98+97+65/9+56=
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时间：2011-10-15 08:14
1+2+3+4+5+7+6+9+8+6+3+5+7+89+1+2+45+78+65 +1+1+1+1+21+34+5+1+2+4+56+6=?_百度作业帮
1+2+3+4+5+7+6+9+8+6+3+5+7+89+1+2+45+78+65 +1+1+1+1+21+34+5+1+2+4+56+6=?
1+2+3+4+5+7+6+9+8+6+3+5+7+89+1+2+45+78+65 +1+1+1+1+21+34+5+1+2+4+56+6=?
用计算器算一下就行啦请问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+46+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+8_百度作业帮
请问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+46+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+8
请问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+46+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+98+100等于几?要把题打下来哦,复制就行了.一道数学题28语文96分,数学100分,英语65分.英语80分.语文100分,数学97分,英语65分,9分,英语81.1分.英语96分.语文41分,数学97分,英语99分.数学96分,英语96分.语文72分,英语80分.语文56分,98.3分,英语100分_百度作业帮
一道数学题28语文96分,数学100分,英语65分.英语80分.语文100分,数学97分,英语65分,9分,英语81.1分.英语96分.语文41分,数学97分,英语99分.数学96分,英语96分.语文72分,英语80分.语文56分,98.3分,英语100分
一道数学题28语文96分,数学100分,英语65分.英语80分.语文100分,数学97分,英语65分,9分,英语81.1分.英语96分.语文41分,数学97分,英语99分.数学96分,英语96分.语文72分,英语80分.语文56分,98.3分,英语100分.语文79分,英语99分.语文80分,数学92分,英语90分.语文71分,数学100分,英语94.请问,我从一到六年级的语、数、英和在一起算,那平均分是多少?
(96+100+…＋100＋94.5)÷（12×3）＝86.675
都加在一起除以12结果是260.025，也就是说你一学期的平均成绩时260.025，再说应该按每科算呀，为什么想算和呢？
额,建议你用计算器``
口算真的有点难
小学的题目？是不是那种加法交换律（用个位数相加刚好整十整百的）？？？
下次把基本功搞扎实再来提问吧 像这种题我就不喜欢用什么简便算法
用Excel 不就很容易吗？一输入 就可以啦！
用Excel 不就很容易吗？ 哈哈 算呀 ，简单呀
小孩,你不厚道哦
用Excel 学学把你.........................还用计算器
数学：(12*100-36.3)/12=96.975以此类推
=86.675下次把基本功搞扎实再来提问吧 像这种题我就不喜欢用什么简便算法用Excel 学学把你.........................还用计算器
把所有的成绩加起来，再除以36，等于86.675。
86.675厄 我倒
以85分为标准分，用各个数减它，得1.675，再加85可得：86.675
260.025=86.675 选择吧
。。。有难度，不会~~~~
86.675...算死
是不是写成一年级（100-4）+100+（100-35）+（100-15）+（100-5）+（100-20）然后100-（减去数值的和）÷（12×3）
把他们都加起来 在除(6*2*3)就可以了
86.675！！！！简单死了，还用计算器！！！
86.675为什么用别人算！很懒哦~~~~~~
你应该自己算让我们算也要加悬赏啊！1"fitfclust" <-
function(x=NULL,curve=NULL,timeindex=NULL,data=NULL, q = 5, h = 1, p = 5,
K = 2, tol = 0.001, maxit = 20, pert =
0.01, grid = seq(0, 1, length = 100), hard = F, plot= F,trace=F)
# This is the main function to implement the FClust procedure.
library(splines)
if (is.null(data))
data <- list(x=x,curve=curve,timeindex=timeindex)
initfit <- fclustinit(data = data, pert = pert, grid = grid, h = h,
p = p, q = q, K = K)
# Initialize the parameters
parameters <- initfit$parameters
vars <- initfit$vars
S <- initfit$S
FullS <- initfit$FullS
sigma.old <- 0
sigma.new <- 1
tol & (ind <= maxit)) {
parameters <- fclustMstep(parameters, data, vars, S, tol, p, hard)
vars <- fclustEstep(parameters, data, vars, S, hard)
sigma.old <- sigma.new
sigma.new <- parameters$sigma[1]
if (trace)
print(paste("Iteration", ind,": Sigma = ",sigma.new))
# Plot cluster mean curves.
cluster.mean <- matrix(0,K,dim(FullS)[1])
for(k in 1:K)
cluster.mean[k,] <- FullS %*% (parameters$lambda.zero + parameters$Lambda %*% parameters$alpha[k,
plot(grid,grid,ylim=range(cluster.mean),type='n',ylab="Cluster Mean")
for(k in 1:K)
lines(grid,cluster.mean[k,], col = 4, lwd = 2)
ind <- ind + 1
# Enforce parameter constraint (7)
cfit <- fclustconst(data, parameters, vars, FullS)
list(data=data,parameters = cfit$parameters, vars = cfit$vars, FullS = FullS,grid=grid)
"fclustinit" <-
function(data, pert = 0, grid = seq(0.01, 1, length = 100), h = 1, p = 2, q = 5,K = K){
S <- FullS <- NULL
# This function initializes all the parameters.
# Produce spline basis matrix
FullS <- cbind(1, ns(grid, df = (q - 1)))
FullS <- svd(FullS)$u
S <- FullS[data$timeindex,
N <- length(table(data$curve))
# Compute initial estimate of basis coefficients.
points <- matrix(0,N,sum(q))
for (i in 1:N){
Si <- S[data$curve==i,]
xi <- data$x[data$curve==i]
points[i,]
class <- kmeans(points, K, 10)$cluster
else class <- rep(1, N)
# Initial estimates for the posterior probs of cluster membership.
piigivej <- matrix(0, N, K)
piigivej[col(piigivej) == class] <- 1
# Calculate coefficeints for cluster means.
classmean <- matrix(0,K,q)
for (k in 1:K)
classmean[k,] <- apply(points[class==k,],2,mean)
# Initialize lambda.zero, Lambda and alpha as defined in paper.
lambda.zero <- apply(classmean, 2, mean)
Lambda <- as.matrix(svd(scale(classmean, scale = F))$v[, 1:h])
alpha <- scale(classmean, scale = F)%*%Lambda
# Calculate estimates for gamma and gprod.
gamma <- t(t(points) - lambda.zero - (Lambda %*% t(alpha[class,
gprod <- NULL
for(i in 1:N)
gprod <- cbind(gprod, (gamma[i,
]) %*% t(gamma[i,
gamma <- array(gamma[, rep(1:sum(q), rep(K, sum(q)))], c(N, K, sum(q)))
gcov <- matrix(0, sum(q), N * sum(q))
list(S = S, FullS = FullS, parameters = list(lambda.zero = lambda.zero,
Lambda = Lambda, alpha = alpha), vars = list(gamma = gamma,
gprod = gprod, gcov = gcov, piigivej = piigivej))
"fclustMstep" <-
function(parameters, data, vars, S, tol, p, hard)
