Jaro similarity
You are encouraged to solve this task according to the task description, using any language you may know.
The Jaro distance is a measure of edit distance between two strings; its inverse, called the Jaro similarity, is a measure of two strings' similarity: the higher the value, the more similar the strings are. The score is normalized such that 0 equates to no similarities and 1 is an exact match.
- Definition
The Jaro similarity of two given strings and is
Where:
- is the number of matching characters;
- is half the number of transpositions.
Two characters from and respectively, are considered matching only if they are the same and not farther apart than characters.
Each character of is compared with all its matching characters in . Each difference in position is half a transposition; that is, the number of transpositions is half the number of characters which are common to the two strings but occupy different positions in each one.
- Example
Given the strings DWAYNE and DUANE we find:
We find a Jaro score of:
- Task
Implement the Jaro algorithm and show the similarity scores for each of the following pairs:
- ("MARTHA", "MARHTA")
- ("DIXON", "DICKSONX")
- ("JELLYFISH", "SMELLYFISH")
- See also
- Jaro–Winkler distance on Wikipedia.
11l
F jaro(s, t)
V s_len = s.len
V t_len = t.len
I s_len == 0 & t_len == 0
R 1.0
V match_distance = (max(s_len, t_len) I/ 2) - 1
V s_matches = [0B] * s_len
V t_matches = [0B] * t_len
V matches = 0
V transpositions = 0
L(i) 0 .< s_len
V start = max(0, i - match_distance)
V end = min(i + match_distance + 1, t_len)
L(j) start .< end
I t_matches[j]
L.continue
I s[i] != t[j]
L.continue
s_matches[i] = 1B
t_matches[j] = 1B
matches++
L.break
I matches == 0
R 0.0
V k = 0
L(i) 0 .< s_len
I !s_matches[i]
L.continue
L !t_matches[k]
k++
I s[i] != t[k]
transpositions++
k++
R ((Float(matches) / s_len) +
(Float(matches) / t_len) +
((matches - transpositions / 2) / matches)) / 3
L(s, t) [(‘MARTHA’, ‘MARHTA’),
(‘DIXON’, ‘DICKSONX’),
(‘JELLYFISH’, ‘SMELLYFISH’)]
print(‘jaro('#.', '#.') = #.10’.format(s, t, jaro(s, t)))- Output:
jaro('MARTHA', 'MARHTA') = 0.9444444444
jaro('DIXON', 'DICKSONX') = 0.7666666667
jaro('JELLYFISH', 'SMELLYFISH') = 0.8962962963
Action!
DEFINE STRING="CHAR ARRAY" ; sys.act
DEFINE ASCII_SpaceBar="32"
INT FUNC JaroDistance(STRING str1, str2)
STRING Z(15)
INT S1, S2, J, M, N, L, I, K, skip, Max, Min
INT Result
Result=0
S1=str1(0)
S2=str2(0)
IF S1>S2 THEN
SCopy(Z,str1)
SCopy(str1,str2)
SCopy(str2,Z)
M=S1
S1=S2
S2=M
FI
J=1 M=0 N=0 L=S2/2 SCopy(Z,str2)
FOR I=1 TO S1 DO
skip=0
IF str1(I)=str2(J) THEN
M==+1
str2(J)=ASCII_SpaceBar
skip=1
FI
IF skip=0 THEN
Max=1
IF Max<(I-L) THEN Max=I-L FI
Min=S2
IF Min>(I+L-1) THEN Min=I+L-1 FI
FOR K=Max TO Min DO
IF str1(I)=str2(K) THEN
N==+1
M==+1
str2(K)=ASCII_SpaceBar
IF K>J THEN J=K FI
FI
OD
FI
IF J<S2 THEN J==+1 FI
OD
IF M=0 THEN
Result=0 ; Jaro distance
ELSE
N=N/2
Result=((M*100)/S1+(M*100)/S2+(((M-N)*100)/M))/3 ; Jaro distance
FI
; Min=S1 IF Min>S2 THEN Min=S2 FI
; M=Min IF M>3 THEN M=3 FI
; M==+1 L=0 SCopy(str2,Z)
; IF M>Min THEN M=Min FI
; FOR I=1 TO M DO
; IF str1(I)=str2(I) THEN
; L==+1
; ELSE
; EXIT
; FI
; OD
; Result=Result*100 + (((L*100)/10)*(100 - Result)) ; Jaro Winkler distance
; Result=(Result+49)/100
RETURN(Result)
PROC MAIN()
INT result
STRING Word_1(15), Word_2(15)
PUT(125)
PUTE()
SCopy(Word_1,"LIGITA") SCopy(Word_2,"LIGA")
PrintF("%S - %S%E",Word_1,Word_2)
result=JaroDistance(Word_1,Word_2)
PrintF("Jaro Distance=%U%E%E",result)
SCopy(Word_1,"ZEILANE") SCopy(Word_2,"ZEIDONE")
PrintF("%S - %S%E",Word_1,Word_2)
result=JaroDistance(Word_1,Word_2)
PrintF("Jaro Distance=%U%E%E",result)
SCopy(Word_1,"JELLYFISH") SCopy(Word_2,"SMELLYFISH")
PrintF("%S - %S%E",Word_1,Word_2)
result=JaroDistance(Word_1,Word_2)
PrintF("Jaro Distance=%U%E%E",result)
RETURN- Output:
MARTHA, MARHTA: 94 DIXON, DICKSONX: 76 JELLYFISH, SMELLYFISH: 89
Ada
with Ada.Text_IO;
procedure Jaro_Distances is
type Jaro_Measure is new Float;
function Jaro_Distance (Left, Right : in String) return Jaro_Measure
is
Left_Matches : array (Left'Range) of Boolean := (others => False);
Right_Matches : array (Right'Range) of Boolean := (others => False);
Matches : Natural := 0;
Transpositions : Natural := 0;
begin
if Left'Length = 0 and Right'Length = 0 then
return 1.000;
end if;
declare
Match_Distance : constant Natural := Natural'Max (Left'Length, Right'Length) / 2 - 1;
begin
for L in Left'Range loop
declare
First : constant Natural := Natural'Max (Right'First, Right'First + L - Left'First - Match_Distance);
Last : constant Natural := Natural'Min (L - Left'First + Match_Distance + Right'First, Right'Last);
begin
for R in First .. Last loop
if
not Right_Matches (R) and
Left (L) = Right (R)
then
Left_Matches (L) := True;
Right_Matches (R) := True;
Matches := Matches + 1;
exit;
end if;
end loop;
end;
end loop;
end;
if Matches = 0 then
return 0.000;
end if;
declare
R : Natural := Right'First;
begin
for L in Left'Range loop
if Left_Matches (L) then
while not Right_Matches (R) loop
R := R + 1;
end loop;
if Left (L) /= Right (R) then
Transpositions := Transpositions + 1;
end if;
R := R + 1;
end if;
end loop;
end;
declare
Match : constant Float := Float (Matches);
Term_1 : constant Float := Match / Float (Left'Length);
Term_2 : constant Float := Match / Float (Right'Length);
Term_3 : constant Float := (Match - Float (Transpositions) / 2.0) / Match;
begin
return Jaro_Measure ((Term_1 + Term_2 + Term_3) / 3.0);
end;
end Jaro_Distance;
procedure Show_Jaro (Left, Right : in String)
is
package Jaro_IO is
new Ada.Text_IO.Float_IO (Jaro_Measure);
use Ada.Text_IO;
Distance : constant Jaro_Measure := Jaro_Distance (Left, Right);
begin
Jaro_IO.Put (Distance, Fore => 1, Aft => 5, Exp => 0);
Set_Col (10); Put (Left);
Set_Col (22); Put (Right);
New_Line;
end Show_Jaro;
S1 : constant String := " MARTHA VS MARHTA ";
begin
Show_Jaro ("DWAYNE", "DUANE");
Show_Jaro ("DIXON", "DICKSONX");
Show_Jaro ("JELLYFISH", "SMELLYFISH");
Show_Jaro (S1 (3 .. 8), S1 (13 .. 18));
end Jaro_Distances;
- Output:
0.82222 DWAYNE DUANE 0.76667 DIXON DICKSONX 0.89630 JELLYFISH SMELLYFISH 0.94444 MARTHA MARHTA
ARM Assembly
/* ARM assembly Raspberry PI */
/* program jarodist.s */
/* Constantes */
.equ BUFFERSIZE, 100
.equ STDIN, 0 @ Linux input console
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ READ, 3 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
.equ SIZESTRING, 256
/* Initialized data */
.data
szCarriageReturn: .asciz "\n"
szMessResult: .ascii " Jaro distance * 1000 = " @ message result
sMessValeur: .fill 12, 1, ' '
.asciz "\n"
szMessDeb: .asciz "For : "
szMessSep: .asciz " and "
szString1: .asciz "DWAYNE"
szString1A: .asciz "DUANE"
szString2: .asciz "MARTHA"
szString2A: .asciz "MARHTA"
szString3: .asciz "DIXON"
szString3A: .asciz "DICKSONX"
szString4: .asciz "JELLYFISH"
szString4A: .asciz "SMELLYFISH"
/* UnInitialized data */
.bss
iTabString1: .skip 4 * SIZESTRING
iTabString2: .skip 4 * SIZESTRING
sBuffer: .skip BUFFERSIZE
/* code section */
.text
.global main
main: @ entry of program
ldr r0,iAdrszString1 @ address string 1
ldr r1,iAdrszString1A @ address string 2
bl preparation @ compute jaro distance
ldr r0,iAdrszString2 @ address string 1
ldr r1,iAdrszString2A @ address string 2
bl preparation @ compute jaro distance
ldr r0,iAdrszString3 @ address string 1
ldr r1,iAdrszString3A @ address string 2
bl preparation @ compute jaro distance
ldr r0,iAdrszString4 @ address string 1
ldr r1,iAdrszString4A @ address string 2
bl preparation @ compute jaro distance
100: @ standard end of the program
mov r0, #0 @ return code
pop {fp,lr} @restaur 2 registers
mov r7, #EXIT @ request to exit program
swi 0 @ perform the system call
iAdrsMessValeur: .int sMessValeur
iAdrsBuffer: .int sBuffer
iAdrszMessResult: .int szMessResult
iAdrszCarriageReturn: .int szCarriageReturn
iAdrszMessDeb: .int szMessDeb
iAdrszMessSep: .int szMessSep
iAdrszString1: .int szString1
iAdrszString1A: .int szString1A
iAdrszString2: .int szString2
iAdrszString2A: .int szString2A
iAdrszString3: .int szString3
iAdrszString3A: .int szString3A
iAdrszString4: .int szString4
iAdrszString4A: .int szString4A
/******************************************************************/
/* preparation compute */
/******************************************************************/
/* r0 contains the address of the first string */
/* r1 contains the address of the second string */
preparation:
push {r2,lr} @ save registers
mov r2,r0 @ save first address
ldr r0,iAdrszMessDeb @ display the two strings
bl affichageMess
mov r0,r2
bl affichageMess
ldr r0,iAdrszMessSep
bl affichageMess
mov r0,r1
bl affichageMess
mov r0,r2 @ address string 1
@ and r1 contains address string 2
bl jaroDistance @ compute jaro distance
@ conversion register to string
ldr r1,iAdrsMessValeur
bl conversion10 @ conversion register to string
ldr r0,iAdrszMessResult
bl affichageMess @ display message
100:
pop {r2,lr} @ restaur registers
bx lr @ return
/******************************************************************/
/* Compute Jaro distance */
/******************************************************************/
/* r0 contains the address of the first string */
/* r1 contains the address of the second string */
/* r0 returns jaro distance * 1000 because not use float compute !!! */
jaroDistance:
push {r1-r11,lr} @ save registers
mov r6,r0 @ save address string 1
bl strLength @ size string
cmp r0,#0 @ empty string ?
beq 100f
mov r4,r0
mov r0,r1
bl strLength @ size string 2
cmp r0,#0 @ empty string ?
beq 100f
mov r5,r0
mov r2,#0 @ initialisation tables 1 and 2
mov r3,#0
ldr r7,iadriTabString1
ldr r8,iadriTabString2
1: @loop start
str r3,[r7,r2,lsl #2]
str r3,[r8,r2,lsl #2]
add r2,#1
cmp r2,#SIZESTRING
blt 1b
cmp r4,r5 @ compute match distance
lsrle r3,r5,#1 @ length max / 2
lsrgt r3,r4,#1
sub r3,#1 @ - 1
sub r4,#1 @ last index string 1
sub r5,#1 @ last index string 2
mov r11,#0 @ match counter
mov r2,#0 @ index loop
2: @ loop match
subs r7,r2,r3
movlt r7,#0 @ compute start
add r8,r2,r3
add r8,#1
cmp r8,r5
movgt r8,r5 @ compute end
3:
ldr r10,iadriTabString2 @ load element table 2 at location r7
ldr r9,[r10,r7,lsl #2]
cmp r9,#0 @ if not zero continue
bne 4f
ldrb r9,[r6,r2] @ compare characters of two strings
ldrb r10,[r1,r7]
cmp r9,r10
bne 4f @ not equal
ldr r10,iadriTabString2 @ match
mov r9,#1 @ store 1 in two tables
str r9,[r10,r7,lsl #2]
ldr r10,iadriTabString1
str r9,[r10,r2,lsl #2]
add r11,#1 @ increment counter match
b 5f @ end loop 2
4:
add r7,#1 @ following character string 2
cmp r7,r8 @ end ?
ble 3b
5:
add r2,#1 @ following character string 1
cmp r2,r4 @ end string ?
ble 2b
cmp r11,#0 @ return if 0 match
moveq r0,#0
beq 100f
/* compute transposition */
mov r2,#0 @ loop indice
mov r3,#0 @ indice string 2
mov r7,#0 @ counter transposition
6:
ldr r10,iadriTabString1 @ character match ?
