0x52b78f8>

\$fim
function (x = c(x11, x21), w = c(w1, w2), b = c(b1, b2))
{
Mat = matrix(c(+w[1] * 1/(exp(b[1] + b[2] * x[1])) * exp(b[1] +
b[2] * x[1]) * exp(b[1] + b[2] * x[1]) + w[2] * 1/(exp(b[1] +
b[2] * x[2])) * exp(b[1] + b[2] * x[2]) * exp(b[1] +
b[2] * x[2]), +w[1] * 1/(exp(b[1] + b[2] * x[1])) * exp(b[1] +
b[2] * x[1]) * x[1] * exp(b[1] + b[2] * x[1]) + w[2] *
1/(exp(b[1] + b[2] * x[2])) * exp(b[1] + b[2] * x[2]) *
x[2] * exp(b[1] + b[2] * x[2]), +w[1] * 1/(exp(b[1] +
b[2] * x[1])) * exp(b[1] + b[2] * x[1]) * exp(b[1] +
b[2] * x[1]) * x[1] + w[2] * 1/(exp(b[1] + b[2] * x[2])) *
exp(b[1] + b[2] * x[2]) * exp(b[1] + b[2] * x[2]) * x[2],
+w[1] * 1/(exp(b[1] + b[2] * x[1])) * exp(b[1] + b[2] *
x[1]) * x[1] * exp(b[1] + b[2] * x[1]) * x[1] + w[2] *
1/(exp(b[1] + b[2] * x[2])) * exp(b[1] + b[2] * x[2]) *
x[2] * exp(b[1] + b[2] * x[2]) * x[2]), 2, 2)
d = Mat
return(d)
}
<environment: 0x246d000>

\$fim.mpfr
function (x = c(x11, x21), w = c(w1, w2), b = c(b1, b2))
{
Mat = new("mpfrMatrix", c(+mpfr(w[1], precBits = 54) * 1/(exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54))) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + mpfr(w[2], precBits = 54) * 1/(exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54))) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54)) * exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)), +mpfr(w[1], precBits = 54) * 1/(exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54))) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * mpfr(x[1],
precBits = 54) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) + mpfr(w[2],
precBits = 54) * 1/(exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54))) * exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) * mpfr(x[2], precBits = 54) * exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)), +mpfr(w[1], precBits = 54) * 1/(exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54))) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) * mpfr(x[1], precBits = 54) + mpfr(w[2],
precBits = 54) * 1/(exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54))) * exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54)) * mpfr(x[2],
precBits = 54), +mpfr(w[1], precBits = 54) * 1/(exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54))) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * mpfr(x[1],
precBits = 54) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * mpfr(x[1],
precBits = 54) + mpfr(w[2], precBits = 54) * 1/(exp(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54))) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54)) * mpfr(x[2],
precBits = 54) * exp(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54)) * mpfr(x[2],
precBits = 54)), Dim = c(2L, 2L))
d = Mat
return(d)
}
<environment: 0x246d000>

\$fim
function (x = c(x11, x21), w = c(w1, w2), b = c(b1, b2))
{
Mat = matrix(c(+w[1] * 1/(b[1] * exp(-b[2] * x[1])) * exp(-b[2] *
x[1]) * exp(-b[2] * x[1]) + w[2] * 1/(b[1] * exp(-b[2] *
x[2])) * exp(-b[2] * x[2]) * exp(-b[2] * x[2]), +w[1] *
1/(b[1] * exp(-b[2] * x[1])) * -(b[1] * (exp(-b[2] *
x[1]) * x[1])) * exp(-b[2] * x[1]) + w[2] * 1/(b[1] *
exp(-b[2] * x[2])) * -(b[1] * (exp(-b[2] * x[2]) * x[2])) *
exp(-b[2] * x[2]), +w[1] * 1/(b[1] * exp(-b[2] * x[1])) *
exp(-b[2] * x[1]) * -(b[1] * (exp(-b[2] * x[1]) * x[1])) +
w[2] * 1/(b[1] * exp(-b[2] * x[2])) * exp(-b[2] * x[2]) *
-(b[1] * (exp(-b[2] * x[2]) * x[2])), +w[1] * 1/(b[1] *
exp(-b[2] * x[1])) * -(b[1] * (exp(-b[2] * x[1]) * x[1])) *
-(b[1] * (exp(-b[2] * x[1]) * x[1])) + w[2] * 1/(b[1] *
exp(-b[2] * x[2])) * -(b[1] * (exp(-b[2] * x[2]) * x[2])) *
-(b[1] * (exp(-b[2] * x[2]) * x[2]))), 2, 2)
d = Mat
return(d)
}
<environment: 0x3e66540>

\$fim.mpfr
function (x = c(x11, x21), w = c(w1, w2), b = c(b1, b2))
{
Mat = new("mpfrMatrix", c(+mpfr(w[1], precBits = 54) * 1/(mpfr(b[1],
precBits = 54) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54))) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + mpfr(w[2], precBits = 54) * 1/(mpfr(b[1],
precBits = 54) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54))) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)), +mpfr(w[1], precBits = 54) * 1/(mpfr(b[1],
precBits = 54) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54))) * -(mpfr(b[1], precBits = 54) * (exp(-mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * mpfr(x[1],
precBits = 54))) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) + mpfr(w[2], precBits = 54) * 1/(mpfr(b[1],
precBits = 54) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54))) * -(mpfr(b[1], precBits = 54) * (exp(-mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54)) * mpfr(x[2],
precBits = 54))) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)), +mpfr(w[1], precBits = 54) * 1/(mpfr(b[1],
precBits = 54) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54))) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54)) * -(mpfr(b[1], precBits = 54) * (exp(-mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * mpfr(x[1],
precBits = 54))) + mpfr(w[2], precBits = 54) * 1/(mpfr(b[1],
precBits = 54) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54))) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54)) * -(mpfr(b[1], precBits = 54) * (exp(-mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54)) * mpfr(x[2],
precBits = 54))), +mpfr(w[1], precBits = 54) * 1/(mpfr(b[1],
precBits = 54) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54))) * -(mpfr(b[1], precBits = 54) * (exp(-mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * mpfr(x[1],
precBits = 54))) * -(mpfr(b[1], precBits = 54) * (exp(-mpfr(b[2],
precBits = 54) * mpfr(x[1], precBits = 54)) * mpfr(x[1],
precBits = 54))) + mpfr(w[2], precBits = 54) * 1/(mpfr(b[1],
precBits = 54) * exp(-mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54))) * -(mpfr(b[1], precBits = 54) * (exp(-mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54)) * mpfr(x[2],
precBits = 54))) * -(mpfr(b[1], precBits = 54) * (exp(-mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54)) * mpfr(x[2],
precBits = 54)))), Dim = c(2L, 2L))
d = Mat
return(d)
}
<environment: 0x3e66540>

\$fim
function (x = c(x11, x21, x31), w = c(w1, w2, w3), b = c(b1,
b2, b3))
{
Mat = matrix(c(+w[1] * 1/(1) * x[1]/(b[2] + x[1] + b[3] *
(x[1])^2) * x[1]/(b[2] + x[1] + b[3] * (x[1])^2) + w[2] *
1/(1) * x[2]/(b[2] + x[2] + b[3] * (x[2])^2) * x[2]/(b[2] +
x[2] + b[3] * (x[2])^2) + w[3] * 1/(1) * x[3]/(b[2] +
x[3] + b[3] * (x[3])^2) * x[3]/(b[2] + x[3] + b[3] *
(x[3])^2), +w[1] * 1/(1) * -((b[1] * x[1])/(b[2] + x[1] +
b[3] * (x[1])^2)^2) * x[1]/(b[2] + x[1] + b[3] * (x[1])^2) +
w[2] * 1/(1) * -((b[1] * x[2])/(b[2] + x[2] + b[3] *
(x[2])^2)^2) * x[2]/(b[2] + x[2] + b[3] * (x[2])^2) +
