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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
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Task/Numerical-integration/Common-Lisp/numerical-integration.lisp Normal file
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(defun left-rectangle (f a b n &aux (d (/ (- b a) n)))
(* d (loop for x from a below b by d summing (funcall f x))))
(defun right-rectangle (f a b n &aux (d (/ (- b a) n)))
(* d (loop for x from b above a by d summing (funcall f x))))
(defun midpoint-rectangle (f a b n &aux (d (/ (- b a) n)))
(* d (loop for x from (+ a (/ d 2)) below b by d summing (funcall f x))))
(defun trapezium (f a b n &aux (d (/ (- b a) n)))
(* (/ d 2)
(+ (funcall f a)
(* 2 (loop for x from (+ a d) below b by d summing (funcall f x)))
(funcall f b))))
(defun simpson (f a b n)
(loop with h = (/ (- b a) n)
with sum1 = (funcall f (+ a (/ h 2)))
with sum2 = 0
for i from 1 below n
do (incf sum1 (funcall f (+ a (* h i) (/ h 2))))
do (incf sum2 (funcall f (+ a (* h i))))
finally (return (* (/ h 6)
(+ (funcall f a)
(funcall f b)
(* 4 sum1)
(* 2 sum2))))))