ldr r9,[r10,r2,lsl #2]
cmp r9,#0
beq 8f @ no
ldr r10,iadriTabString2
7:
ldr r9,[r10,r3,lsl #2] @ yes, search match in table 2
cmp r9,#0
addeq r3,#1
beq 7b
ldrb r9,[r6,r2] @ compare characters
ldrb r10,[r1,r3]
cmp r9,r10
addne r7,#1 @ not equals add 1 to counter
add r3,#1 @ following characters string 2
8:
add r2,#1 @ following characters string 1
cmp r2,r4 @ end string ?
ble 6b @ no loop
lsr r7,#1 @ counter / 2
/* Final */
mov r6,#1000 @ factor 1000 for not use float compute !!!
mul r9,r6,r11 @ compute match * 1000
mul r7,r6,r7 @ compute transposition * 1000
mov r0,r9 @ match
add r1,r4,#1 @ size string 1
bl division
mov r8,r2
mov r0,r9 @ match
add r1,r5,#1 @ size string 2
bl division
add r8,r2
sub r0,r9,r7 @ compute match - transposition
mov r1,r11 @ match
bl division
add r8,r2
mov r0,r8 @ division total / 3
mov r1,#3
bl division
mov r0,r2 @ return value
100:
pop {r1-r11,lr} @ restaur registers
bx lr @ return
iadriTabString1: .int iTabString1
iadriTabString2: .int iTabString2
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr} @ save registres
mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index
cmp r1,#0 @ if 0 its over
addne r2,r2,#1 @ else add 1 in the length
bne 1b @ and loop
@ so here r2 contains the length of the message
mov r1,r0 @ address message in r1
mov r0,#STDOUT @ code to write to the standard output Linux
mov r7, #WRITE @ code call system "write"
svc #0 @ call systeme
pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */
bx lr @ return
/******************************************************************/
/* Converting a register to a decimal unsigned */
/******************************************************************/
/* r0 contains value and r1 address area */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes */
.equ LGZONECAL, 10
conversion10:
push {r1-r4,lr} @ save registers
mov r3,r1
mov r2,#LGZONECAL
1: @ start loop
bl divisionpar10U @unsigned r0 <- dividende. quotient ->r0 reste -> r1
add r1,#48 @ digit
strb r1,[r3,r2] @ store digit on area
cmp r0,#0 @ stop if quotient = 0
subne r2,#1 @ else previous position
bne 1b @ and loop
@ and move digit from left of area
mov r4,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
add r2,#1
add r4,#1
cmp r2,#LGZONECAL
ble 2b
@ and move spaces in end on area
mov r0,r4 @ result length
mov r1,#' ' @ space
3:
strb r1,[r3,r4] @ store space in area
add r4,#1 @ next position
cmp r4,#LGZONECAL
ble 3b @ loop if r4 <= area size
100:
pop {r1-r4,lr} @ restaur registres
bx lr @return
/***************************************************/
/* division par 10 unsigned */
/***************************************************/
/* r0 dividende */
/* r0 quotient */
/* r1 remainder */
divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0 @ save value
//mov r3,#0xCCCD @ r3 <- magic_number lower raspberry 3
//movt r3,#0xCCCC @ r3 <- magic_number higter raspberry 3
ldr r3,iMagicNumber @ r3 <- magic_number raspberry 1 2
umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2 @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr @ leave function
iMagicNumber: .int 0xCCCCCCCD
/***************************************************/
/* calcul size string */
/***************************************************/
/* r0 string address */
/* r0 returns size string */
strLength:
push {r1,r2,lr}
mov r1,#0 @ init counter
1:
ldrb r2,[r0,r1] @ load byte of string index r1
cmp r2,#0 @ end string ?
addne r1,#1 @ no -> +1 counter
bne 1b @ and loop
100:
mov r0,r1
pop {r1,r2,lr}
bx lr
/***************************************************/
/* integer division unsigned */
/***************************************************/
division:
/* r0 contains dividend */
/* r1 contains divisor */
/* r2 returns quotient */
/* r3 returns remainder */
push {r4, lr}
mov r2, #0 @ init quotient
mov r3, #0 @ init remainder
mov r4, #32 @ init counter bits
b 2f
1: @ loop
movs r0, r0, LSL #1 @ r0 <- r0 << 1 updating cpsr (sets C if 31st bit of r0 was 1)
adc r3, r3, r3 @ r3 <- r3 + r3 + C. This is equivalent to r3 ? (r3 << 1) + C
cmp r3, r1 @ compute r3 - r1 and update cpsr
subhs r3, r3, r1 @ if r3 >= r1 (C=1) then r3 <- r3 - r1
adc r2, r2, r2 @ r2 <- r2 + r2 + C. This is equivalent to r2 <- (r2 << 1) + C
2:
subs r4, r4, #1 @ r4 <- r4 - 1
bpl 1b @ if r4 >= 0 (N=0) then loop
pop {r4, lr}
bx lrArturo
loop [
["MARTHA" "MARHTA"]
["DIXON" "DICKSONX"]
["JELLYFISH" "SMELLYFISH"]
] 'pair ->
print [pair "-> Jaro similarity:" round.to: 3 jaro first pair last pair]
- Output:
[MARTHA MARHTA] -> Jaro similarity: 0.944 [DIXON DICKSONX] -> Jaro similarity: 0.767 [JELLYFISH SMELLYFISH] -> Jaro similarity: 0.896
AWK
# syntax: GAWK -f JARO_DISTANCE.AWK
BEGIN {
main("DWAYNE","DUANE")
main("MARTHA","MARHTA")
main("DIXON","DICKSONX")
main("JELLYFISH","SMELLYFISH")
exit(0)
}
function main(str1,str2) {
printf("%9.7f '%s' '%s'\n",jaro(str1,str2),str1,str2)
}
function jaro(str1,str2, begin,end,i,j,k,leng1,leng2,match_distance,matches,str1_arr,str2_arr,transpositions) {
leng1 = length(str1)
leng2 = length(str2)
if (leng1 == 0 && leng2 == 0) { # both strings are empty
return(1)
}
if (leng1 == 0 || leng2 == 0) { # only one string is empty
return(0)
}
match_distance = int(max(leng1,leng2)/2-1)
for (i=1; i<=leng1; i++) { # find matches
begin = int(max(0,i-match_distance))
end = int(min(i+match_distance+1,leng2))
for (j=begin; j<=end; j++) {
if (str2_arr[j]) { continue }
if (substr(str1,i,1) != substr(str2,j,1)) { continue }
str1_arr[i] = 1
str2_arr[j] = 1
matches++
break
}
}
if (matches == 0) {
return(0)
}
k = 0
for (i=1; i<=leng1; i++) { # count transpositions
if (!str1_arr[i]) { continue }
while (!str2_arr[k]) {
k++
}
if (substr(str1,i,1) != substr(str2,k,1)) {
transpositions++
}
k++
}
transpositions /= 2
return((matches/leng1)+(matches/leng2)+((matches-transpositions)/matches))/3
}
function max(x,y) { return((x > y) ? x : y) }
function min(x,y) { return((x < y) ? x : y) }
- Output:
0.8222222 'DWAYNE' 'DUANE' 0.9444444 'MARTHA' 'MARHTA' 0.7666667 'DIXON' 'DICKSONX' 0.8962963 'JELLYFISH' 'SMELLYFISH'
BBC BASIC
PRINT "Jaro similarity between the two strings:"
PROCDescribeJaro("MARTHA", "MARHTA")
PROCDescribeJaro("DIXON", "DICKSONX")
PROCDescribeJaro("JELLYFISH", "SMELLYFISH")
PROCDescribeJaro("DWAYNE", "DUANE")
PROCDescribeJaro("a", "b")
PROCDescribeJaro("", "")
END
DEF FNMax(a, b)=(a + b + ABS(a - b)) / 2
DEF FNMin(a, b)=(a + b - ABS(a - b)) / 2
DEF PROCDescribeJaro(word1$, word2$)
LOCAL d%, i%, j%, k%, l1%, l2%, m%, t%
PRINT " '" word1$ "' and '" word2$ "'" TAB(30) "= ";
IF word1$ == "" IF word2$ == "" PRINT;1 : ENDPROC
l1%=LENword1$
l2%=LENword2$
IF l1% < l2% SWAP l1%, l2% SWAP word1$, word2$
d%=l1% / 2 - 1
j%=1
FOR i%=1 TO l2%
IF MID$(word2$, i%, 1) == MID$(word1$, j%, 1) THEN
m%+=1
MID$(word1$, j%)=" "
ELSE
FOR k%=FNMax(1, i% - d%) TO FNMin(l1%, i% + d%)
IF MID$(word2$, i%, 1) == MID$(word1$, k%, 1) THEN
t%+=1
m%+=1
MID$(word1$, k%)=" "
IF k% > j% j%=k%
ENDIF
NEXT
ENDIF
j%+=1
NEXT
IF m% == 0 THEN
PRINT;0
ELSE
PRINT;(m% / l2% + m% / l1% + ((m% - (t% >> 1)) / m%)) / 3
ENDIF
ENDPROC
- Output:
Jaro similarity between the two strings: 'MARTHA' and 'MARHTA' = 0.944444444 'DIXON' and 'DICKSONX' = 0.766666667 'JELLYFISH' and 'SMELLYFISH' = 0.896296296 'DWAYNE' and 'DUANE' = 0.822222222 'a' and 'b' = 0 '' and '' = 1
C
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <stdio.h>
#define TRUE 1
#define FALSE 0
#define max(a, b) ((a) > (b) ? (a) : (b))
#define min(a, b) ((a) < (b) ? (a) : (b))
double jaro(const char *str1, const char *str2) {
// length of the strings
int str1_len = strlen(str1);
int str2_len = strlen(str2);
// if both strings are empty return 1
// if only one of the strings is empty return 0
if (str1_len == 0) return str2_len == 0 ? 1.0 : 0.0;
// max distance between two chars to be considered matching
// floor() is ommitted due to integer division rules
int match_distance = (int) max(str1_len, str2_len)/2 - 1;
// arrays of bools that signify if that char in the matching string has a match
int *str1_matches = calloc(str1_len, sizeof(int));
int *str2_matches = calloc(str2_len, sizeof(int));
// number of matches and transpositions
double matches = 0.0;
double transpositions = 0.0;
// find the matches
for (int i = 0; i < str1_len; i++) {
// start and end take into account the match distance
int start = max(0, i - match_distance);
int end = min(i + match_distance + 1, str2_len);
for (int k = start; k < end; k++) {
// if str2 already has a match continue
if (str2_matches[k]) continue;
// if str1 and str2 are not
if (str1[i] != str2[k]) continue;
// otherwise assume there is a match
str1_matches[i] = TRUE;
str2_matches[k] = TRUE;
matches++;
break;
}
}
// if there are no matches return 0
if (matches == 0) {
free(str1_matches);
free(str2_matches);
return 0.0;
}
// count transpositions
int k = 0;
for (int i = 0; i < str1_len; i++) {
// if there are no matches in str1 continue
if (!str1_matches[i]) continue;
// while there is no match in str2 increment k
while (!str2_matches[k]) k++;
// increment transpositions
if (str1[i] != str2[k]) transpositions++;
k++;
}
// divide the number of transpositions by two as per the algorithm specs
// this division is valid because the counted transpositions include both
// instances of the transposed characters.
