langs a-z

Task/Matrix-exponentiation-operator/OCaml/matrix-exponentiation-operator-1.ocaml

@@ -0,0 +1,58 @@
+(* identity matrix *)
+let eye n =
+  let a = Array.make_matrix n n 0.0 in
+  for i=0 to n-1 do
+    a.(i).(i) <- 1.0
+  done;
+  (a)
+;;
+
+(* matrix dimensions *)
+let dim a = Array.length a, Array.length a.(0);;
+
+(* make matrix from list in row-major order *)
+let matrix p q v =
+  if (List.length v) <> (p * q)
+  then failwith "bad dimensions"
+  else
+    let a = Array.make_matrix p q (List.hd v) in
+    let rec g i j = function
+    | [] -> a
+    | x::v ->
+        a.(i).(j) <- x;
+        if j+1 < q
+        then g i (j+1) v
+        else g (i+1) 0 v
+    in
+    g 0 0 v
+;;
+
+(* matrix product *)
+let matmul a b =
+  let n, p = dim a
+  and q, r = dim b in
+  if p <> q then failwith "bad dimensions" else
+  let c = Array.make_matrix n r 0.0 in
+  for i=0 to n-1 do
+    for j=0 to r-1 do
+      for k=0 to p-1 do
+        c.(i).(j) <- c.(i).(j) +. a.(i).(k) *. b.(k).(j)
+      done
+    done
+  done;
+  (c)
+;;
+
+(* generic exponentiation, usual algorithm *)
+let pow one mul a n =
+  let rec g p x = function
+  | 0 -> x
+  | i ->
+      g (mul p p) (if i mod 2 = 1 then mul p x else x) (i/2)
+  in
+  g a one n
+;;
+
+(* example with integers *)
+pow 1 ( * ) 2 16;;
+(* - : int = 65536 *)

Task/Matrix-exponentiation-operator/OCaml/matrix-exponentiation-operator-2.ocaml

@@ -0,0 +1,13 @@
+let matpow a n =
+  let p, q = dim a in
+  if p <> q then failwith "bad dimensions" else
+  pow (eye p) matmul a n;;
+
+matpow (matrix 2 2 [ 1.0; 1.0; 1.0; 0.0 ]) 10;;
+(* - : float array array = [|[|89.; 55.|]; [|55.; 34.|]|] *)
+
+(* use as infix operator *)
+let ( ^^ ) = matpow;;
+
+[| [| 1.0; 1.0|]; [| 1.0; 0.0 |] |] ^^ 10;;
+(* - : float array array = [|[|89.; 55.|]; [|55.; 34.|]|] *)

Task/Matrix-exponentiation-operator/Octave/matrix-exponentiation-operator.octave

@@ -0,0 +1,6 @@
+M = [ 3, 2; 2, 1 ];
+M^0
+M^1
+M^2
+M^(-1)
+M^0.5

Task/Matrix-exponentiation-operator/PARI-GP/matrix-exponentiation-operator.pari

@@ -0,0 +1 @@
+M^n

Task/Matrix-exponentiation-operator/Perl-6/matrix-exponentiation-operator.pl6

@@ -0,0 +1,36 @@
+subset SqMat of Array where { .elems == all(.[]».elems) }
+
+multi infix:<*>(SqMat $a, SqMat $b) {[
+    for ^$a -> $r {[
+        for ^$b[0] -> $c {
+            [+] ($a[$r][] Z* $b[].map: *[$c])
+        }
+    ]}
+]}
+
+multi infix:<**> (SqMat $m, Int $n is copy where { $_ >= 0 }) {
+    my $tmp = $m;
+    my $out = [for ^$m -> $i { [ for ^$m -> $j { +($i == $j) } ] } ];
+    loop {
+	$out = $out * $tmp if $n +& 1;
+	last unless $n +>= 1;
+	$tmp = $tmp * $tmp;
+    }
+
+    $out;
+}
+
+multi show (SqMat $m) {
+    my $size = 1;
+    for ^$m X ^$m -> $i, $j { $size max= $m[$i][$j].Str.chars; }
+    say join "\n", $m».fmt("%{$size}s");
+}
+
+my @m = [1, 2, 0],
+	[0, 3, 1],
+	[1, 0, 0];
+
+for 0 .. 10 -> $order {
+    say "### Order $order";
+    show @m ** $order;
+}

