! #1/20 1696970693 501 20 100644 28 ` __.SYMDEF SORTED#1/28 1696908991 501 20 100644 692 ` approx,derivative.lisp(in-package :lizfcm.approx) (defun central-derivative-at (f x &optional (delta 0.01)) (let* ((x2 (+ x delta)) (x1 (- x delta)) (y2 (apply f (list x2))) (y1 (apply f (list x1)))) (/ (- y2 y1) (- x2 x1)))) (defun forward-derivative-at (f x &optional (delta 0.01)) (let* ((x2 (+ x delta)) (x1 x) (y2 (apply f (list x2))) (y1 (apply f (list x1)))) (/ (- y2 y1) (- x2 x1)))) (defun backward-derivative-at (f x &optional (delta 0.01)) (let* ((x2 x) (x1 (- x delta)) (y2 (apply f (list x2))) (y1 (apply f (list x1)))) (/ (- y2 y1) (- x2 x1)))) #1/28 1696908123 501 20 100644 324 ` approx,maceps.lisp(in-package :lizfcm.approx) (defun compute-maceps (f a init) (let ((h init) (err init)) (loop collect (list a h err) do (setf h (/ h 2) err (abs (- (funcall f (+ a h)) (funcall f a)))) while (> err 0)))) #1/28 1696908999 501 20 100644 228 ` approx,package.lisp(in-package :cl-user) (defpackage lizfcm.approx (:use :cl) (:export :central-derivative-at :forward-derivative-at :backward-derivative-at :compute-maceps)) #1/20 1696969272 501 20 100644 1556 ` lizfcm.asd(asdf:defsystem "lizfcm" :version "0.1.0" :author "Elizabeth Hunt" :license "MIT" :components ((:file "utils,within-range" :depends-on ("utils,package")) (:file "utils,table" :depends-on ("utils,package")) (:file "utils,package") (: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"))) (asdf:defsystem "lizfcm/tests" :author "Elizabeth Hunt" :license "MIT" :depends-on (:fiveam :lizfcm) :components ((:file "tests,table" :depends-on ("tests,suite")) (:file "tests,maceps" :depends-on ("tests,suite")) (:file "tests,approx" :depends-on ("tests,suite")) (:file "tests,vector" :depends-on ("tests,suite")) (:file "tests,suite")) :perform (asdf:test-op (o c) (uiop:symbol-call :fiveam :run! (uiop:find-symbol* :lizfcm-test-suite :lizfcm/tests)))) #1/28 1696908986 501 20 100644 1396 ` tests,approx.lisp(defpackage lizfcm/tests.approx (:use :cl :fiveam :lizfcm.approx :lizfcm.utils :lizfcm/tests) (:export :approx-suite)) (in-package :lizfcm/tests.approx) (def-suite approx-suite :in lizfcm-test-suite) (in-suite approx-suite) (test central-derivative-at :description "derivative at is within bounds" (let ((f (lambda (x) (* x x))) (x 2) (accepted-delta 0.02) (f-prime-at-x 4) (delta 0.01)) (is (within-range-p (central-derivative-at f x delta) f-prime-at-x accepted-delta)))) (test fwd-derivative-at :description "forward derivative at is within bounds" (let ((f (lambda (x) (* x x))) (x 2) (accepted-delta 0.02) (f-prime-at-x 4) (delta 0.01)) (is (within-range-p (forward-derivative-at f x delta) f-prime-at-x accepted-delta)))) (test bwd-derivative-at :description "backward derivative at is within bounds" (let ((f (lambda (x) (* x x))) (x 2) (accepted-delta 0.02) (f-prime-at-x 4) (delta 0.01)) (is (within-range-p (backward-derivative-at f x delta) f-prime-at-x accepted-delta)))) #1/28 1696908124 501 20 100644 1092 ` tests,maceps.lisp(defpackage lizfcm/tests.maceps (:use :cl :fiveam :lizfcm.approx :lizfcm.utils :lizfcm/tests) (:export :approx-suite)) (in-package :lizfcm/tests.maceps) (def-suite maceps-suite :in lizfcm-test-suite) (in-suite maceps-suite) (test maceps :description "double precision provides precision about (mac eps of single precision) squared" (let* ((maceps-computation-double (compute-maceps (lambda (x) x) 1.0d0 1.0d0)) (maceps-computation-single (compute-maceps (lambda (x) x) 1.0 1.0)) (last-double-h (cadar (last maceps-computation-double))) (last-single-h (cadar (last maceps-computation-single)))) (is (within-range-p (- last-double-h (* last-single-h last-single-h)) 0 last-single-h)))) #1/20 1696908124 501 20 100644 260 ` tests,suite.lisp(in-package :cl-user) (defpackage lizfcm/tests (:use :cl :fiveam) (:export :run! :lizfcm-test-suite)) (in-package :lizfcm/tests) (def-suite lizfcm-test-suite :description "The ultimate parent test suite") #1/20 1696908124 501 20 100644 996 ` tests,table.lisp(defpackage lizfcm/tests.table (:use :cl :fiveam :lizfcm.utils :lizfcm/tests) (:export :approx-suite)) (in-package :lizfcm/tests.table) (def-suite table-suite :in lizfcm-test-suite) (in-suite table-suite) (defun fib (n) (cond ((< n 2) n) (t (+ (fib (- n 1)) (fib (- n 2)))))) (test table-of-fib-vals :description "table generates correctly" (let* ((headers '("n" "fib(n)")) (n-values '((1) (2) (3) (4))) (expected `(("n" "fib(n)") (1 ,(fib 1)) (2 ,(fib 2)) (3 ,(fib 3)) (4 ,(fib 4)))) (tabled (lizfcm.utils:table (:headers headers :domain-order (n) :domain-values n-values) (fib n)))) (is (equal expected tabled)))) #1/28 1696970521 501 20 100644 1356 ` tests,vector.lisp(defpackage lizfcm/tests.vector (:use :cl :fiveam :lizfcm.vector :lizfcm.utils :lizfcm/tests) (:export :vector-suite)) (in-package :lizfcm/tests.vector) (def-suite vector-suite :in lizfcm-test-suite) (in-suite vector-suite) (test p-norm :description "computes p-norm" (let ((v '(1 1)) (length (sqrt 2)) (2-norm (p-norm 2))) (is (within-range-p (funcall 2-norm v) length 0.00001)))) (test vector-distance :description "computes distance via norm" (let ((v1 '(0 0)) (v2 '(1 1)) (dist (sqrt 2))) (is (within-range-p (distance v1 v2 (p-norm 2)) 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 #1/28 1696908123 501 20 100644 140 ` utils,package.lisp(in-package :cl-user) (defpackage lizfcm.utils (:use :cl) (:export :within-range-p :table)) #1/20 1696908123 501 20 100644 364 ` utils,table.lisp(in-package :lizfcm.utils) (defmacro table ((&key headers domain-order domain-values) &body body) `(cons ,headers (mapcar (lambda (tuple) (destructuring-bind ,domain-order tuple (append tuple (list ,@body)))) ,domain-values))) #1/28 1696908124 501 20 100644 172 ` utils,within-range.lisp(in-package :lizfcm.utils) (defun within-range-p (x true-value delta) (and (< x (+ true-value delta)) (> x (- true-value delta)))) #1/28 1696908124 501 20 100644 172 ` vector,distance.lisp(in-package :lizfcm.vector) (defun distance (v1 v2 norm) (let* ((d (mapcar #'- v1 v2)) (length (funcall norm d))) length)) #1/20 1696908124 501 20 100644 300 ` vector,norm.lisp(in-package :lizfcm.vector) (defun p-norm (p) (lambda (v) (expt (reduce #'+ (mapcar (lambda (x) (abs (expt x p))) v)) (/ 1 p)))) (defun max-norm (v) (reduce #'max v)) #1/28 1696962268 501 20 100644 172 ` vector,package.lisp(in-package :cl-user) (defpackage lizfcm.vector (:use :cl) (:export :p-norm :max-norm :distance :least-squares-reg)) #1/20 1696970639 501 20 100644 1732 ` main.lisp(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))) #1/36 1696962277 501 20 100644 68 ` vector,least-squares-reg.lisp(in-package :lizfcm.vector) #1/36 1696969388 501 20 100644 524 ` vector,least-squares.lisp(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)))