transpositions /= 2.0;
// free the allocated memory
free(str1_matches);
free(str2_matches);
// return the Jaro distance
return ((matches / str1_len) +
(matches / str2_len) +
((matches - transpositions) / matches)) / 3.0;
}
int main() {
printf("%f\n", jaro("MARTHA", "MARHTA"));
printf("%f\n", jaro("DIXON", "DICKSONX"));
printf("%f\n", jaro("JELLYFISH", "SMELLYFISH"));
}
- Output:
0.944444 0.766667 0.896296
C#
using System;
public class JaroDistance {
public static double Jaro(string s, string t) {
int s_len = s.Length;
int t_len = t.Length;
if (s_len == 0 && t_len == 0) return 1;
int match_distance = Math.Max(s_len, t_len) / 2 - 1;
bool[] s_matches = new bool[s_len];
bool[] t_matches = new bool[t_len];
int matches = 0;
int transpositions = 0;
for (int i = 0; i < s_len; i++) {
int start = Math.Max(0, i - match_distance);
int end = Math.Min(i + match_distance + 1, t_len);
for (int j = start; j < end; j++) {
if (t_matches[j]) continue;
if (s[i] != t[j]) continue;
s_matches[i] = true;
t_matches[j] = true;
matches++;
break;
}
}
if (matches == 0) return 0;
int k = 0;
for (int i = 0; i < s_len; i++) {
if (!s_matches[i]) continue;
while (!t_matches[k]) k++;
if (s[i] != t[k]) transpositions++;
k++;
}
return (((double)matches / s_len) +
((double)matches / t_len) +
(((double)matches - transpositions / 2.0) / matches)) / 3.0;
}
public static void Main(string[] args) {
Console.WriteLine(Jaro("MARTHA", "MARHTA"));
Console.WriteLine(Jaro("DIXON", "DICKSONX"));
Console.WriteLine(Jaro("JELLYFISH", "SMELLYFISH"));
}
}
- Output:
0.944444444444445 0.766666666666667 0.896296296296296
C++
#include <algorithm>
#include <iostream>
#include <string>
double jaro(const std::string s1, const std::string s2) {
const uint l1 = s1.length(), l2 = s2.length();
if (l1 == 0)
return l2 == 0 ? 1.0 : 0.0;
const uint match_distance = std::max(l1, l2) / 2 - 1;
bool s1_matches[l1];
bool s2_matches[l2];
std::fill(s1_matches, s1_matches + l1, false);
std::fill(s2_matches, s2_matches + l2, false);
uint matches = 0;
for (uint i = 0; i < l1; i++)
{
const int end = std::min(i + match_distance + 1, l2);
for (int k = std::max(0u, i - match_distance); k < end; k++)
if (!s2_matches[k] && s1[i] == s2[k])
{
s1_matches[i] = true;
s2_matches[k] = true;
matches++;
break;
}
}
if (matches == 0)
return 0.0;
double t = 0.0;
uint k = 0;
for (uint i = 0; i < l1; i++)
if (s1_matches[i])
{
while (!s2_matches[k]) k++;
if (s1[i] != s2[k]) t += 0.5;
k++;
}
const double m = matches;
return (m / l1 + m / l2 + (m - t) / m) / 3.0;
}
int main() {
using namespace std;
cout << jaro("MARTHA", "MARHTA") << endl;
cout << jaro("DIXON", "DICKSONX") << endl;
cout << jaro("JELLYFISH", "SMELLYFISH") << endl;
return 0;
}
Clojure
(ns test-project-intellij.core
(:gen-class))
(defn find-matches [s t]
" find match locations in the two strings "
" s_matches is set to true wherever there is a match in t and t_matches is set conversely "
(let [s_len (count s)
t_len (count t)
match_distance (int (- (/ (max s_len t_len) 2) 1))
matches 0
transpositions 0
fn-start (fn [i] (max 0 (- i match_distance))) ; function to compute starting position
fn-end (fn [i] (min (+ i match_distance 1) (- t_len 1))) ] ; function to compute end position
(loop [i 0
start (fn-start i)
end (fn-end i)
k start
s_matches (vec (repeat (count s) false))
t_matches (vec (repeat (count t) false))
matches 0]
(if (< i s_len)
(if (<= k end)
(if (get t_matches k)
; continue with next k
(recur i start end (inc k) s_matches t_matches matches)
(if (= (get s i) (get t k))
; match a position, so update matches, s_matches, t_matches to reflect match
(recur (inc i) (fn-start (inc i)) (fn-end (inc i)) (fn-start (inc i)) (assoc s_matches i true) (assoc t_matches k true) (inc matches))
; no match so try next k
(recur i start end (inc k) s_matches t_matches matches)))
; End of k iterations, so increment i and set k to start based upon i
(recur (inc i) (fn-start (inc i)) (fn-end (inc i)) (fn-start (inc i)) s_matches t_matches matches))
; End of i iterations
[matches s_matches t_matches]))))
(defn count-transpositions [s t s_matches t_matches]
" Utility function to count the number of transpositions "
(let [s_len (count s)]
(loop [i 0
k 0
transpositions 0]
(if (< i s_len)
; still elements in s (since i < s_len)
(if (not (get s_matches i nil))
; skip to next i since there are no matches in s
(recur (inc i) k transpositions)
; checking for match in t
(if (not (get t_matches k nil))
; keeping looping around as long as there are no matches in t
(recur i (inc k) transpositions)
(if (not= (get s i) (get t k))
; increment transposition count (if strings don't equal at match location)
(recur (inc i) (inc k) (inc transpositions))
; was a match, so advance i and k without increasing transpositions count
(recur (inc i) (inc k) transpositions))))
; Return count
transpositions))))
(defn jaro [s t]
" Main Jaro Distance routine"
(if (= s t)
1
(let [[matches s_matches t_matches] (find-matches s t)]
(if (= 0 matches)
0
(let [s_len (count s)
t_len (count t)
transpositions (count-transpositions s t s_matches t_matches)]
(float (/ (+ (/ matches s_len) (/ matches t_len) (/ (- matches (/ transpositions 2)) matches)) 3)))))))
(println (jaro "MARTHA" "MARHTA"))
(println (jaro "DIXON" "DICKSONX"))
(println (jaro "JELLYFISH" "SMELLYFISH"))
- Output:
0.9444444 0.76666665 0.8962963
CLU
max = proc [T: type] (a, b: T) returns (T)
where T has lt: proctype (T,T) returns (bool)
if a<b then return(b) else return(a) end
end max
min = proc [T: type] (a, b: T) returns (T)
where T has lt: proctype (T,T) returns (bool)
if a<b then return(a) else return(b) end
end min
jaro = proc (s1, s2: string) returns (real)
s1_len: int := string$size(s1)
s2_len: int := string$size(s2)
if s1_len = 0 & s2_len = 0 then return(1.0)
elseif s1_len = 0 | s2_len = 0 then return(0.0)
end
dist: int := max[int](s1_len, s2_len)/2 - 1
s1_match: array[bool] := array[bool]$fill(1,s1_len,false)
s2_match: array[bool] := array[bool]$fill(1,s2_len,false)
matches: real := 0.0
transpositions: real := 0.0
for i: int in int$from_to(1, s1_len) do
start: int := max[int](1, i-dist)
end_: int := min[int](i+dist, s2_len)
for k: int in int$from_to(start, end_) do
if s2_match[k] then continue end
if s1[i] ~= s2[k] then continue end
s1_match[i] := true
s2_match[k] := true
matches := matches + 1.0
break
end
end
if matches=0.0 then return(0.0) end
k: int := 1
for i: int in int$from_to(1, s1_len) do
if ~s1_match[i] then continue end
while ~s2_match[k] do k := k + 1 end
if s1[i] ~= s2[k] then
transpositions := transpositions + 1.0
end
k := k+1
end
transpositions := transpositions / 2.0
return( ((matches / real$i2r(s1_len)) +
(matches / real$i2r(s2_len)) +
((matches - transpositions) / matches)) / 3.0)
end jaro
start_up = proc ()
po: stream := stream$primary_output()
stream$putl(po, f_form(jaro("MARTHA", "MARHTA"), 1, 6))
stream$putl(po, f_form(jaro("DIXON", "DICKSONX"), 1, 6))
stream$putl(po, f_form(jaro("JELLYFISH", "SMELLYFISH"), 1, 6))
end start_up- Output:
0.944444 0.766667 0.896296
COBOL
identification division.
program-id. JaroDistance.
environment division.
configuration section.
repository.
function length intrinsic
function trim intrinsic
function max intrinsic
function min intrinsic
.
data division.
working-storage section.
77 s pic x(255).
77 t pic x(255).
77 s-length pic 9(3).
77 t-length pic 9(3).
77 i pic 9(3).
77 j pic 9(3).
77 k pic 9(3).
77 start-pos pic 9(3).
77 end-pos pic 9(3).
77 match-distance pic 9(3).
77 matches pic 9(3).
77 transpositions pic 9(3).
77 distance pic 9v9(8).
01 jaro-table.
05 filler occurs 255.
10 filler pic 9(1).
88 s-matches value 1 when set to false is 0.
10 filler pic 9(1).
88 t-matches value 1 when set to false is 0.
procedure division.
main.
move "MARTHA" to s
move "MARHTA" to t
perform jaro-calc-and-show
move "DIXON" to s
move "DICKSONX" to t
perform jaro-calc-and-show
move "JELLYFISH" to s
move "SMELLYFISH" to t
perform jaro-calc-and-show
stop run
.
jaro-calc-and-show.
perform jaro-distance
display trim(s) " -> " trim(t) ", distance=" distance
.
jaro-distance.
move length(trim(s)) to s-length
move length(trim(t)) to t-length
if s-length = zeros and t-length = zeros
move 1 to distance
exit paragraph
end-if
compute match-distance = max(s-length, t-length) / 2 - 1
move low-values to jaro-table
move zeros to matches
move zeros to transpositions
perform varying i from 1 by 1 until i > s-length
move max(1, i - match-distance) to start-pos
move min(i + match-distance, t-length) to end-pos
perform varying j from start-pos by 1 until j > end-pos
if t-matches(j) or s(i:1) <> t(j:1)
exit perform cycle
end-if,
set s-matches(i), t-matches(j) to true
add 1 to matches
exit perform
end-perform
end-perform
if matches = zeros
move matches to distance
exit paragraph
end-if
move 1 to k
perform varying i from 1 by 1 until i > s-length
if not s-matches(i)
exit perform cycle
end-if
perform until t-matches(k)
add 1 to k
end-perform
if s(i:1) <> t(k:1)
add 1 to transpositions
end-if
add 1 to k
end-perform
compute distance = ((matches / s-length) + (matches / t-length) +
((matches - transpositions / 2) / matches)) / 3
.
- Output:
MARTHA -> MARHTA, distance=0.94444444 DIXON -> DICKSONX, distance=0.76666666 JELLYFISH -> SMELLYFISH, distance=0.89629629
CoffeeScript
jaro = (s1, s2) ->
l1 = s1.length
l2 = s2.length
if l1 == 0 then return if l2 == 0 then 1.0 else 0.0
match_distance = Math.max(l1, l2) / 2 - 1
s1_matches = []
s2_matches = []
m = 0
for i in [0...l1]
end = Math.min(i + match_distance + 1, l2)
for k in [Math.max(0, i - match_distance)...end]
if !s2_matches[k] and s1[i] == s2[k]
s1_matches[i] = true
s2_matches[k] = true
m++
break
if m == 0
0.0
else
t = 0.0
k = 0
for i in [0...l1]
if s1_matches[i]
until s2_matches[k] then k++
if s1[i] != s2[k++] then t += 0.5
(m / l1 + m / l2 + (m - t) / m) / 3.0
console.log jaro "MARTHA", "MARHTA"
console.log jaro "DIXON", "DICKSONX"
console.log jaro "JELLYFISH", "SMELLYFISH"
- Output:
0.9444444444444445 0.7666666666666666 0.8962962962962964
Crystal
def jaro(s, t)
return 1.0 if s == t
s_len = s.size
t_len = t.size
match_distance = ({s_len, t_len}.max // 2) - 1
s_matches = Array.new(s_len, false)
t_matches = Array.new(t_len, false)
matches = 0.0
s_len.times do |i|
j_start = {0, i - match_distance}.max
j_end = {i + match_distance, t_len - 1}.min
(j_start..j_end).each do |j|
t_matches[j] && next # -> next if t_matches[j]
s[i] == t[j] || next # -> next unless s[i] == t[j]
s_matches[i] = true
t_matches[j] = true
matches += 1.0
break
end
end
return 0.0 if matches == 0.0
k = 0
transpositions = 0.0
s_len.times do |i|
s_matches[i] || next # -> next unless s_matches[i]
while ! t_matches[k]; k += 1 end # -> k += 1 until t_matches[k]
s[i] == t[k] || (transpositions += 1.0) # -> (transpositions += 1.0) unless s[i] == t[k]
k += 1
end
((matches / s_len) + (matches / t_len) +
((matches - transpositions / 2.0) / matches)) / 3.0
end
%w( MARTHA MARHTA
DIXON DICKSONX
JELLYFISH SMELLYFISH
).each_slice(2) { |(s ,t)| puts "jaro(#{s}, #{t}) = #{"%.10f" % jaro(s, t)}" }
- Output:
jaro(MARTHA, MARHTA) = 0.9444444444 jaro(DIXON, DICKSONX) = 0.7666666667 jaro(JELLYFISH, SMELLYFISH) = 0.8962962963
D
auto jaro(in string s1, in string s2) {
int s1_len = cast(int) s1.length;
int s2_len = cast(int) s2.length;
if (s1_len == 0 && s2_len == 0) return 1;
import std.algorithm.comparison: min, max;
auto match_distance = max(s1_len, s2_len) / 2 - 1;
auto s1_matches = new bool[s1_len];
auto s2_matches = new bool[s2_len];
int matches = 0;
for (auto i = 0; i < s1_len; i++) {
auto start = max(0, i - match_distance);
auto end = min(i + match_distance + 1, s2_len);
for (auto j = start; j < end; j++)
if (!s2_matches[j] && s1[i] == s2[j]) {
s1_matches[i] = true;
s2_matches[j] = true;
matches++;
break;
}
}
if (matches == 0) return 0;
auto t = 0.0;
auto k = 0;
for (auto i = 0; i < s1_len; i++)
if (s1_matches[i]) {
while (!s2_matches[k]) k++;
if (s1[i] != s2[k++]) t += 0.5;
}
double m = matches;
return (m / s1_len + m / s2_len + (m - t) / m) / 3.0;
}
void main() {
import std.stdio: writeln;
writeln(jaro( "MARTHA", "MARHTA"));
writeln(jaro( "DIXON", "DICKSONX"));
writeln(jaro("JELLYFISH", "SMELLYFISH"));
}
0.944444 0.766667 0.896296
Delphi
See Pascal.
EasyLang
func jarodistance s1$ s2$ .
s1$[] = strchars s1$
s2$[] = strchars s2$
matchstd = higher len s1$[] len s2$[] / 2 - 1
for i1 to len s1$[]
for i2 to len s2$[]
if s1$[i1] = s2$[i2]
if abs (i2 - i1) <= matchstd
m += 1
if i2 = i1
p += 1
.
.
.
.