# This function implements the M step of the EM algorithm.
K <- dim(parameters$alpha)[1]
alpha <- parameters$alpha
Lambda <- parameters$Lambda
gamma <- vars$gamma
gcov <- vars$gcov
curve <- data$curve
piigivej <- vars$piigivej
N <- dim(gamma)[1]
K <- dim(alpha)[1]
h <- dim(alpha)[2]
n <- length(curve)
q <- dim(S)[2]
sigma.old <- 2
sigma <- 1
# Compute pi.
parameters$pi <- rep(1/K, K)
else parameters$pi <- apply(vars$piigivej, 2, mean)
# Compute rank p estimate of Gamma
ind <- matrix(rep(c(rep(c(1, rep(0, q - 1)), N), 0), q)[1:(N*q^2)], N * q, q)
gsvd <- svd(vars$gprod %*% ind/N)
gsvd$d[ - (1:p)] <- 0
parameters$Gamma <- gsvd$u %*% diag(gsvd$d) %*% t(gsvd$u)
# This loop iteratively calculates alpha and then Lambda and stops
# when they have converged.
loopnumber
tol) & (loopnumber <10)){
sigma.old <- sigma
# Calculate lambda.zero.
gamma.pi <- diag(S %*% t(apply(gamma * as.vector(piigivej),
c(1, 3), sum)[curve,
alpha.pi <- t(matrix(apply(alpha, 2, function(x, piigivej,K)
{rep(1, K) %*% (piigivej * x)}
, t(piigivej), K), N, h)[curve,
lambda.zero <- solve(t(S) %*% S) %*% t(S) %*% (data$x - diag(
S %*% Lambda %*% alpha.pi) - gamma.pi)
x <- data$x - S %*% lambda.zero
# Calculate alpha.
for(i in 1.:K) {
S.Lam <- S %*% Lambda
] <- solve(t(S.Lam.pi) %*% S.Lam) %*%
t(S.Lam.pi) %*% (x - diag(S %*% t(gamma[curve, i,
else print("Warning: empty cluster")
# Calculate Lambda given alpha. This is done by iterating
# through each column of Lambda holding the other columns fixed.
for(m in 1:h) {
pi.alphasq <- apply(t(piigivej) * (alpha^2)[, m], 2,sum)[curve]
pi.alpha <- apply(t(piigivej) * alpha[, m], 2, sum)[curve]
S.Lambda <- t(S %*% Lambda)
if(h != 1) {
temp <- NULL
for(i in 1:K) {
temp <- cbind(temp, as.vector(rep(1, h - 1) %*% matrix((S.Lambda *
], h - 1,dim(S)[1])) * alpha[i, m])
otherLambda <- (temp * piigivej[curve,
])%*%rep(1, K)
else otherLambda <- 0
gamma.pi.alpha <- apply(gamma * as.vector(piigivej) *
rep(alpha[, m], rep(N, K)), c(1, 3), sum)[curve,
Lambda[, m] <- solve(t(S * pi.alphasq) %*% S) %*% t(S) %*%
(x * pi.alpha - otherLambda - (S *gamma.pi.alpha) %*% rep(1, sum(q)))
# Calculate sigma
ind <- matrix(rep(c(rep(F, q), rep(T, N * q)),N)
[1:(N * N * q)], N, N * q, byrow = T)[rep(1:N, table(curve)),]
mat1 <- matrix(rep(S, N), n, N * q)
mat3 <- t(mat1)
mat3[t(ind)] <- 0
ind2 <- matrix(rep(c(rep(F, q), rep(T, N * q)),
N)[1:(N * N * q)], N, N * q, byrow = T)[rep(1:N, rep(q, N)),]
mat2 <- matrix(rep(t(gcov), N), N * q, N * q,byrow = T)
mat2[ind2] <- 0
econtrib <- 0
for(i2 in 1:K) {
vect1 <- x - S %*% Lambda %*% alpha[
] - (S * gamma[curve, i2,
]) %*% rep(1, q)
econtrib <- econtrib + t(piigivej[curve,i2] * vect1) %*% vect1
sigma <- as.vector((econtrib + sum(diag(mat1 %*% mat2 %*% mat3)))/n)
loopnumber <- loopnumber + 1
parameters$lambda.zero <- as.vector(lambda.zero)
parameters$alpha <- alpha
parameters$Lambda <- Lambda
parameters$sigma <- sigma
parameters
"fclustEstep" <-
function(parameters, data, vars, S, hard)
# This function performs the E step of the EM algorithm by
# calculating the expected values of gamma and gamma %*% t(gamma)
# given the current parameter estimates.
par <- parameters
N <- dim(vars$gamma)[1]
K <- dim(vars$gamma)[2]
q <- dim(vars$gamma)[3]
Gamma <- par$Gamma
Lambda.alpha <- par$lambda.zero + par$Lambda %*% t(par$alpha)
vars$gprod <- vars$gcov <- NULL
for(j in 1:N) {
# Calculate expected value of gamma.
Sj <- S[data$curve == j,
nj <- sum(data$curve == j)
invvar <- diag(1/rep(par$sigma, nj))
Cgamma <- Gamma - Gamma %*% t(Sj) %*% solve(diag(nj) + Sj %*%
Gamma %*% t(Sj) %*% invvar) %*% invvar %*% Sj %*% Gamma
centx <- data$x[data$curve == j] - Sj %*% Lambda.alpha
vars$gamma[j,
] <- t(Cgamma %*% t(Sj) %*% invvar %*% centx)
# Calculate pi i given j.
covx <- Sj %*% par$Gamma %*% t(Sj) + solve(invvar)
d <- exp( - diag(t(centx) %*% solve(covx) %*% centx)/2) * par$pi
vars$piigivej[j,
] <- d/sum(d)
if(hard) {
m <- order( - d)[1]
vars$piigivej[j,
vars$piigivej[j, m] <- 1
# Calculate expected value of gamma %*% t(gamma).
vars$gprod <- cbind(vars$gprod, t(matrix(vars$gamma[j,
K, q)) %*% (matrix(vars$gamma[j,
], K, q) * vars$
piigivej[j,
]) + Cgamma)
vars$gcov <- cbind(vars$gcov, Cgamma)
"fclustconst" <-
function(data, parameters, vars, S)
# This function enforces the constraint (7) from the paper on the
# parameters. This means that the alphas can be interpreted as the
# number of standard deviations that the groups are apart etc.
par <- parameters
A <- t(S) %*% solve(par$sigma * diag(dim(S)[1]) + S %*% par$Gamma %*%
t(S)) %*% S
svdA <- svd(A)
sqrtA <- diag(sqrt(svdA$d)) %*% t(svdA$u)
negsqrtA <- svdA$u %*% diag(1/sqrt(svdA$d))
finalsvd <- svd(sqrtA %*% par$Lambda)
par$Lambda
par$alpha <- t(diag(finalsvd$d) %*% t(finalsvd$v) %*% t(par$alpha))
else par$alpha <- t(finalsvd$d * t(finalsvd$v) %*% t(par$alpha))
meanalpha <- apply(par$alpha, 2, mean)
par$alpha <- t(t(par$alpha) - meanalpha)
par$lambda.zero <- par$lambda.zero + par$Lambda %*% meanalpha
list(parameters = par, vars = vars)
"nummax" <-
function(X)
ind <- rep(1, dim(X)[1])
for(i in 2:dim(X)[2]) {
ind[test] <- i
m[test] <- X[test, i]
list(ind = ind, max = m)
"fclust.pred" <-
function(fit,data=NULL,reweight=F)
# This function produces the alpha hats used to provide a low
# dimensional pictorial respresentation of each curve. It also
# produces a class prediction for each curve. It takes as
# input the fit from fldafit (for predictions on the original data)
# or the fit and a new data set (for predictions on new data).
if (is.null(data))
data <- fit$data
FullS <- fit$FullS
par <- fit$parameters
curve <- data$curve
time <- data$time
N <- length(table(curve))
h <- dim(par$alpha)[2]
alpha.hat <- matrix(0, N, h)
K <- dim(fit$par$alpha)[1]
distance <- matrix(0, N, K)
Calpha <- array(0, c(N, h, h))
for(i in 1:N) {
Sij <- FullS[time[curve == i],
xij <- data$x[curve == i]
n <- length(xij)
Sigma <- par$sigma * diag(n) + Sij %*% par$Gamma %*% t(Sij)
