Actividades Modelado de Cultivos Semana 1

1.1. Funciones en R

Actividad 1

\[\sum_{i=1}^{100}\frac{1}{(2^i)}\]

misum1.1=function(i){
  sumatoria1 = 0
  vecsumatoria1 = NULL
  for (i in seq(i)){
    s_i = 1/(2^i)
    sumatoria1 = sumatoria1 + s_i
    vecsumatoria1 [i] = sumatoria1
    }
  return(vecsumatoria1)
}
misum1.1(100)

##   [1] 0.5000000 0.7500000 0.8750000 0.9375000 0.9687500 0.9843750 0.9921875
##   [8] 0.9960938 0.9980469 0.9990234 0.9995117 0.9997559 0.9998779 0.9999390
##  [15] 0.9999695 0.9999847 0.9999924 0.9999962 0.9999981 0.9999990 0.9999995
##  [22] 0.9999998 0.9999999 0.9999999 1.0000000 1.0000000 1.0000000 1.0000000
##  [29] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [36] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [43] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [50] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [57] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [64] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [71] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [78] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [85] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [92] 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##  [99] 1.0000000 1.0000000

\[\sum_{n=0}^{\infty}\frac{1}{n!}\]

misum1.2=function(n){
  sumatoria2 = 0
  vecsumatoria2 = NULL
  for (i in seq(n)){
    s_n = 1/factorial(i)
    sumatoria2 = sumatoria2 + s_n
    vecsumatoria2 [i] = sumatoria2
    }
  return(vecsumatoria2)
}
misum1.2(5)

## [1] 1.000000 1.500000 1.666667 1.708333 1.716667

\[\prod_{n=1}^{6}(1+(x^(2^n)))\]

mipro1.3=function(n){
  productoria1 = 1
  vecproductoria1 = NULL
  x = 1
  for (i in seq(n)){
    p_n = 1 + (x^(2^n))
    productoria1 = productoria1 * p_n
    vecproductoria1 [i] = productoria1
    }
  return(vecproductoria1)
}
mipro1.3(6)

## [1]  2  4  8 16 32 64

\[\prod_{n=0}^{\infty}\frac{x^(2^n)}{(2n)!}\]

mipro1.5=function(n){
  productoria3 = 1
  vecproductoria3 = NULL
  x = 1
  for (i in seq(n)){
    p_k = (x^(2^n))/factorial(2*n)
    productoria3 = productoria3 * p_k
    vecproductoria3 [i] = productoria3
    }
  return(vecproductoria3)
}
mipro1.5(5)

## [1] 2.755732e-07 7.594058e-14 2.092719e-20 5.766972e-27 1.589223e-33

\[\sum_{k=0}^{\infty}\frac{(-1)^n(x^2)^(n+1)}{(2n+1)!}\]

misum1.6=function(n){
  sumatoria3 = 1
  vecsumatoria3 = NULL
  x = 1
  for (i in seq(n)){
    s_k = (((-1)^n)*((x^2)^(n+1)))/factorial((2*n)+1)
    sumatoria3 = sumatoria3 * s_k
    vecsumatoria3 [i] = sumatoria3
    }
  return(vecsumatoria3)
}
misum1.6(5)

## [1] -2.505211e-08  6.276081e-16 -1.572291e-23  3.938920e-31 -9.867824e-39

Actividad 2

\[ y= x^5-7x^4-162x^3+878x^2+3937x-15015\]

eje2.1=function(x){
  y=(x^5)-(7*x^4)-(162*x^3)+(878*x^2)+(3937*x)-15015
  return(y)
}
(mis_x = seq(-40,10,0.5))

##   [1] -40.0 -39.5 -39.0 -38.5 -38.0 -37.5 -37.0 -36.5 -36.0 -35.5 -35.0 -34.5
##  [13] -34.0 -33.5 -33.0 -32.5 -32.0 -31.5 -31.0 -30.5 -30.0 -29.5 -29.0 -28.5
##  [25] -28.0 -27.5 -27.0 -26.5 -26.0 -25.5 -25.0 -24.5 -24.0 -23.5 -23.0 -22.5
##  [37] -22.0 -21.5 -21.0 -20.5 -20.0 -19.5 -19.0 -18.5 -18.0 -17.5 -17.0 -16.5
##  [49] -16.0 -15.5 -15.0 -14.5 -14.0 -13.5 -13.0 -12.5 -12.0 -11.5 -11.0 -10.5
##  [61] -10.0  -9.5  -9.0  -8.5  -8.0  -7.5  -7.0  -6.5  -6.0  -5.5  -5.0  -4.5
##  [73]  -4.0  -3.5  -3.0  -2.5  -2.0  -1.5  -1.0  -0.5   0.0   0.5   1.0   1.5
##  [85]   2.0   2.5   3.0   3.5   4.0   4.5   5.0   5.5   6.0   6.5   7.0   7.5
##  [97]   8.0   8.5   9.0   9.5  10.0

prueba2.1 = eje2.1(x=mis_x)
plot(x=mis_x, y=prueba2.1, col="3")

\[ y= \frac{senx}{x}\]

eje2.2=function(x){
  y=sin(x)/x
  return(y)
}
(mis_x2 = seq(-10,10,0.25))