Task/Matrix-exponentiation-operator/Seed7/matrix-exponentiation-operator.seed7

@@ -0,0 +1,92 @@
+$ include "seed7_05.s7i";
+  include "float.s7i";
+
+const type: matrix is array array float;
+
+const func string: str (in matrix: mat) is func
+  result
+    var string: stri is "";
+  local
+    var integer: row is 0;
+    var integer: column is 0;
+  begin
+    for row range 1 to length(mat) do
+      for column range 1 to length(mat[row]) do
+        stri &:= str(mat[row][column]);
+        if column < length(mat[row]) then
+          stri &:= ", ";
+        end if;
+      end for;
+      if row < length(mat) then
+        stri &:= "\n";
+      end if;
+    end for;
+  end func;
+
+enable_output(matrix);
+
+const func matrix: (in matrix: mat1) * (in matrix: mat2) is func
+  result
+    var matrix: product is matrix.value;
+  local
+    var integer: row is 0;
+    var integer: column is 0;
+    var integer: k is 0;
+  begin
+    product := length(mat1) times length(mat1) times 0.0;
+    for row range 1 to length(mat1) do
+      for column range 1 to length(mat1) do
+        product[row][column] := 0.0;
+        for k range 1 to length(mat1) do
+          product[row][column] +:= mat1[row][k] * mat2[k][column];
+        end for;
+      end for;
+    end for;
+  end func;
+
+const func matrix: (in var matrix: base) ** (in var integer: exponent) is func
+  result
+    var matrix: power is matrix.value;
+  local
+    var integer: row is 0;
+    var integer: column is 0;
+  begin
+    if exponent < 0 then
+      raise NUMERIC_ERROR;
+    else
+      if odd(exponent) then
+        power := base;
+      else
+        # Create identity matrix
+        power := length(base) times length(base) times 0.0;
+        for row range 1 to length(base) do
+          for column range 1 to length(base) do
+            if row = column then
+              power[row][column] := 1.0;
+            end if;
+          end for;
+        end for;
+      end if;
+      exponent := exponent div 2;
+      while exponent > 0 do
+        base := base * base;
+        if odd(exponent) then
+          power := power * base;
+        end if;
+        exponent := exponent div 2;
+      end while;
+    end if;
+  end func;
+
+const proc: main is func
+  local
+    var matrix: m is [] (
+      [] (4.0, 3.0),
+      [] (2.0, 1.0));
+    var integer: exponent is 0;
+  begin
+    for exponent range [] (0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23) do
+      writeln("m ** " <& exponent <& " =");
+      writeln(m ** exponent);
+    end for;
+  end func;

Task/Matrix-exponentiation-operator/TI-89-BASIC/matrix-exponentiation-operator.ti-89

@@ -0,0 +1 @@
+[3,2;4,1]^4

Task/Matrix-exponentiation-operator/Ursala/matrix-exponentiation-operator-1.ursala

@@ -0,0 +1,5 @@
+#import nat
+#import lin
+
+id  = @h ^|CzyCK33/1.! 0.!*
+mex = ||id@l mmult:-0^|DlS/~& iota

Task/Matrix-exponentiation-operator/Ursala/matrix-exponentiation-operator-2.ursala

@@ -0,0 +1 @@
+mex = ~&ar^?\id@al (~&lr?/mmult@llPrX ~&r)^/~&alrhPX mmult@falrtPXPRiiX

Task/Matrix-exponentiation-operator/Ursala/matrix-exponentiation-operator-3.ursala

@@ -0,0 +1,3 @@
+#cast %eLLL
+
+test = mex/*<<3.,2.>,<2.,1.>> <0,1,2,3,4,10>