# Calculate covariance for each alpha hat.
InvCalpha <- t(par$Lambda) %*% t(Sij) %*% solve(Sigma) %*% Sij %*%
par$Lambda
] <- solve(InvCalpha)
# Calculate each alpha hat.
alpha.hat[i,
] <- Calpha[i,
] %*% t(par$Lambda) %*% t(
Sij) %*% solve(Sigma) %*% (xij - Sij %*% par$lambda.zero)
# Calculate the matrix of distances, relative to the
# appropriate metric of each curve from each class centroid.
for (k in 1:K){
y <- as.vector(alpha.hat[i,])-fit$par$alpha[k,]
distance[i,k] <- t(y)%*%InvCalpha %*%y}}
# Calculate final class predictions for each curve.
class.pred <- rep(1, N)
log.pi <- log(fit$par$pi)
if (!reweight)
log.pi <- rep(0,K)
probs <- t(exp(log.pi-t(distance)/2))
probs <- probs/apply(probs,1,sum)
m <- probs[,1]
if(K != 1)
for(k in 2:K) {
class.pred[test] <- k
m[test] <- probs[test, k]
list(Calpha = Calpha, alpha.hat = alpha.hat, class.pred = class.pred,
distance = distance, m = m,probs=probs)
"fclust.curvepred" <-
function(fit, data=NULL, index=NULL, tau = 0.95, tau1 = 0.975)
if (is.null(data))
data <- fit$data
if (is.null(index))
index <- 1:length(table(data$curve))
tau2 <- tau/tau1
sigma <- fit$par$sigma
Gamma <- fit$par$Gamma
Lambda <- fit$par$Lambda
alpha <- fit$par$alpha
lambda.zero <- as.vector(fit$par$lambda.zero)
S <- fit$FullS
N <- length(index)
upci <-lowci <- uppi <- lowpi <- gpred <- matrix(0,N,nrow(S))
etapred <- matrix(0,N,ncol(S))
Lambda.alpha <- lambda.zero + Lambda %*% t(alpha)
for (i in index){
y <- data$x[data$curve == i]
Si <- S[data$time[data$curve == i],
ni <- dim(Si)[1]
invvar <- diag(1/rep(sigma, ni))
covx <- Si %*% Gamma %*% t(Si) + solve(invvar)
centx <- data$x[data$curve == i] - Si %*% Lambda.alpha
d <- exp( - diag(t(centx) %*% solve(covx) %*% centx)/2) * fit$par$pi
pi <- d/sum(d)
K <- length(pi)
mu <- lambda.zero + Lambda %*% t(alpha * pi) %*% rep(1, K)
cov <- (Gamma - Gamma %*% t(Si) %*% solve(diag(ni) + Si %*% Gamma %*%
t(Si)/sigma) %*% Si %*% Gamma/sigma)/sigma
etapred[ind,] <- mu + cov %*% t(Si) %*% (y - Si %*% mu)
ord <- order( - pi)
numb <- sum(cumsum(pi[ord]) <= tau1) + 1
v <- diag(S %*% (cov * sigma) %*% t(S))
pse <- sqrt(v + sigma)
se <- sqrt(v)
lower.p <- upper.p <- lower.c <- upper.c <- matrix(0, nrow(S), numb)
for(j in 1:numb) {
mu <- lambda.zero + Lambda %*% alpha[ord[j],
mean <- S %*% (mu + cov %*% t(Si) %*% (y - Si %*% mu))
upper.p[, j] <- mean + qnorm(tau2) * pse
lower.p[, j] <- mean - qnorm(tau2) * pse
upper.c[, j] <- mean + qnorm(tau2) * se
lower.c[, j] <- mean - qnorm(tau2) * se
upci[ind,] <- nummax(upper.c)$max
lowci[ind,] <-
- nummax( - lower.c)$max
uppi[ind,] <- nummax(upper.p)$max
lowpi[ind,] <-
- nummax( - lower.p)$max
gpred[ind,] <- as.vector(S %*%etapred[ind,])
ind <- ind+1
meancurves <- S%*%Lambda.alpha
list(etapred = etapred, gpred = gpred,
upci = upci,lowci = lowci,
uppi = uppi, lowpi = lowpi,index=index,grid=fit$grid,data=data,meancurves=meancurves)
"fclust.discrim" <-
function(fit,absvalue=F){
S <- fit$FullS
sigma <- fit$par$sigma
n <- nrow(S)
Gamma <- fit$par$Gamma
Sigma <- S%*%Gamma%*%t(S)+sigma*diag(n)
Lambda <- fit$par$Lambda
discrim <- solve(Sigma)%*%S%*%Lambda
if (absvalue)
discrim <- abs(discrim)
n <- ncol(discrim)
nrows <- ceiling(sqrt(n))
par(mfrow=c(nrows,nrows))
for (i in 1:n){
plot(fit$grid,discrim[,i],ylab=paste("Discriminant Function ",i),xlab="Time",type='n')
lines(fit$grid,discrim[,i],lwd=3)
abline(0,0)}}
"fclust.plotcurves" <-
function(object=NULL,fit=NULL,index=NULL,ci=T,pi=T,clustermean=F){
if (is.null(object))
object <- fclust.curvepred(fit)
if (is.null(index))
index <- 1:length(table(object$data$curve))
r <- ceiling(sqrt(length(index)))
par(mfrow=c(r,r))
for (i in index){
grid <- object$grid
upci <- object$upci[i,]
uppi <- object$uppi[i,]
lowci <- object$lowci[i,]
lowpi <- object$lowpi[i,]
gpred <- object$gpred[i,]
meancurves <- (object$mean)
if (clustermean)
yrange <- c(min(c(lowpi,meancurves)),max(c(uppi,meancurves)))
yrange <- c(min(lowpi),max(uppi))
plot(grid,grid,ylim=yrange,ylab="Predictions",xlab="Time",type='n',
main=paste("Curve ",i))
if (clustermean)
in 1:ncol(meancurves))
lines(grid,meancurves[,k],col=6,lty=2,lwd=2)
lines(grid,upci,col=3)
lines(grid,lowci,col=3)}
lines(grid,uppi,col=4)
lines(grid,lowpi,col=4)}
lines(grid,gpred,col=2,lwd=2)
lines(grid[object$data$time[object$data$curve==i]],object$data$x[object$data$curve==i],lwd=2)
points(grid[object$data$time[object$data$curve==i]],object$data$x[object$data$curve==i],pch=19,cex=1.5)
"simdata" <-
structure(list(x = c(-0.744, -0.710,
-0.774, -0.801, -0.887, -0.542,
-0.043, -0.017, 0.139, 0.111,
-0.911, -0.019, -0.034, -0.344,
-0.244, -0.014, -0.494, -0.988,
-0.149, 0.303, -0.189, -0.310,
-0.844, -0.501, -0.119, -0.793,
-0.505, -0.451, 0.983, 0.723,
-0.803, -0.990, -0.444, -0.510,
-0.117, -0.606, -0.032, -0.116,
0.704, 0.912, -0.055, -0.792,
-0.500, -0.697, -0.563, -0.978,
-0.385, -0.917, -0.318, 0.226,
-0.796, -0.946, -0.913, -0.629,
-0.515, -0.510, -0.498, -0.034,
-0.813, 0.146, -0.864, -0.852,
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61, 61, 61, 61, 61, 61, 61, 62, 62, 62, 62, 62, 62, 62, 62, 62,
62, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 64, 64, 64, 64, 64,
64, 64, 64, 64, 64, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 66,
66, 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67,
67, 67, 67, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 69, 69, 69,
69, 69, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 70, 70, 70,
70, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 72, 72, 72, 72, 72,
