R Under development (unstable) (2024-10-16 r87241 ucrt) -- "Unsuffered Consequences" Copyright (C) 2024 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > if(!require("GNE"))stop("this test requires package GNE.") Loading required package: GNE Loading required package: alabama Loading required package: numDeriv Loading required package: nleqslv Loading required package: BB Loading required package: SQUAREM > > > # (1) associated objective functions > # > > dimx <- c(2, 2, 3) > > #Gr_x_j O_i(x) > grfullob <- function(x, i, j) + { + x <- x[1:7] + if(i == 1) + { + grad <- 3*(x - 1:7)^2 + } + if(i == 2) + { + grad <- 1:7*(x - 1:7)^(0:6) + } + if(i == 3) + { + s <- x[5]^2 + x[6]^2 + x[7]^2 - 5 + grad <- c(1, 0, 1, 0, 4*x[5]*s, 4*x[6]*s, 4*x[7]*s) + + } + grad[j] + } > > > #Gr_x_k Gr_x_j O_i(x) > hefullob <- function(x, i, j, k) + { + x <- x[1:7] + if(i == 1) + { + he <- diag( 6*(x - 1:7) ) + } + if(i == 2) + { + he <- diag( c(0, 2, 6, 12, 20, 30, 42)*(x - 1:7)^c(0, 0:5) ) + } + if(i == 3) + { + s <- x[5]^2 + x[6]^2 + x[7]^2 + + he <- rbind(rep(0, 7), rep(0, 7), rep(0, 7), rep(0, 7), + c(0, 0, 0, 0, 4*s+8*x[5]^2, 8*x[5]*x[6], 8*x[5]*x[7]), + c(0, 0, 0, 0, 8*x[5]*x[6], 4*s+8*x[6]^2, 8*x[6]*x[7]), + c(0, 0, 0, 0, 8*x[5]*x[7], 8*x[6]*x[7], 4*s+8*x[7]^2) ) + } + he[j,k] + } > > > > # (2) constraint linked functions > # > > dimlam <- dimw <- c(1, 2, 2) > > #constraint function g_i(x) > g <- function(x, i) + { + x <- x[1:7] + #cat(x[1:5], "|", i, "\n") + if(i == 1) + res <- sum( x^(1:7) ) -7 + if(i == 2) + res <- c(sum(x) + prod(x) - 14, 20 - sum(x)) + if(i == 3) + res <- c(sum(x^2) + 1, 100 - sum(x)) + #cat("res", res + par$a, "\n") + res + } > > > #Gr_x_j g_i(x) > grfullg <- function(x, i, j) + { + x <- x[1:7] + if(i == 1) + { + grad <- (1:7) * x ^ (0:6) + } + if(i == 2) + { + grad <- 1 + sapply(1:7, function(i) prod(x[-i])) + grad <- cbind(grad, -1) + } + if(i == 3) + { + grad <- cbind(2*x, -1) + } + + + if(i == 1) + res <- grad[j] + if(i != 1) + res <- grad[j,] + as.numeric(res) + } > > > > #Gr_x_k Gr_x_j g_i(x) > hefullg <- function(x, i, j, k) + { + x <- x[1:7] + if(i == 1) + { + he1 <- diag( c(0, 2, 6, 12, 20, 30, 42) * x ^ c(0, 0, 1:5) ) + } + if(i == 2) + { + he1 <- matrix(0, 7, 7) + he1[1, -1] <- sapply(2:7, function(i) prod(x[-c(1, i)])) + he1[2, -2] <- sapply(c(1, 3:7), function(i) prod(x[-c(2, i)])) + he1[3, -3] <- sapply(c(1:2, 4:7), function(i) prod(x[-c(3, i)])) + he1[4, -4] <- sapply(c(1:3, 