\(Taller\)

#Ejercicio 1

prod<-function(k){
producto=1
for(i in seq(k)){
p_i=(4*i^2)/((2*i^2)-1)
producto=producto*p_1
}
return(producto)
}

######Ejercicio 5

####Vector1
sec<-seq(from=3, to=6,by=0.1)
vector=c(2.71828^sec* cos(sec))
#Vector 2
i=NULL; ope=NULL; vector2=NULL
for(i in 1:25){ope<-2^i/i; vector2<-c(vector2,ope)}
round(vector2,2)
##  [1]       2.00       2.00       2.67       4.00       6.40      10.67
##  [7]      18.29      32.00      56.89     102.40     186.18     341.33
## [13]     630.15    1170.29    2184.53    4096.00    7710.12   14563.56
## [19]   27594.11   52428.80   99864.38  190650.18  364722.09  699050.67
## [25] 1342177.28
#Vector 3
paste("Tratamiento", 1:30)
##  [1] "Tratamiento 1"  "Tratamiento 2"  "Tratamiento 3"  "Tratamiento 4" 
##  [5] "Tratamiento 5"  "Tratamiento 6"  "Tratamiento 7"  "Tratamiento 8" 
##  [9] "Tratamiento 9"  "Tratamiento 10" "Tratamiento 11" "Tratamiento 12"
## [13] "Tratamiento 13" "Tratamiento 14" "Tratamiento 15" "Tratamiento 16"
## [17] "Tratamiento 17" "Tratamiento 18" "Tratamiento 19" "Tratamiento 20"
## [21] "Tratamiento 21" "Tratamiento 22" "Tratamiento 23" "Tratamiento 24"
## [25] "Tratamiento 25" "Tratamiento 26" "Tratamiento 27" "Tratamiento 28"
## [29] "Tratamiento 29" "Tratamiento 30"
#Vector 4
paste("Gen", 1:10, sep = "")
##  [1] "Gen1"  "Gen2"  "Gen3"  "Gen4"  "Gen5"  "Gen6"  "Gen7"  "Gen8"  "Gen9" 
## [10] "Gen10"
#Vector 5
v5=replicate(n = 20, rnorm(40, 3, 0.3) )
med=colMeans(v5)
#Vector 6
de=apply(v5, 2, sd)
#Vector 7
cv=de/med

######Ejercicio 6

ma<-c(1,1,3,2,9,3,-4,5,1)#Con esta no funcionó
datosma2<-c(1,2,-4,1,9,5,3,3,1)
mat2<-matrix(datosma2, nrow = 3, ncol = 3)
#Inversa de la matriz
solve(mat2)
##             [,1]        [,2]        [,3]
## [1,] -0.05084746  0.11864407 -0.20338983
## [2,] -0.11864407  0.11016949  0.02542373
## [3,]  0.38983051 -0.07627119  0.05932203
#Matriz transpuesta
t(mat2)
##      [,1] [,2] [,3]
## [1,]    1    2   -4
## [2,]    1    9    5
## [3,]    3    3    1
#Determinante matriz
det(mat2)
## [1] 118
#Traza
sum(diag(mat2))
## [1] 11
#Rango
qr(mat2)$rank
## [1] 3
#Dimensión
dim(mat2)
## [1] 3 3
#Multiplicación con *-->Útil elemento a elemento por ella misma o un escalar
mat2*mat2
##      [,1] [,2] [,3]
## [1,]    1    1    9
## [2,]    4   81    9
## [3,]   16   25    1
#Multiplicación con %*%
mat2%*%mat2
##      [,1] [,2] [,3]
## [1,]   -9   25    9
## [2,]    8   98   36
## [3,]    2   46    4
# Multiplicación: A^3
mat2*mat2*mat2
##      [,1] [,2] [,3]
## [1,]    1    1   27
## [2,]    8  729   27
## [3,]  -64  125    1
mat2%*%mat2%*%mat2
##      [,1] [,2] [,3]
## [1,]    5  261   57
## [2,]   60 1070  354
## [3,]   78  436  148
#Nota: Con * cada término (ubicado en una columna y fila específico) de la matriz A se multiplica con el término (ubicado en la misma fila y columna  ) de B
# Con %*% se multiplica cada fila por columna

