lambdaway :: haversine

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_h1 haversine formula

_p Following [[rosettacode|https://rosettacode.org/wiki/Haversine_formula]], implement a great-circle distance function, or use a library function, to show the great-circle distance between:

_ul Nashville, TN, USA, which is: N 36°7.2', W 86°40.2'    {b (36.12,   -86.67)}
_ul Los Angeles, CA, USA, which is: N 33°56.4', W 118°24.0'    {b (33.94,  -118.40) }

{pre
 '{def haversine
 {def radians {lambda {:a} {* {/ {PI} 180} :a}}}
 {lambda {:lat1 :lon1 :lat2 :lon2}
  {let { {:diam {* 6372.8 2}} 
         {:dLat {radians {- :lat2 :lat1}}}
         {:dLon {radians {- :lon2 :lon1}}}
         {:lat1 {radians :lat1}}
         {:lat2 {radians :lat2}}
       } {* :diam
            {asin {sqrt {+ {pow {sin {/ :dLat 2}} 2}
                           {* {cos :lat1} 
                              {cos :lat2} 
                              {pow {sin {/ :dLon 2}} 2} }}}}}}}} 
-> {def haversine
 {def radians {lambda {:a} {* {/ {PI} 180} :a}}}
 {lambda {:lat1 :lon1 :lat2 :lon2}
  {let { {:diam {* 6372.8 2}} 
         {:dLat {radians {- :lat2 :lat1}}}
         {:dLon {radians {- :lon2 :lon1}}}
         {:lat1 {radians :lat1}}
         {:lat2 {radians :lat2}}
       } {* :diam
            {asin {sqrt {+ {pow {sin {/ :dLat 2}} 2}
                           {* {cos :lat1} {cos :lat2} 
                              {pow {sin {/ :dLon 2}} 2} }}}}}}}}

'{haversine 36.12 -86.67 33.94 -118.40}
-> {haversine 36.12 -86.67 33.94 -118.40}
}

_h2 translations

{pre
'{def deg2dec
 {lambda {:s :w}
  {let { {:s {if {or {W.equal? :s W}
                     {W.equal? :s S}} then - else +}}
         {:dm {S.replace ° by space in
              {S.replace ' by in :w}}}
         } :s{S.get 0 :dm}.{round {* {/ 100 60} {S.get 1 :dm}}}}}}
-> {def deg2dec
 {lambda {:s :w}
  {let { {:s {if {or {W.equal? :s W} {W.equal? :s S}} then - else +}}
         {:dm {S.replace ° by space in
              {S.replace ' by in :w}}}
         } :s{S.get 0 :dm}.{round {* {/ 100 60} {S.get 1 :dm}}}}}}

'{haversine
 {deg2dec N 36°7.2'}
 {deg2dec W 86°40.2'}
 {deg2dec N 33°56.4'}
 {deg2dec W 118°24.0'}} 
-> {haversine
 {deg2dec N 36°7.2'}
 {deg2dec W 86°40.2'}
 {deg2dec N 33°56.4'}
 {deg2dec W 118°24.0'}}

}