5:7), function(i) prod(x[-c(4, i)])) + he1[5, -5] <- sapply(c(1:4, 6:7), function(i) prod(x[-c(5, i)])) + he1[6, -6] <- sapply(c(1:5, 7:7), function(i) prod(x[-c(6, i)])) + he1[7, -7] <- sapply(1:6, function(i) prod(x[-c(7, i)])) + he2 <- matrix(0, 7, 7) + } + if(i == 3) + { + he1 <- diag(rep(2, 7)) + he2 <- matrix(0, 7, 7) + } + if(i != 1) + return( c(he1[j, k], he2[j, k]) ) + else + return( he1[j, k] ) + } > > > dimmu <- 3 > > #constraint function h(x) > h <- function(x) + { + x <- x[1:7] + c(prod(x) - 1, sum(x^2) -2, sum(x^3) -3) + } > grh <- function(x, j) + { + x <- x[1:7] + c(prod(x[-j]), 2*x[j], 3*x[j]^2) + } > heh <- function(x, j, k) + { + x <- x[1:7] + c(prod(x[-c(j,k)]), 2*(j==k), 6*x[j]*(j==k)) + } > > > > # (3) compute H > # > > z <- rexp(sum(dimx) + 2*sum(dimlam) + 2*sum(dimmu)) > > n <- sum(dimx) > m <- sum(dimlam) > x <- z[1:n] > lam <- z[(n+1):(n+m)] > mu <- z[(n+m+1):(n+m+dimmu)] > w <- z[(n+m+dimmu+1):(n+2*m+2*dimmu)] > > resphi <- funCER(z, dimx, dimlam, grobj=grfullob, constr=g, grconstr=grfullg, joint=h, grjoint=grh, dimmu=dimmu, echo=TRUE) [1] 2 2 3 [1] 1 2 2 [1] 23 > > > check <- c(grfullob(x, 1, 1) + lam[1] * grfullg(x, 1, 1) + mu %*% grh(x, 1), + grfullob(x, 1, 2) + lam[1] * grfullg(x, 1, 2) + mu %*% grh(x, 2), + grfullob(x, 2, 3) + lam[2:3] %*% grfullg(x, 2, 3) + mu %*% grh(x, 3), + grfullob(x, 2, 4) + lam[2:3] %*% grfullg(x, 2, 4) + mu %*% grh(x, 4), + grfullob(x, 3, 5) + lam[4:5] %*% grfullg(x, 3, 5) + mu %*% grh(x, 5), + grfullob(x, 3, 6) + lam[4:5] %*% grfullg(x, 3, 6) + mu %*% grh(x, 6), + grfullob(x, 3, 7) + lam[4:5] %*% grfullg(x, 3, 7) + mu %*% grh(x, 7), + g(x, 1) + w[1], + g(x, 2) + w[2:3], + g(x, 3) + w[4:5], + h(x) + w[6:8], + c(lam, mu) * w) > > #check > cat("\n\n________________________________________\n\n") ________________________________________ > > #part A > print(cbind(check, res=as.numeric(resphi))[1:length(x), ]) check res [1,] 12.979344 12.979344 [2,] 13.177258 13.177258 [3,] 22.021647 22.021647 [4,] -139.100152 -139.100152 [5,] -1.181297 -1.181297 [6,] -2.406006 -2.406006 [7,] 12.058087 12.058087 > #part B > print(cbind(check, res=as.numeric(resphi))[(length(x)+1):length(z), ]) check res [1,] 13.96229508 13.96229508 [2,] -8.22476764 -8.22476764 [3,] 15.44513723 15.44513723 [4,] 5.97867430 5.97867430 [5,] 97.09504781 97.09504781 [6,] 3.34495570 3.34495570 [7,] 4.16416749 4.16416749 [8,] 4.83751608 4.83751608 [9,] 0.09910011 0.09910011 [10,] 0.20960418 0.20960418 [11,] 0.01879120 0.01879120 [12,] 0.23550377 0.23550377 [13,] 2.20788557 2.20788557 [14,] 6.69917917 6.69917917 [15,] 0.78092838 0.78092838 [16,] 8.97776566 8.97776566 > > > if(sum(abs(check - resphi)) > .Machine$double.eps^(2/3)) + stop("wrong result") > > > > # (4) compute Jac H > # > > resjacphi <- jacCER(z, dimx, dimlam, heobj=hefullob, constr=g, grconstr=grfullg, + heconstr=hefullg, joint=h, grjoint=grh, hejoint=heh, dimmu=dimmu) > > > #check > cat("\n\n________________________________________\n\n") ________________________________________ > > > cat("\n\npart A\n\n") part A > > > cat("\n\npart A\n\n") part A > > > checkA <- + rbind( + c(hefullob(x, 1, 1, 1) + lam[1]*hefullg(x, 1, 1, 1) + mu%*%heh(x, 1, 1), + hefullob(x, 1, 1, 2) + lam[1]*hefullg(x, 1, 1, 2) + mu%*%heh(x, 1, 2), + hefullob(x, 1, 1, 3) + lam[1]*hefullg(x, 1, 1, 3) + mu%*%heh(x, 1, 3), + hefullob(x, 1, 1, 4) + lam[1]*hefullg(x, 1, 1, 4) + mu%*%heh(x, 1, 4), + hefullob(x, 1, 1, 5) + lam[1]*hefullg(x, 1, 1, 5) + mu%*%heh(x, 1, 5), + hefullob(x, 1, 1, 6) + lam[1]*hefullg(x, 1, 1, 6) + mu%*%heh(x, 1, 6), + hefullob(x, 1, 1, 7) + lam[1]*hefullg(x, 1, 1, 7) + mu%*%heh(x, 1, 7) + ), + c(hefullob(x, 1, 2, 1) + lam[1]*hefullg(x, 1, 2, 1) + mu%*%heh(x, 2, 1), + hefullob(x, 1, 2, 2) + lam[1]*hefullg(x, 1, 2, 2) + mu%*%heh(x, 2, 2), + hefullob(x, 1, 2, 3) + lam[1]*hefullg(x, 1, 2, 3) + mu%*%heh(x, 2, 3), + hefullob(x, 1, 2, 4) + lam[1]*hefullg(x, 1, 2, 4) + mu%*%heh(x, 2, 4), + hefullob(x, 1, 2, 5) + lam[1]*hefullg(x, 1, 2, 5) + mu%*%heh(x, 2, 5), + hefullob(x, 1, 2, 6) + lam[1]*hefullg(x, 1, 2, 6) + mu%*%heh(x, 2, 6), + hefullob(x, 1, 2, 7) + lam[1]*hefullg(x, 1, 2, 7) + mu%*%heh(x, 2, 7) + ), + c(hefullob(x, 2, 3, 1) + lam[2:3]%*%hefullg(x, 2, 3, 1) + mu%*%heh(x, 3, 1), + hefullob(x, 2, 3, 2) + lam[2:3]%*%hefullg(x, 2, 3, 2) + mu%*%heh(x, 3, 2), + hefullob(x, 2, 3, 3) + lam[2:3]%*%hefullg(x, 2, 3, 3) + mu%*%heh(x, 3, 3), + hefullob(x, 2, 3, 4) + lam[2:3]%*%hefullg(x, 2, 3, 4) + mu%*%heh(x, 3, 4), + hefullob(x, 2, 3, 5) + lam[2:3]%*%hefullg(x, 2, 3, 5) + mu%*%heh(x, 3, 5), + hefullob(x, 2, 3, 6) + lam[2:3]%*%hefullg(x, 2, 3, 6) + mu%*%heh(x, 3, 6), + hefullob(x, 2, 3, 7) + lam[2:3]%*%hefullg(x, 2, 3, 7) + mu%*%heh(x, 3, 7) + ), + c(hefullob(x, 2, 4, 1) + lam[2:3]%*%hefullg(x, 2, 4, 1) + mu%*%heh(x, 4, 1), + hefullob(x, 2, 4, 2) + lam[2:3]%*%hefullg(x, 2, 4, 