w[3] * 1/(1) * -((b[1] * x[3])/(b[2] + x[3] + b[3] *
(x[3])^2)^2) * x[3]/(b[2] + x[3] + b[3] * (x[3])^2),
+w[1] * 1/(1) * -((b[1] * x[1]) * (x[1])^2/(b[2] + x[1] +
b[3] * (x[1])^2)^2) * x[1]/(b[2] + x[1] + b[3] *
(x[1])^2) + w[2] * 1/(1) * -((b[1] * x[2]) * (x[2])^2/(b[2] +
x[2] + b[3] * (x[2])^2)^2) * x[2]/(b[2] + x[2] +
b[3] * (x[2])^2) + w[3] * 1/(1) * -((b[1] * x[3]) *
(x[3])^2/(b[2] + x[3] + b[3] * (x[3])^2)^2) * x[3]/(b[2] +
x[3] + b[3] * (x[3])^2), +w[1] * 1/(1) * x[1]/(b[2] +
x[1] + b[3] * (x[1])^2) * -((b[1] * x[1])/(b[2] +
x[1] + b[3] * (x[1])^2)^2) + w[2] * 1/(1) * x[2]/(b[2] +
x[2] + b[3] * (x[2])^2) * -((b[1] * x[2])/(b[2] +
x[2] + b[3] * (x[2])^2)^2) + w[3] * 1/(1) * x[3]/(b[2] +
x[3] + b[3] * (x[3])^2) * -((b[1] * x[3])/(b[2] +
x[3] + b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -((b[1] *
x[1])/(b[2] + x[1] + b[3] * (x[1])^2)^2) * -((b[1] *
x[1])/(b[2] + x[1] + b[3] * (x[1])^2)^2) + w[2] *
1/(1) * -((b[1] * x[2])/(b[2] + x[2] + b[3] * (x[2])^2)^2) *
-((b[1] * x[2])/(b[2] + x[2] + b[3] * (x[2])^2)^2) +
w[3] * 1/(1) * -((b[1] * x[3])/(b[2] + x[3] + b[3] *
(x[3])^2)^2) * -((b[1] * x[3])/(b[2] + x[3] +
b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -((b[1] *
x[1]) * (x[1])^2/(b[2] + x[1] + b[3] * (x[1])^2)^2) *
-((b[1] * x[1])/(b[2] + x[1] + b[3] * (x[1])^2)^2) +
w[2] * 1/(1) * -((b[1] * x[2]) * (x[2])^2/(b[2] +
x[2] + b[3] * (x[2])^2)^2) * -((b[1] * x[2])/(b[2] +
x[2] + b[3] * (x[2])^2)^2) + w[3] * 1/(1) * -((b[1] *
x[3]) * (x[3])^2/(b[2] + x[3] + b[3] * (x[3])^2)^2) *
-((b[1] * x[3])/(b[2] + x[3] + b[3] * (x[3])^2)^2),
+w[1] * 1/(1) * x[1]/(b[2] + x[1] + b[3] * (x[1])^2) *
-((b[1] * x[1]) * (x[1])^2/(b[2] + x[1] + b[3] *
(x[1])^2)^2) + w[2] * 1/(1) * x[2]/(b[2] + x[2] +
b[3] * (x[2])^2) * -((b[1] * x[2]) * (x[2])^2/(b[2] +
x[2] + b[3] * (x[2])^2)^2) + w[3] * 1/(1) * x[3]/(b[2] +
x[3] + b[3] * (x[3])^2) * -((b[1] * x[3]) * (x[3])^2/(b[2] +
x[3] + b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -((b[1] *
x[1])/(b[2] + x[1] + b[3] * (x[1])^2)^2) * -((b[1] *
x[1]) * (x[1])^2/(b[2] + x[1] + b[3] * (x[1])^2)^2) +
w[2] * 1/(1) * -((b[1] * x[2])/(b[2] + x[2] + b[3] *
(x[2])^2)^2) * -((b[1] * x[2]) * (x[2])^2/(b[2] +
x[2] + b[3] * (x[2])^2)^2) + w[3] * 1/(1) * -((b[1] *
x[3])/(b[2] + x[3] + b[3] * (x[3])^2)^2) * -((b[1] *
x[3]) * (x[3])^2/(b[2] + x[3] + b[3] * (x[3])^2)^2),
+w[1] * 1/(1) * -((b[1] * x[1]) * (x[1])^2/(b[2] + x[1] +
b[3] * (x[1])^2)^2) * -((b[1] * x[1]) * (x[1])^2/(b[2] +
x[1] + b[3] * (x[1])^2)^2) + w[2] * 1/(1) * -((b[1] *
x[2]) * (x[2])^2/(b[2] + x[2] + b[3] * (x[2])^2)^2) *
-((b[1] * x[2]) * (x[2])^2/(b[2] + x[2] + b[3] *
(x[2])^2)^2) + w[3] * 1/(1) * -((b[1] * x[3]) *
(x[3])^2/(b[2] + x[3] + b[3] * (x[3])^2)^2) * -((b[1] *
x[3]) * (x[3])^2/(b[2] + x[3] + b[3] * (x[3])^2)^2)),
3, 3)
d = Mat
return(d)
}
<environment: 0x3bfdbc8>

\$fim.mpfr
function (x = c(x11, x21, x31), w = c(w1, w2, w3), b = c(b1,
b2, b3))
{
Mat = new("mpfrMatrix", c(+mpfr(w[1], precBits = 54) * 1/(1) *
mpfr(x[1], precBits = 54)/(mpfr(b[2], precBits = 54) +
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2) * mpfr(x[1], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[1], precBits = 54))^2) + mpfr(w[2],
precBits = 54) * 1/(1) * mpfr(x[2], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[2], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[2], precBits = 54))^2) * mpfr(x[2],
precBits = 54)/(mpfr(b[2], precBits = 54) + mpfr(x[2],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[2],
precBits = 54))^2) + mpfr(w[3], precBits = 54) * 1/(1) *
mpfr(x[3], precBits = 54)/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2) * mpfr(x[3], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[3], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[3], precBits = 54))^2), +mpfr(w[1],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[1], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) * mpfr(x[1], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[1], precBits = 54))^2) + mpfr(w[2],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[2], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) * mpfr(x[2], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[2], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[2], precBits = 54))^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[3], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2) * mpfr(x[3], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[3], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[3], precBits = 54))^2), +mpfr(w[1],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[1], precBits = 54)) * (mpfr(x[1], precBits = 54))^2/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
mpfr(x[1], precBits = 54)/(mpfr(b[2], precBits = 54) +
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2) + mpfr(w[2], precBits = 54) *
1/(1) * -((mpfr(b[1], precBits = 54) * mpfr(x[2], precBits = 54)) *
(mpfr(x[2], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) * mpfr(x[2], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[2], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[2], precBits = 54))^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[3], precBits = 54)) * (mpfr(x[3], precBits = 54))^2/(mpfr(b[2],
precBits = 54) + mpfr(x[3], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2) *
mpfr(x[3], precBits = 54)/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2), +mpfr(w[1], precBits = 54) *
1/(1) * mpfr(x[1], precBits = 54)/(mpfr(b[2], precBits = 54) +
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2) * -((mpfr(b[1], precBits = 54) *
mpfr(x[1], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) + mpfr(w[2], precBits = 54) *
1/(1) * mpfr(x[2], precBits = 54)/(mpfr(b[2], precBits = 54) +
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2) * -((mpfr(b[1], precBits = 54) *
mpfr(x[2], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3], precBits = 54) *
1/(1) * mpfr(x[3], precBits = 54)/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2) * -((mpfr(b[1], precBits = 54) *
mpfr(x[3], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2), +mpfr(w[1], precBits = 54) *
1/(1) * -((mpfr(b[1], precBits = 54) * mpfr(x[1], precBits = 54))/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[1], precBits = 54))/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) +
mpfr(w[2], precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[2], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) * -((mpfr(b[1],
precBits = 54) * mpfr(x[2], precBits = 54))/(mpfr(b[2],
precBits = 54) + mpfr(x[2], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) +
mpfr(w[3], precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[3], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2) * -((mpfr(b[1],
