# Chapter 6 逻辑斯谛回归与最大熵模型

``````require(magrittr)

iris1 <- iris[1:100, 1:4]
iris1[, "Classes"] <- c(rep(1,50), rep(0,50))

##逻辑斯谛回归模型的梯度下降算法
#全部向量用列向量表示
nc <- ncol(iris1)
nr <- nrow(iris1)
lambda <- 0.0005
eps <- 0.0003
set.seed(2017)
wi <- matrix(rnorm(nc - 1, 0, 0.5), nc - 1, 1)
gradient <- matrix(NA, nc - 1, 1)
k <- 1  #记录迭代步数

while (TRUE) {
print(paste0("迭代解：", wi))
print(paste0("迭代步数：", k))
for (i in seq(nc - 1)) {
for (j in seq(nr)) {
exp_ <- exp(as.matrix(iris1[j, 1:(nc - 1)]) %*% wi)
grad_  <- 1 / (exp_ + 1) *
exp_ * iris1[j, i] - iris1[j, nc] * iris1[j, i]
}
}

#梯度的模

#更新w
w <- wi + lambda * p
m <- norm(w - wi, type = c("2"))
print(paste0("m：", m))
if (m < eps) {
w_wanted <- w
print(paste0("w_wanted：", w_wanted))
break
}
wi <- w
k <- k + 1
}

proba <- c()
for (i in seq(nr)) {
nominator <- exp(as.matrix(iris1[i, 1:(nc - 1)]) %*% w_wanted)
denominator <- 1 + exp(as.matrix(iris1[i, 1:(nc - 1)]) %*%
w_wanted)
p <- nominator / denominator
proba <- append(proba, p)
}

which(proba > 0.5)``````
``````rm(list = ls())
sapply(c("tm",             #version: 0.7-1  重要!!!!!!!!!
"SnowballC",      #version: 0.5.1
"stringr"),       #version: 1.2.0
require,
character.only = TRUE)

options(stringsAsFactors = FALSE)
datapath <- "~/Reuters25178/training"
category <- c("gnp", "gold", "moneysupply")

#训练数据集
gnp.train.dir <- paste0(getwd(),"/Reuters21578/training/gnp")
gold.train.dir <- paste0(getwd(),"/Reuters21578/training/gold")
money.train.dir <- paste0(getwd(),"/Reuters21578/training/money-supply")

# 测试数据集
gnptest.dir <- paste0(getwd(),"/Reuters21578/test/gnp")
goldtest.dir <- paste0(getwd(),"/Reuters21578/test/gold")
moneysupplytest.dir <- paste0(getwd(),"/Reuters21578/test/money-supply")

cleanupDataCorpus <- function(dataCorpus) {
cleanDataCorpus <- tm_map(dataCorpus, removePunctuation)
cleanDataCorpus <- tm_map(cleanDataCorpus, removeNumbers)
cleanDataCorpus <- tm_map(cleanDataCorpus,
content_transformer(str_replace_all),
pattern = "[[:punct:]]", replacement = " ")
cleanDataCorpus <- tm_map(cleanDataCorpus, content_transformer(tolower))
cleanDataCorpus <- tm_map(cleanDataCorpus, removeWords,
c("said", "u.s", stopwords("english")))
cleanDataCorpus <- tm_map(cleanDataCorpus, stemDocument)
#tm包version为0.7-1，该句可注释掉
#cleanDataCorpus <- tm_map(cleanDataCorpus, PlainTextDocument)
return(cleanDataCorpus)
}

gnp.corpus <- Corpus(DirSource(directory = gnp.train.dir,
encoding = "ASCII"))
gol.corpus <- Corpus(DirSource(directory = gold.train.dir,
encoding = "ASCII"))
mon.corpus <- Corpus(DirSource(directory = money.train.dir,
encoding = "ASCII"))

gnp.cleancorpus <- cleanupDataCorpus(gnp.corpus)
gol.cleancorpus <- cleanupDataCorpus(gol.corpus)
mon.cleancorpus <- cleanupDataCorpus(mon.corpus)

gnp.tdm <- TermDocumentMatrix(gnp.cleancorpus)
gol.tdm <- TermDocumentMatrix(gol.cleancorpus)
mon.tdm <- TermDocumentMatrix(mon.cleancorpus)

inspect(gnp.tdm[1:10,1:10])