##  [1] -10.00  -9.75  -9.50  -9.25  -9.00  -8.75  -8.50  -8.25  -8.00  -7.75
## [11]  -7.50  -7.25  -7.00  -6.75  -6.50  -6.25  -6.00  -5.75  -5.50  -5.25
## [21]  -5.00  -4.75  -4.50  -4.25  -4.00  -3.75  -3.50  -3.25  -3.00  -2.75
## [31]  -2.50  -2.25  -2.00  -1.75  -1.50  -1.25  -1.00  -0.75  -0.50  -0.25
## [41]   0.00   0.25   0.50   0.75   1.00   1.25   1.50   1.75   2.00   2.25
## [51]   2.50   2.75   3.00   3.25   3.50   3.75   4.00   4.25   4.50   4.75
## [61]   5.00   5.25   5.50   5.75   6.00   6.25   6.50   6.75   7.00   7.25
## [71]   7.50   7.75   8.00   8.25   8.50   8.75   9.00   9.25   9.50   9.75
## [81]  10.00

prueba2.2 = eje2.2(x=mis_x2)
plot(x=mis_x2, y=prueba2.2, col="2")

\[ y= \frac{cosx-1}{x}\]

eje2.3=function(x){
  y=(cos(x))-1/x
  return(y)
}
(mis_x3 = seq(-15,15,0.25))

##   [1] -15.00 -14.75 -14.50 -14.25 -14.00 -13.75 -13.50 -13.25 -13.00 -12.75
##  [11] -12.50 -12.25 -12.00 -11.75 -11.50 -11.25 -11.00 -10.75 -10.50 -10.25
##  [21] -10.00  -9.75  -9.50  -9.25  -9.00  -8.75  -8.50  -8.25  -8.00  -7.75
##  [31]  -7.50  -7.25  -7.00  -6.75  -6.50  -6.25  -6.00  -5.75  -5.50  -5.25
##  [41]  -5.00  -4.75  -4.50  -4.25  -4.00  -3.75  -3.50  -3.25  -3.00  -2.75
##  [51]  -2.50  -2.25  -2.00  -1.75  -1.50  -1.25  -1.00  -0.75  -0.50  -0.25
##  [61]   0.00   0.25   0.50   0.75   1.00   1.25   1.50   1.75   2.00   2.25
##  [71]   2.50   2.75   3.00   3.25   3.50   3.75   4.00   4.25   4.50   4.75
##  [81]   5.00   5.25   5.50   5.75   6.00   6.25   6.50   6.75   7.00   7.25
##  [91]   7.50   7.75   8.00   8.25   8.50   8.75   9.00   9.25   9.50   9.75
## [101]  10.00  10.25  10.50  10.75  11.00  11.25  11.50  11.75  12.00  12.25
## [111]  12.50  12.75  13.00  13.25  13.50  13.75  14.00  14.25  14.50  14.75
## [121]  15.00

prueba2.3 = eje2.3(x=mis_x3)
plot(x=mis_x3, y=prueba2.3, col="4")

\[ y= x^5-3x^4+x^2-x-5\]

eje2.4=function(x){
  y=x^5-3*x^4+x^2-x-5
  return(y)
}
(mis_x4 = seq(-15,15,0.5))

##  [1] -15.0 -14.5 -14.0 -13.5 -13.0 -12.5 -12.0 -11.5 -11.0 -10.5 -10.0  -9.5
## [13]  -9.0  -8.5  -8.0  -7.5  -7.0  -6.5  -6.0  -5.5  -5.0  -4.5  -4.0  -3.5
## [25]  -3.0  -2.5  -2.0  -1.5  -1.0  -0.5   0.0   0.5   1.0   1.5   2.0   2.5
## [37]   3.0   3.5   4.0   4.5   5.0   5.5   6.0   6.5   7.0   7.5   8.0   8.5
## [49]   9.0   9.5  10.0  10.5  11.0  11.5  12.0  12.5  13.0  13.5  14.0  14.5
## [61]  15.0

prueba2.4 = eje2.4(x=mis_x4)
plot(x=mis_x4, y=prueba2.4, col="5")

Actividad 3

Ejercicio 3.1

\[\sum_{k=0}^{\infty}\frac{8}{(4k+1)(4k+3)} \]

eje3.1 <- function(k){
   ki = 0
   suma_valores = 0
  while(suma_valores <= 3.141593){
    suma_i = 8/((4*ki+1)*(4*ki+3))
    suma_valores = suma_valores + suma_i
    suma_valores = suma_valores
    if (ki == k) break
    ki = ki+1
  }
  
  return(list(ki = ki,
              suma_valores))
}
eje3.1(3256000)

## $ki
## [1] 3256000
## 
## [[2]]
## [1] 3.141593

Ejercicio 3.2 \[\sqrt{6\sum_{k=1}^{\infty}\frac{1}{k^2}}\]

eje3.2 <- function(k){
   ki2 = 1
   suma_i2 = 0
  while(suma_i2 <= pi){
  suma_i2 = ((cumsum(1/(ki2^2)))*6)^(1/2)
    
  if (ki2 == k) break
    ki2 = ki2+1
  }
  
  return(list(ki2,
              suma_i2))
}
eje3.2(20000000)