precBits = 54) * mpfr(x[3], precBits = 54))/(mpfr(b[2],
precBits = 54) + mpfr(x[3], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2),
+mpfr(w[1], precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[1], precBits = 54)) * (mpfr(x[1], precBits = 54))^2/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[1], precBits = 54))/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) +
mpfr(w[2], precBits = 54) * 1/(1) * -((mpfr(b[1],
precBits = 54) * mpfr(x[2], precBits = 54)) *
(mpfr(x[2], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) * -((mpfr(b[1],
precBits = 54) * mpfr(x[2], precBits = 54))/(mpfr(b[2],
precBits = 54) + mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) +
mpfr(w[3], precBits = 54) * 1/(1) * -((mpfr(b[1],
precBits = 54) * mpfr(x[3], precBits = 54)) *
(mpfr(x[3], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2) * -((mpfr(b[1],
precBits = 54) * mpfr(x[3], precBits = 54))/(mpfr(b[2],
precBits = 54) + mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2),
+mpfr(w[1], precBits = 54) * 1/(1) * mpfr(x[1], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[1], precBits = 54))^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[1], precBits = 54)) *
(mpfr(x[1], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) + mpfr(w[2],
precBits = 54) * 1/(1) * mpfr(x[2], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[2], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[2], precBits = 54))^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[2], precBits = 54)) *
(mpfr(x[2], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3],
precBits = 54) * 1/(1) * mpfr(x[3], precBits = 54)/(mpfr(b[2],
precBits = 54) + mpfr(x[3], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[3], precBits = 54))^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[3], precBits = 54)) *
(mpfr(x[3], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2), +mpfr(w[1],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[1], precBits = 54))/(mpfr(b[2], precBits = 54) +
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) * -((mpfr(b[1],
precBits = 54) * mpfr(x[1], precBits = 54)) * (mpfr(x[1],
precBits = 54))^2/(mpfr(b[2], precBits = 54) + mpfr(x[1],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[1],
precBits = 54))^2)^2) + mpfr(w[2], precBits = 54) *
1/(1) * -((mpfr(b[1], precBits = 54) * mpfr(x[2],
precBits = 54))/(mpfr(b[2], precBits = 54) + mpfr(x[2],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[2],
precBits = 54))^2)^2) * -((mpfr(b[1], precBits = 54) *
mpfr(x[2], precBits = 54)) * (mpfr(x[2], precBits = 54))^2/(mpfr(b[2],
precBits = 54) + mpfr(x[2], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) +
mpfr(w[3], precBits = 54) * 1/(1) * -((mpfr(b[1],
precBits = 54) * mpfr(x[3], precBits = 54))/(mpfr(b[2],
precBits = 54) + mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[3], precBits = 54)) *
(mpfr(x[3], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2), +mpfr(w[1],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[1], precBits = 54)) * (mpfr(x[1], precBits = 54))^2/(mpfr(b[2],
precBits = 54) + mpfr(x[1], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[1], precBits = 54)) *
(mpfr(x[1], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) + mpfr(w[2],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[2], precBits = 54)) * (mpfr(x[2], precBits = 54))^2/(mpfr(b[2],
precBits = 54) + mpfr(x[2], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[2], precBits = 54)) *
(mpfr(x[2], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -((mpfr(b[1], precBits = 54) *
mpfr(x[3], precBits = 54)) * (mpfr(x[3], precBits = 54))^2/(mpfr(b[2],
precBits = 54) + mpfr(x[3], precBits = 54) + mpfr(b[3],
precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2) *
-((mpfr(b[1], precBits = 54) * mpfr(x[3], precBits = 54)) *
(mpfr(x[3], precBits = 54))^2/(mpfr(b[2], precBits = 54) +
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2)), Dim = c(3L,
3L))
d = Mat
return(d)
}
<environment: 0x3bfdbc8>

\$fim
function (x = c(x11, x21, x31), w = c(w1, w2, w3), b = c(b1,
b2, b3))
{
Mat = matrix(c(+w[1] * 1/(1) * -(x[1]/(b[1] + b[2] * x[1] +
b[3] * (x[1])^2)^2) * -(x[1]/(b[1] + b[2] * x[1] + b[3] *
(x[1])^2)^2) + w[2] * 1/(1) * -(x[2]/(b[1] + b[2] * x[2] +
b[3] * (x[2])^2)^2) * -(x[2]/(b[1] + b[2] * x[2] + b[3] *
(x[2])^2)^2) + w[3] * 1/(1) * -(x[3]/(b[1] + b[2] * x[3] +
b[3] * (x[3])^2)^2) * -(x[3]/(b[1] + b[2] * x[3] + b[3] *
(x[3])^2)^2), +w[1] * 1/(1) * -(x[1] * x[1]/(b[1] + b[2] *
x[1] + b[3] * (x[1])^2)^2) * -(x[1]/(b[1] + b[2] * x[1] +
b[3] * (x[1])^2)^2) + w[2] * 1/(1) * -(x[2] * x[2]/(b[1] +
b[2] * x[2] + b[3] * (x[2])^2)^2) * -(x[2]/(b[1] + b[2] *
x[2] + b[3] * (x[2])^2)^2) + w[3] * 1/(1) * -(x[3] *
x[3]/(b[1] + b[2] * x[3] + b[3] * (x[3])^2)^2) * -(x[3]/(b[1] +
b[2] * x[3] + b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -(x[1] *
(x[1])^2/(b[1] + b[2] * x[1] + b[3] * (x[1])^2)^2) *
-(x[1]/(b[1] + b[2] * x[1] + b[3] * (x[1])^2)^2) + w[2] *
1/(1) * -(x[2] * (x[2])^2/(b[1] + b[2] * x[2] + b[3] *
(x[2])^2)^2) * -(x[2]/(b[1] + b[2] * x[2] + b[3] * (x[2])^2)^2) +
w[3] * 1/(1) * -(x[3] * (x[3])^2/(b[1] + b[2] * x[3] +
b[3] * (x[3])^2)^2) * -(x[3]/(b[1] + b[2] * x[3] +
b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -(x[1]/(b[1] +
b[2] * x[1] + b[3] * (x[1])^2)^2) * -(x[1] * x[1]/(b[1] +
b[2] * x[1] + b[3] * (x[1])^2)^2) + w[2] * 1/(1) * -(x[2]/(b[1] +
b[2] * x[2] + b[3] * (x[2])^2)^2) * -(x[2] * x[2]/(b[1] +
b[2] * x[2] + b[3] * (x[2])^2)^2) + w[3] * 1/(1) * -(x[3]/(b[1] +
b[2] * x[3] + b[3] * (x[3])^2)^2) * -(x[3] * x[3]/(b[1] +
b[2] * x[3] + b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -(x[1] *
x[1]/(b[1] + b[2] * x[1] + b[3] * (x[1])^2)^2) * -(x[1] *
x[1]/(b[1] + b[2] * x[1] + b[3] * (x[1])^2)^2) + w[2] *
1/(1) * -(x[2] * x[2]/(b[1] + b[2] * x[2] + b[3] * (x[2])^2)^2) *
-(x[2] * x[2]/(b[1] + b[2] * x[2] + b[3] * (x[2])^2)^2) +
w[3] * 1/(1) * -(x[3] * x[3]/(b[1] + b[2] * x[3] + b[3] *
(x[3])^2)^2) * -(x[3] * x[3]/(b[1] + b[2] * x[3] +
b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -(x[1] * (x[1])^2/(b[1] +
b[2] * x[1] + b[3] * (x[1])^2)^2) * -(x[1] * x[1]/(b[1] +
b[2] * x[1] + b[3] * (x[1])^2)^2) + w[2] * 1/(1) * -(x[2] *
(x[2])^2/(b[1] + b[2] * x[2] + b[3] * (x[2])^2)^2) *
-(x[2] * x[2]/(b[1] + b[2] * x[2] + b[3] * (x[2])^2)^2) +
w[3] * 1/(1) * -(x[3] * (x[3])^2/(b[1] + b[2] * x[3] +
b[3] * (x[3])^2)^2) * -(x[3] * x[3]/(b[1] + b[2] *
x[3] + b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -(x[1]/(b[1] +
b[2] * x[1] + b[3] * (x[1])^2)^2) * -(x[1] * (x[1])^2/(b[1] +
b[2] * x[1] + b[3] * (x[1])^2)^2) + w[2] * 1/(1) * -(x[2]/(b[1] +
b[2] * x[2] + b[3] * (x[2])^2)^2) * -(x[2] * (x[2])^2/(b[1] +
