Initial data commit

Task/Matrix-exponentiation-operator/Jq/matrix-exponentiation-operator-1.jq

@@ -0,0 +1,24 @@
+# produce an array of length n that is 1 at i and 0 elsewhere
+def indicator(i;n): [range(0;n) | 0] | .[i] = 1;
+
+# Identity matrix:
+def identity(n): reduce range(0;n) as $i ([]; . + [indicator( $i; n )] );
+
+def direct_matrix_exp(n):
+  . as $in
+  | if n == 0 then identity($in|length)
+    else reduce range(1;n) as $i ($in; . as $m | multiply($m; $in))
+    end;
+
+def matrix_exp(n):
+  if n < 4 then direct_matrix_exp(n)
+  else . as $in
+  | ((n|2)|floor) as $m
+  | matrix_exp($m) as $ans
+  | multiply($ans;$ans) as $ans
+  | (n - (2 * $m) ) as $residue
+  | if $residue == 0 then $ans
+    else matrix_exp($residue) as $residue
+    | multiply($ans; $residue )
+    end
+  end;

Task/Matrix-exponentiation-operator/Jq/matrix-exponentiation-operator-2.jq

@@ -0,0 +1,10 @@
+def pi: 4 * (1|atan);
+
+def rotation_matrix(theta):
+  [[(theta|cos), (theta|sin)], [-(theta|sin), (theta|cos)]];
+
+def demo_matrix_exp(n):
+  rotation_matrix( pi / 4 ) | matrix_exp(n) ;
+
+def demo_direct_matrix_exp(n):
+  rotation_matrix( pi / 4 ) | direct_matrix_exp(n) ;

Task/Matrix-exponentiation-operator/Jq/matrix-exponentiation-operator-3.jq

@@ -0,0 +1,5 @@
+# For demo_matrix_exp(10000)
+$ time jq -n -c -f Matrix-exponentiation_operator.rc
+[[1,-1.1102230246251565e-12],[1.1102230246251565e-12,1]]
+user	0m0.490s
+sys	0m0.008s

Task/Matrix-exponentiation-operator/Jq/matrix-exponentiation-operator-4.jq

@@ -0,0 +1,5 @@
+# For demo_direct_matrix_exp(10000)
+$ time jq -n -c -f Matrix-exponentiation_operator.rc
+[[1,-7.849831895612169e-13],[7.849831895612169e-13,1]]
+user	0m0.625s
+sys	0m0.006s