# How to get dpois results for multiple x and multiple lambda?

I'm trying to get a probability matrix from Poisson distribution using a vector of Lambda. what i want to get:

```    x<-seq(1,3,1)
Lambda<-seq(1,2,0.5)
dpois(x,Lambda[1])
[1] 0.36787944 0.18393972 0.06131324
dpois(x,Lambda[2])
[1] 0.3346952 0.2510214 0.1255107
dpois(x,Lambda[3])
[1] 0.2706706 0.2706706 0.1804470
```

when i do it like this:

```     dpois(x,Lambda)
[1] 0.3678794 0.2510214 0.1804470
```

i get the probs of x[i] with Lambda[i] and not for each lambda all probs of x

i want to know how to do it without using a loop...

in other words i would like to insert into dpois() two vectors for x and lambda, and get all the possible probability combination.

For creating pairs of all combinations of vectors you need to use expand.grid function.

```x <- seq(1, 3, 1)
Lambda <- seq(1, 2, 0.5)

grid <- expand.grid(x=x, Lambda=Lambda)
dpois(grid\$x, grid\$Lambda)
```

When R does something in vectorized way, it aligns and repeats shorter vectors to longest vector as in the example below:

```> cbind(1:5, 1:8, 1:2, 1:3)
[,1] [,2] [,3] [,4]
[1,]    1    1    1    1
[2,]    2    2    2    2
[3,]    3    3    1    3
[4,]    4    4    2    1
[5,]    5    5    1    2
[6,]    1    6    2    3
[7,]    2    7    1    1
[8,]    3    8    2    2
```

So the other way around would be to make your longest vector long enough so that the shorter one will be able to repeat enough times so to create all the combinations:

```> x <- 1:2
> y <- 1:3
> cbind(x,y)
x y
[1,] 1 1
[2,] 2 2
[3,] 1 3
Warning message:
In cbind(x, y) :
number of rows of result is not a multiple of vector length (arg 1)
> cbind(rep(x, each=length(y)), y)
y
[1,] 1 1
[2,] 1 2
[3,] 1 3
[4,] 2 1
[5,] 2 2
[6,] 2 3
```

You asked for "a probability matrix" which you can get directly with

```> x<-seq(1,3,1)
> Lamda<-seq(1,2,0.5)
> outer(x, Lamda, dpois)
[,1]      [,2]      [,3]
[1,] 0.36787944 0.3346952 0.2706706
[2,] 0.18393972 0.2510214 0.2706706
[3,] 0.06131324 0.1255107 0.1804470
```

If you want the matrix dimensions labelled you can use

```> res <- outer(x, Lamda, dpois)
> dimnames(res) <- list(x=x, Lamda=Lamda)
> res
Lamda
x            1       1.5         2
1 0.36787944 0.3346952 0.2706706
2 0.18393972 0.2510214 0.2706706
3 0.06131324 0.1255107 0.1804470
```

You can do it in one line and get some labelling using names<-()

```> outer(`names<-`(x,x), `names<-`(Lamda,Lamda), dpois)
1       1.5         2
1 0.36787944 0.3346952 0.2706706
2 0.18393972 0.2510214 0.2706706
3 0.06131324 0.1255107 0.1804470
```

...but I think that's a bit too clever, I prefer an extra line or two and clarity :-}