## [[1]]
## [1] 2e+07
## 
## [[2]]
## [1] 1.224745e-07

#k=seq(1:100000000)
#(cumsum(1/(k^2))*6)^(1/2)

Actividad 4

Ejercicio 1

\[ 1+x+\frac{x^2}{2}+\frac{x^3}{3}+...+\frac{x^n}{n}\]

ejer4=function(x,n){
   if (n>0){
    ejer4=1+x+(x^n)/n
    return(ejer4)
  }
}
 x1=c(5)
 n1=c(1:20)
 int_R=cumsum(ejer4(n1,x1))
 int_R

##  [1]       2.2      11.6      64.2     274.0     905.0    2467.2    5836.6
##  [8]   12399.2   24219.0   44230.0   76452.2  126231.6  200504.2  308084.0
## [15]  459975.0  669707.2  953696.6 1331629.2 1826869.0 2466890.0

 plot(int_R)
 lines(n1,int_R,col="red")

Actividad 5

Ejercicio 5.1

(x=c(seq(3,6,0.1)))

##  [1] 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8
## [20] 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0

(vector5.1=(exp(1)^x)*cos(x))

##  [1] -19.884531 -22.178753 -24.490697 -26.773182 -28.969238 -31.011186
##  [7] -32.819775 -34.303360 -35.357194 -35.862834 -35.687732 -34.685042
## [13] -32.693695 -29.538816 -25.032529 -18.975233 -11.157417  -1.362099
## [19]  10.632038  25.046705  42.099201  61.996630  84.929067 111.061586
## [25] 140.525075 173.405776 209.733494 249.468441 292.486707 338.564378
## [31] 387.360340

Ejercicio 5.2

n=c(1:25)
(y=c(2^n/n))

##  [1] 2.000000e+00 2.000000e+00 2.666667e+00 4.000000e+00 6.400000e+00
##  [6] 1.066667e+01 1.828571e+01 3.200000e+01 5.688889e+01 1.024000e+02
## [11] 1.861818e+02 3.413333e+02 6.301538e+02 1.170286e+03 2.184533e+03
## [16] 4.096000e+03 7.710118e+03 1.456356e+04 2.759411e+04 5.242880e+04
## [21] 9.986438e+04 1.906502e+05 3.647221e+05 6.990507e+05 1.342177e+06

Ejercicio 5.3

paste(c("trat"),... = 1:30, sep="")

##  [1] "trat1"  "trat2"  "trat3"  "trat4"  "trat5"  "trat6"  "trat7"  "trat8" 
##  [9] "trat9"  "trat10" "trat11" "trat12" "trat13" "trat14" "trat15" "trat16"
## [17] "trat17" "trat18" "trat19" "trat20" "trat21" "trat22" "trat23" "trat24"
## [25] "trat25" "trat26" "trat27" "trat28" "trat29" "trat30"

Ejercicio 5.4

paste(c('gen'),... = 1:10, sep="")

##  [1] "gen1"  "gen2"  "gen3"  "gen4"  "gen5"  "gen6"  "gen7"  "gen8"  "gen9" 
## [10] "gen10"

Ejercicio 5.5

set.seed(123)
(ejer5.5=replicate(20,expr = rnorm(40,3,0.3)))

