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