gnp.tdm <- removeSparseTerms(gnp.tdm, 0.7)
gol.tdm <- removeSparseTerms(gol.tdm, 0.7)
mon.tdm <- removeSparseTerms(mon.tdm, 0.7)

gnp.matx <- t(data.matrix(gnp.tdm))
gol.matx <- t(data.matrix(gol.tdm))
mon.matx <- t(data.matrix(mon.tdm))

gnp.df <- as.data.frame(gnp.matx)
gol.df <- as.data.frame(gol.matx)
mon.df <- as.data.frame(mon.matx)

gnptest.corpus <- Corpus(DirSource(directory = gnptest.dir,
encoding = "ASCII"))
goltest.corpus <- Corpus(DirSource(directory = goldtest.dir,
encoding = "ASCII"))
montest.corpus <- Corpus(DirSource(directory = moneysupplytest.dir,
encoding = "ASCII"))

gnptest.cleancorpus <- cleanupDataCorpus(gnptest.corpus)
goltest.cleancorpus <- cleanupDataCorpus(goltest.corpus)
montest.cleancorpus <- cleanupDataCorpus(montest.corpus)

gnptest.tdm <- TermDocumentMatrix(gnptest.cleancorpus)
goltest.tdm <- TermDocumentMatrix(goltest.cleancorpus)
montest.tdm <- TermDocumentMatrix(montest.cleancorpus)

gnptest.tdm <- removeSparseTerms(gnptest.tdm, 0.7)
goltest.tdm <- removeSparseTerms(goltest.tdm, 0.7)
montest.tdm <- removeSparseTerms(montest.tdm, 0.7)

gnptest.matx <- t(data.matrix(gnptest.tdm))
goltest.matx <- t(data.matrix(goltest.tdm))
montest.matx <- t(data.matrix(montest.tdm))

gnptest.df <- as.data.frame(gnptest.matx)
goltest.df <- as.data.frame(goltest.matx)
montest.df <- as.data.frame(montest.matx)

##转换为矩阵，gnp.df / gnptest.df 不允许重复的行名
gnp.df.mat <- as.matrix(gnp.df)
gnptest.df.mat <- as.matrix(gnptest.df)

gnptestfiltered1 <- data.frame(gnptest.df.mat[, intersect(colnames(gnptest.df.mat),
colnames(gnp.df.mat))])
gnptestfiltered1[1, ]

col.names = colnames(gnp.df.mat))

gnptestfiltered <- rbind.fill(gnptestfiltered1, gnptestfiltered2)
gnptestfiltered[1,]

ncol(gnptestfiltered)

##转换为矩阵，gol.df / goltest.df 不允许重复的行名
gol.df.mat <- as.matrix(gol.df)
goltest.df.mat <- as.matrix(goltest.df)

goltestfiltered1 <- data.frame(goltest.df.mat[, intersect(colnames(goltest.df.mat),
colnames(gol.df.mat))])

col.names = colnames(gol.df.mat))

goltestfiltered <- rbind.fill(goltestfiltered1,
goltestfiltered2)

ncol(goltestfiltered)

##转换为矩阵，mon.df / montest.df 不允许重复的行名
mon.df.mat <- as.matrix(mon.df)
montest.df.mat <- as.matrix(montest.df)

montestfiltered1 <- data.frame(montest.df.mat[, intersect(colnames(montest.df.mat),
colnames(mon.df.mat))])

col.names = colnames(mon.df.mat))

montestfiltered <- rbind.fill(montestfiltered1, montestfiltered2)

ncol(montestfiltered)

gnp.df <- cbind(gnp.df, category = rep("gnp"))
gol.df <- cbind(gol.df, category = rep("gold"))
mon.df <- cbind(mon.df, category = rep("money_supply"))

gnptestfiltered <- cbind(gnptestfiltered, category = rep("gnp"))
goltestfiltered <- cbind(goltestfiltered, category = rep("gold"))
montestfiltered <- cbind(montestfiltered, category = rep("money_supply"))

##############训练用
tdmStackCateg <- rbind.fill(gnp.df, gol.df, mon.df)

nrow(gnp.df); nrow(gol.df); nrow(mon.df)

nrow(tdmStackCateg)

tdmStackCateg[is.na(tdmStackCateg)] <- 0

ncol(gnp.df); ncol(gol.df); ncol(mon.df)

ncol(tdmStackCateg)