72, 72, 72, 72, 72, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 74,
74, 74, 74, 74, 74, 74, 74, 74, 74, 75, 75, 75, 75, 75, 75, 75,
75, 75, 75, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 77, 77, 77,
77, 77, 77, 77, 77, 77, 77, 78, 78, 78, 78, 78, 78, 78, 78, 78,
78, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 80, 80, 80, 80, 80,
80, 80, 80, 80, 80, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 82,
82, 82, 82, 82, 82, 82, 82, 82, 82, 83, 83, 83, 83, 83, 83, 83,
83, 83, 83, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 85, 85, 85,
85, 85, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 86, 86, 86, 86,
86, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88,
88, 88, 88, 88, 88, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 90,
90, 90, 90, 90, 90, 90, 90, 90, 90, 91, 91, 91, 91, 91, 91, 91,
91, 91, 91, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 93, 93, 93,
93, 93, 93, 93, 93, 93, 93, 94, 94, 94, 94, 94, 94, 94, 94, 94,
94, 95, 95, 95, 95, 95, 95, 95, 95, 95, 95, 96, 96, 96, 96, 96,
96, 96, 96, 96, 96, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 98,
98, 98, 98, 98, 98, 98, 98, 98, 98, 99, 99, 99, 99, 99, 99, 99,
99, 99, 99, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100)),
gamma = structure(c(0.1933, -0.454,
0.326, 0.717, -0.5151,
0.9358, -0.3,
0.866, -0.562, -0.5168,
-0.079, 0.7028, -0.654,
-0.666, 0.,
0.787, 0.2608, -0.679,
0.20577, -0.777, -0.4202,
-0.7011, -0.8,
-0.797, -0.5518, -0.1376,
0.849, -0.7,
0., 0.2401,
-0.4585, -0.4,
0.4132, -0.8,
-0., -0.064,
-0.822, -0.6058, -0.2312,
-0.546, -0.,
0.833, -0.5,
0.753, -0.795, -0.5221,
0.369, -0.2,
0.8, 0.294,
0.8015, -0.216, 0.3153,
0.559, 0.0312, -0.822,
0.6506, -0.055, -0.8464,
0.34, -0.393, 0.511,
-0.407, -0.377, -0.559,
-0.962, 0.,
0.334, 0.897, 0.3385,
-0., -0.116,
-0.7708, -0.208, 0.1661,
-0.316, 0.266, -0.3580,
-0.111, 0.8422, -0.7190,
-0.1406, -0.8604, -0.496,
-0.7, -0.0915,
-0.8954, -0.0,
-0., 0.461,
-0.595, 0.4934, -0.4649,
-0.341, 0.8886, -0.644,
-0.71, 0.338,
0., -0.5371,
-0.84681, -0.3565, -0.945,
0.6874, -0.442, -0.725,
0.172, -0.784, -0.9201,
-0.2815, -0.6938, -0.0498,
0.4, 0.1991,
0.600, 0.264, 0.8194,
-0.8, -0.1508,
0.3122, -0.968, -0.703,
0.842, -0.,
-0.2971, -0.505, -0.8875,
0.1597, -0.1010, -0.9199,
0.565, -0.6607, -0.54152,
-0., -0.4838,
-0.595, -0.1943, -0.48,
0.235, 0.963, -0.373,
0.235, -0.4,
0.1174, -0.25,
-0., 0.2879,
-0.129, -0.486, 0.0154,
0.9057, -0.992, -0.9127,
0.9272, -0.2,
0.6, -0.39235,
-0.0783, -0.907, 0.423,
-0., 0.7936,
0.9, -0.5952,
-0.2337, -0.9,
-0.92, -0.13,
0.719, 0.3,
-0.64541, -0.8617, -0.15532,
-0., 0.2691,
-0.2022, -0.121, -0.0287,
-0.9, -0.8952,
0.180, -0.4835,
-0.3015, -0.0,
0.7744, -0.0944, -0.364,
-0.527, 0.202, 0.4899,
0.0977, -0.2857, -0.5956,
0.6836, -0.8532, -0.319,
0.8811, -0.164, -0.268,
-0.4, 0.3462,
-0.3, 0.06,
-0.844, -0.6331, -0.114,
-0.4278, -0.6153, -0.772,
0.698, 0.7,
-0.4, 0.3320,
0.424, -0.6769, -0.684,
-0.206, -0.619, -0.7511,
-0.031, 0.362, 0.986,
-0.418, -0.1322, -0.0996,
0.433, 0.4,
-0., 0.4488,
0.3789, -0.46,
-0.550, -0.0019, -0.5229,
0.93, -0.2556,
0.2953, -0.587, -0.808,
-0.6, -0.81978,
0.6765, -0.356, -0.1184,
0.8, -0.8130,
-0.815, 0.6,
0.316, -0.2277, -0.921,
-0.69952, -0.2911, -0.3116,
0.7, -0.8866,
0.06, -0.9929,
-0.3059, -0.,
0.4053, -0.3418, -0.5314,
-0.45994, -0.1293, -0.5009,
-0.8, 0.3875,
-0., -0.5605,
-0., 0.297,
-0.7392, -0.8798, -0.506,
0.246, -0.2254, -0.4091,
-0.164, -0.2,
0.3631, -0.36, -0.8163,
0.269, 0.,
0.4948, -0.31, 0.2287,
-0.2699, -0.8,
-0.32, 0.75,
0., 0.9731,
0.152, 0.9462, -0.3424,
0.627, 0.264, -0.977187,
0.654, 0.269, 0.491,
-0.055, -0.080, -0.518756,
-0.721, 0.278, 0.4951,
0.535, -0.1312, -0.200,
0.0, 0.490,
0.64, 0.315, -0.98636,
-0.2, 0.0881,
-0.8459, -0.4035, -0.848,
-0.0814, -0.42,
0.5, -0.452,
-0.5, 0.90795,
-0.613, -0.7186, -0.5498,
0.486, -0.5285, -0.3903,
0.5053, -0.38434, -0.656,
-0.4, -0.546,
0.650, 0.5,
-0.983, 0.3158, -0.3998,
0.775, -0.53,
0.3230, -0.31,
0., 0.34467,
0.8, -0.3933,
-0.9, -0.106,
0.7897, -0.772, -0.501,
-0.6, -0.563,
-0., 0.5162,
-0.220, 0.8172, -0.7622,
0.14, -0.646, -0.6405,
-0.6515, -0.175, 0.64834,
-0.7, 0.4942,
0.2586, -0.961, -0.598,
-0.61, -0.495,
-0.319, -0.7,
-0.2, -0.833,
0.3, -0.0213,
0.861, -0..128,
-0.352, 0.534, -0.882,
0., -0.347,
-0.5, 0.274,
0., 0.9967,
-0., -0.30559,
-0.6309, -0.730, 0.4747,
0.0, -0.872,
0.752, 0.922, 0.80398,
0., -0.8596,
-0., 0.5408,
0.008, 0.425, -0.2848
), .Dim = as.integer(c(100, 5)))), .Names = c("x", "timeindex",
"curve", "gamma"))}
1+2+3+4+5+7+6+9+8+6+3+5+7+89+1+2+45+78+65 +1+1+1+1+21+34+5+1+2+4+56+6=?
1+2+3+4+5+7+6+9+8+6+3+5+7+89+1+2+45+78+65 +1+1+1+1+21+34+5+1+2+4+56+6=?
用计算器算一下就行啦请问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+46+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+8_百度作业帮
请问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+46+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+8
请问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+46+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+98+100等于几?要把题打下来哦,复制就行了.一道数学题28语文96分,数学100分,英语65分.英语80分.语文100分,数学97分,英语65分,9分,英语81.1分.英语96分.语文41分,数学97分,英语99分.数学96分,英语96分.语文72分,英语80分.语文56分,98.3分,英语100分_百度作业帮
一道数学题28语文96分,数学100分,英语65分.英语80分.语文100分,数学97分,英语65分,9分,英语81.1分.英语96分.语文41分,数学97分,英语99分.数学96分,英语96分.语文72分,英语80分.语文56分,98.3分,英语100分
一道数学题28语文96分,数学100分,英语65分.英语80分.语文100分,数学97分,英语65分,9分,英语81.1分.英语96分.语文41分,数学97分,英语99分.数学96分,英语96分.语文72分,英语80分.语文56分,98.3分,英语100分.语文79分,英语99分.语文80分,数学92分,英语90分.语文71分,数学100分,英语94.请问,我从一到六年级的语、数、英和在一起算,那平均分是多少?