#Matriz
datmatrix<-c(0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0)
mat3<-matrix(datmatrix, nrow = 6, ncol = 6)
row(mat3)#asigna a cada fila de la matriz un número de manera ascendente
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    1    1    1    1    1
## [2,]    2    2    2    2    2    2
## [3,]    3    3    3    3    3    3
## [4,]    4    4    4    4    4    4
## [5,]    5    5    5    5    5    5
## [6,]    6    6    6    6    6    6
col(mat3)#asigna a cada columna de la matriz un número de manera ascendente
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    2    3    4    5    6
## [2,]    1    2    3    4    5    6
## [3,]    1    2    3    4    5    6
## [4,]    1    2    3    4    5    6
## [5,]    1    2    3    4    5    6
## [6,]    1    2    3    4    5    6
nrow(mat3)#Número de filas
## [1] 6
NROW(mat3)#Igual que nrow
## [1] 6
NCOL(mat3)#Número de columnas
## [1] 6
ncol(mat3)#Igual que NCOL
## [1] 6
anyNA(mat3)#Identificar si hay valores no disponibles
## [1] FALSE
as.matrix(mat3)#convertir datos en una matriz
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    0    1    0    0    0    0
## [2,]    1    0    1    0    0    0
## [3,]    0    1    0    1    0    0
## [4,]    0    0    1    0    1    0
## [5,]    0    0    0    1    0    1
## [6,]    0    0    0    0    1    0
as.raw(mat3)
##  [1] 00 01 00 00 00 00 01 00 01 00 00 00 00 01 00 01 00 00 00 00 01 00 01 00 00
## [26] 00 00 01 00 01 00 00 00 00 01 00
colnames(mat3)#debería dar el nombre de cada columna de mi matriz
## NULL
colSums(mat3)#Sumatoria de cada columna de mi matriz
## [1] 1 2 2 2 2 1
cummax(mat3)#reemplaza por el valor máximo de los datos, el primer cero no se reemplaza porque es por decirlo así el primer máximo, luego 1 es el nuevo máximo entonces de ahí para adelante si reemplaza el cero por 1
##  [1] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
cummin(mat3)#reemplaza por el mínimo de los datos
##  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
cumprod(mat3)#multiplicación acumulativa
##  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
cumsum(mat3)#suma acumulativa
##  [1]  0  1  1  1  1  1  2  2  3  3  3  3  3  4  4  5  5  5  5  5  6  6  7  7  7
## [26]  7  7  8  8  9  9  9  9  9 10 10
det(mat3)
## [1] -1
diag(mat3)
## [1] 0 0 0 0 0 0
diff(mat3)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1   -1    1    0    0    0
## [2,]   -1    1   -1    1    0    0
## [3,]    0   -1    1   -1    1    0
## [4,]    0    0   -1    1   -1    1
## [5,]    0    0    0   -1    1   -1
dimnames(mat3)
## NULL
exp(mat3)
##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
## [1,] 1.000000 2.718282 1.000000 1.000000 1.000000 1.000000
## [2,] 2.718282 1.000000 2.718282 1.000000 1.000000 1.000000
## [3,] 1.000000 2.718282 1.000000 2.718282 1.000000 1.000000
## [4,] 1.000000 1.000000 2.718282 1.000000 2.718282 1.000000
## [5,] 1.000000 1.000000 1.000000 2.718282 1.000000 2.718282
## [6,] 1.000000 1.000000 1.000000 1.000000 2.718282 1.000000
is.matrix(mat3)
## [1] TRUE
is.unsorted(mat3)
## [1] TRUE
is.vector(mat3)
## [1] FALSE
isSymmetric(mat3)
## [1] TRUE
length(mat3)
## [1] 36
lengths(mat3)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    1    1    1    1    1
## [2,]    1    1    1    1    1    1
## [3,]    1    1    1    1    1    1
## [4,]    1    1    1    1    1    1
## [5,]    1    1    1    1    1    1
## [6,]    1    1    1    1    1    1
log10(mat3)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -Inf    0 -Inf -Inf -Inf -Inf
## [2,]    0 -Inf    0 -Inf -Inf -Inf
## [3,] -Inf    0 -Inf    0 -Inf -Inf
## [4,] -Inf -Inf    0 -Inf    0 -Inf
## [5,] -Inf -Inf -Inf    0 -Inf    0
## [6,] -Inf -Inf -Inf -Inf    0 -Inf
lower.tri(mat3)
##       [,1]  [,2]  [,3]  [,4]  [,5]  [,6]
## [1,] FALSE FALSE FALSE FALSE FALSE FALSE
## [2,]  TRUE FALSE FALSE FALSE FALSE FALSE
## [3,]  TRUE  TRUE FALSE FALSE FALSE FALSE
## [4,]  TRUE  TRUE  TRUE FALSE FALSE FALSE
## [5,]  TRUE  TRUE  TRUE  TRUE FALSE FALSE
## [6,]  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
margin.table(mat3)
## [1] 10
marginSums(mat3)
## [1] 10
max(mat3)
## [1] 1
max.col(mat3)
## [1] 2 1 2 5 4 5
mean(mat3)
## [1] 0.2777778
min(mat3)
## [1] 0
nchar(mat3)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    1    1    1    1    1
## [2,]    1    1    1    1    1    1
## [3,]    1    1    1    1    1    1
## [4,]    1    1    1    1    1    1
## [5,]    1    1    1    1    1    1
## [6,]    1    1    1    1    1    1
norm(mat3)
## [1] 2
order(mat3)
##  [1]  1  3  4  5  6  8 10 11 12 13 15 17 18 19 20 22 24 25 26 27 29 31 32 33 34
## [26] 36  2  7  9 14 16 21 23 28 30 35
pmax(mat3)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    0    1    0    0    0    0
## [2,]    1    0    1    0    0    0
## [3,]    0    1    0    1    0    0
## [4,]    0    0    1    0    1    0
## [5,]    0    0    0    1    0    1
## [6,]    0    0    0    0    1    0
pmin(mat3)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    0    1    0    0    0    0
## [2,]    1    0    1    0    0    0
## [3,]    0    1    0    1    0    0
## [4,]    0    0    1    0    1    0
## [5,]    0    0    0    1    0    1
## [6,]    0    0    0    0    1    0
range(mat3)
## [1] 0 1
rank(mat3)
##  [1] 13.5 31.5 13.5 13.5 13.5 13.5 31.5 13.5 31.5 13.5 13.5 13.5 13.5 31.5 13.5
## [16] 31.5 13.5 13.5 13.5 13.5 31.5 13.5 31.5 13.5 13.5 13.5 13.5 31.5 13.5 31.5
## [31] 13.5 13.5 13.5 13.5 31.5 13.5
solve(mat3)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    0    1    0   -1    0    1
## [2,]    1    0    0    0    0    0
## [3,]    0    0    0    1    0   -1
## [4,]   -1    0    1    0    0    0
## [5,]    0    0    0    0    0    1
## [6,]    1    0   -1    0    1    0
sort(mat3)
##  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1
sum(mat3)
## [1] 10
t(mat3)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    0    1    0    0    0    0
## [2,]    1    0    1    0    0    0
## [3,]    0    1    0    1    0    0
## [4,]    0    0    1    0    1    0
## [5,]    0    0    0    1    0    1
## [6,]    0    0    0    0    1    0
upper.tri(mat3)
##       [,1]  [,2]  [,3]  [,4]  [,5]  [,6]
## [1,] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
## [2,] FALSE FALSE  TRUE  TRUE  TRUE  TRUE
## [3,] FALSE FALSE FALSE  TRUE  TRUE  TRUE
## [4,] FALSE FALSE FALSE FALSE  TRUE  TRUE
## [5,] FALSE FALSE FALSE FALSE FALSE  TRUE
## [6,] FALSE FALSE FALSE FALSE FALSE FALSE
which.max(mat3)
## [1] 2

