Matrix-exponentiation operator: Difference between revisions
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( scratchpad ) { { 3 2 } { 2 1 } } 4 my-m^n .
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=={{header|Fortran}}==
{{works with|Fortran|90 and later}}
<lang fortran>module matmod
implicit none
! Overloading the ** operator does not work because the compiler cannot
! differentiate between matrix exponentiation and the elementwise raising
! of an array to a power therefore we define a new operator
interface operator (.matpow.)
module procedure matrix_exp
end interface
contains
function matrix_exp(m, n) result (res)
real, intent(in) :: m(:,:)
integer, intent(in) :: n
real :: res(size(m,1),size(m,2))
integer :: i
if(n == 0) then
res = 0
do i = 1, size(m,1)
res(i,i) = 1
end do
return
end if
res = m
do i = 2, n
res = matmul(res, m)
end do
end function matrix_exp
end module matmod
program Matrix_exponentiation
use matmod
implicit none
integer, parameter :: n = 3
real, dimension(n,n) :: m1, m2
integer :: i, j
m1 = reshape((/ (i, i = 1, n*n) /), (/ n, n /), order = (/ 2, 1 /))
do i = 0, 4
m2 = m1 .matpow. i
do j = 1, size(m2,1)
write(*,*) m2(j,:)
end do
write(*,*)
end do
end program Matrix_exponentiation</lang>
Output
<pre> 1.00000 0.00000 0.00000
0.00000 1.00000 0.00000
0.00000 0.00000 1.00000
1.00000 2.00000 3.00000
4.00000 5.00000 6.00000
7.00000 8.00000 9.00000
30.0000 36.0000 42.0000
66.0000 81.0000 96.0000
102.000 126.000 150.000
468.000 576.000 684.000
1062.00 1305.00 1548.00
1656.00 2034.00 2412.00
7560.00 9288.00 11016.0
17118.0 21033.0 24948.0
26676.0 32778.0 38880.0</pre>
=={{header|GAP}}==
<lang gap># Matrix exponentiation is built-in
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