(96+100+…＋100＋94.5)÷（12×3）＝86.675
都加在一起除以12结果是260.025，也就是说你一学期的平均成绩时260.025，再说应该按每科算呀，为什么想算和呢？
额,建议你用计算器``
口算真的有点难
小学的题目？是不是那种加法交换律（用个位数相加刚好整十整百的）？？？
下次把基本功搞扎实再来提问吧 像这种题我就不喜欢用什么简便算法
用Excel 不就很容易吗？一输入 就可以啦！
用Excel 不就很容易吗？ 哈哈 算呀 ，简单呀
小孩,你不厚道哦
用Excel 学学把你.........................还用计算器
数学：(12*100-36.3)/12=96.975以此类推
=86.675下次把基本功搞扎实再来提问吧 像这种题我就不喜欢用什么简便算法用Excel 学学把你.........................还用计算器
把所有的成绩加起来，再除以36，等于86.675。
86.675厄 我倒
以85分为标准分，用各个数减它，得1.675，再加85可得：86.675
260.025=86.675 选择吧
。。。有难度，不会~~~~
86.675...算死
是不是写成一年级（100-4）+100+（100-35）+（100-15）+（100-5）+（100-20）然后100-（减去数值的和）÷（12×3）
把他们都加起来 在除(6*2*3)就可以了
86.675！！！！简单死了，还用计算器！！！
86.675为什么用别人算！很懒哦~~~~~~
你应该自己算让我们算也要加悬赏啊！1"fitfclust" <-
function(x=NULL,curve=NULL,timeindex=NULL,data=NULL, q = 5, h = 1, p = 5,
K = 2, tol = 0.001, maxit = 20, pert =
0.01, grid = seq(0, 1, length = 100), hard = F, plot= F,trace=F)
# This is the main function to implement the FClust procedure.
library(splines)
if (is.null(data))
data <- list(x=x,curve=curve,timeindex=timeindex)
initfit <- fclustinit(data = data, pert = pert, grid = grid, h = h,
p = p, q = q, K = K)
# Initialize the parameters
parameters <- initfit$parameters
vars <- initfit$vars
S <- initfit$S
FullS <- initfit$FullS
sigma.old <- 0
sigma.new <- 1
tol & (ind <= maxit)) {
parameters <- fclustMstep(parameters, data, vars, S, tol, p, hard)
vars <- fclustEstep(parameters, data, vars, S, hard)
sigma.old <- sigma.new
sigma.new <- parameters$sigma[1]
if (trace)
print(paste("Iteration", ind,": Sigma = ",sigma.new))
# Plot cluster mean curves.
cluster.mean <- matrix(0,K,dim(FullS)[1])
for(k in 1:K)
cluster.mean[k,] <- FullS %*% (parameters$lambda.zero + parameters$Lambda %*% parameters$alpha[k,
plot(grid,grid,ylim=range(cluster.mean),type='n',ylab="Cluster Mean")
for(k in 1:K)
lines(grid,cluster.mean[k,], col = 4, lwd = 2)
ind <- ind + 1
# Enforce parameter constraint (7)
cfit <- fclustconst(data, parameters, vars, FullS)
list(data=data,parameters = cfit$parameters, vars = cfit$vars, FullS = FullS,grid=grid)
"fclustinit" <-
function(data, pert = 0, grid = seq(0.01, 1, length = 100), h = 1, p = 2, q = 5,K = K){
S <- FullS <- NULL
# This function initializes all the parameters.
# Produce spline basis matrix
FullS <- cbind(1, ns(grid, df = (q - 1)))
FullS <- svd(FullS)$u
S <- FullS[data$timeindex,
N <- length(table(data$curve))
# Compute initial estimate of basis coefficients.
points <- matrix(0,N,sum(q))
for (i in 1:N){
Si <- S[data$curve==i,]
xi <- data$x[data$curve==i]
points[i,]
class <- kmeans(points, K, 10)$cluster
else class <- rep(1, N)
# Initial estimates for the posterior probs of cluster membership.
piigivej <- matrix(0, N, K)
piigivej[col(piigivej) == class] <- 1
# Calculate coefficeints for cluster means.
classmean <- matrix(0,K,q)
for (k in 1:K)
classmean[k,] <- apply(points[class==k,],2,mean)
# Initialize lambda.zero, Lambda and alpha as defined in paper.
lambda.zero <- apply(classmean, 2, mean)
Lambda <- as.matrix(svd(scale(classmean, scale = F))$v[, 1:h])
alpha <- scale(classmean, scale = F)%*%Lambda
# Calculate estimates for gamma and gprod.
gamma <- t(t(points) - lambda.zero - (Lambda %*% t(alpha[class,
gprod <- NULL
for(i in 1:N)
gprod <- cbind(gprod, (gamma[i,
]) %*% t(gamma[i,
gamma <- array(gamma[, rep(1:sum(q), rep(K, sum(q)))], c(N, K, sum(q)))
gcov <- matrix(0, sum(q), N * sum(q))
list(S = S, FullS = FullS, parameters = list(lambda.zero = lambda.zero,
Lambda = Lambda, alpha = alpha), vars = list(gamma = gamma,
gprod = gprod, gcov = gcov, piigivej = piigivej))
"fclustMstep" <-
function(parameters, data, vars, S, tol, p, hard)
# This function implements the M step of the EM algorithm.
K <- dim(parameters$alpha)[1]
alpha <- parameters$alpha
Lambda <- parameters$Lambda
gamma <- vars$gamma
gcov <- vars$gcov
curve <- data$curve
piigivej <- vars$piigivej
N <- dim(gamma)[1]
K <- dim(alpha)[1]
h <- dim(alpha)[2]
n <- length(curve)
q <- dim(S)[2]
sigma.old <- 2
sigma <- 1
# Compute pi.
parameters$pi <- rep(1/K, K)
else parameters$pi <- apply(vars$piigivej, 2, mean)
# Compute rank p estimate of Gamma
ind <- matrix(rep(c(rep(c(1, rep(0, q - 1)), N), 0), q)[1:(N*q^2)], N * q, q)
gsvd <- svd(vars$gprod %*% ind/N)
gsvd$d[ - (1:p)] <- 0
parameters$Gamma <- gsvd$u %*% diag(gsvd$d) %*% t(gsvd$u)
# This loop iteratively calculates alpha and then Lambda and stops
# when they have converged.
loopnumber
tol) & (loopnumber <10)){
sigma.old <- sigma
# Calculate lambda.zero.
gamma.pi <- diag(S %*% t(apply(gamma * as.vector(piigivej),
c(1, 3), sum)[curve,
alpha.pi <- t(matrix(apply(alpha, 2, function(x, piigivej,K)
{rep(1, K) %*% (piigivej * x)}
, t(piigivej), K), N, h)[curve,
lambda.zero <- solve(t(S) %*% S) %*% t(S) %*% (data$x - diag(
S %*% Lambda %*% alpha.pi) - gamma.pi)
x <- data$x - S %*% lambda.zero
# Calculate alpha.
for(i in 1.:K) {
S.Lam <- S %*% Lambda
] <- solve(t(S.Lam.pi) %*% S.Lam) %*%
t(S.Lam.pi) %*% (x - diag(S %*% t(gamma[curve, i,
else print("Warning: empty cluster")