.
t = (m - p) / 2
return 1 / 3 * (m / len s1$[] + m / len s2$[] + (m - t) / m)
.
print jarodistance "MARTHA" "MARHTA"
print jarodistance "DIXON" "DICKSONX"
print jarodistance "JELLYFISH" "SMELLYFISH"
- Output:
0.94 0.68 0.89
Elixir
defmodule Jaro do
def distance(s, t) when is_binary(s) and is_binary(t), do:
distance(to_charlist(s), to_charlist(t))
def distance(x, x), do: 1.0
def distance(s, t) do
s_len = length(s)
t_len = length(t)
{s_matches, t_matches, matches} = matching(s, t, s_len, t_len)
if matches == 0 do
0.0
else
{k, transpositions} = transposition(s, t, s_matches, t_matches)
((matches / s_len) +
(matches / t_len) +
((matches - transpositions/2) / matches)) / 3
end
end
defp matching(s, t, s_len, t_len) do
match_distance = div(max(s_len, t_len), 2) - 1
ac0 = {List.duplicate(false, s_len), List.duplicate(false, t_len), 0}
Enum.reduce(0..s_len-1, ac0, fn i,acc ->
j_start = max(0, i-match_distance)
j_end = min(i+match_distance, t_len-1)
Enum.reduce_while(j_start..j_end, acc, fn j,{sm,tm,m} ->
if Enum.at(tm, j) or Enum.at(s, i) != Enum.at(t, j) do
{:cont, {sm, tm, m}}
else
{:halt, { List.replace_at(sm, i, true),
List.replace_at(tm, j, true),
m + 1 }}
end
end)
end)
end
defp transposition(s, t, s_matches, t_matches) do
Enum.reduce(0..length(s)-1, {0,0}, fn i,{k,transpositions} ->
if Enum.at(s_matches, i) do
k = k + (Enum.drop(t_matches, k)
|> Enum.take_while(fn matche -> not matche end)
|> length)
if Enum.at(s, i) == Enum.at(t, k), do: {k+1, transpositions},
else: {k+1, transpositions+1}
else
{k, transpositions}
end
end)
end
end
~w( MARTHA MARHTA
DIXON DICKSONX
JELLYFISH SMELLYFISH )c
|> Enum.chunk(2)
|> Enum.each(fn [s,t] ->
:io.format "jaro(~s, ~s) = ~.10f~n", [inspect(s), inspect(t), Jaro.distance(s, t)]
end)
- Output:
jaro('MARTHA', 'MARHTA') = 0.9444444444
jaro('DIXON', 'DICKSONX') = 0.7666666667
jaro('JELLYFISH', 'SMELLYFISH') = 0.8962962963
Elixir has a built-in function (String.jaro_distance).
Emacs Lisp
(let ()
(defun jaro (s1 s2)
(let (mw mflags1 mflags2 fn-reset-mflags fn-reset-all-mflags fn-cnt-trans)
(setq mflags1 (make-vector (length s1) nil))
(setq mflags2 (make-vector (length s2) nil))
(setq mw (1- (/ (max (length s1) (length s2)) 2)))
(setq fn-reset-mflags
(lambda (idx)
(let ((start (max 0 (- idx mw)))
(end (min (1- (length s2)) (+ idx mw))))
(cl-loop for i from start to end do
(when (and (not (elt mflags1 idx))
(not (elt mflags2 i)))
(when (equal (elt s1 idx) (elt s2 i))
(aset mflags1 idx 't)
(aset mflags2 i 't) ) ) ) ) ) )
(setq fn-reset-all-mflags
(lambda ()
(dotimes (idx (length s1))
(funcall fn-reset-mflags idx) ) ) )
(setq fn-cnt-trans
(lambda ()
(let ((cur2 0) (transposition 0))
(dotimes (cur1 (length s1))
(when (aref mflags1 cur1)
(while (not (aref mflags2 cur2))
(setq cur2 (1+ cur2)) )
(when (not (equal (aref s1 cur1)
(aref s2 cur2)))
(setq transposition (1+ transposition)) )
(setq cur2 (1+ cur2))
)
)
transposition ) ) )
(funcall fn-reset-all-mflags)
(let ((m (seq-count (lambda (f) f) mflags1))
(tr (funcall fn-cnt-trans)))
;;(message "matches: %s, transposition: %s, |s1|: %d |s2|: %d" m tr (length s1) (length s2))
(if (= m 0)
0
(progn (/ (+ (/ (float m) (length s1)) (/ (float m) (length s2)) (/ (float (- m (/ (float tr) 2))) m) ) 3))
) ) ) )
(let ((params '(("MARTHA" "MARHTA")
("DIXON" "DICKSONX")
("JELLYFISH" "SMELLYFISH"))))
(dolist (p params)
(message "jaro(%s, %s) = %f"
(nth 0 p) (nth 1 p)
(jaro (nth 0 p) (nth 1 p)))
)
)
)
- Output:
jaro(MARTHA, MARHTA) = 0.944444 jaro(DIXON, DICKSONX) = 0.766667 jaro(JELLYFISH, SMELLYFISH) = 0.896296
F#
// Calculate Jaro distance of 2 strings. Nigel Galloway: August 7th., 2020
let fG n g=Seq.map2(fun n g->if g=1 then Some n else None) n g |> Seq.choose id
let J (n:string) (g:string)=
let s1,s2=n.Length,g.Length
let w,m1,m2=(max s1 s2)/2-1,Array.zeroCreate<int>s1,Array.zeroCreate<int>s2
g|>Seq.iteri(fun i g->match [max(i-w) 0..min(i+w)(s1-1)]|>Seq.tryFind(fun i->n.[i]=g&&m1.[i]=0) with Some n->m1.[n]<-1;m2.[i]<-1 |_->())
let t=float(Seq.fold2(fun Σ n g->Σ + (if n<>g then 1 else 0)) 0 (fG n m1) (fG g m2))/2.0
let m=float(m2|>Array.sum) in if m=0.0 then m else ((m/float s1)+(m/float s2)+((m-t)/m))/3.0
printfn "MARTHA MARHTA->%f" (J "MARTHA" "MARHTA")
printfn "DIXON DICKSONX->%f" (J "DIXON" "DICKSONX")
printfn "JELLYFISH SMELLYFISH->%f" (J "JELLYFISH" "SMELLYFISH")
- Output:
MARTHA MARHTA->0.944444 DIXON DICKSONX->0.766667 JELLYFISH SMELLYFISH->0.896296
Factor
USING: formatting fry generalizations kernel locals make math
math.order sequences sequences.extras ;
IN: rosetta-code.jaro-distance
: match? ( s1 s2 n -- ? )
[ pick nth swap indices nip ] [ 2nip ]
[ drop [ length ] bi@ max 2/ 1 - ] 3tri
'[ _ - abs _ <= ] any? ;
: matches ( s1 s2 -- seq )
over length <iota> [
[ [ nip swap nth ] [ match? ] 3bi [ , ] [ drop ] if ]
2with each
] "" make ;
: transpositions ( s1 s2 -- n )
2dup swap [ matches ] 2bi@ [ = not ] 2count 2/ ;
:: jaro ( s1 s2 -- x )
s1 s2 matches length :> m
s1 length :> |s1|
s2 length :> |s2|
s1 s2 transpositions :> t
m zero? [ 0 ] [ m |s1| / m |s2| / m t - m / + + 1/3 * ] if ;
: jaro-demo ( -- )
"DWAYNE" "DUANE"
"MARTHA" "MARHTA"
"DIXON" "DICKSONX"
"JELLYFISH" "SMELLYFISH" [
2dup jaro dup >float "%u %u jaro -> %u (~%.5f)\n" printf
] 2 4 mnapply ;
MAIN: jaro-demo
- Output:
"DWAYNE" "DUANE" jaro -> 37/45 (~0.82222) "MARTHA" "MARHTA" jaro -> 17/18 (~0.94444) "DIXON" "DICKSONX" jaro -> 23/30 (~0.76667) "JELLYFISH" "SMELLYFISH" jaro -> 121/135 (~0.89630)
FreeBASIC
' version 09-10-2016
' compile with: fbc -s console
#Macro max(x, y)
IIf((x) > (y), (x), (y))
#EndMacro
#Macro min(x, y)
IIf((x) < (y), (x), (y))
#EndMacro
Function jaro(word1 As String, word2 As String) As Double
If Len(word1) > Len(word2) Then Swap word1, word2
Dim As Long i, j, j1, m, t
Dim As Long s1 = Len(word1)
Dim As Long s2 = Len(word2)
Dim As Long max_dist = s2 \ 2 -1 ' integer division
For i = 0 To s1 -1
If word1[i] = word2[j] Then
m = m +1
word2[j] = 32
Else
For j1 = max(0, i - max_dist) To min(s2 -1, i + max_dist)
If word1[i] = word2[j1] Then
t = t +1
m = m +1
word2[j1] = 32
If j1 > j Then j = j1
End If
Next
End If
j = j + 1
Next
If m = 0 Then Return 0
t = t \ 2
Return (m / s1 + m / s2 + ((m - t) / m)) / 3
End Function
' ------=< MAIN >=------
Print
Print " jaro (MARTHA, MARHTA) ="; jaro("MARTHA", "MARHTA")
Print " jaro (DIXON, DICKSONX) ="; jaro("DIXON", "DICKSONX")
Print " jaro (JELLYFISH, SMELLYFISH) ="; jaro("JELLYFISH", "SMELLYFISH")
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
- Output:
jaro (MARTHA, MARHTA) = 0.9444444444444444 jaro (DIXON, DICKSONX) = 0.7666666666666667 jaro (JELLYFISH, SMELLYFISH) = 0.8962962962962963
Go
package main
import "fmt"
func jaro(str1, str2 string) float64 {
if len(str1) == 0 && len(str2) == 0 {
return 1
}
if len(str1) == 0 || len(str2) == 0 {
return 0
}
match_distance := len(str1)
if len(str2) > match_distance {
match_distance = len(str2)
}
match_distance = match_distance/2 - 1
str1_matches := make([]bool, len(str1))
str2_matches := make([]bool, len(str2))
matches := 0.
transpositions := 0.
for i := range str1 {
start := i - match_distance
if start < 0 {
start = 0
}
end := i + match_distance + 1
if end > len(str2) {
end = len(str2)
}
for k := start; k < end; k++ {
if str2_matches[k] {
continue
}
if str1[i] != str2[k] {
continue
}
str1_matches[i] = true
str2_matches[k] = true
matches++
break
}
}
if matches == 0 {
return 0
}
k := 0
for i := range str1 {
if !str1_matches[i] {
continue
}
for !str2_matches[k] {
k++
}
if str1[i] != str2[k] {
transpositions++
}
k++
}
transpositions /= 2
return (matches/float64(len(str1)) +
matches/float64(len(str2)) +
(matches-transpositions)/matches) / 3
}
func main() {
fmt.Printf("%f\n", jaro("MARTHA", "MARHTA"))
fmt.Printf("%f\n", jaro("DIXON", "DICKSONX"))
fmt.Printf("%f\n", jaro("JELLYFISH", "SMELLYFISH"))
}
- Output:
0.944444 0.766667 0.896296
Haskell
import Data.List (elemIndex, intercalate, sortOn)
import Data.Maybe (mapMaybe)
import Text.Printf (printf)
---------------------- JARO DISTANCE ---------------------
jaro :: Ord a => [a] -> [a] -> Float
jaro x y
| 0 == m = 0
| otherwise =
(1 / 3)
* ( (m / s1) + (m / s2) + ((m - t) / m))
where
f = fromIntegral . length
[m, t] =
[f, fromIntegral . transpositions]
<*> [matches x y]
[s1, s2] = [f] <*> [x, y]
matches :: Eq a => [a] -> [a] -> [(Int, a)]
matches s1 s2 =
let [(l1, xs), (l2, ys)] =
sortOn
fst
((length >>= (,)) <$> [s1, s2])
r = quot l2 2 - 1
in mapMaybe
( \(c, n) ->
-- Initial chars out of range ?
let offset = max 0 (n - (r + 1))
in -- Any offset for this char within range.
elemIndex c (drop offset (take (n + r) ys))
>>= (\i -> Just (offset + i, c))
)
(zip xs [1 ..])