b[2] * x[2] + b[3] * (x[2])^2)^2) + w[3] * 1/(1) * -(x[3]/(b[1] +
b[2] * x[3] + b[3] * (x[3])^2)^2) * -(x[3] * (x[3])^2/(b[1] +
b[2] * x[3] + b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -(x[1] *
x[1]/(b[1] + b[2] * x[1] + b[3] * (x[1])^2)^2) * -(x[1] *
(x[1])^2/(b[1] + b[2] * x[1] + b[3] * (x[1])^2)^2) +
w[2] * 1/(1) * -(x[2] * x[2]/(b[1] + b[2] * x[2] + b[3] *
(x[2])^2)^2) * -(x[2] * (x[2])^2/(b[1] + b[2] * x[2] +
b[3] * (x[2])^2)^2) + w[3] * 1/(1) * -(x[3] * x[3]/(b[1] +
b[2] * x[3] + b[3] * (x[3])^2)^2) * -(x[3] * (x[3])^2/(b[1] +
b[2] * x[3] + b[3] * (x[3])^2)^2), +w[1] * 1/(1) * -(x[1] *
(x[1])^2/(b[1] + b[2] * x[1] + b[3] * (x[1])^2)^2) *
-(x[1] * (x[1])^2/(b[1] + b[2] * x[1] + b[3] * (x[1])^2)^2) +
w[2] * 1/(1) * -(x[2] * (x[2])^2/(b[1] + b[2] * x[2] +
b[3] * (x[2])^2)^2) * -(x[2] * (x[2])^2/(b[1] + b[2] *
x[2] + b[3] * (x[2])^2)^2) + w[3] * 1/(1) * -(x[3] *
(x[3])^2/(b[1] + b[2] * x[3] + b[3] * (x[3])^2)^2) *
-(x[3] * (x[3])^2/(b[1] + b[2] * x[3] + b[3] * (x[3])^2)^2)),
3, 3)
d = Mat
return(d)
}
<environment: 0x227fc88>

\$fim.mpfr
function (x = c(x11, x21, x31), w = c(w1, w2, w3), b = c(b1,
b2, b3))
{
Mat = new("mpfrMatrix", c(+mpfr(w[1], precBits = 54) * 1/(1) *
-(mpfr(x[1], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-(mpfr(x[1], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) +
mpfr(w[2], precBits = 54) * 1/(1) * -(mpfr(x[2], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[2],
precBits = 54))^2)^2) * -(mpfr(x[2], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[2],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[2],
precBits = 54))^2)^2) + mpfr(w[3], precBits = 54) *
1/(1) * -(mpfr(x[3], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2) *
-(mpfr(x[3], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2),
+mpfr(w[1], precBits = 54) * 1/(1) * -(mpfr(x[1], precBits = 54) *
mpfr(x[1], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-(mpfr(x[1], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) +
mpfr(w[2], precBits = 54) * 1/(1) * -(mpfr(x[2],
precBits = 54) * mpfr(x[2], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) * -(mpfr(x[2],
precBits = 54)/(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) +
mpfr(w[3], precBits = 54) * 1/(1) * -(mpfr(x[3],
precBits = 54) * mpfr(x[3], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2) * -(mpfr(x[3],
precBits = 54)/(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2),
+mpfr(w[1], precBits = 54) * 1/(1) * -(mpfr(x[1], precBits = 54) *
(mpfr(x[1], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-(mpfr(x[1], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) +
mpfr(w[2], precBits = 54) * 1/(1) * -(mpfr(x[2],
precBits = 54) * (mpfr(x[2], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) * -(mpfr(x[2],
precBits = 54)/(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) +
mpfr(w[3], precBits = 54) * 1/(1) * -(mpfr(x[3],
precBits = 54) * (mpfr(x[3], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2) * -(mpfr(x[3],
precBits = 54)/(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2),
+mpfr(w[1], precBits = 54) * 1/(1) * -(mpfr(x[1], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[1],
precBits = 54))^2)^2) * -(mpfr(x[1], precBits = 54) *
mpfr(x[1], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) +
mpfr(w[2], precBits = 54) * 1/(1) * -(mpfr(x[2],
precBits = 54)/(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) *
-(mpfr(x[2], precBits = 54) * mpfr(x[2], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -(mpfr(x[3], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[3],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[3],
precBits = 54))^2)^2) * -(mpfr(x[3], precBits = 54) *
mpfr(x[3], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2),
+mpfr(w[1], precBits = 54) * 1/(1) * -(mpfr(x[1], precBits = 54) *
mpfr(x[1], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-(mpfr(x[1], precBits = 54) * mpfr(x[1], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) + mpfr(w[2],
precBits = 54) * 1/(1) * -(mpfr(x[2], precBits = 54) *
mpfr(x[2], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) *
-(mpfr(x[2], precBits = 54) * mpfr(x[2], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -(mpfr(x[3], precBits = 54) *
mpfr(x[3], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2) *
-(mpfr(x[3], precBits = 54) * mpfr(x[3], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2), +mpfr(w[1],
precBits = 54) * 1/(1) * -(mpfr(x[1], precBits = 54) *
(mpfr(x[1], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-(mpfr(x[1], precBits = 54) * mpfr(x[1], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) + mpfr(w[2],
precBits = 54) * 1/(1) * -(mpfr(x[2], precBits = 54) *
(mpfr(x[2], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) *
-(mpfr(x[2], precBits = 54) * mpfr(x[2], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -(mpfr(x[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2) *
-(mpfr(x[3], precBits = 54) * mpfr(x[3], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2), +mpfr(w[1],
precBits = 54) * 1/(1) * -(mpfr(x[1], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[1],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[1],
precBits = 54))^2)^2) * -(mpfr(x[1], precBits = 54) *
(mpfr(x[1], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) +
mpfr(w[2], precBits = 54) * 1/(1) * -(mpfr(x[2],
precBits = 54)/(mpfr(b[1], precBits = 54) + mpfr(b[2],
precBits = 54) * mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) *
-(mpfr(x[2], precBits = 54) * (mpfr(x[2], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -(mpfr(x[3], precBits = 54)/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) * mpfr(x[3],
precBits = 54) + mpfr(b[3], precBits = 54) * (mpfr(x[3],
precBits = 54))^2)^2) * -(mpfr(x[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2),
+mpfr(w[1], precBits = 54) * 1/(1) * -(mpfr(x[1], precBits = 54) *
mpfr(x[1], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-(mpfr(x[1], precBits = 54) * (mpfr(x[1], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) + mpfr(w[2],
precBits = 54) * 1/(1) * -(mpfr(x[2], precBits = 54) *
mpfr(x[2], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) *
-(mpfr(x[2], precBits = 54) * (mpfr(x[2], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -(mpfr(x[3], precBits = 54) *
mpfr(x[3], precBits = 54)/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2) *
-(mpfr(x[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2), +mpfr(w[1],
precBits = 54) * 1/(1) * -(mpfr(x[1], precBits = 54) *
(mpfr(x[1], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[1], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54))^2)^2) *