####算法输入用
which(colnames(tdmStackCateg) == "category") #[1] 48
ncol(tdmStackCateg) #[1] 68
#将"category"列放置最后一列
tdmStackCateg <- tdmStackCateg[, c(1:47, 49:68, 48)]
tdmStackCateg[,"rowid"] <- rownames(tdmStackCateg)
``````require(magrittr)
require(tibble)
nr_tdm <- nrow(tdmStackCateg)
len_lab <- tdmStackCateg[, "category"] %>%
unique(.) %>%
length(.)

#定义特征函数, 0-1特征函数, 词频特征函数
nc_tdm <- ncol(tdmStackCateg)
#最后两个是"category", "rowid"
voc <- colnames(tdmStackCateg)[-c(nc_tdm - 1, nc_tdm)]

#voc属于哪个lab?
voc_lab <- matrix(NA ,length(voc),2)
for (i in seq(length(voc))) {
idx_cat <- which(colnames(tdmStackCateg) == "category")
sub <- tdmStackCateg[, c(i,idx_cat)]
idx <- which(sub[, 1] != 0)
sub <- sub[idx, ]
colnames(sub) <- c("voc","categ")
dd <- ddply(sub, ~ categ, summarize,sum = sum(voc))
voc_lab[i, 1] <- voc[i]
voc_lab[i, 2] <- dd[which.max(dd[,"sum"]), "categ"]
}
voc_lab

#####特征函数1
featfun1 <- function(x = tdmStackCateg[1, 1:length(voc)],
y = tdmStackCateg[1, "category"],
i = 1) {
lab <- voc_lab[which(voc_lab[, 1] == voc[i]), 2]
if (y == lab) {
fvalue <- x[, voc[i]]
if (fvalue != 0) {
fvalue <- x[, voc[i]]   #如果词频不为0，则特征值取词频
} else {
fvalue <- 0.1           #如果词频为0，则特征值取0.1，"绝对折扣"
}
} else {
fvalue <- 0
}
fvalue
}

featfun1(x = tdmStackCateg[11, 1:length(voc)],
y = tdmStackCateg[11, "category"],
i = 40)  #第11个样本点，第40个特征函数
featfun1(x = tdmStackCateg[11, 1:length(voc)],
y = tdmStackCateg[11, "category"],
i = 43)  #第11个样本点，第43个特征函数

colnames(tdmStackCateg)
voc

matx_tdmSC <- as.matrix(tdmStackCateg[, 1:length(voc)])

#假设计算f(doc1,lab310)的第一至第length(voc)个特征函数的值
val <- c()
for (k in seq(length(voc))) {
val_ <- featfun1(x = tdmStackCateg[1, 1:length(voc)],
y = tdmStackCateg[310, "category"],
i = k)
val <- append(val, val_)
}
val

#对于所有的样本，计算f#
f_sharp_matx <- matrix(NA, nr_tdm, 1)
for (j in seq(nr_tdm)) {
feature_sharp <- 0
for (k in seq(length(voc))) {
feature_ <- featfun1(x = tdmStackCateg[j, 1:length(voc)],
y = tdmStackCateg[j, "category"],
i = k)
feature_sharp <- feature_sharp + feature_
}
f_sharp_matx[j, 1] <- feature_sharp
}

f_sharp_matx
max(f_sharp_matx) #[1] 163.3

###定义函数pxy，求联合分布概率
pxy <- function(x = tdmStackCateg[1, "rowid"],
y = tdmStackCateg[1, "category"]) {
v <- tdmStackCateg %>%
subset(., rowid == x & category == y) %>%
nrow(.)
p <- v / nr_tdm
p
}

pxy(x = tdmStackCateg[1, "rowid"],
y = tdmStackCateg[1, "category"])

###定义函数px，求边缘分布px
px <- function(x=tdmStackCateg[1, "rowid"]) {
v <- tdmStackCateg %>%
subset(., rowid == x) %>%
nrow(.)
p <- v / nr_tdm
p
}

px(x = tdmStackCateg[10, "rowid"])

###定义函数pyx，求最大熵模型pyx
wi <- matrix(0, length(voc), 1)
lab <- tdmStackCateg[, "category"]
pyx <- function(xx = tdmStackCateg[1, 1:length(voc)],
yy = tdmStackCateg[1, "category"],
w = wi) {
fea <- matrix(NA, length(voc), 1)
for (k in seq(length(voc))) {
fea[k, 1] <- featfun1(x = xx, y = yy, i = k)
}
nominator <- exp(t(w) %*% fea)
denominator <- 0
feat <- matrix(NA, length(voc), 1)
for (j in seq(length(lab))) {
for (v in seq(length(voc))) {
feat[v, 1] <- featfun1(x = xx, y = lab[j], i = v)
}
denominator_ <- exp(t(w) %*% feat)
denominator <- denominator + denominator_
}
p <- (nominator / denominator) %>%
as.numeric()
p
}

pyx(xx = tdmStackCateg[1, 1:length(voc)],
yy = tdmStackCateg[1, "category"],
w = wi)

#定义函数EPF_nomin
#k=1,则计算针对第1个特征函数的EPF_nomin
EPF_nomin <- function(k) {
valu <- 0
for (j in seq(nr_tdm)) {
pxy <- pxy(x = tdmStackCateg[j, "rowid"],
y = tdmStackCateg[j, "category"])
feat <- featfun1(x = tdmStackCateg[j, 1:length(voc)],
y = tdmStackCateg[j, "category"],
i = k)
valu_ <- pxy * feat
valu <- valu + valu_
}
valu
}

EPF_nomin(1)

#定义函数EPF_denomin
#k=1, W=matrix(0, length(voc), 1) 则计算针对第1个特征函数的EPF_denomin
EPF_denomin <- function(k, W) {
valu <- 0
for (j in seq(nr_tdm)) {
px <- px(x = tdmStackCateg[j, "rowid"])
pyx <- pyx(xx = tdmStackCateg[j, 1:length(voc)],
yy = tdmStackCateg[j, "category"],
w = W)
feat <- featfun1(x = tdmStackCateg[j, 1:length(voc)],
y = tdmStackCateg[j, "category"],
i = k)
valu_ <- px * pyx * feat
valu <- valu + valu_
}
valu
}

len_voc <- length(voc)
mat_voc <- matrix(0, len_voc, 1)
EPF_denomin(1, mat_voc)``````
``````###算法6.1，改进的迭代尺度算法IIS
eps <- 0.001
bigM <- max(f_sharp_matx)
W <- matrix(0, len_voc, 1)
k <- 1  #记录迭代步数
nominator_ <- matrix(NA, len_voc, 1)
for (i in seq(len_voc)) {
nominator_[i, 1] <- EPF_nomin(i) %>%
round(., 6)  ##放while循环之外
}