transpositions :: Ord a => [(Int, a)] -> Int
transpositions =
length
. filter (uncurry (>))
. (zip <*> tail)
--------------------------- TEST -------------------------
main :: IO ()
main =
mapM_ putStrLn $
fmap
( \(s1, s2) ->
intercalate
" -> "
[s1, s2, printf "%.3f\n" $ jaro s1 s2]
)
[ ("DWAYNE", "DUANE"),
("MARTHA", "MARHTA"),
("DIXON", "DICKSONX"),
("JELLYFISH", "SMELLYFISH")
]
- Output:
DWAYNE -> DUANE -> 0.822 MARTHA -> MARHTA -> 0.944 DIXON -> DICKSONX -> 0.767 JELLYFISH -> SMELLYFISH -> 0.896
Haxe
class Jaro {
private static function jaro(s1: String, s2: String): Float {
var s1_len = s1.length;
var s2_len = s2.length;
if (s1_len == 0 && s2_len == 0) return 1;
var match_distance = Std.int(Math.max(s1_len, s2_len)) / 2 - 1;
var matches = { s1: [for(n in 0...s1_len) false], s2: [for(n in 0...s2_len) false] };
var m = 0;
for (i in 0...s1_len) {
var start = Std.int(Math.max(0, i - match_distance));
var end = Std.int(Math.min(i + match_distance + 1, s2_len));
for (j in start...end)
if (!matches.s2[j] && s1.charAt(i) == s2.charAt(j)) {
matches.s1[i] = true;
matches.s2[j] = true;
m++;
break;
}
}
if (m == 0) return 0;
var k = 0;
var t = 0.;
for (i in 0...s1_len)
if (matches.s1[i]) {
while (!matches.s2[k]) k++;
if (s1.charAt(i) != s2.charAt(k++)) t += 0.5;
}
return (m / s1_len + m / s2_len + (m - t) / m) / 3.0;
}
public static function main() {
Sys.println(jaro( "MARTHA", "MARHTA"));
Sys.println(jaro( "DIXON", "DICKSONX"));
Sys.println(jaro("JELLYFISH", "SMELLYFISH"));
}
}
- Output:
0.944444444444445 0.766666666666667 0.896296296296296
IS-BASIC
100 PROGRAM "Jaro.bas"
110 DO
120 READ IF MISSING EXIT DO:A$,B$
130 PRINT A$;", ";B$;":";JARO(A$,B$)
140 LOOP
150 DEF JARO(A$,B$)
160 LET J=1:LET M,T,JARO=0:LET S1=LEN(A$):LET S2=LEN(B$)
170 IF S1>S2 THEN
180 LET Z$=A$:LET A$=B$:LET B$=Z$
190 LET Z=S1:LET S1=S2:LET S2=Z
200 END IF
210 LET MAXDIST=INT(S2/2)
220 FOR I=1 TO S1
230 IF A$(I)=B$(J) THEN
240 LET M=M+1:CALL CHANGE(B$," ",J)
250 ELSE
260 FOR K=MAX(1,I-MAXDIST) TO MIN(S2,I+MAXDIST)
270 IF A$(I)=B$(K) THEN
280 LET T=T+1:LET M=M+1:CALL CHANGE(B$," ",K)
290 IF K>J THEN LET J=K
300 END IF
310 NEXT
320 END IF
330 IF J<S2 THEN LET J=J+1
340 NEXT
350 IF M<>0 THEN
360 LET T=INT(T/2)
370 LET JARO=(M/S1+M/S2+((M-T)/M))/3
380 END IF
390 END DEF
400 DEF CHANGE(REF S$,C$,POS)
410 LET S$=S$(:POS-1)&C$&S$(POS+1:)
420 END DEF
430 DATA MARTHA,MARHTA
440 DATA DIXON,DICKSONX
450 DATA JELLYFISH,SMELLYFISH
460 DATA DWAYNE,DUANEJ
Implementation:
jaro=: dyad define
d=. ((x >.&# y)%2)-1
e=. (x =/y) * d >: |x -/&(i.@#) y
xm=. (+./"1 e)#x
ym=. (+./"2 e)#y
m=. xm <.&# ym
t=. (+/xm ~:&(m&{.) ym)%2
s1=. #x
s2=. #y
((m%s1)+(m%s2)+(m-t)%m)%3
)
Task examples:
'MARTHA' jaro 'MARHTA'
0.944444
'DIXON' jaro 'DICKSONX'
0.766667
'JELLYFISH' jaro 'SMELLYFISH'
0.896296
Java
public class JaroDistance {
public static double jaro(String s, String t) {
int s_len = s.length();
int t_len = t.length();
if (s_len == 0 && t_len == 0) return 1;
int match_distance = Integer.max(s_len, t_len) / 2 - 1;
boolean[] s_matches = new boolean[s_len];
boolean[] t_matches = new boolean[t_len];
int matches = 0;
int transpositions = 0;
for (int i = 0; i < s_len; i++) {
int start = Integer.max(0, i-match_distance);
int end = Integer.min(i+match_distance+1, t_len);
for (int j = start; j < end; j++) {
if (t_matches[j]) continue;
if (s.charAt(i) != t.charAt(j)) continue;
s_matches[i] = true;
t_matches[j] = true;
matches++;
break;
}
}
if (matches == 0) return 0;
int k = 0;
for (int i = 0; i < s_len; i++) {
if (!s_matches[i]) continue;
while (!t_matches[k]) k++;
if (s.charAt(i) != t.charAt(k)) transpositions++;
k++;
}
return (((double)matches / s_len) +
((double)matches / t_len) +
(((double)matches - transpositions/2.0) / matches)) / 3.0;
}
public static void main(String[] args) {
System.out.println(jaro( "MARTHA", "MARHTA"));
System.out.println(jaro( "DIXON", "DICKSONX"));
System.out.println(jaro("JELLYFISH", "SMELLYFISH"));
}
}
- Output:
0.9444444444444445 0.7666666666666666 0.8962962962962964
jq
Works with gojq, the Go implementation of jq
def jaro($s1; $s2):
($s1|length) as $le1
| ($s2|length) as $le2
| if $le1 == 0 and $le2 == 0 then 1
elif $le1 == 0 or $le2 == 0 then 0
else ((((if $le2 > $le1 then $le2 else $le1 end) / 2) | floor) - 1) as $dist
| {matches: 0, matches2: [], matches2: [], transpos: 0 }
| reduce range(0; $le1) as $i (.;
(($i - $dist) | if . < 0 then 0 else . end) as $start
| (($i + $dist + 1) | if . > $le2 then $le2 else . end) as $stop
| .k = $start
| until(.k >= $stop;
if (.matches2[.k] or $s1[$i:$i+1] != $s2[.k:.k+1])|not
then .matches1[$i] = true
| .matches2[.k] = true
| .matches += 1
| .k = $stop
else .k += 1
end) )
| if .matches == 0 then 0
else .k = 0
| reduce range(0; $le1) as $i (.;
if .matches1[$i]
then until(.k >= $le2 or .matches2[.k]; .k += 1)
| if .k < $le2 and ($s1[$i:$i+1] != $s2[.k:.k+1]) then .transpos += 1 else . end
| .k += 1
else .
end )
| .transpos /= 2
| (.matches/$le1 + .matches/$le2 + ((.matches - .transpos)/.matches)) / 3
end
end ;
def task:
[["MARTHA","MARHTA"],
["DIXON", "DICKSONX"],
["JELLYFISH","SMELLYFISH"],
["ABC","DEF"]][]
| (jaro(.[0]; .[1]) * 1000 | floor / 1000) as $d
| "jaro(\(.[0]); \(.[1])) => \($d)";
task- Output:
jaro(MARTHA; MARHTA) => 0.944 jaro(DIXON; DICKSONX) => 0.766 jaro(JELLYFISH; SMELLYFISH) => 0.896 jaro(ABC; DEF) => 0
Julia
function jarodistance(s1, s2)
m = t = p = 0
matchstd = max(length(s1), length(s2)) / 2 - 1
for (i1, c1) in enumerate(s1)
for (i2, c2) in enumerate(s2)
(c1 == c2) && (abs(i2 - i1) ≤ matchstd) && (m += 1)
(c1 == c2) && (i2 == i1) && (p += 1)
end
end
t = (m - p) / 2
1 / 3 * (m / length(s1) + m / length(s2) + (m - t) / m)
end
@show jarodistance("MARTHA", "MARHTA")
@show jarodistance("DIXON", "DICKSONX")
@show jarodistance("JELLYFISH", "SMELLYFISH")
- Output:
jarodistance("MARTHA", "MARHTA") = 0.9444444444444444
jarodistance("DIXON", "DICKSONX") = 0.6833333333333332
jarodistance("JELLYFISH", "SMELLYFISH") = 0.8870370370370371
Kotlin
object Jaro {
fun distance(s1: String, s2: String): Double {
val s1_len = s1.length
val s2_len = s2.length
if (s1_len == 0 && s2_len == 0) return 1.0
val match_distance = Math.max(s1_len, s2_len) / 2 - 1
val s1_matches = BooleanArray(s1_len)
val s2_matches = BooleanArray(s2_len)
var matches = 0
for (i in 0..s1_len - 1) {
val start = Math.max(0, i - match_distance)
val end = Math.min(i + match_distance + 1, s2_len)
(start..end - 1).find { j -> !s2_matches[j] && s1[i] == s2[j] } ?. let {
s1_matches[i] = true
s2_matches[it] = true
matches++
}
}
if (matches == 0) return 0.0
var t = 0.0
var k = 0
(0..s1_len - 1).filter { s1_matches[it] }.forEach { i ->
while (!s2_matches[k]) k++
if (s1[i] != s2[k]) t += 0.5
k++
}
val m = matches.toDouble()
return (m / s1_len + m / s2_len + (m - t) / m) / 3.0
}
}
fun main(args: Array<String>) {
println(Jaro.distance("MARTHA", "MARHTA"))
println(Jaro.distance("DIXON", "DICKSONX"))
println(Jaro.distance("JELLYFISH", "SMELLYFISH"))
}
Mathematica / Wolfram Language
ClearAll[JaroDistance]
JaroDistance[s_String, t_String] := Module[{slen, tlen, maxdistance, smatches, tmatches, matches, transpositions, start, end, k, schar, tchar},
slen = StringLength[s];
tlen = StringLength[t];
schar = Characters[s];
tchar = Characters[t];
If[slen == tlen == 0,
1
,
maxdistance = Floor[Max[slen, tlen]/2] - 1;
smatches = ConstantArray[False, slen];
tmatches = ConstantArray[False, tlen];
matches = transpositions = 0;
Do[
start = Max[0, i - maxdistance];
end = Min[i + maxdistance + 1, tlen];
start = Max[1, i - maxdistance];
end = Min[i + maxdistance + 1, tlen];
Do[
If[! tmatches[[j]],
If[schar[[i]] == tchar[[j]],
smatches[[i]] = True;
tmatches[[j]] = True;
matches++;
Break[];
]
]
,
{j, start, end}
]
,
{i, slen}
];
If[matches == 0,
0
,
k = 1;
Do[
If[smatches[[i]],
While[! tmatches[[k]],
k++;
];
If[schar[[i]] != tchar[[k]],
transpositions++;
];
k++;
]
,
{i, slen}
];
N@(matches/slen + matches/tlen + (matches - transpositions/2)/matches)/3
]
]
]
JaroDistance["DWAYNE", "DUANE"]
JaroDistance["MARTHA", "MARHTA"]
JaroDistance["DIXON", "DICKSONX"]
JaroDistance["JELLYFISH", "SMELLYFISH"]
- Output:
0.822222 0.944444 0.766667 0.896296
Nim
import lenientops
func jaro(s1, s2: string): float =
if s1.len == 0 and s2.len == 0: return 1
if s1.len == 0 or s2.len == 0: return 0
let matchDistance = max(s1.len, s2.len) div 2 - 1
var s1Matches = newSeq[bool](s1.len)
var s2Matches = newSeq[bool](s2.len)
var matches = 0
for i in 0..s1.high:
for j in max(0, i - matchDistance)..min(i + matchDistance, s2.high):
if not s2Matches[j] and s1[i] == s2[j]:
s1Matches[i] = true
s2Matches[j] = true
inc matches
break
if matches == 0: return 0
var transpositions = 0.0
var k = 0
for i in ..s1.high:
if not s1Matches[i]: continue
while not s2Matches[k]: inc k
if s1[i] != s2[k]: transpositions += 0.5
inc k
result = (matches / s1.len + matches / s2.len + (matches - transpositions) / matches) / 3
echo jaro("MARTHA", "MARHTA")
echo jaro("DIXON", "DICKSONX")
echo jaro("JELLYFISH", "SMELLYFISH")
- Output:
0.9444444444444445 0.7666666666666666 0.8962962962962964
Objeck
class JaroDistance {
function : Main(args : String[]) ~ Nil {
Jaro("MARTHA", "MARHTA")->PrintLine();
Jaro("DIXON", "DICKSONX")->PrintLine();
Jaro("JELLYFISH", "SMELLYFISH")->PrintLine();
}
function : Jaro(s : String, t : String) ~ Float {
s_len := s->Size();
t_len := t->Size();
if (s_len = 0 & t_len = 0) { return 1; };
match_distance := Int->Max(s_len, t_len) / 2 - 1;
s_matches := Bool->New[s_len];
t_matches := Bool->New[t_len];
matches := 0;
transpositions := 0;
for (i := 0; i < s_len; i++;) {
start := Int->Max(0, i-match_distance);
end := Int->Min(i+match_distance+1, t_len);
for (j := start; j < end; j++;) {
if (t_matches[j]) { continue; };
if (s->Get( i) <> t->Get( j)) { continue; };
s_matches[i] := true;
t_matches[j] := true;
matches++;
break;
};
};
if (matches = 0) { return 0; };
k := 0;
for (i := 0; i < s_len; i++;) {
if (<>s_matches[i]) { continue; };
while (<>t_matches[k]) { k++; };
if (s->Get( i) <> t->Get( k)) { transpositions++; };
k++;
};
return ((matches->As(Float) / s_len) +
(matches->As(Float) / t_len) +
((matches->As(Float) - transpositions/2.0) / matches)) / 3.0;
}
}- Output:
0.944444 0.766667 0.896296
PARI/GP
This version was translated from Java and Perl.
\\Jaro distance between 2 strings s1 and s2.
