A-M baby

Task/Multiple-regression/Common-Lisp/multiple-regression-1.lisp

@@ -0,0 +1,33 @@
+;; Solve a linear system AX=B where A is symmetric and positive definite, so it can be Cholesky decomposed.
+(defun linsys (A B)
+  (let* ((n (car  (array-dimensions A)))
+         (m (cadr (array-dimensions B)))
+         (y (make-array n        :element-type 'long-float :initial-element 0.0L0))
+         (X (make-array `(,n ,m) :element-type 'long-float :initial-element 0.0L0))
+         (L (chol A))) ; A=LL'
+
+    (loop for col from 0 to (- m 1) do
+       ;; Forward substitution: y = L\B
+       (loop for k from 0 to (- n 1)
+             do (setf (aref y k)
+                      (/ (- (aref B k col)
+                            (loop for j from 0 to (- k 1)
+                                  sum (* (aref L k j)
+                                         (aref y j))))
+                         (aref L k k))))
+
+       ;; Back substitution. x=L'\y
+       (loop for k from (- n 1) downto 0
+             do (setf (aref X k col)
+                      (/ (- (aref y k)
+                            (loop for j from (+ k 1) to (- n 1)
+                                  sum (* (aref L j k)
+                                         (aref X j col))))
+                         (aref L k k)))))
+    X))
+
+;; Solve a linear least squares problem. Ax=b, with A being mxn, with m>n.
+;; Solves the linear system A'Ax=A'b.
+(defun lsqr (A b)
+  (linsys (mmul (mtp A) A)
+          (mmul (mtp A) b)))

Task/Multiple-regression/Common-Lisp/multiple-regression-2.lisp

@@ -0,0 +1,5 @@
+(let ((x (make-array '(1 11) :initial-contents '((0 1 2 3 4 5 6 7 8 9 10))))
+      (y (make-array '(1 11) :initial-contents '((1 6 17 34 57 86 121 162 209 262 321)))))
+  (polyfit x y 2))
+
+#2A((0.9999999999999759d0) (2.000000000000005d0) (3.0d0))