how to calculate distance between observations with coordinate points

[ffguo]

Hi,

I have a problem with calculating distance between observations, which is the variable model. Each observation contains 5 coordinate points, {fxi,fyi}, i=1 to 5; The dataset as following, is there any macro or for loop can do the calculation? Thanks!

obs	model	fx1	fy1	fx2	fy2	fx3	fy3	fx4	fy4	fx5	fy5
1	a	129	16.5	129	22.25	129	59.75	129	90.75	129	112.25
2	b	156.9375	18	156.9375	26.5	156.9375	69	156.9375	109.5	156.9375	137
3	c	140	26	140	31	140	76.5	140	116	140	142.75
4	d	109.7188	24	109.7188	29.5	109.7188	53.75	109.7188	87	109.7188	100.25
5	e	145.5	7	145.5	11.5	145.5	46.5	145.5	90	145.5	110.5
6	f	94.28125	15	94.28125	19.5	94.28125	47.5	94.28125	91.25	94.28125	111.25
7	g	150	28.5	150	34	150	83	150	126	150	172
8	a	147	9.5	147	17	147	62	147	102.5	147	141
9	b	91.4375	12.75	91.4375	17.75	91.4375	48.5	91.4375	82.75	91.4375	89.25
10	c	106.3438	2.25	106.3438	4.75	106.3438	34.5	106.3438	57.5	106.3438	78
11	d	130.9375	9.75	130.9375	14.75	130.9375	51.5	130.9375	79.5	130.9375	99.5
12	e	143.5625	21.5	143.5625	26.5	143.5625	74	143.5625	119.5	143.5625	142

[Reeza]

What would your distance calculation look like? 

Please include sample output. 

[ffguo]

Hi,

The function used to caluculate euclidean distance should be dis(distance between any two oberservation)= sum(squr((fyi1-fyi2)**2+(fxi1-fxi2)**2)),{fxi1,fyi1} from the first observation, the other from the second observation, i=1 to 5. Thanks

[Ksharp]

if it was Eduical distance, 

Data step also can do that.

data have;
infile cards truncover expandtabs;
input obs	model $	fx1	fy1	fx2	fy2	fx3	fy3	fx4	fy4	fx5	fy5;
cards;
1   a   129 16.5    129 22.25   129 59.75   129 90.75 129   112.25
2   b   156.9375    18  156.9375    26.5    156.9375    69  156.9375    109.5   156.9375    137
3   c   140 26  140 31  140 76.5    140 116 140 142.75
4   d   109.7188    24  109.7188    29.5    109.7188    53.75   109.7188    87  109.7188    100.25
5   e   145.5   7   145.5   11.5    145.5   46.5    145.5   90  145.5   110.5
6   f   94.28125    15  94.28125    19.5    94.28125    47.5    94.28125    91.25   94.28125    111.25
7   g   150 28.5    150 34  150 83  150 126 150 172
8   a   147 9.5 147 17  147 62  147 102.5   147 141
9   b   91.4375 12.75   91.4375 17.75   91.4375 48.5    91.4375 82.75   91.4375 89.25
10  c   106.3438    2.25    106.3438    4.75    106.3438    34.5    106.3438    57.5    106.3438    78
11  d   130.9375    9.75    130.9375    14.75   130.9375    51.5    130.9375    79.5    130.9375    99.5
12  e   143.5625    21.5    143.5625    26.5    143.5625    74  143.5625    119.5   143.5625    142
;
run;
proc iml;
var_x='fx1':'fx5';
var_y='fy1':'fy5';
use have;
read all var var_x into x;
read all var var_y into y;
close;

distance= sqrt((y-x)[,##]);

create distance var{distance};
append;
close;

data want;
 merge have distance;
run;

[ffguo]

Hi,

Thanks for help. This seems work but not get the right result, because the function used to caluculate euclidean distance is 

dis(distance between any two oberservation)= sum(squr((fyi1-fyi2)**2+(fxi1-fxi2)**2)),{fxi1,fyi1} from the first observation, the other from the second observation, i=1 to 5. So should the sum equation be modified? Thanks.

[Reeza]

Look at proc distance with method=Euclid. 

[Ksharp]

data have;
infile cards truncover expandtabs;
input obs	model $	fx1	fy1	fx2	fy2	fx3	fy3	fx4	fy4	fx5	fy5;
cards;
1   a   129 16.5    129 22.25   129 59.75   129 90.75 129   112.25
2   b   156.9375    18  156.9375    26.5    156.9375    69  156.9375    109.5   156.9375    137
3   c   140 26  140 31  140 76.5    140 116 140 142.75
4   d   109.7188    24  109.7188    29.5    109.7188    53.75   109.7188    87  109.7188    100.25
5   e   145.5   7   145.5   11.5    145.5   46.5    145.5   90  145.5   110.5
6   f   94.28125    15  94.28125    19.5    94.28125    47.5    94.28125    91.25   94.28125    111.25
7   g   150 28.5    150 34  150 83  150 126 150 172
8   a   147 9.5 147 17  147 62  147 102.5   147 141
9   b   91.4375 12.75   91.4375 17.75   91.4375 48.5    91.4375 82.75   91.4375 89.25
10  c   106.3438    2.25    106.3438    4.75    106.3438    34.5    106.3438    57.5    106.3438    78
11  d   130.9375    9.75    130.9375    14.75   130.9375    51.5    130.9375    79.5    130.9375    99.5
12  e   143.5625    21.5    143.5625    26.5    143.5625    74  143.5625    119.5   143.5625    142
;
run;
data want1;
 set have;
 array x{*} fx:;
 array y{*} fy:;
 sum=0;
 do i=1 to dim(x);
  sum+(y{i}-x{i})**2;
 end;
  distance=sqrt(sum);
 drop sum i;
run;

[Reeza]

@Ksharp I think the OP wants distance between different rows. 

[ffguo]

Correctly. But each row composed of 5 {fxi,fyi} points. If I used Proc distance, I won't get correct result. For proc distance with Euclid, the calculate function will be dist=sqrt[(fx11-fx12)**2+(fy11-fy12)**2+ (fx21-fx22)**2+ (fy21-fy22)**2+...+ (fx51-fx52)**2+ (fy51-fy52)**2]. However, what I want to get is: dist=sqrt[(fx11-fx12)**2+(fy11-fy12)**2]+ sqrt[(fx21-fx22)**2+(fy21-fy22)**2]+...+sqrt[(fx51-fx52)**2+ (fy51-fy52)**2].

[Reeza]

Are you sure? Post the code you've used please.

[ffguo]

proc distance data=use method= euclid out=want;
var interval(fx1 fy1 fx2 fy2 fx3 fy3 fx4 fy4 fx5 fy5);
id model;
run;
the distance between fist obs and second obs is 79.1, however, the correct value should be 156.6.

[Reeza]

It might be worth switching it to a long format then and grouping to be able to use the formula.

Otherwise a SQL cross join as long as you're willing to type  out the formula.

proc sql;

select a.*, b.fx1 as fx12, b.fy1 as fy12 ...,

sqrt[(fx11-fx12)**2+(fy11-fy12)**2]+ sqrt[(fx21-fx22)**2+(fy21-fy22)**2]+...+sqrt[(fx51-fx52)**2+ (fy51-fy52)**2] as dist

from have as a

cross join have as b;

quit;