\\ 4/12/16 aev
jaroDist(s1,s2)={
my(vt1=Vecsmall(s1),vt2=Vecsmall(s2),n1=#s1,n2=#s2,d,
md=max(n1,n2)\2-1,cs,ce,mc=0,tr=0,k=1,ds,
s1m=vector(n1,z,0),s2m=vector(n2,z,0));
if(!n1||!n2, return(0));
for(i=1,n1,
cs=max(1,i-md);
ce=min(i+md+1,n2);
for(j=cs,ce,
if(s2m[j],next);
if(vt1[i]!=vt2[j], next);
mc++; s1m[i]=1; s2m[j]=1; break;
);\\fend j
);\\fend i
if(!mc, return(0));
for(i=1,n1,
if(!s1m[i], next);
while(!s2m[k], k++);
if(vt1[i]!=vt2[k], tr++);
k++
);\\fend i
d=(mc/n1+mc/n2+(mc-tr/2)/mc)/3.0;
ds=Strprintf("%.5f",d);
print(" *** Jaro distance is: ",ds," for strings: ",s1,", ",s2);
return(d);
}
{ \\ Testing:
jaroDist("MARTHA","MARHTA");
jaroDist("DIXON","DICKSONX");
jaroDist("JELLYFISH","SMELLYFISH");
jaroDist("DWAYNE","DUANE");
}- Output:
*** Jaro distance is: 0.94444 for strings: MARTHA, MARHTA *** Jaro distance is: 0.76667 for strings: DIXON, DICKSONX *** Jaro distance is: 0.89630 for strings: JELLYFISH, SMELLYFISH *** Jaro distance is: 0.82222 for strings: DWAYNE, DUANE
Pascal
program Jaro_distance;
uses SysUtils, Math;
//converted from C source by /u/bleuge
function ssJaroWinkler(s1, s2: string): double;
var
l1, l2, match_distance, matches, i, k, trans: integer;
bs1, bs2: array[1..255] of boolean; //used to avoid getmem, max string length is 255
begin
l1 := length(s1);
l2 := length(s2);
fillchar(bs1, sizeof(bs1), 0); //set booleans to false
fillchar(bs2, sizeof(bs2), 0);
if l1 = 0 then
if l2 = 0 then
exit(1)
else
exit(0);
match_distance := (max(l1, l2) div 2) - 1;
matches := 0;
trans := 0;
for i := 1 to l1 do
begin
for k := max(1, i - match_distance) to min(i + match_distance, l2) do
begin
if bs2[k] then
continue;
if s1[i] <> s2[k] then
continue;
bs1[i] := true;
bs2[k] := true;
inc(matches);
break;
end;
end;
if matches = 0 then
exit(0);
k := 1;
for i := 1 to l1 do
begin
if (bs1[i] = false) then
continue;
while (bs2[k] = false) do
inc(k);
if s1[i] <> s2[k] then
inc(trans);
inc(k);
end;
trans := trans div 2;
result := ((matches / l1) + (matches / l2) + ((matches - trans) / matches)) / 3;
end;
begin
//test
writeln(formatfloat('0.######', ssJaroWinkler('DWAYNE', 'DUANE')));
writeln(formatfloat('0.######', ssJaroWinkler('MARTHA', 'MARHTA')));
writeln(formatfloat('0.######', ssJaroWinkler('DIXON', 'DICKSONX')));
writeln(formatfloat('0.######', ssJaroWinkler('JELLYFISH', 'SMELLYFISH')));
{$IFNDEF LINUX}readln;{$ENDIF}
end.
- Output:
0,822222 0,944444 0,766667 0,896296
Perl
use strict;
use warnings;
use List::Util qw(min max);
sub jaro {
my($s, $t) = @_;
my(@s_matches, @t_matches, $matches);
return 1 if $s eq $t;
my($s_len, @s) = (length $s, split //, $s);
my($t_len, @t) = (length $t, split //, $t);
my $match_distance = int (max($s_len, $t_len) / 2) - 1;
for my $i (0 .. $#s) {
my $start = max(0, $i - $match_distance);
my $end = min($i + $match_distance + 1, $t_len);
for my $j ($start .. $end - 1) {
next if $t_matches[$j] or $s[$i] ne $t[$j];
($s_matches[$i], $t_matches[$j]) = (1, 1);
$matches++ and last;
}
}
return 0 unless $matches;
my($k, $transpositions) = (0, 0);
for my $i (0 .. $#s) {
next unless $s_matches[$i];
$k++ until $t_matches[$k];
$transpositions++ if $s[$i] ne $t[$k];
$k++;
}
( $matches/$s_len + $matches/$t_len + (($matches - $transpositions/2) / $matches) ) / 3;
}
printf "%.3f\n", jaro(@$_[0], @$_[1]) for
['MARTHA', 'MARHTA'], ['DIXON', 'DICKSONX'], ['JELLYFISH', 'SMELLYFISH'],
['I repeat myself', 'I repeat myself'], ['', ''];
- Output:
0.944 0.767 0.896 1.000 1.000
Phix
function jaro(string str1, str2) str1 = trim(upper(str1)) str2 = trim(upper(str2)) integer len1 = length(str1), len2 = length(str2), match_distance = floor(max(len1,len2)/2)-1, match_count = 0, half_transposed = 0 if len1==0 then return len2==0 end if -- count the number of matches sequence m1 = repeat(false,len1), m2 = repeat(false,len2) for i=1 to len1 do for k=max(1,i-match_distance) to min(len2,i+match_distance) do if not m2[k] then if str1[i]=str2[k] then m1[i] = true m2[k] = true match_count += 1 exit end if end if end for end for if match_count==0 then return 0 end if -- count the number of half-transpositions integer k = 1 for i=1 to len1 do if m1[i] then while not m2[k] do k += 1 end while half_transposed += (str1[i]!=str2[k]) k += 1 end if end for integer transpositions = floor(half_transposed/2), not_transposed = match_count - transpositions -- -- return the average of: -- percentage/fraction of the first string matched, -- percentage/fraction of the second string matched, and -- percentage/fraction of matches that were not transposed. -- return (match_count/len1 + match_count/len2 + not_transposed/match_count)/3 end function constant testcouples = {{"CRATE","TRACE"}, {"JONES","JOHNSON"}, {"ABCVWXYZ","CABVWXYZ"}, {"DWAYNE","DUANE"}, {"MARTHA", "MARHTA"}, {"DIXON", "DICKSONX"}, {"JELLYFISH", "SMELLYFISH"}} for i=1 to length(testcouples) do string {s1, s2} = testcouples[i] printf(1,"%f <== jaro(\"%s\", \"%s\")\n",{jaro(s1,s2),s1,s2}) end for
- Output:
0.733333 <== jaro("CRATE", "TRACE")
0.790476 <== jaro("JONES", "JOHNSON")
0.958333 <== jaro("ABCVWXYZ", "CABVWXYZ")
0.822222 <== jaro("DWAYNE", "DUANE")
0.944444 <== jaro("MARTHA", "MARHTA")
0.766667 <== jaro("DIXON", "DICKSONX")
0.896296 <== jaro("JELLYFISH", "SMELLYFISH")
Python
Procedural
'''Jaro distance'''
from __future__ import division
def jaro(s, t):
'''Jaro distance between two strings.'''
s_len = len(s)
t_len = len(t)
if s_len == 0 and t_len == 0:
return 1
match_distance = (max(s_len, t_len) // 2) - 1
s_matches = [False] * s_len
t_matches = [False] * t_len
matches = 0
transpositions = 0
for i in range(s_len):
start = max(0, i - match_distance)
end = min(i + match_distance + 1, t_len)
for j in range(start, end):
if t_matches[j]:
continue
if s[i] != t[j]:
continue
s_matches[i] = True
t_matches[j] = True
matches += 1
break
if matches == 0:
return 0
k = 0
for i in range(s_len):
if not s_matches[i]:
continue
while not t_matches[k]:
k += 1
if s[i] != t[k]:
transpositions += 1
k += 1
return ((matches / s_len) +
(matches / t_len) +
((matches - transpositions / 2) / matches)) / 3
def main():
'''Tests'''
for s, t in [('MARTHA', 'MARHTA'),
('DIXON', 'DICKSONX'),
('JELLYFISH', 'SMELLYFISH')]:
print("jaro(%r, %r) = %.10f" % (s, t, jaro(s, t)))
if __name__ == '__main__':
main()
- Output:
jaro('MARTHA', 'MARHTA') = 0.9444444444
jaro('DIXON', 'DICKSONX') = 0.7666666667
jaro('JELLYFISH', 'SMELLYFISH') = 0.8962962963
Composition of pure functions
'''Jaro distance between two strings'''
from functools import reduce
import itertools
# --------------------- JARO FUNCTION ----------------------
# jaro :: String -> String -> Float
def jaro(x):
'''The Jaro distance between two strings.'''
def go(s1, s2):
m, t = ap(compose(Tuple, len))(
transpositionSum
)(matches(s1, s2))
return 0 if 0 == m else (
(1 / 3) * ((m / len(s1)) + (
m / len(s2)
) + ((m - t) / m))
)
return lambda y: go(x, y)
# -------------------------- TEST --------------------------
# main :: IO ()
def main():
'''Sample word pairs'''
print(
fTable('Jaro distances:\n')(str)(
showPrecision(3)
)(
uncurry(jaro)
)([
("DWAYNE", "DUANE"),
("MARTHA", "MARHTA"),
("DIXON", "DICKSONX"),
("JELLYFISH", "SMELLYFISH")
])
)
# ----------------- JARO HELPER FUNCTIONS ------------------
# transpositionSum :: [(Int, Char)] -> Int
def transpositionSum(xs):
'''A count of the transpositions in xs.'''
def f(a, xy):
x, y = xy
return 1 + a if fst(x) > fst(y) else a
return reduce(f, zip(xs, xs[1:]), 0)
# matches :: String -> String -> [(Int, Char)]
def matches(s1, s2):
'''A list of (Index, Char) correspondences
between the two strings s1 and s2.'''
[(_, xs), (l2, ys)] = sorted(map(
ap(compose(Tuple, len))(list), [s1, s2]
))
r = l2 // 2 - 1
# match :: (Int, (Char, Int)) -> (Int, Char)
def match(a, nc):
n, c = nc
offset = max(0, n - (1 + r))
def indexChar(x):
return a + [(offset + x, c)]
return maybe(a)(indexChar)(
elemIndex(c)(
drop(offset)(take(n + r)(ys))
)
)
return reduce(match, enumerate(xs), [])
# ------------------- GENERIC FUNCTIONS --------------------
# Just :: a -> Maybe a
def Just(x):
'''Constructor for an inhabited Maybe (option type) value.
Wrapper containing the result of a computation.
'''
return {'type': 'Maybe', 'Nothing': False, 'Just': x}
# Nothing :: Maybe a
def Nothing():
'''Constructor for an empty Maybe (option type) value.
Empty wrapper returned where a computation is not possible.
'''
return {'type': 'Maybe', 'Nothing': True}
# Tuple (,) :: a -> b -> (a, b)
def Tuple(x):
'''Constructor for a pair of values,
possibly of two different types.
'''
def go(y):
return (
x + (y,)
) if isinstance(x, tuple) else (x, y)
return go
# ap :: (a -> b -> c) -> (a -> b) -> a -> c
def ap(f):
'''Applicative instance for functions.
'''
def go(g):
def fxgx(x):
return f(x)(
g(x)
)
return fxgx
return go
# compose :: ((a -> a), ...) -> (a -> a)
def compose(*fs):
'''Composition, from right to left,
of a series of functions.
'''
def go(f, g):
def fg(x):
return f(g(x))
return fg
return reduce(go, fs, lambda x: x)
# drop :: Int -> [a] -> [a]
# drop :: Int -> String -> String
def drop(n):
'''The sublist of xs beginning at
(zero-based) index n.
'''
def go(xs):
if isinstance(xs, (list, tuple, str)):
return xs[n:]
else:
take(n)(xs)
return xs
return go
# elemIndex :: Eq a => a -> [a] -> Maybe Int
def elemIndex(x):
'''Just the index of the first element in xs
which is equal to x,
or Nothing if there is no such element.
'''
def go(xs):
try:
return Just(xs.index(x))
except ValueError:
return Nothing()
return go
# fst :: (a, b) -> a
def fst(tpl):
'''First member of a pair.'''
return tpl[0]
# maybe :: b -> (a -> b) -> Maybe a -> b
def maybe(v):
'''Either the default value v, if m is Nothing,
or the application of f to x,
where m is Just(x).
'''
return lambda f: lambda m: v if (
None is m or m.get('Nothing')
) else f(m.get('Just'))
# showPrecision Int -> Float -> String
def showPrecision(n):
'''A string showing a floating point number
at a given degree of precision.'''
return lambda x: str(round(x, n))
# fTable :: String -> (a -> String) ->
# (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
'''Heading -> x display function -> fx display function ->
f -> xs -> tabular string.
'''
def gox(xShow):
def gofx(fxShow):
def gof(f):
def goxs(xs):
ys = [xShow(x) for x in xs]
w = max(map(len, ys))
def arrowed(x, y):
return y.rjust(w, ' ') + (
' -> ' + fxShow(f(x))
)
return s + '\n' + '\n'.join(
map(arrowed, xs, ys)
)
return goxs
return gof
return gofx
return gox
# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
islice = itertools.islice
def go(xs):
return (
xs[0:n]
if isinstance(xs, (list, tuple))
else list(islice(xs, n))
)
return go
# uncurry :: (a -> b -> c) -> ((a, b) -> c)
def uncurry(f):
'''A function over a tuple derived from a curried function.'''
return lambda xy: f(xy[0])(
xy[1]
)
# MAIN ---
if __name__ == '__main__':
main()
- Output:
Jaro distances:
('DWAYNE', 'DUANE') -> 0.822
('MARTHA', 'MARHTA') -> 0.944
('DIXON', 'DICKSONX') -> 0.767
('JELLYFISH', 'SMELLYFISH') -> 0.896
Racket
(kinda)
Returns an exact value for the Jaro distance.
#lang racket/base
;; {{trans|C}}
(require data/bit-vector)
(define (jaro-distance str1 str2)
(define str1-len (string-length str1))
(define str2-len (string-length str2))
(cond
[(and (zero? str1-len) (zero? str2-len)) 0]
[(or (zero? str1-len) (zero? str2-len)) 1]
[else
;; vectors of bools that signify if that char in the matching string has a match
(define str1-matches (make-bit-vector str1-len))
(define str2-matches (make-bit-vector str2-len))
(define matches
;; max distance between two chars to be considered matching
(let ((match-distance (sub1 (quotient (max str1-len str2-len) 2))))
(for/fold ((matches 0))
((i (in-range 0 str1-len))
(c1 (in-string str1)))
(define start (max 0 (- i match-distance)))
(define end (min (+ i match-distance 1) str2-len))
(for/fold ((matches matches))
((k (in-range start end))
(c2 (in-string str2 start))
#:unless (bit-vector-ref str2-matches k) ; if str2 already has a match continue
#:when (char=? c1 c2) ; if str1 and str2 are not
#:final #t)
;; otherwise assume there is a match
(bit-vector-set! str1-matches i #t)
(bit-vector-set! str2-matches k #t)
(add1 matches)))))
(cond
[(zero? matches) 0]
[else
(define-values (transpositions*2 k+)
(for/fold ((transpositions 0) (k 0))
((i (in-range 0 str1-len))
(c1 (in-string str1))
(b1 (in-bit-vector str1-matches))
;; if there are no matches in str1 continue
#:when b1)
(define k+ (for/first ((k+ (in-range k str2-len))
(b2 (in-bit-vector str2-matches k))
#:when b2)
k+))
(values
(+ transpositions (if (char=? c1 (string-ref str2 k+)) 0 1)) ; increment transpositions
(add1 k+)))) ;; while there is no match in str2 increment k
;; divide the number of transpositions by two as per the algorithm specs
;; this division is valid because the counted transpositions include both
;; instances of the transposed characters.
