# In bquast/sigmoid: Sigmoid Functions for Machine Learning

The `sigmoid()` function returns the sigmoid value of the input(s), by default this is done using the standard logistic function.

```library(sigmoid)
sigmoid(3)
```

Inputs can also be tensors, such as vectors, matrices, or arrays.

```sigmoid(-5:5)
sigmoid( matrix(-3:5,nrow=3) ) # etc.
```

The `sigmoid()` function is a wrapper, which by default uses the `logistic()` function, it can also use other methods.

## Gompertz

```sigmoid( -5:5, method='Gompertz' )
```

These functions can also be accessed directly.

```Gompertz(-1:-5)
```

## Rectified Linear Unit (ReLU)

Rectified Linear Unit (ReLU)

```sigmoid( -5:5, method='ReLU')
```

Leaky Rectified Linear Unit

```sigmoid( -5:5, method="leakyReLU")
```

## Mappings

These mappings are similar but not identical.

```library(ggplot2)

input = -5:5

df = data.frame(input, logistic(input), Gompertz(input))

ggplot(df, aes(input, logistic(input))) + geom_line() +
geom_line(aes(input,Gompertz(input)), colour='red')
```

## Inverse

The wrapper can also apply the inverse of the method, returning the original values.

```sigmoid( sigmoid(-5:5), inverse=TRUE )
```

Which also works for other methods.

```sigmoid( sigmoid(-5:5, method='Gompertz'), method='Gompertz', inverse=TRUE )
```

In addition to this, the SoftMax algorithm can be pre applied.

```sigmoid( -3:5 )
sigmoid( -3:5, SoftMax = TRUE )
```

Several parameters can be specified (for details see `help(logistic)`, etc.). This can for instance be used to preserve greater entropy.

```x = seq(1,5, by=0.05)
qplot(sigmoid(x))
qplot( sigmoid(x, k=sd(x), x0=mean(x) ) )
```

bquast/sigmoid documentation built on Jan. 11, 2020, 11:16 a.m.