| ;; Polynomial interpolation in Clojure, written as a fold. | |
| ;; | |
| ;; This allows you to generate an estimate of the value of some polynomial at x, | |
| ;; where you have a sequence of points that the polynomial has to pass through. | |
| ;; | |
| ;; See [this namespace](https://github.com/sicmutils/sicmutils/blob/main/src/sicmutils/polynomial/interpolate.cljc#L20) | |
| ;; for a much longer build-up to these simple functions! | |
| (defn prepare [[x fx]] | |
| [x x fx fx]) |
| ;; general impl of https://en.wikipedia.org/wiki/Kahan_summation_algorithm#Further_enhancements | |
| (defn- klein-term [acc delta] | |
| `[sum# (+ ~acc ~delta) | |
| ~delta (if (>= (Math/abs ~(with-meta acc {:tag 'double})) | |
| (Math/abs ~(with-meta delta {:tag 'double}))) | |
| (+ (- ~acc sum#) ~delta) | |
| (+ (- ~delta sum#) ~acc)) | |
| ~acc sum#]) |
| (ns tutorial.petageconvert) | |
| ;; woohoo, some comments! | |
| ;; | |
| ;; A note about `pet-multiplier`... for your keys, symbols are great, but | |
| ;; Clojure provides an additional idea of keywords over Scheme. Keywords like | |
| ;; `:dog` evaluate to themselves, so you don't have to quote them. Symbols are fine, but you have one less thing to remember (the quote). | |
| (def pet-multipler | |
| {'dog 7 'cat 5 'fish 10}) |
We know how to integrate real-valued functions of a real variable. We want to extend this idea to manifolds, in such a way that the integral is independent of the coordinate system used to compute it.
The integral of a real-valued function of a real variable is the limit of a sum of products of the values of the function on subintervals and the lengths of the increments of the independent variable in those subintervals:
| ;; here were the deps I needed for this... I don't know enough vega-lite to go without the Hanami example I had | |
| ;; already built, so excuse me there! | |
| {:paths ["dev"] | |
| :deps {io.github.nextjournal/clerk {:local/root "../clerk"} | |
| notespace-sicmutils {:mvn/version "0.16.2"} | |
| aerial.hanami/aerial.hanami {:mvn/version "0.12.7"} | |
| sicmutils/sicmutils {:git/url "https://github.com/sicmutils/sicmutils" | |
| :sha "8658c0c8883b8225a742b9422061f40b852f375d"}}} |
| (defn install-fn-printers! | |
| "NOTE: If you are using Emacs + cider-nrepl, these two `print-method` | |
| implementations will not be installed. I'm currently working on a fix to get | |
| this enabled in the Emacs environment... But if you want to test this feature | |
| out, simply execute these forms. | |
| https://github.com/clojure-emacs/cider-nrepl/blob/master/src/cider/nrepl/print_method.clj#L42-L71 | |
| TODO write a with-methods instead to do this..." | |
| [] | |
| #?(:clj |
| (defn ^:no-doc careful-def [ns] | |
| #?(:cljs | |
| (fn [sym form] | |
| `(def ~sym ~form)) | |
| :clj | |
| (let [ns-sym (ns-name ns) | |
| nsm (ns-map ns) | |
| remote? (fn [sym] | |
| (when-let [v (nsm sym)] |
| shadow-cljs - running: lein run -m shadow.cljs.devtools.cli --npm clj-repl | |
| Syntax error (UnsatisfiedLinkError) compiling at (/private/var/folders/xw/0lq56zhn4hb4lknppw_k086c0000gn/T/form-init10880055894866318920.clj:1:126). | |
| /private/var/folders/xw/0lq56zhn4hb4lknppw_k086c0000gn/T/jna5901602065421044698.tmp: dlopen(/private/var/folders/xw/0lq56zhn4hb4lknppw_k086c0000gn/T/jna5901602065421044698.tmp, 1): no suitable image found. Did find: | |
| /private/var/folders/xw/0lq56zhn4hb4lknppw_k086c0000gn/T/jna5901602065421044698.tmp: no matching architecture in universal wrapper | |
| /private/var/folders/xw/0lq56zhn4hb4lknppw_k086c0000gn/T/jna5901602065421044698.tmp: no matching architecture in universal wrapper | |
| Full report at: | |
| /var/folders/xw/0lq56zhn4hb4lknppw_k086c0000gn/T/clojure-14930451110325842276.edn |
| (/ | |
| (+ (* -717897987691852588770249/1125899906842624 (expt x 74) (sqrt x) (cos (+ (* x (sqrt x)) (* 3 (sqrt x))))) | |
| (* -17947449692296314719256225/562949953421312 (expt x 73) (sqrt x) (cos (+ (* x (sqrt x)) (* 3 (sqrt x))))) | |
| (* -412791342922815238542893175/1125899906842624 (expt x 73) (sin (+ (* x (sqrt x)) (* 3 (sqrt x))))) | |
| (* -879425034922519421243555025/1125899906842624 (expt x 72) (sqrt x) (cos (+ (* x (sqrt x)) (* 3 (sqrt x))))) | |
| (* -19640492446602933741106062225/1125899906842624 (expt x 72) (sin (+ (* x (sqrt x)) (* 3 (sqrt x))))) | |
| (* 23549048157369686724410751225/281474976710656 (expt x 71) (sqrt x) (cos (+ (* x (sqrt x)) (* 3 (sqrt x))))) | |
| (* -57162627269963762380831076625/140737488355328 (expt x 71) (sin (+ (* x (sqrt x)) (* 3 (sqrt x))))) | |
| (* 1180872394115405245080929164125/281474976710656 (expt x 70) (sqrt x) (cos (+ (* x (sqrt x)) (* 3 (sqrt x))))) | |
| (* 80027678177949267333163507275/8796093022208 (expt x 70) (sin (+ (* x (sqrt x)) (* 3 (sqrt x))))) |
| ;; | |
| ;; [[jacobian]] handles this main logic. [[jacobian]] can only take a structural | |
| ;; input. [[euclidean]] and [[multivariate]] below widen handle, respectively, | |
| ;; optionally-structural and multivariable arguments. | |
| (defn- jacobian | |
| "Takes: | |
| - some function `f` of a single [[s/structure?]] argument | |
| - the unperturbed structural `input` |