(define transpositions (quotient transpositions*2 2))
;; return the Jaro distance
(/ (+ (/ matches str1-len)
(/ matches str2-len)
(/ (- matches transpositions) matches))
3)])]))
(module+ test
(jaro-distance "MARTHA" "MARHTA"); 0.944444
(exact->inexact (jaro-distance "MARTHA" "MARHTA")); 0.944444
(jaro-distance "DIXON" "DICKSONX"); 0.766667
(exact->inexact (jaro-distance "DIXON" "DICKSONX")); 0.766667
(jaro-distance "JELLYFISH" "SMELLYFISH"); 0.896296
(exact->inexact (jaro-distance "JELLYFISH" "SMELLYFISH"))); 0.896296
- Output:
The exact->inexact calls in the tests give an inexact, floating point version of the rational values.
17/18 0.9444444444444444 23/30 0.7666666666666667 121/135 0.8962962962962963
Raku
(formerly Perl 6)
sub jaro ($s, $t) {
return 1 if $s eq $t;
my $s-len = + my @s = $s.comb;
my $t-len = + my @t = $t.comb;
my $match-distance = ($s-len max $t-len) div 2 - 1;
my ($matches, @s-matches, @t-matches);
for ^@s -> $i {
my $start = 0 max $i - $match-distance;
my $end = $i + $match-distance min ($t-len - 1);
for $start .. $end -> $j {
next if @t-matches[$j] or @s[$i] ne @t[$j];
(@s-matches[$i], @t-matches[$j]) = (1, 1);
$matches++ and last;
}
}
return 0 unless $matches;
my ($k, $transpositions) = (0, 0);
for ^@s -> $i {
next unless @s-matches[$i];
$k++ until @t-matches[$k];
$transpositions++ if @s[$i] ne @t[$k];
$k++;
}
( $matches/$s-len + $matches/$t-len + (($matches - $transpositions/2) / $matches) ) / 3
}
say jaro(.key, .value).fmt: '%.3f' for
'MARTHA' => 'MARHTA', 'DIXON' => 'DICKSONX', 'JELLYFISH' => 'SMELLYFISH',
'I repeat myself' => 'I repeat myself', '' => '';
- Output:
0.944 0.767 0.896 1.000 1.000
REXX
/*REXX program computes the Jaro distance between two strings (or a list of strings).*/
@.= /*define a default for the @. array. */
parse arg @.1 /*obtain an optional character string. */
if @.1='' then do; @.1= 'MARTHA MARHTA' /*Nothing specified? Use the defaults.*/
@.2= 'DIXON DICKSONX'
@.3= 'JELLYFISH SMELLYFISH'
@.4= 'DWAYNE DUANE'
end /* [↑] embedded blanks are shown as is.*/
do j=1 while @.j\=='' /*process all the strings in the list. */
d= jaroD(@.j)
say 'Jaro distance is ' format(d, , 8) " for strings: " @.j
end /*j*/ /* └──── digits past the decimal point.*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
jaroD: procedure; arg s.1 s.2 .; L1= length(s.1); L2= length(s.2); m= 0
if L1==0 | L2==0 then return 0 /*check if any string is a null string.*/
f= max(L1, L2) % 2 - 1 /*calculate furthest distanced allowed.*/
r.= 0 /* [↓] see if the char is near enough.*/
do k=1 for L1; p= pos( substr(s.1, k, 1), s.2, max(1, k-f) )
r.k= p
if p\==0 & abs(p-k)<=f then m= m+1 /*if near enough, count it as a match. */
else r.k= 0 /* ··· otherwise, don't count it.*/
end /*k*/
t= 0
do o=1 for L1; om= o - 1; if r.o==0 | r.om==0 then iterate
if pos( substr(s.1, o, 1), s.2)==0 then iterate
if r.o<r.om then t= t + 1
end /*o*/ /* [↑] count number of transpositions.*/
if m==0 then return 0
return (m/L1 + m/L2 + (m-t)/m) / 3
- output when using the default inputs:
Jaro distance is 0.94444444 for strings: MARTHA MARHTA Jaro distance is 0.76666667 for strings: DIXON DICKSONX Jaro distance is 0.89629630 for strings: JELLYFISH SMELLYFISH Jaro distance is 0.82222222 for strings: DWAYNE DUANE
Ring
# Project : Jaro distance
decimals(12)
see " jaro (MARTHA, MARHTA) = " + jaro("MARTHA", "MARHTA") + nl
see " jaro (DIXON, DICKSONX) = " + jaro("DIXON", "DICKSONX") + nl
see " jaro (JELLYFISH, SMELLYFISH) = " + jaro("JELLYFISH", "SMELLYFISH") + nl
func jaro(word1, word2)
if len(word1) > len(word2)
swap(word1, word2)
ok
j = 1
t = 0
m = 0
s1 = len(word1)
s2 = len(word2)
maxdist = (s2 / 2) -1
for i = 1 to s1
if word1[i] = word2[j] and j < max(len(word2), len(word2)) + 1
m = m +1
word2[j] = char(32)
else
for j1 = max(1, i - maxdist) to min(s2 -1, i + maxdist)
if word1[i] = word2[j1]
t = t +1
m = m +1
word2[j1] = char(32)
if j1 > j and j1 < max(len(word2), len(word2)) + 1
j = j1
ok
ok
next
ok
if j < max(len(word2), len(word2))
j = j + 1
ok
next
if m = 0
return 0
ok
t = floor(t / 2)
return (m / s1 + m / s2 + ((m - t) / m)) / 3
func swap(a, b)
temp = a
a = b
b = temp
return [a, b]Output:
jaro (MARTHA, MARHTA) = 0.944444444444 jaro (DIXON, DICKSONX) = 0.766666666667 jaro (JELLYFISH, SMELLYFISH) = 0.896296296296
Ruby
def jaro(s, t)
return 1.0 if s == t
s_len = s.size
t_len = t.size
match_distance = ([s_len, t_len].max / 2) - 1
s_matches = []
t_matches = []
matches = 0.0
s_len.times do |i|
j_start = [0, i-match_distance].max
j_end = [i+match_distance, t_len-1].min
(j_start..j_end).each do |j|
t_matches[j] && next
s[i] == t[j] || next
s_matches[i] = true
t_matches[j] = true
matches += 1.0
break
end
end
return 0.0 if matches == 0.0
k = 0
transpositions = 0.0
s_len.times do |i|
s_matches[i] || next
k += 1 until t_matches[k]
s[i] == t[k] || (transpositions += 1.0)
k += 1
end
((matches / s_len) +
(matches / t_len) +
((matches - transpositions/2.0) / matches)) / 3.0
end
%w(
MARTHA MARHTA
DIXON DICKSONX
JELLYFISH SMELLYFISH
).each_slice(2) do |s,t|
puts "jaro(#{s.inspect}, #{t.inspect}) = #{'%.10f' % jaro(s, t)}"
end
- Output:
jaro("MARTHA", "MARHTA") = 0.9444444444
jaro("DIXON", "DICKSONX") = 0.7666666667
jaro("JELLYFISH", "SMELLYFISH") = 0.8962962963
Rust
use std::cmp;
pub fn jaro(s1: &str, s2: &str) -> f64 {
let s1_len = s1.len();
let s2_len = s2.len();
if s1_len == 0 && s2_len == 0 { return 1.0; }
let match_distance = cmp::max(s1_len, s2_len) / 2 - 1;
let mut s1_matches = vec![false; s1_len];
let mut s2_matches = vec![false; s2_len];
let mut m: isize = 0;
for i in 0..s1_len {
let start = cmp::max(0, i as isize - match_distance as isize) as usize;
let end = cmp::min(i + match_distance + 1, s2_len);
for j in start..end {
if !s2_matches[j] && s1.as_bytes()[i] == s2.as_bytes()[j] {
s1_matches[i] = true;
s2_matches[j] = true;
m += 1;
break;
}
}
}
if m == 0 { return 0.0; }
let mut t = 0.0;
let mut k = 0;
for i in 0..s1_len {
if s1_matches[i] {
while !s2_matches[k] { k += 1; }
if s1.as_bytes()[i] != s2.as_bytes()[k] { t += 0.5; }
k += 1;
}
}
let m = m as f64;
(m / s1_len as f64 + m / s2_len as f64 + (m - t) / m) / 3.0
}
fn main() {
let pairs = [("MARTHA", "MARHTA"), ("DIXON", "DICKSONX"), ("JELLYFISH", "SMELLYFISH")];
for p in pairs.iter() { println!("{}/{} = {}", p.0, p.1, jaro(p.0, p.1)); }
}
- Output:
MARTHA/MARHTA = 0.9444444444444445 DIXON/DICKSONX = 0.7666666666666666 JELLYFISH/SMELLYFISH = 0.8962962962962964
Scala
object Jaro extends App {
def distance(s1: String, s2: String): Double = {
val s1_len = s1.length
val s2_len = s2.length
if (s1_len == 0 && s2_len == 0) return 1.0
val match_distance = Math.max(s1_len, s2_len) / 2 - 1
val s1_matches = Array.ofDim[Boolean](s1_len)
val s2_matches = Array.ofDim[Boolean](s2_len)
var matches = 0
for (i <- 0 until s1_len) {
val start = Math.max(0, i - match_distance)
val end = Math.min(i + match_distance + 1, s2_len)
start until end find { j => !s2_matches(j) && s1(i) == s2(j) } match {
case Some(j) =>
s1_matches(i) = true
s2_matches(j) = true
matches += 1
case None =>
}
}
if (matches == 0) return 0.0
var t = 0.0
var k = 0
0 until s1_len filter s1_matches foreach { i =>
while (!s2_matches(k)) k += 1
if (s1(i) != s2(k)) t += 0.5
k += 1
}
val m = matches.toDouble
(m / s1_len + m / s2_len + (m - t) / m) / 3.0
}
val strings = List(("MARTHA", "MARHTA"), ("DIXON", "DICKSONX"), ("JELLYFISH", "SMELLYFISH"))
strings.foreach { s => println(distance(s._1, s._2)) }
}
Sidef
func jaro(s, t) {
return 1 if (s == t)
var s_len = s.len
var t_len = t.len
var match_distance = ((s_len `max` t_len) // 2 - 1)
var s_matches = []
var t_matches = []
var matches = 0
var transpositions = 0
for i (^s_len) {
var start = (0 `max` i-match_distance)
var end = (i+match_distance `min` t_len-1)
for k (start..end) {
t_matches[k] && next
s[i] == t[k] || next
s_matches[i] = true
t_matches[k] = true
matches++
break
}
}
return 0 if (matches == 0)
var k = 0
for i (^s_len) {
s_matches[i] || next
while (!t_matches[k]) { ++k }
s[i] == t[k] || ++transpositions
++k
}
((matches / s_len) +
(matches / t_len) +
((matches - transpositions/2) / matches)) / 3
}
for pair in [
[%c"MARTHA", %c"MARHTA"],
[%c"DIXON", %c"DICKSONX"],
[%c"JELLYFISH", %c"SMELLYFISH"],
] {
say "jaro(#{pair.map{.join.dump}.join(', ')}) = #{'%.10f' % jaro(pair...)}"
}
- Output:
jaro("MARTHA", "MARHTA") = 0.9444444444
jaro("DIXON", "DICKSONX") = 0.7666666667
jaro("JELLYFISH", "SMELLYFISH") = 0.8962962963
Stata
Here we use the jarowinkler package from SSC. To install the package, type
ssc install jarowinkler
Now the program for the task:
clear
input str20 a str20 b
DWAYNE DUANE
MARTHA MARHTA
DIXON DICKSONX
JELLYFISH SMELLYFISH
end
jarowinkler a b, gen(jw) jaroonly(jaro)
format %8.3f jaro
format %-20s a b
list a b jaro
Output
+--------------------------------+
| a b jaro |
|--------------------------------|
1. | DWAYNE DUANE 0.822 |
2. | MARTHA MARHTA 0.944 |
3. | DIXON DICKSONX 0.767 |
4. | JELLYFISH SMELLYFISH 0.896 |
+--------------------------------+
Swift
func jaroWinklerMatch(_ s: String, _ t: String) -> Double {
let s_len: Int = s.count
let t_len: Int = t.count
if s_len == 0 && t_len == 0 {
return 1.0
}
if s_len == 0 || t_len == 0 {
return 0.0
}
var match_distance: Int = 0
if s_len == 1 && t_len == 1 {
match_distance = 1
} else {
match_distance = ([s_len, t_len].max()!/2) - 1
}
var s_matches = [Bool]()
var t_matches = [Bool]()
for _ in 1...s_len {
s_matches.append(false)
}
for _ in 1...t_len {
t_matches.append(false)
}
var matches: Double = 0.0
var transpositions: Double = 0.0
for i in 0...s_len-1 {
let start = [0, (i-match_distance)].max()!
let end = [(i + match_distance), t_len-1].min()!