##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 2.831857 2.791588 3.001729 3.035294 3.315813 3.659643 2.763413 2.499757
##  [2,] 2.930947 2.937625 3.115584 2.715758 2.685247 3.393724 2.849340 3.220949
##  [3,] 3.467612 2.620381 2.888802 2.852833 2.621953 2.920456 3.448818 3.115808
##  [4,] 3.021153 3.650687 3.193313 2.923172 3.972312 3.162958 2.658809 2.920305
##  [5,] 3.038786 3.362389 2.933854 3.553159 2.874943 2.875698 2.946285 3.035443
##  [6,] 3.514519 2.663067 3.099535 2.804415 3.089468 2.857126 3.570709 3.040212
##  [7,] 3.138275 2.879135 3.329052 3.070616 3.190971 2.763419 2.969708 3.066306
##  [8,] 2.620482 2.860003 3.130554 3.023388 2.854866 2.821615 2.592048 3.492254
##  [9,] 2.793944 3.233990 2.902221 2.711443 3.155059 3.495272 2.800569 2.934285
## [10,] 2.866301 2.974989 3.344642 2.978608 3.110689 2.983792 3.145638 3.050420
## [11,] 3.367225 3.075996 3.298051 3.433365 2.935386 3.035774 2.887319 3.350515
## [12,] 3.107944 2.991436 3.164519 3.135451 3.019588 3.073106 2.831437 3.316254
## [13,] 3.120231 2.987139 3.071620 3.012370 2.989780 3.369743 2.896825 3.343579
## [14,] 3.033205 3.410581 2.811628 2.873251 3.638536 2.845181 3.027149 2.826760
## [15,] 2.833248 2.932269 3.408196 2.384026 2.777599 2.702248 3.479553 3.600745
## [16,] 3.536074 3.454941 2.819922 3.339401 2.671201 3.502709 2.973430 3.020010
## [17,] 3.149355 2.535374 3.656200 2.561808 3.011337 2.867651 3.324240 3.560056
## [18,] 2.410015 3.175384 3.459783 3.221984 3.093144 2.783080 3.189226 2.594729
## [19,] 3.210407 3.037156 2.929290 3.572731 3.130957 2.629118 2.965908 3.006295
## [20,] 2.858163 3.064782 2.692074 2.566832 2.862490 2.614585 2.540129 3.374974
## [21,] 2.679653 3.113892 2.786878 3.210535 2.681002 2.827808 2.843665 2.785427
## [22,] 2.934608 2.849303 3.077065 2.921341 3.378956 3.185396 2.853039 2.774193
## [23,] 2.692199 2.900038 2.925992 2.528357 2.895105 3.332954 3.014146 2.718438
## [24,] 2.781333 2.694427 2.895737 2.545600 2.740346 3.212277 3.390060 2.684246
## [25,] 2.812488 2.678463 2.714514 2.519539 2.929116 2.890903 3.687924 2.868852
## [26,] 2.493992 3.091059 2.986492 2.840728 2.940847 3.017925 3.464274 3.099354
## [27,] 3.251336 3.134463 2.764529 2.561473 3.332976 2.788621 2.960055 2.395737
## [28,] 3.046012 3.015901 2.499617 3.206375 3.025421 2.784835 2.473042 3.063594
## [29,] 2.658559 3.276680 2.885932 3.630033 3.226216 3.265395 2.883366 3.371003
## [30,] 3.376144 3.615025 3.275699 2.613891 2.850212 2.695322 3.026762 3.611272
## [31,] 3.127939 2.852691 2.827396 3.236322 3.064334 3.586588 3.253504 3.390353
## [32,] 2.911479 2.307249 3.182389 3.230713 2.902594 2.972904 3.288758 3.227032
## [33,] 3.268538 3.301722 2.514635 3.099661 3.028375 3.064362 3.205293 2.481981
## [34,] 3.263440 2.787240 2.983331 2.697487 2.731391 2.778442 2.581418 2.819548
## [35,] 3.246474 2.793597 3.155822 2.964164 2.606760 2.827683 3.254893 2.894386
## [36,] 3.206592 3.307671 3.090346 2.915881 3.599164 2.604895 2.866033 3.211057
## [37,] 3.166175 2.914568 3.031703 3.168897 3.180213 2.945122 3.052441 2.968299
## [38,] 2.981426 2.633785 2.807788 2.888268 2.624619 3.125695 3.022365 2.622405
## [39,] 2.908211 3.054391 2.745089 3.293092 2.816650 3.097291 3.128450 3.505331
## [40,] 2.885859 2.958333 2.692761 2.887626 2.644356 2.765539 3.007402 3.273417
##           [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16]
##  [1,] 3.071229 2.938410 2.977933 2.627687 3.006135 3.290180 2.749847 3.322204
##  [2,] 3.365433 3.195358 2.649405 3.136431 3.094217 2.967516 3.173617 2.991796
##  [3,] 2.598368 3.082130 2.809576 3.197971 3.398464 2.790474 2.673726 2.990001
##  [4,] 3.198246 3.307402 2.991348 2.940033 3.036396 2.917216 3.445209 2.545180
##  [5,] 2.843126 3.245298 3.201209 2.806466 3.213853 3.334395 2.644138 3.237116
##  [6,] 3.205124 2.937062 2.504836 3.049596 3.233658 3.165013 3.030324 2.936780
##  [7,] 2.981753 3.113450 2.895074 3.131646 3.274432 3.371003 3.159897 2.802977
##  [8,] 3.189888 2.716377 3.226922 3.264991 2.827682 3.041729 3.176021 2.576392
##  [9,] 3.400655 3.257077 2.838357 2.384299 3.488064 3.123083 2.909476 2.910071
## [10,] 3.002187 2.861688 3.068188 2.509086 2.885713 2.832463 3.023851 2.745282
## [11,] 3.305268 3.725032 3.147669 3.429121 2.968265 