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# 3B. Merge & Amend

Two arguments `x` and `y` can be merged by interleaving their items (necessarily of a common shape) as determined by a Boolean list of shape `x +&# y`. For example:

       x=: >;:'That they hunted from hill'
       y=: >;:'second time me to plain'
       b=: 0 1 1 0 0 1 0 0 1 1
       mrg=: 1 : '/:@/:@(x."_) { ,'
       x([ ; ] ; (,.b)"_ ; b mrg)y
    +----------------------+
    |That  |second|0|That  |
    |they  |time  |1|second|
    |hunted|me    |1|time  |
    |from  |to    |0|they  |
    |hill  |plain |0|hunted|
    |      |      |1|me    |
    |      |      |0|from  |
    |      |      |0|hill  |
    |      |      |1|to    |
    |      |      |1|plain |
    +----------------------+

The form of the function `b mrg` obtained by applying the adverb `mrg` suggests the form of a function `MRG` to be applied to a Boolean left argument and a right argument formed as the catenation of the original arguments. Thus:

       b mrg
    /:@/:@(0 1 1 0 0 1 0 0 1 1"_) { ,

       MRG=: /:@/:@[ { ]
       b MRG x,y
    That
    second
    time
    they
    hunted
    me
    from
    hill
    to
    plain

The argument b need not be Boolean, but may be anything of the requisite number of items that is in the domain of `/:`. For example:

       b=: 0 2 2 1 0 2 2 2 0 0 1 1 2 1 2 1 1 1 1 1
       y0=: 'abcd' [ y1=: '123456789' [ y2=: 'zzzzzzz'
       b MRG y0,y1,y2
    azz1bzzzcd23z4z56789

`a0=: mrg=: 1 : '/:@/:@(x."_) { ,'` | `x b mrg y` merges x and y
`m1=: MRG=: /:@/:@[ { ]` | `b MRG x,y` is equivalent to above
`d2=: alt=: ,@,.` | Merge items from x and y alternately

For example:

       x=: 'temr rtes'
       y=: 'h axbohr '
       x alt y
    the marx brothers

An argument can be amended by replacing those cells selected by an index, by the cells of another argument. For example:

       x=: 'ABCD' [ y=: 'abcdefghij'
       i=: 4 2 8 6
       i{y
    ecig

       ]z=: x i} y
    abBdAfDhCj

       m=: a.{~(a. i. 'A')+i.5 5
       ]i=: 2 # &.> i. # m
    +-------------------+
    |0 0|1 1|2 2|3 3|4 4|
    +-------------------+

       x=: '+-*%^'
       m ; (i{m) ; x ; x i} m
    +-----------------------+
    |ABCDE|AGMSY|+-*%^|+BCDE|
    |FGHIJ|     |     |F-HIJ|
    |KLMNO|     |     |KL*NO|
    |PQRST|     |     |PQR%T|
    |UVWXY|     |     |UVWX^|
    +-----------------------+

Amendment can also be made by using a function that selects a portion of its argument. For example:

       IR=: @(i.@$@])     NB. Adverb to select indices of (ravelled) table right argument
       A=: IR }           NB. Adverb to amend selected portion of right argument
       d=: (<0 1)&|:      NB. Function to select diagonal of a table
       '+-*%^' (] ; d@] ; ]IR ; d IR ; d IR } ; d A) m
    +---------------------------------------------------+
    |ABCDE|AGMSY| 0  1  2  3  4|0 6 12 18 24|+BCDE|+BCDE|
    |FGHIJ|     | 5  6  7  8  9|            |F-HIJ|F-HIJ|
    |KLMNO|     |10 11 12 13 14|            |KL*NO|KL*NO|
    |PQRST|     |15 16 17 18 19|            |PQR%T|PQR%T|
    |UVWXY|     |20 21 22 23 24|            |UVWX^|UVWX^|
    +---------------------------------------------------+
       NB. m; diag m; Indices of ravelled m; Indices of diagonal; Amendments

       ur=: 2 _3&{.      NB. Select upper right corner
       (2 3$'+-*%^!') (] ; ur@] ; ]IR ; ur IR ; ur IR } ; ur A) m
    +------------------------------------------+
    |ABCDE|CDE| 0  1  2  3  4|2 3 4|AB+-*|AB+-*|
    |FGHIJ|HIJ| 5  6  7  8  9|7 8 9|FG%^!|FG%^!|
    |KLMNO|   |10 11 12 13 14|     |KLMNO|KLMNO|
    |PQRST|   |15 16 17 18 19|     |PQRST|PQRST|
    |UVWXY|   |20 21 22 23 24|     |UVWXY|UVWXY|
    +------------------------------------------+

`a3=: IR=: @(i.@$@])` | `f IR` selects indices of ravelled rgt arg
`m4=: d=: (<0 1)&|:` | Function to select diagonal of table
`m5=: ur=: 2 _3&{.` | Function to select upper right corner

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