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+(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)))
+