Data commit

Task/QR-decomposition/Racket/qr-decomposition-1.rkt

@@ -0,0 +1,6 @@
+> (require math)
+> (matrix-qr (matrix [[12 -51   4]
+                      [ 6 167 -68]
+                      [-4  24 -41]]))
+(array #[#[6/7 -69/175 -58/175] #[3/7 158/175 6/175] #[-2/7 6/35 -33/35]])
+(array #[#[14 21 -14] #[0 175 -70] #[0 0 35]])

Task/QR-decomposition/Racket/qr-decomposition-2.rkt

@@ -0,0 +1,29 @@
+#lang racket
+(require math/matrix math/array)
+(define-values (T I col size)
+  (values ; short names
+   matrix-transpose identity-matrix matrix-col matrix-num-rows))
+
+(define (scale c A) (matrix-scale A c))
+(define (unit n i) (build-matrix n 1 (λ (j _) (if (= j i) 1 0))))
+
+(define (H u)
+  (matrix- (I (size u))
+           (scale (/ 2 (matrix-dot u u))
+                  (matrix* u (T u)))))
+
+(define (normal a)
+  (define a0 (matrix-ref a 0 0))
+  (matrix- a (scale (* (sgn a0) (matrix-2norm a))
+                    (unit (size a) 0))))
+
+(define (QR A)
+  (define n (size A))
+  (for/fold ([Q (I n)] [R A]) ([i (- n 1)])
+    (define Hi (H (normal (submatrix R (:: i n) (:: i (+ i 1))))))
+    (define Hi* (if (= i 0) Hi (block-diagonal-matrix (list (I i) Hi))))
+    (values (matrix* Q Hi*) (matrix* Hi* R))))
+
+(QR (matrix [[12 -51   4]
+               [ 6 167 -68]
+               [-4  24 -41]]))

Task/QR-decomposition/Racket/qr-decomposition-3.rkt

@@ -0,0 +1,6 @@
+(array #[#[6/7 69/175 -58/175]
+             #[3/7 -158/175 6/175]
+             #[-2/7 -6/35 -33/35]])
+(array #[#[14 21 -14]
+             #[0 -175 70]
+             #[0 0 35]])