# Calculate Lambda given alpha. This is done by iterating
# through each column of Lambda holding the other columns fixed.
for(m in 1:h) {
pi.alphasq <- apply(t(piigivej) * (alpha^2)[, m], 2,sum)[curve]
pi.alpha <- apply(t(piigivej) * alpha[, m], 2, sum)[curve]
S.Lambda <- t(S %*% Lambda)
if(h != 1) {
temp <- NULL
for(i in 1:K) {
temp <- cbind(temp, as.vector(rep(1, h - 1) %*% matrix((S.Lambda *
], h - 1,dim(S)[1])) * alpha[i, m])
otherLambda <- (temp * piigivej[curve,
])%*%rep(1, K)
else otherLambda <- 0
gamma.pi.alpha <- apply(gamma * as.vector(piigivej) *
rep(alpha[, m], rep(N, K)), c(1, 3), sum)[curve,
Lambda[, m] <- solve(t(S * pi.alphasq) %*% S) %*% t(S) %*%
(x * pi.alpha - otherLambda - (S *gamma.pi.alpha) %*% rep(1, sum(q)))
# Calculate sigma
ind <- matrix(rep(c(rep(F, q), rep(T, N * q)),N)
[1:(N * N * q)], N, N * q, byrow = T)[rep(1:N, table(curve)),]
mat1 <- matrix(rep(S, N), n, N * q)
mat3 <- t(mat1)
mat3[t(ind)] <- 0
ind2 <- matrix(rep(c(rep(F, q), rep(T, N * q)),
N)[1:(N * N * q)], N, N * q, byrow = T)[rep(1:N, rep(q, N)),]
mat2 <- matrix(rep(t(gcov), N), N * q, N * q,byrow = T)
mat2[ind2] <- 0
econtrib <- 0
for(i2 in 1:K) {
vect1 <- x - S %*% Lambda %*% alpha[
] - (S * gamma[curve, i2,
]) %*% rep(1, q)
econtrib <- econtrib + t(piigivej[curve,i2] * vect1) %*% vect1
sigma <- as.vector((econtrib + sum(diag(mat1 %*% mat2 %*% mat3)))/n)
loopnumber <- loopnumber + 1
parameters$lambda.zero <- as.vector(lambda.zero)
parameters$alpha <- alpha
parameters$Lambda <- Lambda
parameters$sigma <- sigma
parameters
"fclustEstep" <-
function(parameters, data, vars, S, hard)
# This function performs the E step of the EM algorithm by
# calculating the expected values of gamma and gamma %*% t(gamma)
# given the current parameter estimates.
par <- parameters
N <- dim(vars$gamma)[1]
K <- dim(vars$gamma)[2]
q <- dim(vars$gamma)[3]
Gamma <- par$Gamma
Lambda.alpha <- par$lambda.zero + par$Lambda %*% t(par$alpha)
vars$gprod <- vars$gcov <- NULL
for(j in 1:N) {
# Calculate expected value of gamma.
Sj <- S[data$curve == j,
nj <- sum(data$curve == j)
invvar <- diag(1/rep(par$sigma, nj))
Cgamma <- Gamma - Gamma %*% t(Sj) %*% solve(diag(nj) + Sj %*%
Gamma %*% t(Sj) %*% invvar) %*% invvar %*% Sj %*% Gamma
centx <- data$x[data$curve == j] - Sj %*% Lambda.alpha
vars$gamma[j,
] <- t(Cgamma %*% t(Sj) %*% invvar %*% centx)
# Calculate pi i given j.
covx <- Sj %*% par$Gamma %*% t(Sj) + solve(invvar)
d <- exp( - diag(t(centx) %*% solve(covx) %*% centx)/2) * par$pi
vars$piigivej[j,
] <- d/sum(d)
if(hard) {
m <- order( - d)[1]
vars$piigivej[j,
vars$piigivej[j, m] <- 1
# Calculate expected value of gamma %*% t(gamma).
vars$gprod <- cbind(vars$gprod, t(matrix(vars$gamma[j,
K, q)) %*% (matrix(vars$gamma[j,
], K, q) * vars$
piigivej[j,
]) + Cgamma)
vars$gcov <- cbind(vars$gcov, Cgamma)
"fclustconst" <-
function(data, parameters, vars, S)
# This function enforces the constraint (7) from the paper on the
# parameters. This means that the alphas can be interpreted as the
# number of standard deviations that the groups are apart etc.
par <- parameters
A <- t(S) %*% solve(par$sigma * diag(dim(S)[1]) + S %*% par$Gamma %*%
t(S)) %*% S
svdA <- svd(A)
sqrtA <- diag(sqrt(svdA$d)) %*% t(svdA$u)
negsqrtA <- svdA$u %*% diag(1/sqrt(svdA$d))
finalsvd <- svd(sqrtA %*% par$Lambda)
par$Lambda
par$alpha <- t(diag(finalsvd$d) %*% t(finalsvd$v) %*% t(par$alpha))
else par$alpha <- t(finalsvd$d * t(finalsvd$v) %*% t(par$alpha))
meanalpha <- apply(par$alpha, 2, mean)
par$alpha <- t(t(par$alpha) - meanalpha)
par$lambda.zero <- par$lambda.zero + par$Lambda %*% meanalpha
list(parameters = par, vars = vars)
"nummax" <-
function(X)
ind <- rep(1, dim(X)[1])
for(i in 2:dim(X)[2]) {
ind[test] <- i
m[test] <- X[test, i]
list(ind = ind, max = m)
"fclust.pred" <-
function(fit,data=NULL,reweight=F)
# This function produces the alpha hats used to provide a low
# dimensional pictorial respresentation of each curve. It also
# produces a class prediction for each curve. It takes as
# input the fit from fldafit (for predictions on the original data)
# or the fit and a new data set (for predictions on new data).
if (is.null(data))
data <- fit$data
FullS <- fit$FullS
par <- fit$parameters
curve <- data$curve
time <- data$time
N <- length(table(curve))
h <- dim(par$alpha)[2]
alpha.hat <- matrix(0, N, h)
K <- dim(fit$par$alpha)[1]
distance <- matrix(0, N, K)
Calpha <- array(0, c(N, h, h))
for(i in 1:N) {
Sij <- FullS[time[curve == i],
xij <- data$x[curve == i]
n <- length(xij)
Sigma <- par$sigma * diag(n) + Sij %*% par$Gamma %*% t(Sij)
# Calculate covariance for each alpha hat.
InvCalpha <- t(par$Lambda) %*% t(Sij) %*% solve(Sigma) %*% Sij %*%
par$Lambda
] <- solve(InvCalpha)
# Calculate each alpha hat.
alpha.hat[i,
] <- Calpha[i,
] %*% t(par$Lambda) %*% t(
Sij) %*% solve(Sigma) %*% (xij - Sij %*% par$lambda.zero)
# Calculate the matrix of distances, relative to the
# appropriate metric of each curve from each class centroid.
for (k in 1:K){
y <- as.vector(alpha.hat[i,])-fit$par$alpha[k,]