while (TRUE) {
print(paste0("迭代解：", W))
print(paste0("迭代步数：", k))
theta <- matrix(NA, len_voc, 1)
for (i in seq(len_voc)) {
nominator <- nominator_[i, 1]
denominator <- EPF_denomin(i, W)
theta[i, 1] <- (log(nominator / denominator) / bigM) %>%
round(., 6)
print(paste0("i = ", i))
}
WI <- W + theta
if (all(WI - W < eps)) {
W_wanted <- WI
print(paste0("W_wanted：", W_wanted))
break
}
W <- WI
k <- k + 1
}``````
``````######算法6.2，最大熵模型学习的BFGS算法
require(MASS)
#ginv() 求逆
###开始执行，顺序执行，从k <- 1 开始
k <- 1
eps <- 0.001
lambda <- 0.0005
len_voc <- length(voc)
W <- matrix(0, len_voc, 1)
#B 是用于逼近海赛矩阵H的，B应该是 W 的函数，且B是正定对称矩阵，
#那么，B <- diag(1, len_voc, len_voc)是否有问题? 详见220页，92页
B <- diag(1, len_voc, len_voc)
g <- matrix(NA, len_voc, 1)
##计算算法6.2第2步的gk
for (j in seq(len_voc)) {
g[j, 1] <- EPF_denomin(j, W) - EPF_nomin(j) #计算梯度
}

gk <- norm(g, type = c("2"))
if (gk < eps) {
W_wanted <- W
print(paste0("W_wanted: ", W_wanted))
break
}

while (TRUE) {
pk <- -(ginv(B) %*% g)
W2 <- W + lambda * pk
##计算算法6.2第6步的gk2
g2 <- matrix(NA, len_voc, 1)
for (j in seq(len_voc)) {
g2[j, 1] <- EPF_denomin(j, W2) - EPF_nomin(j) #计算梯度
gk2 <- norm(g2, type = c("2"))
if (gk2 < eps) {
W_wanted2 <- W2
print(paste0("W_wanted2: ", W_wanted2))
break
}
yk <- g2 - g
thetak <- W2 - W
nomi_y <- t(yk) %*% yk        #得到一个数
denomi_y <- t(yk) %*% thetak  #得到一个数
nomi_theta <- B %*% thetak %*% t(thetak) %*% B#得到一个矩阵
denomi_theta <- t(thetak) %*% B %*% thetak    #得到一个数

part1 <- nomi_y / denomi_y
part2 <- nomi_theta / denomi_theta

if (denomi_y > 0) {   #校正公式
B <- B + part1 - part2
} else {
B <- B
}
g <- g2
k <- k + 1
}``````
``````// 算法6.1, 改进的迭代尺度算法IIS, IIS.cpp

