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Matrix-exponentiation operator: Difference between revisions
→{{header|Nim}}
ReeceGoding (talk | contribs) m (→Infix operator) |
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/* matrix([-1/5, 2/5],
[4/5, -3/5]) */</lang>
=={{header|Nim}}==
<lang Nim>import sequtils, strutils
type Matrix[N: static int; T] = array[1..N, array[1..N, T]]
func `*`[N, T](a, b: Matrix[N, T]): Matrix[N, T] =
for i in 1..N:
for j in 1..N:
for k in 1..N:
result[i][j] += a[i][k] * b[k][j]
func identityMatrix[N; T](): Matrix[N, T] =
for i in 1..N:
result[i][i] = T(1)
func `^`[N, T](m: Matrix[N, T]; n: Natural): Matrix[N, T] =
if n == 0: return identityMatrix[N, T]()
if n == 1: return m
var n = n
var m = m
result = identityMatrix[N, T]()
while n > 0:
if (n and 1) != 0:
result = result * m
n = n shr 1
m = m * m
proc `$`(m: Matrix): string =
var lg = 0
for i in 1..m.N:
for j in 1..m.N:
lg = max(lg, len($m[i][j]))
for i in 1..m.N:
echo m[i].mapIt(align($it, lg)).join(" ")
when isMainModule:
let m1: Matrix[3, int] = [[ 3, 2, -1],
[-1, 0, 5],
[ 2, -1, 3]]
echo m1^10
import math
const
C30 = sqrt(3.0) / 2
S30 = 1 / 2
let m2: Matrix[2, float] = [[C30, -S30], [S30, C30]] # 30° rotation matrix.
echo m2^12 # Nearly the identity matrix.</lang>
{{out}}
<pre>572880 154352 321344
480752 261648 306176
473168 161936 413472
0.9999999999999993 -3.885780586188048e-16
3.885780586188048e-16 0.9999999999999993</pre>
=={{header|OCaml}}==
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