Actividad 9

pH=c(6.12,5.13,5.84,6.53,6.12,6.30,6.04,5.79,5.94,6.03,6.12)
tiempo= seq(from=30, to=330,by=30)
plot(tiempo,pH, pch=17,col="darkviolet", type="b")
grid(lty=5, col="orange")
text(90,5.2,"θ =1.34")

#Cálculo de pendiente
tiempotramo=c(30,60,90)
pHtramo=c(5.13,5.84,6.53)
mod=lm(pHtramo~tiempotramo)
theta=atan(mod$coefficients[2 ])
pendiente=theta*180/pi

#Ejericio 12

pp<-rbeta(30,0.8,0.5)
datos<-data.frame(pp)#Data.frame crear tabla a partir de rbeta
ppmult<-datos*100
mpp=mean(ppmult)
## Warning in mean.default(ppmult): argument is not numeric or logical: returning
## NA
vectors<-c(44.15,82.26,86.66,36.00,98.73,97.78,90.41,77.45,17.22,18.59,99.72,42.94,78.45,42.08,34.41,6.34,58.09,32.05,92.00,57.26,80.77,69.16,16.62,69.97,24.74,16.10,77.26,67.24,6.13,56.03)
desvi<-sd(vectors)
datos_2sd=100*sum(ppmult>(mpp-2*desvi)& ppmult<(mpp+2*desvi))/length(ppmult)
sumacu=cumsum(vectors)
which.max(vectors)
## [1] 11
which.min(vectors)
## [1] 29

#Actividad 13

x<-c(1,2,5,9,11)
y<-c(2,5,1,0,23)
intersect(x,y)#Me da los intersectos entre ambos vectores
## [1] 1 2 5
setdiff(x,y)#devuelve las filas en x que no están en y
## [1]  9 11
setdiff(y,x)#devuelve las filas en y que no están en x
## [1]  0 23
union(x,y)#une ambos vectores
## [1]  1  2  5  9 11  0 23

#Actividad 14

set.seed(123)
td<-rbeta(30,2,1)
datoss<-data.frame(td)#Data.frame crear tabla a partir de rbeta
tdmult<-datoss*25


tdmult[tdmult>20 ]#Valores mayores a 20
##  [1] 24.23301 24.44851 20.19500 23.53852 20.42654 21.56602 22.20562 23.61541
##  [9] 22.44633 22.37667 22.13464 21.50145 20.76335
mean(tdmult[tdmult>=4])#sacar la media solo con los valores >=4
## [1] 17.33406
tdmult[tdmult==0|tdmult==1]#No me da da
## numeric(0)