2) + mu%*%heh(x, 4, 2), + hefullob(x, 2, 4, 3) + lam[2:3]%*%hefullg(x, 2, 4, 3) + mu%*%heh(x, 4, 3), + hefullob(x, 2, 4, 4) + lam[2:3]%*%hefullg(x, 2, 4, 4) + mu%*%heh(x, 4, 4), + hefullob(x, 2, 4, 5) + lam[2:3]%*%hefullg(x, 2, 4, 5) + mu%*%heh(x, 4, 5), + hefullob(x, 2, 4, 6) + lam[2:3]%*%hefullg(x, 2, 4, 6) + mu%*%heh(x, 4, 6), + hefullob(x, 2, 4, 7) + lam[2:3]%*%hefullg(x, 2, 4, 7) + mu%*%heh(x, 4, 7) + ), + c(hefullob(x, 3, 5, 1) + lam[4:5]%*%hefullg(x, 3, 5, 1) + mu%*%heh(x, 5, 1), + hefullob(x, 3, 5, 2) + lam[4:5]%*%hefullg(x, 3, 5, 2) + mu%*%heh(x, 5, 2), + hefullob(x, 3, 5, 3) + lam[4:5]%*%hefullg(x, 3, 5, 3) + mu%*%heh(x, 5, 3), + hefullob(x, 3, 5, 4) + lam[4:5]%*%hefullg(x, 3, 5, 4) + mu%*%heh(x, 5, 4), + hefullob(x, 3, 5, 5) + lam[4:5]%*%hefullg(x, 3, 5, 5) + mu%*%heh(x, 5, 5), + hefullob(x, 3, 5, 6) + lam[4:5]%*%hefullg(x, 3, 5, 6) + mu%*%heh(x, 5, 6), + hefullob(x, 3, 5, 7) + lam[4:5]%*%hefullg(x, 3, 5, 7) + mu%*%heh(x, 5, 7) + ), + c(hefullob(x, 3, 6, 1) + lam[4:5]%*%hefullg(x, 3, 6, 1) + mu%*%heh(x, 6, 1), + hefullob(x, 3, 6, 2) + lam[4:5]%*%hefullg(x, 3, 6, 2) + mu%*%heh(x, 6, 2), + hefullob(x, 3, 6, 3) + lam[4:5]%*%hefullg(x, 3, 6, 3) + mu%*%heh(x, 6, 3), + hefullob(x, 3, 6, 4) + lam[4:5]%*%hefullg(x, 3, 6, 4) + mu%*%heh(x, 6, 4), + hefullob(x, 3, 6, 5) + lam[4:5]%*%hefullg(x, 3, 6, 5) + mu%*%heh(x, 6, 5), + hefullob(x, 3, 6, 6) + lam[4:5]%*%hefullg(x, 3, 6, 6) + mu%*%heh(x, 6, 6), + hefullob(x, 3, 6, 7) + lam[4:5]%*%hefullg(x, 3, 6, 7) + mu%*%heh(x, 6, 7) + ), + c(hefullob(x, 3, 7, 1) + lam[4:5]%*%hefullg(x, 3, 7, 1) + mu%*%heh(x, 7, 1), + hefullob(x, 3, 7, 2) + lam[4:5]%*%hefullg(x, 3, 7, 2) + mu%*%heh(x, 7, 2), + hefullob(x, 3, 7, 3) + lam[4:5]%*%hefullg(x, 3, 7, 3) + mu%*%heh(x, 7, 3), + hefullob(x, 3, 7, 4) + lam[4:5]%*%hefullg(x, 3, 7, 4) + mu%*%heh(x, 7, 4), + hefullob(x, 3, 7, 5) + lam[4:5]%*%hefullg(x, 3, 7, 5) + mu%*%heh(x, 7, 5), + hefullob(x, 3, 7, 6) + lam[4:5]%*%hefullg(x, 3, 7, 6) + mu%*%heh(x, 7, 6), + hefullob(x, 3, 7, 7) + lam[4:5]%*%hefullg(x, 3, 7, 7) + mu%*%heh(x, 7, 7) + ) + ) > > > print(resjacphi[1:n, 1:n] - checkA) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0 [2,] 0 -1.776357e-15 0 0 0.000000e+00 0.000000e+00 0 [3,] 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0 [4,] 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0 [5,] 0 0.000000e+00 0 0 1.776357e-15 0.000000e+00 0 [6,] 0 0.000000e+00 0 0 0.000000e+00 -3.552714e-15 