Numeric error propagation: Difference between revisions

=={{header|Common Lisp}}==

<lang lisp>(defstruct uncertain-number

(value 0 :type number)

(uncertainty 0 :type number))

(defmethod print-object ((n uncertain-number) stream)

(format stream "~,2F ± ~,2F" (uncertain-number-value n) (uncertain-number-uncertainty n)))

(defun add (n1 n2)

(let* ((value1 (uncertain-number-value n1))

(value2 (uncertain-number-value n2))

(uncertainty1 (uncertain-number-uncertainty n1))

(uncertainty2 (uncertain-number-uncertainty n2))

(value (+ value1 value2))

(uncertainty (sqrt (+ (* uncertainty1 uncertainty1)

(* uncertainty2 uncertainty2)))))

(make-uncertain-number :value value :uncertainty uncertainty)))

(defun negate (n)

(make-uncertain-number :value (- (uncertain-number-value n))

:uncertainty (uncertain-number-uncertainty n)))

(defun subtract (n1 n2)

(add n1 (negate n2)))

(defun multiply (n1 n2)

(let* ((value1 (uncertain-number-value n1))

(value2 (uncertain-number-value n2))

(uncertainty-ratio-1 (/ (uncertain-number-uncertainty n1) value1))

(uncertainty-ratio-2 (/ (uncertain-number-uncertainty n2) value2))

(value (* value1 value2))

(uncertainty (sqrt (* value

value

(+ (* uncertainty-ratio-1 uncertainty-ratio-1)

(* uncertainty-ratio-2 uncertainty-ratio-2))))))

(make-uncertain-number :value value :uncertainty uncertainty)))

(defun inverse (n)

(make-uncertain-number :value (/ (uncertain-number-value n))

:uncertainty (uncertain-number-uncertainty n)))

(defun divide (n1 n2)

(multiply n1 (inverse n2)))

(defun exponentiate (base exp)

(let* ((base-value (uncertain-number-value base))

(uncertainty-ratio (/ (uncertain-number-uncertainty base) base-value))

(value (expt base-value exp))

(uncertainty (abs (* value exp uncertainty-ratio))))

(make-uncertain-number :value value :uncertainty uncertainty)))

(defun solve ()

(let* ((x1 (make-uncertain-number :value 100 :uncertainty 1.1))

(y1 (make-uncertain-number :value 50 :uncertainty 1.2))

(x2 (make-uncertain-number :value 200 :uncertainty 2.2))

(y2 (make-uncertain-number :value 100 :uncertainty 2.3))

(d (exponentiate (add (exponentiate (subtract x1 x2) 2)

(exponentiate (subtract y1 y2) 2))

1/2)))

(format t "d = ~A~%" d)))</lang>

{{out}}

<pre>d = 111.80 ± 2.49</pre>