distance[i,k] <- t(y)%*%InvCalpha %*%y}}
# Calculate final class predictions for each curve.
class.pred <- rep(1, N)
log.pi <- log(fit$par$pi)
if (!reweight)
log.pi <- rep(0,K)
probs <- t(exp(log.pi-t(distance)/2))
probs <- probs/apply(probs,1,sum)
m <- probs[,1]
if(K != 1)
for(k in 2:K) {
class.pred[test] <- k
m[test] <- probs[test, k]
list(Calpha = Calpha, alpha.hat = alpha.hat, class.pred = class.pred,
distance = distance, m = m,probs=probs)
"fclust.curvepred" <-
function(fit, data=NULL, index=NULL, tau = 0.95, tau1 = 0.975)
if (is.null(data))
data <- fit$data
if (is.null(index))
index <- 1:length(table(data$curve))
tau2 <- tau/tau1
sigma <- fit$par$sigma
Gamma <- fit$par$Gamma
Lambda <- fit$par$Lambda
alpha <- fit$par$alpha
lambda.zero <- as.vector(fit$par$lambda.zero)
S <- fit$FullS
N <- length(index)
upci <-lowci <- uppi <- lowpi <- gpred <- matrix(0,N,nrow(S))
etapred <- matrix(0,N,ncol(S))
Lambda.alpha <- lambda.zero + Lambda %*% t(alpha)
for (i in index){
y <- data$x[data$curve == i]
Si <- S[data$time[data$curve == i],
ni <- dim(Si)[1]
invvar <- diag(1/rep(sigma, ni))
covx <- Si %*% Gamma %*% t(Si) + solve(invvar)
centx <- data$x[data$curve == i] - Si %*% Lambda.alpha
d <- exp( - diag(t(centx) %*% solve(covx) %*% centx)/2) * fit$par$pi
pi <- d/sum(d)
K <- length(pi)
mu <- lambda.zero + Lambda %*% t(alpha * pi) %*% rep(1, K)
cov <- (Gamma - Gamma %*% t(Si) %*% solve(diag(ni) + Si %*% Gamma %*%
t(Si)/sigma) %*% Si %*% Gamma/sigma)/sigma
etapred[ind,] <- mu + cov %*% t(Si) %*% (y - Si %*% mu)
ord <- order( - pi)
numb <- sum(cumsum(pi[ord]) <= tau1) + 1
v <- diag(S %*% (cov * sigma) %*% t(S))
pse <- sqrt(v + sigma)
se <- sqrt(v)
lower.p <- upper.p <- lower.c <- upper.c <- matrix(0, nrow(S), numb)
for(j in 1:numb) {
mu <- lambda.zero + Lambda %*% alpha[ord[j],
mean <- S %*% (mu + cov %*% t(Si) %*% (y - Si %*% mu))
upper.p[, j] <- mean + qnorm(tau2) * pse
lower.p[, j] <- mean - qnorm(tau2) * pse
upper.c[, j] <- mean + qnorm(tau2) * se
lower.c[, j] <- mean - qnorm(tau2) * se
upci[ind,] <- nummax(upper.c)$max
lowci[ind,] <-
- nummax( - lower.c)$max
uppi[ind,] <- nummax(upper.p)$max
lowpi[ind,] <-
- nummax( - lower.p)$max
gpred[ind,] <- as.vector(S %*%etapred[ind,])
ind <- ind+1
meancurves <- S%*%Lambda.alpha
list(etapred = etapred, gpred = gpred,
upci = upci,lowci = lowci,
uppi = uppi, lowpi = lowpi,index=index,grid=fit$grid,data=data,meancurves=meancurves)
"fclust.discrim" <-
function(fit,absvalue=F){
S <- fit$FullS
sigma <- fit$par$sigma
n <- nrow(S)
Gamma <- fit$par$Gamma
Sigma <- S%*%Gamma%*%t(S)+sigma*diag(n)
Lambda <- fit$par$Lambda
discrim <- solve(Sigma)%*%S%*%Lambda
if (absvalue)
discrim <- abs(discrim)
n <- ncol(discrim)
nrows <- ceiling(sqrt(n))
par(mfrow=c(nrows,nrows))
for (i in 1:n){
plot(fit$grid,discrim[,i],ylab=paste("Discriminant Function ",i),xlab="Time",type='n')
lines(fit$grid,discrim[,i],lwd=3)
abline(0,0)}}
"fclust.plotcurves" <-
function(object=NULL,fit=NULL,index=NULL,ci=T,pi=T,clustermean=F){
if (is.null(object))
object <- fclust.curvepred(fit)
if (is.null(index))
index <- 1:length(table(object$data$curve))
r <- ceiling(sqrt(length(index)))
par(mfrow=c(r,r))
for (i in index){
grid <- object$grid
upci <- object$upci[i,]
uppi <- object$uppi[i,]
lowci <- object$lowci[i,]
lowpi <- object$lowpi[i,]
gpred <- object$gpred[i,]
meancurves <- (object$mean)
if (clustermean)
yrange <- c(min(c(lowpi,meancurves)),max(c(uppi,meancurves)))
yrange <- c(min(lowpi),max(uppi))
plot(grid,grid,ylim=yrange,ylab="Predictions",xlab="Time",type='n',
main=paste("Curve ",i))
if (clustermean)
in 1:ncol(meancurves))
lines(grid,meancurves[,k],col=6,lty=2,lwd=2)
lines(grid,upci,col=3)
lines(grid,lowci,col=3)}
lines(grid,uppi,col=4)
lines(grid,lowpi,col=4)}
lines(grid,gpred,col=2,lwd=2)
lines(grid[object$data$time[object$data$curve==i]],object$data$x[object$data$curve==i],lwd=2)
points(grid[object$data$time[object$data$curve==i]],object$data$x[object$data$curve==i],pch=19,cex=1.5)
"simdata" <-
structure(list(x = c(-0.744, -0.710,
-0.774, -0.801, -0.887, -0.542,
-0.043, -0.017, 0.139, 0.111,
-0.911, -0.019, -0.034, -0.344,
-0.244, -0.014, -0.494, -0.988,
-0.149, 0.303, -0.189, -0.310,
-0.844, -0.501, -0.119, -0.793,
-0.505, -0.451, 0.983, 0.723,
-0.803, -0.990, -0.444, -0.510,
-0.117, -0.606, -0.032, -0.116,
0.704, 0.912, -0.055, -0.792,
-0.500, -0.697, -0.563, -0.978,
-0.385, -0.917, -0.318, 0.226,
-0.796, -0.946, -0.913, -0.629,
-0.515, -0.510, -0.498, -0.034,
-0.813, 0.146, -0.864, -0.852,
-0.366, -0.692, -0.662, -0.511,
-0.835, -0.253, 0.245, 0.711,
-0.317, -0.7703, -0.378,
-0.158, -0.237, -0.600, -0.207,
-0.862, 0.188, 0.914, -0.574,
-0.632, -0.772, -0.111, -0.095,
-0.874, -0.7144, -0.7018,
0.726, 0.763, -0.689, -0.678,
-0.733, -0.022, -0.735, -0.033,
-0.4934, -0.,
0.979, -0.121, -0.266, -0.976,
-0.845, -0.715, -0.238, -0.717,
-0.685, 0.001, 0.145, -0.531,
-0.340, -0.914, -0.943, -0.2948,
-0.264, -0.358, -0.726, 0.7839,
0.110, -0.288, -0.900, -0.938,
-0.963, -0.892, -0.688, -0.303,
-0.155, 0.435, 0.595, -0.907,
-0.6686, -0.587, -0.118,
-0.919, -0.975, -0.111, 0.1566,
0.98, 0.713, -0.491, -0.202,
-0.996, -0.912, -0.548, -0.816,
-0.8, 0.565, 0.623,
-0.274, -0.696, -0.585, -0.464,
-0.124, -0.203, -0.15, -0.81,
-0., -0.957, -0.454,
-0.459, -0.957, -0.2619,
0.331, 0., 0.681,
0.05, -0.184, -0.869, -0.691,
-0.934, -0.972, -0.414, -0.719,
-0.623, -0.985, 0.189, -0.387,
-0.970, -0.977, -0.819, -0.893,
-0.829, -0.135, -0.84, 0.558,
0.625, -0.859, -0.527, -0.829,
-0.798, -0.398, -0.387, -0.848,
-0.484, -0.063, 0.583, -0.477,
-0.128, -0.768, -0.292, -0.764,
-0.502, -0.954, -0.1943,
0.345, 0.893, -0.5536, -0.773,
-0.136, -0.580, -0.849, -0.396,
-0.169, -0., 0.726,
-0.097, -0.333, -0.366, -0.106,
-0.420, -0.438, -0.284, -0.59539,
0., -0.084, -0.682,
-0.230, -0.794, -0.539, -0.544,