-(mpfr(x[1], precBits = 54) * (mpfr(x[1], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[1], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54))^2)^2) + mpfr(w[2],
precBits = 54) * 1/(1) * -(mpfr(x[2], precBits = 54) *
(mpfr(x[2], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[2], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54))^2)^2) *
-(mpfr(x[2], precBits = 54) * (mpfr(x[2], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[2], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54))^2)^2) + mpfr(w[3],
precBits = 54) * 1/(1) * -(mpfr(x[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2/(mpfr(b[1], precBits = 54) +
mpfr(b[2], precBits = 54) * mpfr(x[3], precBits = 54) +
mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2)^2) *
-(mpfr(x[3], precBits = 54) * (mpfr(x[3], precBits = 54))^2/(mpfr(b[1],
precBits = 54) + mpfr(b[2], precBits = 54) *
mpfr(x[3], precBits = 54) + mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54))^2)^2)), Dim = c(3L,
3L))
d = Mat
return(d)
}
<environment: 0x227fc88>

\$fim
function (x = c(x11, x21, x31, x41), w = c(w1, w2, w3, w4), b = c(b1,
b2, b3))
{
Mat = matrix(c(+w[1] * 1/(1) * 1 * 1 + w[2] * 1/(1) * 1 *
1 + w[3] * 1/(1) * 1 * 1 + w[4] * 1/(1) * 1 * 1, +w[1] *
1/(1) * -exp(-b[3] * x[1]^b[4]) * 1 + w[2] * 1/(1) *
-exp(-b[3] * x[2]^b[4]) * 1 + w[3] * 1/(1) * -exp(-b[3] *
x[3]^b[4]) * 1 + w[4] * 1/(1) * -exp(-b[3] * x[4]^b[4]) *
1, +w[1] * 1/(1) * b[2] * (exp(-b[3] * x[1]^b[4]) * x[1]^b[4]) *
1 + w[2] * 1/(1) * b[2] * (exp(-b[3] * x[2]^b[4]) * x[2]^b[4]) *
1 + w[3] * 1/(1) * b[2] * (exp(-b[3] * x[3]^b[4]) * x[3]^b[4]) *
1 + w[4] * 1/(1) * b[2] * (exp(-b[3] * x[4]^b[4]) * x[4]^b[4]) *
1, +w[1] * 1/(1) * b[2] * (exp(-b[3] * x[1]^b[4]) * (b[3] *
(x[1]^b[4] * log(x[1])))) * 1 + w[2] * 1/(1) * b[2] *
(exp(-b[3] * x[2]^b[4]) * (b[3] * (x[2]^b[4] * log(x[2])))) *
1 + w[3] * 1/(1) * b[2] * (exp(-b[3] * x[3]^b[4]) * (b[3] *
(x[3]^b[4] * log(x[3])))) * 1 + w[4] * 1/(1) * b[2] *
(exp(-b[3] * x[4]^b[4]) * (b[3] * (x[4]^b[4] * log(x[4])))) *
1, +w[1] * 1/(1) * 1 * -exp(-b[3] * x[1]^b[4]) + w[2] *
1/(1) * 1 * -exp(-b[3] * x[2]^b[4]) + w[3] * 1/(1) *
1 * -exp(-b[3] * x[3]^b[4]) + w[4] * 1/(1) * 1 * -exp(-b[3] *
x[4]^b[4]), +w[1] * 1/(1) * -exp(-b[3] * x[1]^b[4]) *
-exp(-b[3] * x[1]^b[4]) + w[2] * 1/(1) * -exp(-b[3] *
x[2]^b[4]) * -exp(-b[3] * x[2]^b[4]) + w[3] * 1/(1) *
-exp(-b[3] * x[3]^b[4]) * -exp(-b[3] * x[3]^b[4]) + w[4] *
1/(1) * -exp(-b[3] * x[4]^b[4]) * -exp(-b[3] * x[4]^b[4]),
+w[1] * 1/(1) * b[2] * (exp(-b[3] * x[1]^b[4]) * x[1]^b[4]) *
-exp(-b[3] * x[1]^b[4]) + w[2] * 1/(1) * b[2] * (exp(-b[3] *
x[2]^b[4]) * x[2]^b[4]) * -exp(-b[3] * x[2]^b[4]) +
w[3] * 1/(1) * b[2] * (exp(-b[3] * x[3]^b[4]) * x[3]^b[4]) *
-exp(-b[3] * x[3]^b[4]) + w[4] * 1/(1) * b[2] *
(exp(-b[3] * x[4]^b[4]) * x[4]^b[4]) * -exp(-b[3] *
x[4]^b[4]), +w[1] * 1/(1) * b[2] * (exp(-b[3] * x[1]^b[4]) *
(b[3] * (x[1]^b[4] * log(x[1])))) * -exp(-b[3] *
x[1]^b[4]) + w[2] * 1/(1) * b[2] * (exp(-b[3] * x[2]^b[4]) *
(b[3] * (x[2]^b[4] * log(x[2])))) * -exp(-b[3] *
x[2]^b[4]) + w[3] * 1/(1) * b[2] * (exp(-b[3] * x[3]^b[4]) *
(b[3] * (x[3]^b[4] * log(x[3])))) * -exp(-b[3] *
x[3]^b[4]) + w[4] * 1/(1) * b[2] * (exp(-b[3] * x[4]^b[4]) *
(b[3] * (x[4]^b[4] * log(x[4])))) * -exp(-b[3] *
x[4]^b[4]), +w[1] * 1/(1) * 1 * b[2] * (exp(-b[3] *
x[1]^b[4]) * x[1]^b[4]) + w[2] * 1/(1) * 1 * b[2] *
(exp(-b[3] * x[2]^b[4]) * x[2]^b[4]) + w[3] * 1/(1) *
1 * b[2] * (exp(-b[3] * x[3]^b[4]) * x[3]^b[4]) +
w[4] * 1/(1) * 1 * b[2] * (exp(-b[3] * x[4]^b[4]) *
x[4]^b[4]), +w[1] * 1/(1) * -exp(-b[3] * x[1]^b[4]) *
b[2] * (exp(-b[3] * x[1]^b[4]) * x[1]^b[4]) + w[2] *
1/(1) * -exp(-b[3] * x[2]^b[4]) * b[2] * (exp(-b[3] *
x[2]^b[4]) * x[2]^b[4]) + w[3] * 1/(1) * -exp(-b[3] *
x[3]^b[4]) * b[2] * (exp(-b[3] * x[3]^b[4]) * x[3]^b[4]) +
w[4] * 1/(1) * -exp(-b[3] * x[4]^b[4]) * b[2] * (exp(-b[3] *
x[4]^b[4]) * x[4]^b[4]), +w[1] * 1/(1) * b[2] *
(exp(-b[3] * x[1]^b[4]) * x[1]^b[4]) * b[2] * (exp(-b[3] *
x[1]^b[4]) * x[1]^b[4]) + w[2] * 1/(1) * b[2] * (exp(-b[3] *
x[2]^b[4]) * x[2]^b[4]) * b[2] * (exp(-b[3] * x[2]^b[4]) *
x[2]^b[4]) + w[3] * 1/(1) * b[2] * (exp(-b[3] * x[3]^b[4]) *
x[3]^b[4]) * b[2] * (exp(-b[3] * x[3]^b[4]) * x[3]^b[4]) +
w[4] * 1/(1) * b[2] * (exp(-b[3] * x[4]^b[4]) * x[4]^b[4]) *
b[2] * (exp(-b[3] * x[4]^b[4]) * x[4]^b[4]),
+w[1] * 1/(1) * b[2] * (exp(-b[3] * x[1]^b[4]) * (b[3] *
(x[1]^b[4] * log(x[1])))) * b[2] * (exp(-b[3] * x[1]^b[4]) *
x[1]^b[4]) + w[2] * 1/(1) * b[2] * (exp(-b[3] * x[2]^b[4]) *
(b[3] * (x[2]^b[4] * log(x[2])))) * b[2] * (exp(-b[3] *
x[2]^b[4]) * x[2]^b[4]) + w[3] * 1/(1) * b[2] * (exp(-b[3] *
x[3]^b[4]) * (b[3] * (x[3]^b[4] * log(x[3])))) *
b[2] * (exp(-b[3] * x[3]^b[4]) * x[3]^b[4]) + w[4] *
1/(1) * b[2] * (exp(-b[3] * x[4]^b[4]) * (b[3] *
(x[4]^b[4] * log(x[4])))) * b[2] * (exp(-b[3] * x[4]^b[4]) *
x[4]^b[4]), +w[1] * 1/(1) * 1 * b[2] * (exp(-b[3] *
x[1]^b[4]) * (b[3] * (x[1]^b[4] * log(x[1])))) +
w[2] * 1/(1) * 1 * b[2] * (exp(-b[3] * x[2]^b[4]) *
(b[3] * (x[2]^b[4] * log(x[2])))) + w[3] * 1/(1) *
1 * b[2] * (exp(-b[3] * x[3]^b[4]) * (b[3] * (x[3]^b[4] *
log(x[3])))) + w[4] * 1/(1) * 1 * b[2] * (exp(-b[3] *
x[4]^b[4]) * (b[3] * (x[4]^b[4] * log(x[4])))), +w[1] *
1/(1) * -exp(-b[3] * x[1]^b[4]) * b[2] * (exp(-b[3] *
x[1]^b[4]) * (b[3] * (x[1]^b[4] * log(x[1])))) +
w[2] * 1/(1) * -exp(-b[3] * x[2]^b[4]) * b[2] * (exp(-b[3] *
x[2]^b[4]) * (b[3] * (x[2]^b[4] * log(x[2])))) +
w[3] * 1/(1) * -exp(-b[3] * x[3]^b[4]) * b[2] * (exp(-b[3] *
x[3]^b[4]) * (b[3] * (x[3]^b[4] * log(x[3])))) +
w[4] * 1/(1) * -exp(-b[3] * x[4]^b[4]) * b[2] * (exp(-b[3] *
x[4]^b[4]) * (b[3] * (x[4]^b[4] * log(x[4])))),
+w[1] * 1/(1) * b[2] * (exp(-b[3] * x[1]^b[4]) * x[1]^b[4]) *
b[2] * (exp(-b[3] * x[1]^b[4]) * (b[3] * (x[1]^b[4] *
log(x[1])))) + w[2] * 1/(1) * b[2] * (exp(-b[3] *
x[2]^b[4]) * x[2]^b[4]) * b[2] * (exp(-b[3] * x[2]^b[4]) *
(b[3] * (x[2]^b[4] * log(x[2])))) + w[3] * 1/(1) *
b[2] * (exp(-b[3] * x[3]^b[4]) * x[3]^b[4]) * b[2] *
(exp(-b[3] * x[3]^b[4]) * (b[3] * (x[3]^b[4] * log(x[3])))) +
w[4] * 1/(1) * b[2] * (exp(-b[3] * x[4]^b[4]) * x[4]^b[4]) *
b[2] * (exp(-b[3] * x[4]^b[4]) * (b[3] * (x[4]^b[4] *
log(x[4])))), +w[1] * 1/(1) * b[2] * (exp(-b[3] *
x[1]^b[4]) * (b[3] * (x[1]^b[4] * log(x[1])))) *
b[2] * (exp(-b[3] * x[1]^b[4]) * (b[3] * (x[1]^b[4] *
log(x[1])))) + w[2] * 1/(1) * b[2] * (exp(-b[3] *
x[2]^b[4]) * (b[3] * (x[2]^b[4] * log(x[2])))) *
b[2] * (exp(-b[3] * x[2]^b[4]) * (b[3] * (x[2]^b[4] *
log(x[2])))) + w[3] * 1/(1) * b[2] * (exp(-b[3] *
x[3]^b[4]) * (b[3] * (x[3]^b[4] * log(x[3])))) *
b[2] * (exp(-b[3] * x[3]^b[4]) * (b[3] * (x[3]^b[4] *
log(x[3])))) + w[4] * 1/(1) * b[2] * (exp(-b[3] *
x[4]^b[4]) * (b[3] * (x[4]^b[4] * log(x[4])))) *
b[2] * (exp(-b[3] * x[4]^b[4]) * (b[3] * (x[4]^b[4] *