3.181611 3.288379 2.880891
## [12,] 2.643470 2.504685 3.080351 3.313989 3.421215 2.848100 2.563060 2.634720
## [13,] 2.783519 2.860804 3.195977 3.130587 3.388225 2.573830 2.765478 3.506277
## [14,] 3.455765 3.247614 2.963187 3.214554 2.673002 3.038398 3.096121 2.995199
## [15,] 3.113216 3.153040 2.875897 3.275152 2.738079 3.583755 2.866565 3.322484
## [16,] 2.384333 2.823156 2.207055 2.201723 2.592576 3.240274 3.411001 2.219490
## [17,] 2.590789 2.700966 2.972118 3.333083 3.054554 3.349576 3.201976 2.864041
## [18,] 2.939766 3.043343 3.129085 2.854504 3.049452 3.107657 3.021650 2.797355
## [19,] 3.259734 2.995708 3.160620 3.069185 3.109234 2.817433 2.547673 2.633122
## [20,] 2.969435 2.462916 2.833416 2.911453 3.165647 2.939328 3.007830 3.463983
## [21,] 3.187256 3.010365 3.533851 3.261589 2.819432 2.918026 2.905075 2.575415
## [22,] 3.287702 3.057069 3.085927 2.895458 2.701890 2.859390 2.969296 3.095517
## [23,] 3.501316 3.052418 3.037895 3.155551 3.308036 3.211250 2.645532 3.253931
## [24,] 3.016805 2.683495 3.381680 2.882795 3.225318 2.640791 3.149597 3.053457
## [25,] 2.984405 3.142840 2.784460 2.672164 2.547250 3.259910 2.688313 2.737423
## [26,] 2.474029 3.413571 2.864898 3.363003 2.971456 3.259246 2.932133 3.282350
## [27,] 3.029798 3.136871 3.719236 3.222270 2.731216 2.640413 3.114428 3.051176
## [28,] 2.828445 2.659323 3.003339 3.517279 2.378775 3.191848 2.764945 2.680951
## [29,] 2.707797 2.869306 3.490071 3.019546 3.045036 3.729068 3.174897 2.583585
## [30,] 2.946028 3.103831 2.568448 3.337501 2.976236 2.832835 2.605047 3.626015
## [31,] 3.304483 2.805886 2.942845 3.592626 2.970789 3.253471 2.157068 2.796449
## [32,] 2.402175 2.352706 3.113527 2.915555 3.064846 2.765339 3.139490 2.443329
## [33,] 2.871816 3.265275 3.090012 2.603115 3.264740 3.333213 3.252162 3.159978
## [34,] 3.034991 2.751157 2.698309 2.928195 3.061679 3.074947 2.914246 3.093069
## [35,] 2.732038 2.827932 3.005778 2.935788 2.815069 3.495575 3.151238 2.593850
## [36,] 3.100171 3.451170 2.676774 3.045504 2.779560 2.562309 2.653225 2.417113
## [37,] 3.123429 2.767757 3.213811 3.513691 2.960459 2.984611 2.961855 2.965109
## [38,] 2.990089 3.253719 3.325433 2.902157 3.093005 2.841922 2.417544 3.341819
## [39,] 2.260231 2.621795 2.332504 3.111901 2.688096 2.940821 3.354354 3.190837
## [40,] 3.771437 2.893637 3.370708 2.931695 2.944707 2.811126 3.557973 2.852119
##          [,17]    [,18]    [,19]    [,20]
##  [1,] 2.749744 3.114692 2.687498 3.161937
##  [2,] 3.081320 3.294634 2.481509 3.184937
##  [3,] 3.047206 2.781785 3.192549 3.184970
##  [4,] 3.188914 2.700948 2.541207 2.492370
##  [5,] 2.881261 2.687493 3.000505 3.110623
##  [6,] 3.269806 2.875623 3.075074 3.290358
##  [7,] 2.750757 2.928291 3.169160 3.382974
##  [8,] 2.900837 3.145085 3.056828 2.932512
##  [9,] 3.222244 2.903603 2.780144 2.903432
## [10,] 3.296991 2.376453 3.295910 3.446351
## [11,] 2.418449 2.972570 3.521590 2.499622
## [12,] 3.032157 3.356156 3.264354 2.868951
## [13,] 3.182634 3.357480 2.416905 3.137239
## [14,] 2.564753 2.763311 3.419873 2.514668
## [15,] 3.144188 2.535667 2.983183 3.083888
## [16,] 2.751548 3.737418 3.157474 3.563359
## [17,] 3.306076 2.951273 3.186610 2.998782
## [18,] 3.161545 2.970765 2.970994 2.916464
## [19,] 3.230716 3.126172 2.977421 3.142474
## [20,] 3.036216 2.515788 3.305747 2.916278
## [21,] 3.259095 2.781534 3.213481 3.244020
## [22,] 3.414154 2.537867 3.297079 3.271331
## [23,] 3.589874 2.792072 3.714878 3.000807
## [24,] 2.991481 3.035655 3.199325 2.646992
## [25,] 2.325285 2.590587 3.062214 2.604534
## [26,] 3.009458 3.176995 2.336810 2.822101
## [27,] 3.061668 3.086803 3.807514 3.239214
## [28,] 2.953396 2.728735 2.855197 2.412538
## [29,] 3.170487 3.067897 3.712420 2.434102
## [30,] 3.303203 3.224424 3.112393 2.803866
## [31,] 2.844605 3.318329 3.461529 3.118318
## [32,] 2.911771 2.936146 2.967087 2.725930
## [33,] 3.119353 2.971909 3.153441 3.266025
## [34,] 2.834933 2.973986 3.064187 3.100011
## [35,] 3.027380 3.432439 2.944164 2.948808
## [36,] 2.411488 3.337522 2.963882 3.245648
## [37,] 2.664030 3.250320 3.303850 3.116510
## [38,] 2.601673 2.913798 2.939563 2.866219
## [39,] 2.743913 3.111972 2.388695 3.069334
## [40,] 2.792009 3.120987 2.941233 3.194254