0 [7,] 0 0.000000e+00 0 0 0.000000e+00 0.000000e+00 0 > > > cat("\n\n________________________________________\n\n") ________________________________________ > cat("\n\npart B\n\n") part B > > > checkB <- + rbind( + cbind(c(grfullg(x, 1, 1), grfullg(x, 1, 2)), c(0, 0), c(0, 0), c(0, 0), c(0, 0)), + cbind(c(0, 0), rbind(grfullg(x, 2, 3), grfullg(x, 2, 4)), c(0, 0), c(0, 0)), + cbind(c(0, 0, 0), c(0, 0, 0), c(0, 0, 0), rbind(grfullg(x, 3, 5), grfullg(x, 3, 6), grfullg(x, 3, 7))) + ) > checkB <- cbind(checkB, rbind(grh(x, 1), grh(x, 2), grh(x, 3), grh(x, 4), grh(x, 5), grh(x, 6), grh(x, 7))) > > print(resjacphi[1:n, (n+1):(n+m+dimmu)] - checkB) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 0 0 0 0 0 0 0 0 [2,] 0 0 0 0 0 0 0 0 [3,] 0 0 0 0 0 0 0 0 [4,] 0 0 0 0 0 0 0 0 [5,] 0 0 0 0 0 0 0 0 [6,] 0 0 0 0 0 0 0 0 [7,] 0 0 0 0 0 0 0 0 > > cat("\n\n________________________________________\n\n") ________________________________________ > cat("\n\npart C\n\n") part C > > checkC <- matrix(0, n, m+dimmu) > > print(resjacphi[1:n, (n+m+dimmu+1):(n+2*m+2*dimmu)] - checkC) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 0 0 0 0 0 0 0 0 [2,] 0 0 0 0 0 0 0 0 [3,] 0 0 0 0 0 0 0 0 [4,] 0 0 0 0 0 0 0 0 [5,] 0 0 0 0 0 0 0 0 [6,] 0 0 0 0 0 0 0 0 [7,] 0 0 0 0 0 0 0 0 > > cat("\n\n________________________________________\n\n") ________________________________________ > cat("\n\npart D\n\n") part D > > > > > checkD <- + t( + cbind( + rbind( + grfullg(x, 1, 1) , + grfullg(x, 1, 2) , + grfullg(x, 1, 3) , + grfullg(x, 1, 4) , + grfullg(x, 1, 5) , + grfullg(x, 1, 6) , + grfullg(x, 1, 7) + ), + rbind( + grfullg(x, 2, 1) , + grfullg(x, 2, 2) , + grfullg(x, 2, 3) , + grfullg(x, 2, 4) , + grfullg(x, 2, 5) , + grfullg(x, 2, 6) , + grfullg(x, 2, 7) + ), + rbind( + grfullg(x, 3, 1) , + grfullg(x, 3, 2) , + grfullg(x, 3, 3) , + grfullg(x, 3, 4) , + grfullg(x, 3, 5) , + grfullg(x, 3, 6) , + grfullg(x, 3, 7) + ) + ) + ) > checkD <- rbind(checkD, cbind(grh(x, 1), grh(x, 2), grh(x, 3), grh(x, 4), grh(x, 5), grh(x, 6), grh(x, 7))) > > > print(resjacphi[(n+1):(n+m+dimmu), 1:n] - checkD) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0 0 0 0 0 0 0 [2,] 0 0 0 0 0 0 0 [3,] 0 0 0 0 0 0 0 [4,] 0 0 0 0 0 0 0 [5,] 0 0 0 0 0 0 0 [6,] 0 0 0 0 0 0 0 [7,] 0 0 0 0 0 0 0 [8,] 0 0 0 0 0 0 0 > > > cat("\n\n________________________________________\n\n") ________________________________________ > cat("\n\npart E\n\n") part