if start > end {
break
}
for j in start...end {
if t_matches[j] {
continue
}
if s[String.Index.init(encodedOffset: i)] != t[String.Index.init(encodedOffset: j)] {
continue
}
// We must have a match
s_matches[i] = true
t_matches[j] = true
matches += 1
break
}
}
if matches == 0 {
return 0.0
}
var k = 0
for i in 0...s_len-1 {
if !s_matches[i] {
continue
}
while !t_matches[k] {
k += 1
}
if s[String.Index.init(encodedOffset: i)] != t[String.Index.init(encodedOffset: k)] {
transpositions += 1
}
k += 1
}
let top = (matches / Double(s_len)) + (matches / Double(t_len)) + (matches - (transpositions / 2)) / matches
return top/3
}
print("DWAYNE/DUANE:", jaroWinklerMatch("DWAYNE", "DUANE"))
print("MARTHA/MARHTA:", jaroWinklerMatch("MARTHA", "MARHTA"))
print("DIXON/DICKSONX:", jaroWinklerMatch("DIXON", "DICKSONX"))
print("JELLYFISH/SMELLYFISH:", jaroWinklerMatch("JELLYFISH", "SMELLYFISH"))
- Output:
DWAYNE/DUANE: 0.822222222222222 MARTHA/MARHTA: 0.944444444444445 DIXON/DICKSONX: 0.766666666666667 JELLYFISH/SMELLYFISH: 0.896296296296296
Tcl
proc jaro {s1 s2} {
set l1 [string length $s1]
set l2 [string length $s2]
set dmax [expr {max($l1, $l2)/2 - 1}] ;# window size to scan for matches
set m1 {} ;# match indices
set m2 {}
for {set i 0} {$i < $l1} {incr i} {
set jmin [expr {$i - $dmax}] ;# don't worry about going out-of-bounds
set jmax [expr {$i + $dmax}] ;# because [string index] will return {} safely
for {set j $jmin} {$j <= $jmax} {incr j} {
if {$j in $m2} continue ;# don't double-count matches
if {[string index $s1 $i] eq [string index $s2 $j]} {
lappend m1 $i
lappend m2 $j
break
}
}
}
set T 0 ;# number of transpositions
set oj -1
foreach j $m2 {
if {$j < $oj} {incr T}
set oj $j
}
set T [expr {$T / 2.0}]
set M [expr {1.0 * [llength $m1]}] ;# number of matches
expr { ( ($M / $l1) + ($M / $l2) + (($M - $T) / $M) ) / 3.0 }
}
foreach {s t} {
DWAYNE DUANE
MARTHA MARHTA
DIXON DICKSONX
JELLYFISH SMELLYFISH
} {
puts "[jaro $s $t]:\t$s / $t"
}
- Output:
0.8222222222222223: DWAYNE / DUANE 0.9722222222222222: MARTHA / MARHTA 0.7666666666666666: DIXON / DICKSONX 0.8962962962962964: JELLYFISH / SMELLYFISH
Turbo-Basic XL
10 DIM Word_1$(20), Word_2$(20), Z$(20)
11 CLS
20 Word_1$="MARTHA" : Word_2$="MARHTA" : ? Word_1$;" - ";Word_2$ : EXEC _JWD_ : ?
30 Word_1$="DIXON" : Word_2$="DICKSONX" : ? Word_1$;" - ";Word_2$ : EXEC _JWD_ : ?
40 Word_1$="JELLYFISH" : Word_2$="SMELLYFISH" : ? Word_1$;" - ";Word_2$ : EXEC _JWD_ : ?
11000 END
12000 REM JaroWinklerDistance INPUT(Word_1$, Word_2$) USE(Z$, I, J, K, L, M, N, S1, S2, Min, Max) RETURN(FLOAT Result)
12000 PROC _JWD_
12010 Result=0 : S1=LEN(Word_1$) : S2=LEN(Word_2$)
12020 IF S1>S2 THEN Z$=Word_1$ : Word_1$=Word_2$ : Word_2$=Z$ : M=S1 : S1=S2 : S2=M
12030 J=1: M=0 : N=0 : L=INT(S2/2) : Z$=Word_2$
12040 FOR I=1 TO S1
12050 IF Word_1$(I,I)=Word_2$(J,J) THEN M=M+1: Word_2$(J,J)=" ": GO# JMP_JWD
12060 Max=1 : IF Max<(I-L) THEN Max=I-L
12070 Min=S2 : IF Min>(I+L-1) THEN Min=I+L-1
12080 FOR K=Max TO Min
12090 IF Word_1$(I,I)=Word_2$(K,K) THEN N=N+1: M=M+1: Word_2$(K,K)=" ": IF K>J THEN J=K
12100 NEXT K
12110 #JMP_JWD : IF J<S2 THEN J=J+1
12120 NEXT I
12130 IF M=0
12140 Result=0 : REM jaro distance
12150 ELSE
12160 N=INT(N/2)
12170 Result=(M/S1+M/S2+((M-N)/M))/3. : REM jaro distance
12180 ENDIF
12190 ? "Jaro Distance=";Result
12200 Min=S1 : IF Min>S2 THEN Min=S2
12210 M=Min : IF M>3 THEN M=3
12220 M=M+1 : L=0 : Word_2$=Z$ : IF M>Min THEN M=Min
12230 FOR I=1 TO M
12240 IF Word_1$(I,I)=Word_2$(I,I)
12250 L=L+1
12260 ELSE
12270 EXIT
12280 ENDIF
12290 NEXT I
12300 Result=Result + (L*0.1*(1.0 - Result)) : REM Winkler
12310 ? "Jaro Winkler Distance=";Result
12320 ENDPROC- Output:
MARTHA, MARHTA: 0.9444444433 DIXON, DICKSONX: 0.7666666666 JELLYFISH, SMELLYFISH: 0.8962962933
VBA
Option Explicit
Function JaroWinkler(text1 As String, text2 As String, Optional p As Double = 0.1) As Double
Dim dummyChar, match1, match2 As String
Dim i, f, t, j, m, l, s1, s2, limit As Integer
i = 1
Do
dummyChar = Chr(i)
i = i + 1
Loop Until InStr(1, text1 & text2, dummyChar, vbTextCompare) = 0
s1 = Len(text1)
s2 = Len(text2)
limit = WorksheetFunction.Max(0, Int(WorksheetFunction.Max(s1, s2) / 2) - 1)
match1 = String(s1, dummyChar)
match2 = String(s2, dummyChar)
For l = 1 To WorksheetFunction.Min(4, s1, s2)
If Mid(text1, l, 1) <> Mid(text2, l, 1) Then Exit For
Next l
l = l - 1
For i = 1 To s1
f = WorksheetFunction.Min(WorksheetFunction.Max(i - limit, 1), s2)
t = WorksheetFunction.Min(WorksheetFunction.Max(i + limit, 1), s2)
j = InStr(1, Mid(text2, f, t - f + 1), Mid(text1, i, 1), vbTextCompare)
If j > 0 Then
m = m + 1
text2 = Mid(text2, 1, f + j - 2) & dummyChar & Mid(text2, f + j)
match1 = Mid(match1, 1, i - 1) & Mid(text1, i, 1) & Mid(match1, i + 1)
match2 = Mid(match2, 1, f + j - 2) & Mid(text1, i, 1) & Mid(match2, f + j)
End If
Next i
match1 = Replace(match1, dummyChar, "", 1, -1, vbTextCompare)
match2 = Replace(match2, dummyChar, "", 1, -1, vbTextCompare)
t = 0
For i = 1 To m
If Mid(match1, i, 1) <> Mid(match2, i, 1) Then t = t + 1
Next i
JaroWinkler = (m / s1 + m / s2 + (m - t / 2) / m) / 3
JaroWinkler = JaroWinkler + (1 - JaroWinkler) * l * WorksheetFunction.Min(0.25, p)
End Function
V (Vlang)
import math
fn jaro(str1 string, str2 string) f64 {
s1_len := str1.len
s2_len := str2.len
if s1_len == 0 && s2_len == 0 {
return 1
}
if s1_len == 0 || s2_len == 0 {
return 0
}
match_distance := math.max<int>(s1_len,s2_len)/2 - 1
mut str1_matches := []bool{len: s1_len}
mut str2_matches := []bool{len: s2_len}
mut matches := 0
mut transpositions := 0.0
for i in 0..s1_len {
start := math.max<int>(0,i - match_distance)
end := math.min<int>(i + match_distance, s2_len)
for k in start..end {
if str2_matches[k] {
continue
}
if str1[i] != str2[k] {
continue
}
str1_matches[i] = true
str2_matches[k] = true
matches++
break
}
}
if matches == 0 {
return 0
}
mut k := 0
for i in 0..s1_len {
if !str1_matches[i] {
continue
}
for !str2_matches[k] {
k++
}
if str1[i] != str2[k] {
transpositions++
}
k++
}
transpositions /= 2
return (matches/f64(s1_len) +
matches/f64(s2_len) +
(matches-transpositions)/matches) / 3
}
fn main() {
println(jaro("MARTHA", "MARHTA"))
println(jaro("DIXON", "DICKSONX"))
println(jaro("JELLYFISH", "SMELLYFISH"))
}- Output:
0.9444444444444445 0.7666666666666666 0.8962962962962964
Wren
import "./fmt" for Fmt
var jaro = Fn.new { |s1, s2|
var le1 = s1.count
var le2 = s2.count
if (le1 == 0 && le2 == 0) return 1
if (le1 == 0 || le2 == 0) return 0
var dist = (le2 > le1) ? le2 : le1
dist = (dist/2).floor - 1
var matches1 = List.filled(le1, false)
var matches2 = List.filled(le2, false)
var matches = 0
var transpos = 0
for (i in 0...s1.count) {
var start = i - dist
if (start < 0) start = 0
var end = i + dist + 1
if (end > le2) end = le2
var k = start
while (k < end) {
if (!(matches2[k] || s1[i] != s2[k])) {
matches1[i] = true
matches2[k] = true
matches = matches + 1
break
}
k = k + 1
}
}
if (matches == 0) return 0
var k = 0
for (i in 0...s1.count) {
if (matches1[i]) {
while(!matches2[k]) k = k + 1
if (s1[i] != s2[k]) transpos = transpos + 1
k = k + 1
}
}
transpos = transpos / 2
return (matches/le1 + matches/le2 + (matches - transpos)/matches) / 3
}
System.print(Fmt.f(0, jaro.call("MARTHA", "MARHTA")))
System.print(Fmt.f(0, jaro.call("DIXON", "DICKSONX")))
System.print(Fmt.f(0, jaro.call("JELLYFISH", "SMELLYFISH")))
- Output:
0.944444 0.766667 0.896296
zkl
//-->String of matched characters, ordered
fcn _jaro(str1,str2, matchDistance){
cs:=Sink(String);
foreach i,c in ([0..].zip(str1)){
str2.find(c,(0).max(i - matchDistance),i + matchDistance) :
if(Void!=_) cs.write(c);
}
cs.close()
}
fcn jaro(str1,str2){
s1Len,s2Len,matchDistance := str1.len(), str2.len(), s1Len.max(s2Len)/2 - 1;
cs12,cs21 := _jaro(str1,str2, matchDistance), _jaro(str2,str1, matchDistance);
matches:=cs12.len().toFloat();
if(not matches) return(0.0);
transpositions:=cs12.walker().zipWith('!=,cs21).filter().sum(0)/2;
( matches/s1Len + matches/s2Len +
((matches - transpositions)/matches) ) / 3.0
}foreach s,t in (T(
T("MARTHA","MARHTA"), T("DIXON","DICKSONX"), T("JELLYFISH","SMELLYFISH"))){
println(0'|jaro("%s","%s") = %.10f|.fmt(s,t,jaro(s,t)));
}- Output:
jaro("MARTHA","MARHTA") = 0.9444444444
jaro("DIXON","DICKSONX") = 0.7666666667
jaro("JELLYFISH","SMELLYFISH") = 0.8962962963
ZX Spectrum Basic
10 LET a$="MARTHA": LET b$="MARHTA": PRINT a$;", ";b$;": ";: GO SUB 1000: PRINT jaro
20 LET a$="DIXON": LET b$="DICKSONX": PRINT a$;", ";b$;": ";: GO SUB 1000: PRINT jaro
30 LET a$="JELLYFISH": LET b$="SMELLYFISH": PRINT a$;", ";b$;": ";: GO SUB 1000: PRINT jaro
900 STOP
1000 REM Jaro subroutine
1010 LET s1=LEN a$: LET s2=LEN b$: LET j=1: LET m=0: LET t=0
1030 IF s1>s2 THEN LET z$=a$: LET a$=b$: LET b$=z$: LET z=s1: LET s1=s2: LET s2=z
1035 LET maxdist=INT (s2/2)
1040 FOR i=1 TO s1
1050 IF a$(i)=b$(j) THEN LET m=m+1: LET b$(j)=" ": GO TO 2000
1080 FOR k=FN x(1,i-maxdist) TO FN n(s2,i+maxdist)
1090 IF a$(i)=b$(k) THEN LET t=t+1: LET m=m+1: LET b$(k)=" ": IF k>j THEN LET j=k
1100 NEXT k
2000 IF j<s2 THEN LET j=j+1:
2010 NEXT i
2020 IF m=0 THEN LET jaro=0: RETURN
2030 LET t=INT (t/2)
2040 LET jaro=(m/s1+m/s2+((m-t)/m))/3
2050 RETURN
5000 REM Functions
5010 DEF FN x(a,b)=(a AND a>b)+(b AND a<b)+(a AND a=b): REM max function
5020 DEF FN n(a,b)=(a AND a<b)+(b AND a>b)+(a AND a=b): REM min function
- Output:
MARTHA, MARHTA: 0.94444444 DIXON, DICKSONX: 0.76666667 JELLYFISH, SMELLYFISH: 0.8962963
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