| Miscellaneous | 128!: |
| 128!:0 y |
QR. Produces the QR decomposition of a complex matrix y
(in the domain of matrix inverse %.),
an Hermitian matrix and a square upper triangular matrix,
individually boxed.
mp=: +/ . * NB. Matrix product A=: j./?. 2 7 4$10 NB. A random complex matrix $A 7 4 'Q R'=: 128!:0 A $Q 7 4 $R 4 4 >./|,(=i.4) - (+|:Q) mp Q NB. Q is Hermitian 2.70972e_16 0~:R NB. R is upper triangular 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 A -: Q mp R 1 |
| 128!:1 y | R Inv. Invert square upper triangular matrix. |
| x 128!:2 y | Apply. x 128!:2 y applies the verb in
string x to y .
For example:
'+/' 128!:2 i.2 5
5 7 9 11 13
'+/' 128!:2"1 i.2 5
10 35
'+/"1' 128!:2 i.2 5
10 35
('+/';'|.';'|."1') 128!:2&.><i.2 5
+-----------+---------+---------+
|5 7 9 11 13|5 6 7 8 9|4 3 2 1 0|
| |0 1 2 3 4|9 8 7 6 5|
+-----------+---------+---------+
'2 3' 128!:2 i.2 5
|syntax error
| '2 3' 128!:2 i.2 5
'@' 128!:2 i.2 5
|syntax error
| '@' 128!:2 i.2 5
The ranks of 128!:2 are 1 _ ,
that is, apply the lists in the left argument to
the right argument in toto. |
| [x] 128!:3 y | CRC. A CRC polynomial is a boolean list or an integer.
The following CRC polynomials p and q are equivalent:
p=: 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 q=: _306674912 _8]\p 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 q -: (_2 _2,30$2) #. p 1 p -: (32$2) #: q 1 x 128!:3 y computes the CRC encoding of string y according to x , which may be p or p;i , where p is a CRC polynomial and i is the initial CRC value. If i is elided then _1 is used. 128!:3 y is equivalent to _306674912 (128!:3) y . The monad x&(128!:3) is supported by special code which pre-computes a look-up table of CRC values for each byte. Examples: f=: 128!:3 f '123456789' _873187034 f 'assiduously avoid any and all asinine alliterations' 1439575093 |
| 128!:4 y | RNG Raw. See Roll/Deal (?).
|
| 128!:5 y | Is NaN. If z=: 128!:5 y , then z has the same shape as y and an atom of z is 1 if and only if the corresponding atom of y is _. (NaN) or contains _. . Examples: (128!:5) 3.45 6 _. 7 0 0 1 0 (128!:5) t=. 2 2$1 2;3 4 5;(<<_. 7);_. 0 0 1 1 (128!:5) < t 1 (128!:5) ;:'Cogito, ergo sum. _.' 0 0 0 0 0 |