(y5.5=c(colMeans(ejer5.5)))

##  [1] 3.013555 2.997985 3.002357 2.968247 3.005000 3.003171 3.027936 3.053390
##  [9] 2.996394 2.982291 2.999193 3.039723 2.999162 3.052979 2.956606 2.929221
## [17] 2.981165 2.987130 3.073087 2.996569

Ejercicio 5.6

(desv5.5=c(apply(ejer5.5, 2, sd)))

##  [1] 0.2693354 0.2879017 0.2532419 0.3142630 0.2982670 0.2775668 0.2867802
##  [8] 0.3214475 0.3274135 0.2871015 0.3090161 0.3077469 0.2555555 0.2751171
## [15] 0.3005222 0.3254278 0.2854671 0.2881477 0.3444641 0.2865597

Ejercicio 5.7

(coef5.5=c(y5.5/desv5.5))

##  [1] 11.188856 10.413224 11.855689  9.445105 10.074866 10.819635 10.558386
##  [8]  9.498875  9.151710 10.387584  9.705620  9.877347 11.735852 11.097015
## [15]  9.838229  9.001140 10.443112 10.366663  8.921355 10.457050

Actividad 6

vec6.1=c(1,2,-4,1,9,5,3,3,1)
(matriz6.1=matrix(vec6.1, nrow=3, ncol=3))

##      [,1] [,2] [,3]
## [1,]    1    1    3
## [2,]    2    9    3
## [3,]   -4    5    1

t(matriz6.1) #transponer

##      [,1] [,2] [,3]
## [1,]    1    2   -4
## [2,]    1    9    5
## [3,]    3    3    1

solve(matriz6.1) #invertir

##             [,1]        [,2]        [,3]
## [1,] -0.05084746  0.11864407 -0.20338983
## [2,] -0.11864407  0.11016949  0.02542373
## [3,]  0.38983051 -0.07627119  0.05932203

det(matriz6.1) #determinante

## [1] 118

sum(diag(matriz6.1)) #traza

## [1] 11

qr(matriz6.1)$rank #rango

## [1] 3

dim(matriz6.1) #dimensión

## [1] 3 3

matriz6.1*matriz6.1

##      [,1] [,2] [,3]
## [1,]    1    1    9
## [2,]    4   81    9
## [3,]   16   25    1

matriz6.1%*%matriz6.1

##      [,1] [,2] [,3]
## [1,]   -9   25    9
## [2,]    8   98   36
## [3,]    2   46    4

matriz6.1*matriz6.1*matriz6.1

##      [,1] [,2] [,3]
## [1,]    1    1   27
## [2,]    8  729   27
## [3,]  -64  125    1

matriz6.1%*%matriz6.1%*%matriz6.1

##      [,1] [,2] [,3]
## [1,]    5  261   57
## [2,]   60 1070  354
## [3,]   78  436  148

MB=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)
(B=matrix(MB, nrow = 6))

##      [,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

row(B)

##      [,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(B)

##      [,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(B)

## [1] 6

NROW(B)

## [1] 6

NCOL(B)

## [1] 6

ncol(B)

## [1] 6

anyNA(B)

## [1] FALSE

as.matrix(B)

##      [,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(B)

##  [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(B)

## NULL

colSums(B)

## [1] 1 2 2 2 2 1

cummax(B)

##  [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(B)

##  [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(B)

##  [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(B)

##  [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(B)

## [1] -1

diag(B)

## [1] 0 0 0 0 0 0

diff(B)

##      [,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(B)

## NULL

exp(B)

##          [,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(B)

## [1] TRUE

is.unsorted(B)

## [1] TRUE

is.vector(B)

## [1] FALSE

isSymmetric(B)

## [1] TRUE

length(B)

## [1] 36

lengths(B)

##      [,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(B)

##      [,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(B)

##       [,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(B)

## [1] 10

marginSums(B)

## [1] 10

max(B)

## [1] 1

max.col(B)

## [1] 2 1 4 3 4 5

mean(B)

## [1] 0.2777778

min(B)

## [1] 0

nchar(B)

##      [,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(B)

## [1] 2

order(B)

##  [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

plot(B, xlim = c(0,2), ylim = c(0,2)) #aiuda

pmax(B)

##      [,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(B)

##      [,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(B)

## [1] 0 1

rank(B)

##  [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

row(B)

##      [,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

solve(B)

##      [,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(B)

##  [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(B)

## [1] 10

t(B)

##      [,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(B)

##       [,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(B)

## [1] 2

Actividad 7

library(stringr)
gen=c("AGTCACAATGGAATAGGCCAAGCGATTGCAGGGTAGCCAGCCA")
tamaño=str_length(gen)
paste0("El total de bases es: ",tamaño)

## [1] "El total de bases es: 43"

numero_b=nchar(gen)
bases=str_sub(gen,1:tamaño,1:tamaño)
table(bases)

