tasks a-s

Task/QR-decomposition/J/qr-decomposition-1.j

@@ -0,0 +1,16 @@
+mp=: +/ . *  NB. matrix product
+h =: +@|:    NB. conjugate transpose
+
+QR=: 3 : 0
+ n=.{:$A=.y
+ if. 1>:n do.
+  A ((% {.@,) ; ]) %:(h A) mp A
+ else.
+  m =.>.n%2
+  A0=.m{."1 A
+  A1=.m}."1 A
+  'Q0 R0'=.QR A0
+  'Q1 R1'=.QR A1 - Q0 mp T=.(h Q0) mp A1
+  (Q0,.Q1);(R0,.T),(-n){."1 R1
+ end.
+)

Task/QR-decomposition/J/qr-decomposition-2.j

@@ -0,0 +1,6 @@
+   QR x:12 _51 4,6 167 _68,:_4 24 _41
+┌────────────────────┬──────────┐
+│ 6r7 _69r175 _58r175│14  21 _14│
+│ 3r7 158r175   6r175│ 0 175 _70│
+│_2r7    6r35  _33r35│ 0   0  35│
+└────────────────────┴──────────┘

Task/QR-decomposition/J/qr-decomposition-3.j

@@ -0,0 +1,4 @@
+   X=:i.# Y=:1 6 17 34 57 86 121 162 209 262 321
+   'Q R'=: QR X ^/ i.3
+   R %.~(|:Q)+/ .* Y
+1 2 3