using namespace Rcpp;

// [[Rcpp::plugins("cpp11")]]

double featfun1_cpp01(CharacterMatrix voc_lab,
CharacterVector voc,
NumericVector x,
String y, int i) {

CharacterVector col0 = voc_lab(_, 0);
CharacterVector st(1);
st[0] = voc[i - 1]; // index, - 1
IntegerVector A = match(st, col0);
String lab = voc_lab(A[0] - 1, 1);  // index, - 1
double fvalue(NA_REAL);
if (lab == y) {
fvalue = x[i - 1];
if (fvalue != 0.0) {
fvalue = x[i - 1];
} else {
fvalue = 0.1;
}
} else {
fvalue = 0.0;
}
return fvalue;
}

double pxy_cpp(DataFrame tdmStackCateg,
String x, String y) {
double nr_tdm = tdmStackCateg.nrows();
CharacterVector rowID = tdmStackCateg["rowid"];
CharacterVector Category = tdmStackCateg["category"];
double counT = 0;
for (int i = 0; i < rowID.length(); i++) {
bool b1 = x == rowID[i];
bool b2 = y == Category[i];
if (b1 && b2) {
counT = counT + 1;
} else {
counT = counT + 0;
}
}
double p = counT / nr_tdm;
return p;
}

double px_cpp(DataFrame tdmStackCateg, String x) {
double nr_tdm = tdmStackCateg.nrows();
CharacterVector rowID = tdmStackCateg["rowid"];
double counT = 0;
for (int i = 0; i < rowID.length(); i++) {
bool b1 = x == rowID[i];
if (b1) {
counT = counT + 1;
} else {
counT = counT + 0;
}
}
double p = counT / nr_tdm;
return p;
}

double pyx_cpp01(DataFrame tdmStackCateg,
CharacterMatrix voc_lab,
CharacterVector voc,
NumericVector xx,
String yy,
NumericMatrix w) {
CharacterVector lab = tdmStackCateg["category"];
int vocLen = voc.length();
NumericVector fea(vocLen);

int wnr = w.nrow(), wnc = w.ncol();
arma::mat W(w.begin(), wnr, wnc, false);
arma::colvec FEA(fea.begin(), vocLen, false);

for (int k = 0; k < voc.length(); k++) {
FEA[k] = featfun1_cpp01(voc_lab, voc, xx, yy, k + 1);
}
arma::colvec nominator_1 = exp(arma::trans(W) * FEA);
double nominator = nominator_1[0];

double denominator = 0.0;
String stri = NA_STRING;
double denominator_1 = NA_REAL;

NumericVector feat(vocLen);
arma::colvec FEAT(feat.begin(), vocLen, false);
for (int j = 0; j < lab.length(); j++) {
stri = lab[j];
for (int v = 0; v < vocLen; v++) {
FEAT[v] = featfun1_cpp01(voc_lab, voc, xx, stri, v + 1);
}
arma::colvec DenoMinator = exp(arma::trans(W) * FEAT);
denominator_1 = DenoMinator[0];
denominator = denominator + denominator_1;
}
double p = nominator / denominator;
return p;
}

double EPF_nomin_cpp(DataFrame tdmStackCateg,
NumericMatrix matx_tdmSC,
CharacterMatrix voc_lab,
CharacterVector voc,
int k) {

double valu = 0.0;
double valu_1 = NA_REAL;

int nr_tdm = tdmStackCateg.nrows();
CharacterVector rowID = tdmStackCateg["rowid"];
CharacterVector lab = tdmStackCateg["category"];

double pxy = NA_REAL;
double feat = NA_REAL;