log(x[4]))))), 4, 4)
d = Mat
return(d)
}
<environment: 0x486e478>

\$fim.mpfr
function (x = c(x11, x21, x31, x41), w = c(w1, w2, w3, w4), b = c(b1,
b2, b3))
{
Mat = new("mpfrMatrix", c(+mpfr(w[1], precBits = 54) * 1/(1) *
1 * 1 + mpfr(w[2], precBits = 54) * 1/(1) * 1 * 1 + mpfr(w[3],
precBits = 54) * 1/(1) * 1 * 1 + mpfr(w[4], precBits = 54) *
1/(1) * 1 * 1, +mpfr(w[1], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * 1 + mpfr(w[2], precBits = 54) * 1/(1) *
-exp(-mpfr(b[3], precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * 1 + mpfr(w[3], precBits = 54) *
1/(1) * -exp(-mpfr(b[3], precBits = 54) * mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54)) * 1 + mpfr(w[4],
precBits = 54) * 1/(1) * -exp(-mpfr(b[3], precBits = 54) *
mpfr(x[4], precBits = 54)^mpfr(b[4], precBits = 54)) *
1, +mpfr(w[1], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * 1 + mpfr(w[2], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * 1 + mpfr(w[3], precBits = 54) * 1/(1) *
mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3], precBits = 54) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) *
1 + mpfr(w[4], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * 1, +mpfr(w[1], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[1],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[1],
precBits = 54))))) * 1 + mpfr(w[2], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[2],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[2],
precBits = 54))))) * 1 + mpfr(w[3], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[3],
precBits = 54))))) * 1 + mpfr(w[4], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[4],
precBits = 54))))) * 1, +mpfr(w[1], precBits = 54) *
1/(1) * 1 * -exp(-mpfr(b[3], precBits = 54) * mpfr(x[1],
precBits = 54)^mpfr(b[4], precBits = 54)) + mpfr(w[2],
precBits = 54) * 1/(1) * 1 * -exp(-mpfr(b[3], precBits = 54) *
mpfr(x[2], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[3], precBits = 54) * 1/(1) * 1 * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[4], precBits = 54) * 1/(1) *
1 * -exp(-mpfr(b[3], precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)), +mpfr(w[1], precBits = 54) * 1/(1) *
-exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * -exp(-mpfr(b[3], precBits = 54) *
mpfr(x[1], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[2], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * -exp(-mpfr(b[3], precBits = 54) *
mpfr(x[2], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[3], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * -exp(-mpfr(b[3], precBits = 54) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[4], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * -exp(-mpfr(b[3], precBits = 54) *
mpfr(x[4], precBits = 54)^mpfr(b[4], precBits = 54)),
+mpfr(w[1], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * -exp(-mpfr(b[3], precBits = 54) *
mpfr(x[1], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[2], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[2],
precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[2], precBits = 54)^mpfr(b[4], precBits = 54)) *
-exp(-mpfr(b[3], precBits = 54) * mpfr(x[2],
precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[3], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) *
-exp(-mpfr(b[3], precBits = 54) * mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[4], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[4], precBits = 54)^mpfr(b[4], precBits = 54)) *
-exp(-mpfr(b[3], precBits = 54) * mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54)),
+mpfr(w[1], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[1], precBits = 54))))) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[2], precBits = 54) * 1/(1) *
mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3], precBits = 54) *
mpfr(x[2], precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[2], precBits = 54))))) *
-exp(-mpfr(b[3], precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[3], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[3],
precBits = 54))))) * -exp(-mpfr(b[3], precBits = 54) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[4], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[4], precBits = 54))))) *
-exp(-mpfr(b[3], precBits = 54) * mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54)),
+mpfr(w[1], precBits = 54) * 1/(1) * 1 * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[2], precBits = 54) *
1/(1) * 1 * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[3], precBits = 54) * 1/(1) *
1 * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[4], precBits = 54) * 1/(1) *
1 * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)), +mpfr(w[1], precBits = 54) * 1/(1) *
-exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[2], precBits = 54) *
1/(1) * -exp(-mpfr(b[3], precBits = 54) * mpfr(x[2],
precBits = 54)^mpfr(b[4], precBits = 54)) * mpfr(b[2],
precBits = 54) * (exp(-mpfr(b[3], precBits = 54) *
mpfr(x[2], precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[2], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[3], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[4], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[4], precBits = 54)^mpfr(b[4], precBits = 54)),
+mpfr(w[1], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[2], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[3], precBits = 54) * 1/(1) *
mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3], precBits = 54) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3], precBits = 54) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) +
mpfr(w[4], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(x[4], precBits = 54)^mpfr(b[4], precBits = 54)) *
mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)), +mpfr(w[1], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[1],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[1],
precBits = 54))))) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[2], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[2],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[2],
precBits = 54))))) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[3], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[3],
precBits = 54))))) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) + mpfr(w[4], precBits = 54) *
1/(1) * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[4],
precBits = 54))))) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)), +mpfr(w[1], precBits = 54) *
1/(1) * 1 * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[1],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[1],
precBits = 54))))) + mpfr(w[2], precBits = 54) *