E > > > checkE <- matrix(0, m+dimmu, m+dimmu) > > print(resjacphi[(n+1):(n+m+dimmu), (n+1):(n+m+dimmu)] - checkE) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 0 0 0 0 0 0 0 0 [2,] 0 0 0 0 0 0 0 0 [3,] 0 0 0 0 0 0 0 0 [4,] 0 0 0 0 0 0 0 0 [5,] 0 0 0 0 0 0 0 0 [6,] 0 0 0 0 0 0 0 0 [7,] 0 0 0 0 0 0 0 0 [8,] 0 0 0 0 0 0 0 0 > > > cat("\n\n________________________________________\n\n") ________________________________________ > cat("\n\npart F\n\n") part F > > > checkF <- diag(m+dimmu) > > print(resjacphi[(n+1):(n+m+dimmu), (n+m+dimmu+1):(n+2*m+2*dimmu)] - checkF) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 0 0 0 0 0 0 0 0 [2,] 0 0 0 0 0 0 0 0 [3,] 0 0 0 0 0 0 0 0 [4,] 0 0 0 0 0 0 0 0 [5,] 0 0 0 0 0 0 0 0 [6,] 0 0 0 0 0 0 0 0 [7,] 0 0 0 0 0 0 0 0 [8,] 0 0 0 0 0 0 0 0 > > > cat("\n\n________________________________________\n\n") ________________________________________ > cat("\n\npart G\n\n") part G > > > checkG <- matrix(0, m+dimmu, n) > > print(resjacphi[(n+m+dimmu+1):(n+2*m+2*dimmu), 1:n] - checkG) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [1,] 0 0 0 0 0 0 0 [2,] 0 0 0 0 0 0 0 [3,] 0 0 0 0 0 0 0 [4,] 0 0 0 0 0 0 0 [5,] 0 0 0 0 0 0 0 [6,] 0 0 0 0 0 0 0 [7,] 0 0 0 0 0 0 0 [8,] 0 0 0 0 0 0 0 > > cat("\n\n________________________________________\n\n") ________________________________________ > cat("\n\npart H\n\n") part H > > > checkH <- diag(w) > > print(resjacphi[(n+m+dimmu+1):(n+2*m+2*dimmu), (n+1):(n+m+dimmu)] - checkH) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 0 0 0 0 0 0 0 0 [2,] 0 0 0 0 0 0 0 0 [3,] 0 0 0 0 0 0 0 0 [4,] 0 0 0 0 0 0 0 0 [5,] 0 0 0 0 0 0 0 0 [6,] 0 0 0 0 0 0 0 0 [7,] 0 0 0 0 0 0 0 0 [8,] 0 0 0 0 0 0 0 0 > > > cat("\n\n________________________________________\n\n") ________________________________________ > cat("\n\npart I\n\n") part I > > > checkI <- diag(c(lam, mu)) > > print(resjacphi[(n+m+dimmu+1):(n+2*m+2*dimmu), (n+m+dimmu+1):(n+2*m+2*dimmu)] - checkI) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 0 0 0 0 0 0 0 0 [2,] 0 0 0 0 0 0 0 0 [3,] 0 0 0 0 0 0 0 0 [4,] 0 0 0 0 0 0 0 0 [5,] 0 0 0 0 0 0 0 0 [6,] 0 0 0 0 0 0 0 0 [7,] 0 0 0 0 0 0 0 0 [8,] 0 0 0 0 0 0 0 0 > > checkjack <- rbind(cbind(checkA, checkB, checkC), cbind(checkD, checkE, checkF), cbind(checkG, checkH, checkI)) > > if(sum(abs(checkjack - resjacphi)) > .Machine$double.eps^(2/3)) + stop("wrong result") > > proc.time() user system elapsed 0.59 0.12 0.70