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Self-Classify =  _ 0 0 Equal

=y classifies the items of the nub of y (that is, ~.y) according to equality with the items of y , producing a boolean table of shape #~.y by #y . For example:
   y=: 3 3 $ 'abcdef'
   y ; (~.y) ; (=y)
+---+---+-----+
|abc|abc|1 0 1|
|def|def|0 1 0|
|abc|   |     |
+---+---+-----+
  x=y is 1 if x is equal to y , and is otherwise 0 .

If x or y is a finite floating-point or complex number, the comparison is made with a tolerance t , normally 2 to the power _44 but also controlled by the fit conjunction !. , as in x=!.0 y . Formally, x=y is 1 if the magnitude of x-y does not exceed t times the larger of the magnitudes of x and y .

Tolerance applies similarly to other verbs as indicated for each, notably to Match (-:), to Floor (<.), and to Signum (*), but not to Grade (/:).
 

Both the monadic and dyadic cases of the verb = apply to nouns of any rank, and to boxed as well as simple nouns. For example:
   ]a=: ;: 'Try and try and try again.'
+---+---+---+---+---+------+
|Try|and|try|and|try|again.|
+---+---+---+---+---+------+

   ~. a
+---+---+---+------+
|Try|and|try|again.|
+---+---+---+------+

   =a
1 0 0 0 0 0
0 1 0 1 0 0
0 0 1 0 1 0
0 0 0 0 0 1

   a = <'and'
0 1 0 1 0 0
Because of the limited precision of the computer, results which should agree (such as 144*(13%144) and 13) may not; the tolerant comparison allows such a comparison to show agreement (a result 1). More or less stringent comparisons may be made by using the conjunction !. to specify a tolerance t , as in the function eq=: =!.t .



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