problem one hw 4

md2pdf.css

@@ -1,3 +0,0 @@
-img {
-  max-width: 100%;
-}

src/lizfcm.asd

@@ -9,6 +9,7 @@
                  (:file "approx,maceps" :depends-on ("approx,package"))
                  (:file "approx,derivative" :depends-on ("approx,package"))
                  (:file "approx,package")
+                 (:file "vector,least-squares")
                  (:file "vector,distance" :depends-on ("vector,norm" "vector,package"))
                  (:file "vector,norm" :depends-on ("vector,package"))
                  (:file "vector,package")))

src/main.lisp

@@ -0,0 +1,60 @@
+(load "lizfcm.asd")
+(ql:quickload :lizfcm)
+
+;; this is a collection showcasing the library developed for math4610, required
+;; from the Shared Library definition
+
+(defun smaceps ()
+  (cadar (last (lizfcm.approx:compute-maceps
+                 (lambda (x) x) 1.0 1.0))))
+
+(defun dmaceps ()
+  (cadar (last (lizfcm.approx:compute-maceps
+                 (lambda (x) x) 1.0d0 1.0d0))))
+
+(defun l2-norm (v)
+  (let ((2-norm (lizfcm.vector:p-norm 2)))
+    (funcall 2-norm v)))
+
+(defun l1-norm (v)
+  (let ((1-norm (lizfcm.vector:p-norm 1)))
+    (funcall 1-norm v)))
+
+(defun linf-norm (v)
+  (lizfcm.vector:max-norm v))
+
+(defun l2-distance (v1 v2)
+  (let ((2-norm (lizfcm.vector:p-norm 2)))
+    (lizfcm.vector:distance v1 v2 2-norm)))
+
+(defun l1-distance (v1 v2)
+  (let ((1-norm (lizfcm.vector:p-norm 1)))
+    (lizfcm.vector:distance v1 v2 1-norm)))
+
+(defun linf-distance (v1 v2)
+  (lizfcm.vector:distance v1 v2 'lizfcm.vector:max-norm))
+
+(defun f (x)
+  (/ (- x 1) (+ x 1)))
+
+(defun fprime (x)
+  (/ 2 (expt (+ x 1) 2)))
+
+(defmacro showcase (s-expr)
+  `(format t "~a = ~a~%" ,(format nil "~a" s-expr) ,s-expr))
+
+(defun main ()
+  (showcase (smaceps))
+  (showcase (dmaceps))
+  (showcase (l2-norm '(1 2)))
+  (showcase (l1-norm '(1 2)))
+  (showcase (linf-norm '(1 2)))
+  (showcase (l1-distance '(1 2) '(-3 4)))
+  (showcase (l2-distance '(1 2) '(-3 4)))
+  (showcase (linf-distance '(1 2) '(-3 4)))
+  (showcase (lizfcm.vector:least-squares-reg '(1 2 3 4 5 6 7)
+                                             '(0.5 3 2 3.5 5 6 7.5)))
+  (showcase (lizfcm.approx:forward-derivative-at 'f 1 0.00001))
+  (showcase (lizfcm.approx:central-derivative-at 'f 1 0.00001))
+  (showcase (lizfcm.approx:backward-derivative-at 'f 1 0.00001)))
+

src/tests,vector.lisp

@@ -29,3 +29,14 @@
                             dist
                             0.00001))))
 
+(test least-squares
+      :description "least squares is correct enough"
+      (let ((x '(0 1 2 3 4))
+            (y '(1 2 3 4 5)))
+        (destructuring-bind (m b) (lizfcm.vector:least-squares-reg x y)
+          (is (within-range-p m 1 0.00001))
+          (is (within-range-p b 1 0.00001))))
+      (let ((x '(1 2 3 4 5 6 7))
+            (y '(0.5 3 2 3.5 5 6 7.5)))
+        (destructuring-bind (m b) (lizfcm.vector:least-squares-reg x y)
+          (is (within-range-p m 1 0.3))))) ;; just a guestimate for best fit

src/vector,least-squares-reg.lisp

@@ -0,0 +1,2 @@
+(in-package :lizfcm.vector)
+

src/vector,least-squares.lisp

@@ -0,0 +1,14 @@
+(in-package :lizfcm.vector)
+
+(defun least-squares-reg (x y)
+  (let* ((n (length x))
+         (sum-y (reduce #'+ y))
+         (sum-x (reduce #'+ x))
+         (sum-xy (reduce #'+ (mapcar #'* x y)))
+         (sum-xsquared (reduce #'+ (mapcar #'* x x)))
+         (b (/ (- (* sum-y sum-xsquared) (* sum-x sum-xy))
+               (- (* n sum-xsquared) (* sum-x sum-x))))
+         (a (/ (- (* n sum-xy) (* sum-x sum-y))
+               (- (* n sum-xsquared) (* sum-x sum-x)))))
+    (list a b)))
+

src/vector,package.lisp

@@ -4,4 +4,5 @@
   (:export
     :p-norm
     :max-norm
-    :distance))
+    :distance
+    :least-squares-reg))