1/(1) * 1 * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[2],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[2],
precBits = 54))))) + mpfr(w[3], precBits = 54) *
1/(1) * 1 * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[3],
precBits = 54))))) + mpfr(w[4], precBits = 54) *
1/(1) * 1 * mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) * (mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54) * log(mpfr(x[4],
precBits = 54))))), +mpfr(w[1], precBits = 54) *
1/(1) * -exp(-mpfr(b[3], precBits = 54) * mpfr(x[1],
precBits = 54)^mpfr(b[4], precBits = 54)) * mpfr(b[2],
precBits = 54) * (exp(-mpfr(b[3], precBits = 54) *
mpfr(x[1], precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[1], precBits = 54))))) +
mpfr(w[2], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[2],
precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[2], precBits = 54))))) +
mpfr(w[3], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[3],
precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[3], precBits = 54))))) +
mpfr(w[4], precBits = 54) * 1/(1) * -exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[4], precBits = 54))))),
+mpfr(w[1], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[1], precBits = 54))))) + mpfr(w[2],
precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[2], precBits = 54))))) + mpfr(w[3],
precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[3], precBits = 54))))) + mpfr(w[4],
precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[4], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[4], precBits = 54))))), +mpfr(w[1],
precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[1], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[1], precBits = 54))))) * mpfr(b[2],
precBits = 54) * (exp(-mpfr(b[3], precBits = 54) *
mpfr(x[1], precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[1], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[1], precBits = 54))))) +
mpfr(w[2], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[2],
precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[2], precBits = 54))))) *
mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[2], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[2], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[2], precBits = 54))))) + mpfr(w[3],
precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[3], precBits = 54))))) * mpfr(b[2],
precBits = 54) * (exp(-mpfr(b[3], precBits = 54) *
mpfr(x[3], precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[3], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[3], precBits = 54))))) +
mpfr(w[4], precBits = 54) * 1/(1) * mpfr(b[2], precBits = 54) *
(exp(-mpfr(b[3], precBits = 54) * mpfr(x[4],
precBits = 54)^mpfr(b[4], precBits = 54)) *
(mpfr(b[3], precBits = 54) * (mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54) * log(mpfr(x[4], precBits = 54))))) *
mpfr(b[2], precBits = 54) * (exp(-mpfr(b[3],
precBits = 54) * mpfr(x[4], precBits = 54)^mpfr(b[4],
precBits = 54)) * (mpfr(b[3], precBits = 54) *
(mpfr(x[4], precBits = 54)^mpfr(b[4], precBits = 54) *
log(mpfr(x[4], precBits = 54)))))), Dim = c(4L,
4L))
d = Mat
return(d)
}
<environment: 0x486e478>

\$fim
function (x = c(x11, x21, x31, x41), w = c(w1, w2, w3, w4), b = c(b1,
b2, b3, b4))
{
Mat = matrix(c(+w[1] * 1/(1) * 1/(1 + b[2] * exp(-b[3] *
x[1]))^b[4] * 1/(1 + b[2] * exp(-b[3] * x[1]))^b[4] +
w[2] * 1/(1) * 1/(1 + b[2] * exp(-b[3] * x[2]))^b[4] *
1/(1 + b[2] * exp(-b[3] * x[2]))^b[4] + w[3] * 1/(1) *
1/(1 + b[2] * exp(-b[3] * x[3]))^b[4] * 1/(1 + b[2] *
exp(-b[3] * x[3]))^b[4] + w[4] * 1/(1) * 1/(1 + b[2] *
exp(-b[3] * x[4]))^b[4] * 1/(1 + b[2] * exp(-b[3] * x[4]))^b[4],
+w[1] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] * x[1]))^(b[4] -
1) * (b[4] * exp(-b[3] * x[1])))/((1 + b[2] * exp(-b[3] *
x[1]))^b[4])^2) * 1/(1 + b[2] * exp(-b[3] * x[1]))^b[4] +
w[2] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[2]))^(b[4] - 1) * (b[4] * exp(-b[3] * x[2])))/((1 +
b[2] * exp(-b[3] * x[2]))^b[4])^2) * 1/(1 + b[2] *
exp(-b[3] * x[2]))^b[4] + w[3] * 1/(1) * -(b[1] *
((1 + b[2] * exp(-b[3] * x[3]))^(b[4] - 1) * (b[4] *
exp(-b[3] * x[3])))/((1 + b[2] * exp(-b[3] *
x[3]))^b[4])^2) * 1/(1 + b[2] * exp(-b[3] * x[3]))^b[4] +
w[4] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[4]))^(b[4] - 1) * (b[4] * exp(-b[3] * x[4])))/((1 +
b[2] * exp(-b[3] * x[4]))^b[4])^2) * 1/(1 + b[2] *
exp(-b[3] * x[4]))^b[4], +w[1] * 1/(1) * b[1] *
((1 + b[2] * exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] *
(b[2] * (exp(-b[3] * x[1]) * x[1]))))/((1 + b[2] *
exp(-b[3] * x[1]))^b[4])^2 * 1/(1 + b[2] * exp(-b[3] *
x[1]))^b[4] + w[2] * 1/(1) * b[1] * ((1 + b[2] *
exp(-b[3] * x[2]))^(b[4] - 1) * (b[4] * (b[2] * (exp(-b[3] *
x[2]) * x[2]))))/((1 + b[2] * exp(-b[3] * x[2]))^b[4])^2 *
1/(1 + b[2] * exp(-b[3] * x[2]))^b[4] + w[3] * 1/(1) *
b[1] * ((1 + b[2] * exp(-b[3] * x[3]))^(b[4] - 1) *
(b[4] * (b[2] * (exp(-b[3] * x[3]) * x[3]))))/((1 +
b[2] * exp(-b[3] * x[3]))^b[4])^2 * 1/(1 + b[2] *
exp(-b[3] * x[3]))^b[4] + w[4] * 1/(1) * b[1] * ((1 +
b[2] * exp(-b[3] * x[4]))^(b[4] - 1) * (b[4] * (b[2] *
(exp(-b[3] * x[4]) * x[4]))))/((1 + b[2] * exp(-b[3] *
x[4]))^b[4])^2 * 1/(1 + b[2] * exp(-b[3] * x[4]))^b[4],
+w[1] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] * x[1]))^b[4] *
log((1 + b[2] * exp(-b[3] * x[1]))))/((1 + b[2] *
exp(-b[3] * x[1]))^b[4])^2) * 1/(1 + b[2] * exp(-b[3] *
x[1]))^b[4] + w[2] * 1/(1) * -(b[1] * ((1 + b[2] *
exp(-b[3] * x[2]))^b[4] * log((1 + b[2] * exp(-b[3] *
x[2]))))/((1 + b[2] * exp(-b[3] * x[2]))^b[4])^2) *
1/(1 + b[2] * exp(-b[3] * x[2]))^b[4] + w[3] * 1/(1) *
-(b[1] * ((1 + b[2] * exp(-b[3] * x[3]))^b[4] * log((1 +
b[2] * exp(-b[3] * x[3]))))/((1 + b[2] * exp(-b[3] *
x[3]))^b[4])^2) * 1/(1 + b[2] * exp(-b[3] * x[3]))^b[4] +
w[4] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[4]))^b[4] * log((1 + b[2] * exp(-b[3] * x[4]))))/((1 +
b[2] * exp(-b[3] * x[4]))^b[4])^2) * 1/(1 + b[2] *
exp(-b[3] * x[4]))^b[4], +w[1] * 1/(1) * 1/(1 +
b[2] * exp(-b[3] * x[1]))^b[4] * -(b[1] * ((1 + b[2] *
exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] * exp(-b[3] *
x[1])))/((1 + b[2] * exp(-b[3] * x[1]))^b[4])^2) +
w[2] * 1/(1) * 1/(1 + b[2] * exp(-b[3] * x[2]))^b[4] *
-(b[1] * ((1 + b[2] * exp(-b[3] * x[2]))^(b[4] -
1) * (b[4] * exp(-b[3] * x[2])))/((1 + b[2] *
exp(-b[3] * x[2]))^b[4])^2) + w[3] * 1/(1) *
1/(1 + b[2] * exp(-b[3] * x[3]))^b[4] * -(b[1] *
((1 + b[2] * exp(-b[3] * x[3]))^(b[4] - 1) * (b[4] *
exp(-b[3] * x[3])))/((1 + b[2] * exp(-b[3] *
x[3]))^b[4])^2) + w[4] * 1/(1) * 1/(1 + b[2] * exp(-b[3] *
x[4]))^b[4] * -(b[1] * ((1 + b[2] * exp(-b[3] * x[4]))^(b[4] -
1) * (b[4] * exp(-b[3] * x[4])))/((1 + b[2] * exp(-b[3] *
x[4]))^b[4])^2), +w[1] * 1/(1) * -(b[1] * ((1 + b[2] *
exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] * exp(-b[3] *
x[1])))/((1 + b[2] * exp(-b[3] * x[1]))^b[4])^2) *
-(b[1] * ((1 + b[2] * exp(-b[3] * x[1]))^(b[4] -
1) * (b[4] * exp(-b[3] * x[1])))/((1 + b[2] *
exp(-b[3] * x[1]))^b[4])^2) + w[2] * 1/(1) *
-(b[1] * ((1 + b[2] * exp(-b[3] * x[2]))^(b[4] -
1) * (b[4] * exp(-b[3] * x[2])))/((1 + b[2] *
exp(-b[3] * x[2]))^b[4])^2) * -(b[1] * ((1 +
b[2] * exp(-b[3] * x[2]))^(b[4] - 1) * (b[4] * exp(-b[3] *
x[2])))/((1 + b[2] * exp(-b[3] * x[2]))^b[4])^2) +
w[3] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[3]))^(b[4] - 1) * (b[4] * exp(-b[3] * x[3])))/((1 +
b[2] * exp(-b[3] * x[3]))^b[4])^2) * -(b[1] *
((1 + b[2] * exp(-b[3] * x[3]))^(b[4] - 1) *
(b[4] * exp(-b[3] * x[3])))/((1 + b[2] * exp(-b[3] *
x[3]))^b[4])^2) + w[4] * 1/(1) * -(b[1] * ((1 +
b[2] * exp(-b[3] * x[4]))^(b[4] - 1) * (b[4] * exp(-b[3] *
x[4])))/((1 + b[2] * exp(-b[3] * x[4]))^b[4])^2) *
-(b[1] * ((1 + b[2] * exp(-b[3] * x[4]))^(b[4] -
1) * (b[4] * exp(-b[3] * x[4])))/((1 + b[2] *
exp(-b[3] * x[4]))^b[4])^2), +w[1] * 1/(1) *
b[1] * ((1 + b[2] * exp(-b[3] * x[1]))^(b[4] - 1) *
(b[4] * (b[2] * (exp(-b[3] * x[1]) * x[1]))))/((1 +
b[2] * exp(-b[3] * x[1]))^b[4])^2 * -(b[1] * ((1 +
b[2] * exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] * exp(-b[3] *
x[1])))/((1 + b[2] * exp(-b[3] * x[1]))^b[4])^2) +
w[2] * 1/(1) * b[1] * ((1 + b[2] * exp(-b[3] * x[2]))^(b[4] -
1) * (b[4] * (b[2] * (exp(-b[3] * x[2]) * x[2]))))/((1 +
b[2] * exp(-b[3] * x[2]))^b[4])^2 * -(b[1] *
((1 + b[2] * exp(-b[3] * x[2]))^(b[4] - 1) *
(b[4] * exp(-b[3] * x[2])))/((1 + b[2] * exp(-b[3] *
x[2]))^b[4])^2) + w[3] * 1/(1) * b[1] * ((1 +
b[2] * exp(-b[3] * x[3]))^(b[4] - 1) * (b[4] * (b[2] *
(exp(-b[3] * x[3]) * x[3]))))/((1 + b[2] * exp(-b[3] *
x[3]))^b[4])^2 * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[3]))^(b[4] - 1) * (b[4] * exp(-b[3] * x[3])))/((1 +
b[2] * exp(-b[3] * x[3]))^b[4])^2) + w[4] * 1/(1) *
b[1] * ((1 + b[2] * exp(-b[3] * x[4]))^(b[4] - 1) *
(b[4] * (b[2] * (exp(-b[3] * x[4]) * x[4]))))/((1 +
b[2] * exp(-b[3] * x[4]))^b[4])^2 * -(b[1] * ((1 +
b[2] * exp(-b[3] * x[4]))^(b[4] - 1) * (b[4] * exp(-b[3] *
x[4])))/((1 + b[2] * exp(-b[3] * x[4]))^b[4])^2),
+w[1] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] * x[1]))^b[4] *
log((1 + b[2] * exp(-b[3] * x[1]))))/((1 + b[2] *
exp(-b[3] * x[1]))^b[4])^2) * -(b[1] * ((1 + b[2] *
exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] * exp(-b[3] *
x[1])))/((1 + b[2] * exp(-b[3] * x[1]))^b[4])^2) +
w[2] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[2]))^b[4] * log((1 + b[2] * exp(-b[3] * x[2]))))/((1 +
b[2] * exp(-b[3] * x[2]))^b[4])^2) * -(b[1] *
((1 + b[2] * exp(-b[3] * x[2]))^(b[4] - 1) *
(b[4] * exp(-b[3] * x[2])))/((1 + b[2] * exp(-b[3] *
x[2]))^b[4])^2) + w[3] * 1/(1) * -(b[1] * ((1 +
b[2] * exp(-b[3] * x[3]))^b[4] * log((1 + b[2] *
exp(-b[3] * x[3]))))/((1 + b[2] * exp(-b[3] * x[3]))^b[4])^2) *
-(b[1] * ((1 + b[2] * exp(-b[3] * x[3]))^(b[4] -
1) * (b[4] * exp(-b[3] * x[3])))/((1 + b[2] *
exp(-b[3] * x[3]))^b[4])^2) + w[4] * 1/(1) *
-(b[1] * ((1 + b[2] * exp(-b[3] * x[4]))^b[4] * log((1 +
b[2] * exp(-b[3] * x[4]))))/((1 + b[2] * exp(-b[3] *
x[4]))^b[4])^2) * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[4]))^(b[4] - 1) * (b[4] * exp(-b[3] * x[4])))/((1 +
b[2] * exp(-b[3] * x[4]))^b[4])^2), +w[1] * 1/(1) *
1/(1 + b[2] * exp(-b[3] * x[1]))^b[4] * b[1] * ((1 +
b[2] * exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] * (b[2] *
(exp(-b[3] * x[1]) * x[1]))))/((1 + b[2] * exp(-b[3] *
x[1]))^b[4])^2 + w[2] * 1/(1) * 1/(1 + b[2] * exp(-b[3] *
x[2]))^b[4] * b[1] * ((1 + b[2] * exp(-b[3] * x[2]))^(b[4] -
1) * (b[4] * (b[2] * (exp(-b[3] * x[2]) * x[2]))))/((1 +
b[2] * exp(-b[3] * x[2]))^b[4])^2 + w[3] * 1/(1) *
1/(1 + b[2] * exp(-b[3] * x[3]))^b[4] * b[1] * ((1 +
b[2] * exp(-b[3] * x[3]))^(b[4] - 1) * (b[4] * (b[2] *
(exp(-b[3] * x[3]) * x[3]))))/((1 + b[2] * exp(-b[3] *
x[3]))^b[4])^2 + w[4] * 1/(1) * 1/(1 + b[2] * exp(-b[3] *
x[4]))^b[4] * b[1] * ((1 + b[2] * exp(-b[3] * x[4]))^(b[4] -
1) * (b[4] * (b[2] * (exp(-b[3] * x[4]) * x[4]))))/((1 +
b[2] * exp(-b[3] * x[4]))^b[4])^2, +w[1] * 1/(1) *
-(b[1] * ((1 + b[2] * exp(-b[3] * x[1]))^(b[4] -
1) * (b[4] * exp(-b[3] * x[1])))/((1 + b[2] *
exp(-b[3] * x[1]))^b[4])^2) * b[1] * ((1 + b[2] *
exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] * (b[2] * (exp(-b[3] *
x[1]) * x[1]))))/((1 + b[2] * exp(-b[3] * x[1]))^b[4])^2 +
w[2] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[2]))^(b[4] - 1) * (b[4] * exp(-b[3] * x[2])))/((1 +
b[2] * exp(-b[3] * x[2]))^b[4])^2) * b[1] * ((1 +
b[2] * exp(-b[3] * x[2]))^(b[4] - 1) * (b[4] *
(b[2] * (exp(-b[3] * x[2]) * x[2]))))/((1 + b[2] *
exp(-b[3] * x[2]))^b[4])^2 + w[3] * 1/(1) * -(b[1] *
((1 + b[2] * exp(-b[3] * x[3]))^(b[4] - 1) * (b[4] *
exp(-b[3] * x[3])))/((1 + b[2] * exp(-b[3] *
x[3]))^b[4])^2) * b[1] * ((1 + b[2] * exp(-b[3] *
x[3]))^(b[4] - 1) * (b[4] * (b[2] * (exp(-b[3] *
x[3]) * x[3]))))/((1 + b[2] * exp(-b[3] * x[3]))^b[4])^2 +
w[4] * 1/(1) * -(b[1] * ((1 + b[2] * exp(-b[3] *
x[4]))^(b[4] - 1) * (b[4] * exp(-b[3] * x[4])))/((1 +
b[2] * exp(-b[3] * x[4]))^b[4])^2) * b[1] * ((1 +
b[2] * exp(-b[3] * x[4]))^(b[4] - 1) * (b[4] *
(b[2] * (exp(-b[3] * x[4]) * x[4]))))/((1 + b[2] *
exp(-b[3] * x[4]))^b[4])^2, +w[1] * 1/(1) * b[1] *
((1 + b[2] * exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] *
(b[2] * (exp(-b[3] * x[1]) * x[1]))))/((1 + b[2] *
exp(-b[3] * x[1]))^b[4])^2 * b[1] * ((1 + b[2] *
exp(-b[3] * x[1]))^(b[4] - 1) * (b[4] * (b[2] * (exp(-b[3] *
x[1]) * x[1]))))/((1 + b[2] * exp(-b[3] * x[1]))^b[4])^2 +
w[2] * 1/(1) * b[1] * ((1 + b[2] * exp(-b[3] * x[2]))^(b[4] -
1) * (b[4] * (b[2] * (exp(-b[3] * x[2]) * x[2]))))/((1 +
b[2] * exp(-b[3] * x[2]))^b[4])^2 * b[1] * ((1 +
b[2] * exp(-b[3] * x[2]))^(b[4] - 1) * (b[4] *
(b[2] * (exp(-b[3] * x[2]) * x[2]))))/((1 + b[2] *
exp(-b[3] * x[2]))^b[4])^2 + w[3] * 1/(1) * b[1] *
((1 + b[2] * exp(-b[3] * x[3]))^(b[4] - 1) * (b[4] *
(b[2] * (exp(-b[3] * x[3]) * x[3]))))/((1 + b[2] *
exp(-b[3] * x[3]))^b[4])^2 * b[1] * ((1 + b[2] *
exp(-b[3] * x[3]))^(b[4] - 1) * (b[4] * (b[2] * (exp(-b[3] *
x[3]) * x[3]))))/((1 + b[2] * exp(-b[3] * x[3]))^b[4])^2 +
w[4] * 1/(1) * b[1] * ((1 + b[2] * exp(-b[3] * x[4]))^(b[4] -
1) * (b[4] * (b[2] * (exp(-b[3] * x[4]) * x[4]))))/((1 +
b[2] * exp(-b[3] * x[4]))^b[4])^2 * b[1] * ((1 +
b[2] * exp(-b[3] * x[4]))^(b[4] - 1) * (b[4] *
(b[2] * (exp(-b[3] * x[4]) * x[4]))))/((1 + b[2] *
exp(-b[3] * x[4]))^b[4])^2, +w[1] * 1/(1) * -(b[1] *
((1 + b[2] * exp(-b[3] * x[1]))^b[4] * log((1 + b[2] *
exp(-b[3] * x[1]))))/((1 + b[2] * exp(-b[3] *
x[1]))^b[4])^2) * b[1] * ((1 + b[2] * exp(-b[3] *
x[1]))^(b[4] - 1) * (b[4] * (b[2] * (exp(-b[3] *```