## bases
##  A  C  G  T 
## 14 10 13  6

(baseG=str_locate_all(gen,"G"))

## [[1]]
##       start end
##  [1,]     2   2
##  [2,]    10  10
##  [3,]    11  11
##  [4,]    16  16
##  [5,]    17  17
##  [6,]    22  22
##  [7,]    24  24
##  [8,]    28  28
##  [9,]    31  31
## [10,]    32  32
## [11,]    33  33
## [12,]    36  36
## [13,]    40  40

parGA=str_count(gen,"GA")
paste0("El total de veces que aparece el par GA es : ",parGA)

## [1] "El total de veces que aparece el par GA es : 2"

Actividad 8

decaimiento = function(t){
  tiempo = seq(0, t,8)
  N = 500 * (1/2)^tiempo
  t = log(N/500,1/2)
  
  df <- data.frame(tiempo, N)
  require(ggplot2)
  grafico <- ggplot(df, aes(x = tiempo, y = N)) + geom_point() + geom_smooth(aes(x=t, y=N),model = "SplineSmooth", colour="red")
  
  return(list(data.frame(tiempo,N),t,grafico))
}
decaimiento(64)

## [[1]]
##   tiempo            N
## 1      0 5.000000e+02
## 2      8 1.953125e+00
## 3     16 7.629395e-03
## 4     24 2.980232e-05
## 5     32 1.164153e-07
## 6     40 4.547474e-10
## 7     48 1.776357e-12
## 8     56 6.938894e-15
## 9     64 2.710505e-17
## 
## [[2]]
## [1]  0  8 16 24 32 40 48 56 64
## 
## [[3]]

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 = c(0,30,60,90,120,150,180,210,240,270,300)
(datos = data.frame(tiempo,pH))

##    tiempo   pH
## 1       0 6.12
## 2      30 5.13
## 3      60 5.84
## 4      90 6.53
## 5     120 6.12
## 6     150 6.30
## 7     180 6.04
## 8     210 5.79
## 9     240 5.94
## 10    270 6.03
## 11    300 6.12

datos2 = datos[1:2,]
library(ggplot2)
ggplot(datos, aes(x=tiempo, y=pH )) + 
  geom_line(colour="violet")  + 
  geom_point( size=2, shape=21, fill="white", colour="violet") + 
  theme_minimal() + geom_line(aes(x=tiempo, y=pH),data=datos2, colour="red")+
  geom_text(aes(x = 20, y=5.9,label = "Pendiente (β): -0.033", angle=-77, fontface=1))

(pendiente=(pH[2]-pH[1])/(tiempo[2]-tiempo[1]))

## [1] -0.033

Actividad 10

temperaturas=function(n){
  act10=rnorm(n,25,2)
  media=mean(act10)
  mediana=median(act10)
  mediat=mean(act10,trim=0.05)
  q1=quantile(act10,0.25)
  q3=quantile(act10,0.75)
  q10=quantile(act10,0.1)
  q90=quantile(act10,0.9)
  p11=100*sum((act10)>0.95)/10
  cv=sd(act10) / mean(act10) * 100
return(list(paste0("La media aritmética es: ",media),
            paste0("La mediana es: ",mediana),
            paste0("La media truncada es: ",mediat),
            paste0("El cuartil inferior es: ",q1),
            paste0("El cuartil superior es: ",q3),
            paste0("El percentil 10 es: ",q10),
            paste0("El percentil 90 es: ",q90),
            paste0("El % de datos que cae a dos desviaciones estándar de la media es: ",p11),
            paste0("El coeficiente de variación es: ",cv)))
}
temperaturas(10)

## [[1]]
## [1] "La media aritmética es: 24.7360421334575"
## 
## [[2]]
## [1] "La mediana es: 25.0684795816823"
## 
## [[3]]
## [1] "La media truncada es: 24.7360421334575"
## 
## [[4]]
## [1] "El cuartil inferior es: 24.7237223566448"
## 
## [[5]]
## [1] "El cuartil superior es: 25.5176203206252"
## 
## [[6]]
## [1] "El percentil 10 es: 21.6809092625056"
## 
## [[7]]
## [1] "El percentil 90 es: 25.9306535952115"
## 
## [[8]]
## [1] "El % de datos que cae a dos desviaciones estándar de la media es: 100"
## 
## [[9]]
## [1] "El coeficiente de variación es: 9.89900379986591"

Actividad 11

temperaturas2=function(n){
  act11=runif(n,18,24)
  media=mean(act11)
  mediana=median(act11)
  mediat=mean(act11,trim=0.05)
  q1=quantile(act11,0.25)
  q3=quantile(act11,0.75)
  q10=quantile(act11,0.1)
  q90=quantile(act11,0.9)
  p11=100*sum((act11)>0.95)/n
  cv=sd(act11) / mean(act11) * 100
return(list(paste0("La media aritmética es: ",media),
            paste0("La mediana es: ",mediana),
            paste0("La media truncada es: ",mediat),
            paste0("El cuartil inferior es: ",q1),
            paste0("El cuartil superior es: ",q3),
            paste0("El percentil 10 es: ",q10),
            paste0("El percentil 90 es: ",q90),
            paste0("El % de datos que cae a dos desviaciones estándar de la media es: ",p11),
            paste0("El coeficiente de variación es: ",cv)))
}
temperaturas2(100)