-0.266, -0.56,
0.187, -0.349, -0.990, -0.067,
-0.002, -0.371, -0.145, -0.327,
-0.872, 0., -0.442,
-0.551, -0.301, -0.381, -0.817,
-0.17, -0.763, -0.733, -0.284,
0.806, -0.301, -0.7693, -0.253,
-0.435, -0.384, -0.216, -0.349,
-0.236, -0.275, -0.6301,
-0.130, -0.331, -0.975, -0.084,
-0.9594, -0.697, -0.261,
-0.746, -0.198, -0.355, -0.511,
-0.379, -0.427, -0.102, -0.401,
-0.522, -0.9,
0.542, 0.186, -0.546, -0.541,
-0.348, -0.191, -0.415, -0.623,
0..168, 0.851, 0.855,
-0.084, -0.510, -0.249, -0.864,
-0.591, -0.943, -0.790, -0.740,
0.362, 0.167, -0.346, -0.186,
-0.336, -0.386, -0.299, -0.067,
-0.747, 0., 0.115,
-0.332, -0.518, -0.491, -0.650,
-0.38, -0.890, -0.0395, -0.19782,
0.713, 0.811, -0.594, -0.736,
-0.398, -0.722, -0.970, -0.840,
-0.639, -0., 0.716,
-0.625, -0.977, -0.38, -0.485,
-0.583, -0.12, -0.372, 0.344,
0.321, 0.585, -0.786, -0.162,
-0.0715, -0.4292, -0.785,
-0.3003, -0.791, -0.457,
-0., -0.325, -0.289,
-0.148, -0.909, -0.605, 0.447,
0.032, 0.702, 0.55, 0.929,
-0.07, -0.366, -0.365, -0.403,
-0.253, -0.096, -0.076, -0.561,
-0., -0.710, -0.331,
-0.350, -0.147, -0.163, -0.161,
-0.641, -0.793, 0.,
-0.149, -0.918, -0.248, -0.898,
-0.987, -0.091, -0.992, -0.626,
-0.65, -0.0965, -0.876, -0.7055,
-0.4581, -0.779, -0.267,
-0.019, -0.166, -0.1032,
0.3, -0.912, -0.012,
-0.013, -0.520, -0.418, -0.411,
-0.077, -0.869, 0.,
-0.358, -0.502, -0.337, -0.118,
-0.707, -0.819, -0.968, -0.162,
0., -0.819, -0.147,
-0.997, -0.336, -0.0794,
-0.592, -0.175, -0.595, 0.0903,
0.381, -0.020, -0.1579, -0.720,
-0.238, -0.102, -0.606, -0.9981,
0.41, 0.277, 0.69, -0.049,
-0.934, -0.686, -0.947, -0.434,
-0.021, -0.8987, -0.356,
-0.286, -0.325, -0.668, -0.758,
-0.346, -0.661, -0.217, -0.134,
-0.436, -0.9,
0.697, -0.191, -0.576, -0.332,
-0.988, -0.952, -0.45, -0.233,
-0.7, 0.108693,
-0.277, -0.474, -0.953, -0.975,
-0.594, -0.877, -0.884, 0.217,
0.455, 0.293, -0.366, -0.694,
-0.167, -0.282, -0.709, -0.254,
-0.1, -0.9, 0.958,
0.0, 0.3785, -0.7992,
-0.5776, -0.103,
-0.3127, -0.6491, -0.6848,
0.2697, -0..22622,
-0.969, -0.5238,
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0.874, 0.55, -0.4682,
-0.8435, -0.2334, -0.180247,
-0.6495, -0.57,
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-0.7658, -0.73615, -0.5511,
-0.7155, -0.9262, -0.4988,
-0.2558, -0.5,
-0.578969, -0.57,
0.461, 0.836, 0.3985, -0.02063,
0.15, -0.61553,
-0.9636, -0.6103, -0.331,
0.3, -0.2253,
-0.9, 0.0174,
0.5, -0.8899,
-0.6305, -0.9,
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0.0306, -0.895,
0.3133, -0.61,
0.82, 0.6019,
-0.33264, -0.5538, -0.19524,
-0.636369, -0.4173, -0.329786,
0.8949, -0.6978, -0.664,
-0.6362, -0.74, -0.8977,
-0.11323, -0.33,
0.880747, -0.47,
-0.0019, -0.0313, -0.2145,
0.9, 0.67078,
0.46334, -0.3565, -0.0467,
-0.6587, -0.9524, -0.73825,
0.3885, -0.40951, -0.73226,
-0.7872, -0.7046, -0.9545,
-0.0698, -0.1208, -0.6120,
0.55, 0.1677,
0.0809, -0.098,
-0.5823, -0.5,
-0.3421, -0.8,
0.6, -0.6349,
-0.8145, -0.304, 0.98127,
0.3475, -0.7869, -5.44e-05,
-0.6659, -0.6307, -0.4862,
-0.3060, -0.681, 0.2479,
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0.7615, -0.962,
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-0.31, 0.2675,
-0.0529, -0.6, 0.1519,
0.0243, -0.4760, -0.4697,
-0.4903, -0.4011, -0.0138,
0.926, 0.4, -0.0859,
0.1, 0.41438,
0.9169, -0.4,
0.3, -0.70672,
-0.3929, -0.5556, -0.3054,
-0.3, 0.56567,
0.2, 0.26222,
0.6147, -0.16652, -0.9155,
0.18637, -0.85465, -0.1454,
-0.4, -0.2471,
0.6194, -0.9e-05,
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0.690, 0.8966,
-0.8935, -0.75946, -0.86945,
0.78185, -0.86989, -0.0265,
-0.7609, -0.5,
0.7, -0.27099,
-0.09076, -0.21,
0.00, -0.0401,
-0.5491, -0.6352, -0.5763,
-0.0513, -0.6362, -0.1848,
-0.1282, -0.4309, -0.02745,
0.94, 0.8218,
0.992, 0.034, -0.90526, -0.21610,
0.28, 0.73473,
-0.0433, -0.173,
0.53, -0.2652,
-0.8356, -0.34,
0.5, -0.25976,
0.89, 0.4976,
0.75, 0.8237,
0.85, 0.2436,
-0.2665, -0.9686, -0.4235,
-0.3, 0.5330,
0.76, 0.6386,
0.77484, -0.8,
-0.5376, -0.3800, -0.6279,
-0.0409, -0.3070, -0.9617,
-0.43197, -0.0752, -0.0345,
0.66, -0.92900,
-0.9564, -0.8696, -0.2777,
-0.1307, -0.3689, -0.3373,
-0.0316, -0.951124, -0.2747,
-0.7801, -0.7031, -0.3859,
-0.0049, -0.237,
0.727620, -0.1747, -0.8264,
-0.2138, -0.6800, -0.209,
-0.3539, -0.8748, -0.04368,
-0.5967, 0.8142,
0.797906, -0.9849, -0.05064,
0.89471, -0.81205, -0.1015,
-0.711, -0.7659, -0.0422,
-0.1696, -0.714,
-0.35, -0.99548,
-0.0053, -0.0577, -0.6184,
-0.7095, -0.4221, -0.2298,
-0.5887, -0.37,
-0.8418, -0.37487, -0.9948,
-0.5548, -0.9,
0.999, 0.22157,
-0.5613, -0.7751, -0.1085,
-0.9398, -0.66,
0.3556, -0.1911, -0.3037,
-0.9, 0.0967,
0.2693, -0.42,
0.64, 0.4379,
0.70742, -0.4,
0.1, 0.8599, -0.47742,
-0.39172, -0.8075, -0.9441,
-0.57, 0.0763,
-0., 0.000314,
0.5, -0.2435,
-0.662, -0.8743,
-0.2714, -0.56,
0.5898, -0.429,
0.11261, -0.7367, -0.4469,
-0.697, 0.9079,
0.23, 0.53440,
0.06346, -0.37212, -0.9606,
-0.363, -0.1324, -0.3152,
-0.84632, -0.561, -0.5107,
0.4, -0.36025,
3.86e-05, -0.6326, -0.983757,
-0.1775, -0.99,
0.24, 0.4252,
0.34, -0.8420,
0.078655, -0.6321, -0.44831,
0.9, 0.8537, -0.4836,
0.3047, -0.1322, -0.53647,
-0.4, 0.1467,
-0.17078, -0.3642, -0.7532,
-0.3485, -0.70102, -0.5456,
0., 0.2031, -0.0742,
-0.125, -0.26957,
-0.1838, -0.9,
0.55, -0.0838,
-0.29241, -0.3497, -0.2586,
0.1, 0.7185, -0.6284,
-0.8121, -0.9893, -0.1051,
-0.7024, -0.4,
0.6129), timeindex = as.integer(c(13, 14, 22, 24,
25, 27, 30, 41, 89, 95, 4, 20, 24, 47, 49, 52, 61, 62, 69, 91,
3, 14, 32, 34, 45, 53, 54, 71, 83, 87, 3, 8, 18, 28, 41, 46,
50, 77, 92, 95, 12, 16, 20, 29, 39, 49, 57, 63, 75, 88, 9, 23,
26, 29, 34, 37, 39, 40, 45, 94, 26, 36, 39, 45, 50, 53, 62, 77,
91, 98, 11, 30, 31, 36, 46, 49, 57, 58, 90, 94, 2, 15, 30, 51,
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