Matrix-exponentiation operator: Difference between revisions
→{{header|R}}: Added an infix solution. It seems more faithful to the task's requirement of using "an operator".
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ReeceGoding (talk | contribs) (→{{header|R}}: Added an infix solution. It seems more faithful to the task's requirement of using "an operator".) |
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=={{header|R}}==
===Library function call===
{{libheader|Biodem}}
<lang R>library(Biodem)
Line 2,693 ⟶ 2,694:
# [2,] 832040 514229</lang>
Note that non-integer powers are not supported with this function.
===Infix operator===
The task wants the implementation to be "as an operator". Given that R lets us define new infix operators, it seems fitting to show how to do this. Ideally, for a matrix a and int n, we'd want to be able to use a^n. R actually has this already, but it's not what the task wants:
<lang r>a<-matrix(c(1,2,3,4),2,2)
a^1
a^2</lang>
{{out}}
<pre>> a^1
[,1] [,2]
[1,] 1 3
[2,] 2 4
> a^2
[,1] [,2]
[1,] 1 9
[2,] 4 16</pre>
As we can see, it instead returns the given matrix with its elements raised to the nth power. Overwriting the ^ operator would be dangerous and rude. However, R's base library suggests an alternative. %*% is already defined as matrix multiplication, so why not use %^% for exponentiation?
<lang r>`%^%`<-function(mat,n)
{
is.wholenumber<-function(x,tol=.Machine$double.eps^0.5){abs(x - round(x))<tol}#See the docs for is.integer
if(is.matrix(mat) && is.numeric(n) && is.wholenumber(n))
{
if(n==0){diag(nrow=nrow(mat))}#Identity matrix of mat's dimensions
else if(n==1){mat}
else if(n>1){mat%*%(mat%^%(n-1))}
else stop("Invalid n.")
}
else stop("Invald input type.")
}
#For output:
a%^%0
a%^%1
a%^%2
a%*%a%*%a#Base R's equivalent of a%^%3
a%^%3
nonSquareMatrix<-matrix(c(1,2,3,4,5,6),nrow=2,ncol=3)
nonSquareMatrix%^%1
nonSquareMatrix%^%2#R's %*% will throw the error for us</lang>
{{out}}
<pre>> a%^%0
[,1] [,2]
[1,] 1 0
[2,] 0 1
> a%^%1
[,1] [,2]
[1,] 1 3
[2,] 2 4
> a%^%2
[,1] [,2]
[1,] 7 15
[2,] 10 22
> a%*%a%*%a#Base R's equivalent of a%^%3
[,1] [,2]
[1,] 37 81
[2,] 54 118
> a%^%3
[,1] [,2]
[1,] 37 81
[2,] 54 118
> nonSquareMatrix<-matrix(c(1,2,3,4,5,6),nrow=2,ncol=3)
> nonSquareMatrix%^%1
[,1] [,2] [,3]
[1,] 1 3 5
[2,] 2 4 6
> nonSquareMatrix%^%2#R's %*% will throw the error for us
Error in mat %*% (mat %^% (n - 1)) : non-conformable arguments</pre>
Our code is far from efficient and could do with more error-checking, but it demonstrates the principle. If we wanted to do this properly, we'd use a library - ideally one that calls C code. Following the previous submission's example, we can just do this:
<lang r>library(Biodem)
`%^%`<-function(mat,n) Biodem::mtx.exp(mat,n)</lang>
And it will work just the same, except for being much faster and throwing an error on nonSquareMatrix%^%1.
=={{header|Racket}}==
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