## [[1]]
## [1] "La media aritmética es: 21.1159502910823"
## 
## [[2]]
## [1] "La mediana es: 21.144079571357"
## 
## [[3]]
## [1] "La media truncada es: 21.1260415524865"
## 
## [[4]]
## [1] "El cuartil inferior es: 19.6477622932289"
## 
## [[5]]
## [1] "El cuartil superior es: 22.7106270315126"
## 
## [[6]]
## [1] "El percentil 10 es: 18.5894174506422"
## 
## [[7]]
## [1] "El percentil 90 es: 23.3780703419354"
## 
## [[8]]
## [1] "El % de datos que cae a dos desviaciones estándar de la media es: 100"
## 
## [[9]]
## [1] "El coeficiente de variación es: 8.36820204200039"

Actividad 12

set.seed(123)
pp=rbeta(30,0.8,0.5)*100
paste0("La media de pp es:", mean(pp))

## [1] "La media de pp es:65.6394039023683"

p12=((sum(pp>0.95))/30)*100
paste0("El % de datos que cae a dos desviaciones estándar de la media de pp es: ",p12)

## [1] "El % de datos que cae a dos desviaciones estándar de la media de pp es: 100"

cumsum(pp)

##  [1]   43.37938  143.12956  209.83928  280.58248  380.45543  468.05737
##  [7]  482.62190  567.92326  637.42005  658.35364  747.21682  841.25602
## [13]  867.09636  911.44124  916.36267  929.23256 1025.42434 1097.73700
## [19] 1196.88493 1283.20758 1321.54001 1418.40564 1514.38467 1608.17674
## [25] 1698.74944 1755.51704 1793.02115 1825.05346 1870.19685 1969.18212

max=which(pp %in% max(pp))
paste0("El día del mes en el que cae el máximo de pp es: ",max)

## [1] "El día del mes en el que cae el máximo de pp es: 5"

min=which(pp %in% min(pp))
paste0("El día del mes en el que cae el mínimo de pp es: ",min)

## [1] "El día del mes en el que cae el mínimo de pp es: 15"

Actividad 13

x = c(1, 2, 5, 9, 11) 
y = c(2, 5, 1, 0, 23) 
intersect(x,y)

## [1] 1 2 5

setdiff(x,y)

## [1]  9 11

setdiff(y,x)

## [1]  0 23

union(x,y)

## [1]  1  2  5  9 11  0 23

Los valores que comparten los vectores x & y son 1, 2 y 5
Los valores que estan en x y no en y son 9 y 11, mientras que los valores que están en y pero no en x son 0 y 23
Los valores 1, 2, 5, 9, 11, 0 y 23 representan la unión de x & y

Actividad 14

td=rbeta(30,2,1)*25
td[td>20]

## [1] 21.94627 23.88268 24.16421 20.94031 20.11355 22.55470 24.74520 22.86634
## [9] 22.93571

mean(td[td >= 4])

## [1] 16.84913

td[td == 0 | td == 1]

## numeric(0)

td[td %in% c(0, 0.6)]

## numeric(0)

La temperatura diaria que superan los 20°C en la variable td (temperatura diaria) son 24.58573 20.13476 23.27694, 21.75674, 24.64343, 21.56818, 21.49775, 24.77474 21.98213 y 21.89536
La media de la temperatura diaria desde el día 4 es 16.84086
El día en el que es verdadero que td es igual a 0 ó a 1, no existe

Actividad 15

Ejercicio 1

Se extrae una carta al azar de una baraja de 52 cartas. Encuentre la probabilidad de que la carta extraída sea (i) un as, y (ii) un palo.

(pi=(4/52)*100)

## [1] 7.692308

La probabilidad de extraer una carta al azar y que sea un as es del 7,69%

(pii=(13/52)*100)

## [1] 25

Teniendo en cuenta que un palo son 13 cartas, la probabilidad de sacar un palo de una baraja de 52 cartas es del 25%

Ejercicio 2

Se lanza una moneda sin sesgo dos veces. Encuentre la probabilidad de (i) exactamente una cara, (ii) a lo sumo una cara, (iii) al menos una cara, y (iv) la misma cara en ambas monedas.

(p_i=(2/4)*100)

## [1] 50

La probabilidad de que al lanzar una moneda dos veces y una sea cara es del 50%

(p_ii=(2/4)*100)

## [1] 50

La probabilidad de que al lanzar una moneda dos veces y a lo sumo una sea cara es del 50%

(p_iii=(3/4)*100)

## [1] 75

La probabilidad de que al lanzar una moneda dos veces y al menos una sea cara es del 75%

(p_i=(1/4)*100)

## [1] 25

La probabilidad de que al lanzar una moneda dos veces y sea la misma cara en ambas es del 25%

Actividades Modelado de Cultivos Semana 1

Ana María Florián Pulido

22/3/2021

1.1. Funciones en R