In AlfonsoRReyes/rDeepThought:

The sigmoid function

basic_sigmoid <- function(x) {
    s <- 1 / (1 + exp (-x))
    return(s)
}

basic_sigmoid(3)
# 9525741

Vector operations

x <- array(c(1, 2, 3))
print(x + 3)

Sigmoid on a vector

sigmoid <- function(x) {
    s <- 1 / ( 1 + exp(-x))
    return(s)
}

x <- array(c(1, 2, 3))
sigmoid(x)

Sigmoid gradient

sigmoid_derivative <- function(x) {
    # Compute the gradient (also called the slope or derivative) of the sigmoid 
    # function with respect to its input x.
    # You can store the output of the sigmoid function into variables and then 
    # use it to calculate the gradient.

    # Arguments:
    # x -- A scalar or numpy array

    # Return:
    # ds -- Your computed gradient.

    s <- 1 / ( 1 + exp(-x))
    ds <- s * (1 - s)
    return(ds)
}

x <- array(c(1, 2, 3))
sigmoid_derivative(x)
# 0.19661193 0.10499359 0.04517666

Reshaping arrays

, in computer science, an image is represented by a 3D array of shape (length,height,depth=3). However, when you read an image as the input of an algorithm you convert it to a vector of shape (length∗height∗3,1). In other words, you "unroll", or reshape, the 3D array into a 1D vector.

Implement image2vector() that takes an input of shape (length, height, 3) and returns a vector of shape (lengthheight3, 1). For example, if you would like to reshape an array v of shape (a, b, c) into a vector of shape (a*b,c) you would do:

image2vector <- function(image){
    # Argument:
    # image -- a numpy array of shape (length, height, depth)
    # 
    # Returns:
    # v -- a vector of shape (length*height*depth, 1)

    v = array(image, dim = c(dim(image)[1] * dim(image)[2] * dim(image)[3], 1))
}    

image =  array(cbind(
    rbind(c( 0.67826139,  0.29380381),
        c( 0.90714982,  0.52835647),
        c( 0.4215251 ,  0.45017551)),

       rbind(c( 0.92814219,  0.96677647),
        c( 0.85304703,  0.52351845),
        c( 0.19981397,  0.27417313)),

       rbind(c( 0.60659855,  0.00533165),
        c( 0.10820313,  0.49978937),
        c( 0.34144279,  0.94630077))),
    dim = c(3,3,2)
)

image

# take row 1 only
image[1,,]

# take column 2
image[,2,]

# take slice 2
image[,,2]

AlfonsoRReyes/rDeepThought documentation built on May 3, 2019, 6:42 p.m.