String stri_rid = NA_STRING;
String stri_lab = NA_STRING;

for (int j = 0; j < nr_tdm; j++) {
stri_rid = rowID[j];
stri_lab = lab[j];
pxy = pxy_cpp(tdmStackCateg, stri_rid, stri_lab);
NumericVector oneVector = matx_tdmSC(j, _);
feat = featfun1_cpp01(voc_lab, voc, oneVector, stri_lab, k);
valu_1 = pxy * feat;
valu = valu + valu_1;
}
return valu;
}

// [[Rcpp::export]]
double EPF_denomin_cpp01(DataFrame tdmStackCateg,
NumericMatrix matx_tdmSC,
CharacterMatrix voc_lab,
CharacterVector voc,
int k,
NumericMatrix W) {
double valu = 0.0;
double valu_1 = NA_REAL;

int nr_tdm = tdmStackCateg.nrows();
CharacterVector rowID = tdmStackCateg["rowid"];
CharacterVector lab = tdmStackCateg["category"];

double px = NA_REAL;
double pyx = NA_REAL;
double feat = NA_REAL;
String stri_rid = NA_STRING;
String stri_lab = NA_STRING;

for (int j = 0; j < nr_tdm; j++) {
stri_rid = rowID[j];
stri_lab = lab[j];
NumericVector oneVector = matx_tdmSC(j, _);
px = px_cpp(tdmStackCateg, stri_rid);
pyx = pyx_cpp01(tdmStackCateg, voc_lab, voc, oneVector, stri_lab, W);
feat = featfun1_cpp01(voc_lab, voc, oneVector, stri_lab, k);
valu_1 = px * pyx * feat;
valu = valu + valu_1;
}
return valu;
}

// [[Rcpp::export]]
NumericMatrix final(double eps,
double bigM,
DataFrame tdmStackCateg,
NumericMatrix matx_tdmSC,
CharacterMatrix voc_lab,
CharacterVector voc,
NumericMatrix W) {
int k = 1;
int len_voc = voc.length();
NumericMatrix nominator_(len_voc, 1);

for (int i = 0; i < len_voc; i++) {
nominator_(i, 0) = EPF_nomin_cpp(tdmStackCateg,
matx_tdmSC,
voc_lab,
voc,
i + 1);
}

NumericMatrix theta(len_voc, 1);
double nominator = NA_REAL;
double denominator = NA_REAL;
NumericMatrix WI = clone(W);
NumericMatrix W_wanted = clone(W);
LogicalMatrix THETA(len_voc, 1);
bool THETA_single = NA_LOGICAL;

while (true) {
Rcpp::Rcout << "the value of theta: " << theta;
Rcpp::Rcout << "k = " << k;
for (int j = 0; j < len_voc; j++) {
nominator = nominator_(j, 0);
denominator = EPF_denomin_cpp01(tdmStackCateg,
matx_tdmSC,
voc_lab,
voc,
j + 1,
W);
theta(j, 0) = log(nominator / denominator) / bigM;
}
for (int k = 0; k < W.nrow(); k++) {
for (int h = 0; h < W.ncol(); h++) {
WI(k, h) = W(k, h) + theta(k, h);
}
}

for (int m = 0; m < len_voc; m++) {
THETA_single = theta(m, 0) < eps;
THETA(m, 0) = THETA_single;
}

if (is_true(all(THETA))) {
W_wanted = WI;
break;
}

W = WI;
k = k + 1;
}
return W_wanted;
}``````
``````rbenchmark::benchmark(EPF_denomin_cpp01(tdmStackCateg = tdmStackCateg,
matx_tdmSC = matx_tdmSC,
voc_lab = voc_lab,
voc = voc,
k = 1,
W = mat_voc),
EPF_denomin(1, mat_voc),
replications = 1)

#                                                                                                                         test
# 2                                                                                                     EPF_denomin(1, mat_voc)
# 1 EPF_denomin_cpp01(tdmStackCateg = tdmStackCateg, matx_tdmSC = matx_tdmSC, voc_lab = voc_lab, voc = voc, k = 1, W = mat_voc)
#   replications elapsed relative user.self sys.self user.child sys.child
# 2            1  113.91    7.242    112.29     0.02         NA        NA
# 1            1   15.73    1.000     15.65     0.01         NA        NA

eps <- 0.001
bigM <- max(f_sharp_matx)
final(eps,
bigM,
tdmStackCateg,
matx_tdmSC,
voc_lab,
voc,
wi)``````
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