JOY - compiled at 15:19:20 on Apr 3 2002 (BDW)
Copyright 2001 by Manfred von Thun
usrlib is loaded
inilib is loaded
agglib is loaded
numlib is loaded
agglib is already loaded
seqlib is loaded
mtrlib is loaded
numlib is already loaded
output from test file mtrtst.joy (* MATRICES and VECTORS *)
user input is indented by one tab
(* VECTORS *)
5 "hello" n-e-vector.
["hello" "hello" "hello" "hello" "hello"]
5 1 n-e-vector.
[1 1 1 1 1]
(* vectors and scalars *)
5 [1 2 3] [+]sv-bin-v.
[6 7 8]
3.13 [10 20 30] [*]sv-bin-v.
[31.3 62.6 93.9]
5 [1 2 3 4 5 6 7 8 9 10] [-]sv-bin-v.
[4 3 2 1 0 -1 -2 -3 -4 -5]
[1 2 3 4 5 6 7 8 9 10] 5 [-]vs-bin-v.
[-4 -3 -2 -1 0 1 2 3 4 5]
[{1 2 3}{4 5 6}{7 8 9}] {2 4 6 8} [and]vs-bin-v.
[{2} {4 6} {8}]
3.14 [[id] [dup *] [dup dup * *]] [i]sv-bin-v.
[3.14 9.8596 30.9591]
[1 2 3 4] [dup] [*] concat [i]vs-bin-v.
[1 4 9 16]
[1.1 2.2 3.3 4.4 5.5] v-negate-v.
[-1.1 -2.2 -3.3 -4.4 -5.5]
[1.1 2.2 3.3 4.4 5.5] v-invert-v.
[0.909091 0.454545 0.30303 0.227273 0.181818]
(* two vectors *)
[1 2 3 4] [11 22 33] vv-samesize.
false
[1 2 3 4] [11 22 33 44] vv-samesize.
true
[1 2 3] [10 20 30] [+]vv-bin-v.
[11 22 33]
[1 2 3] [10 20 30] [*]vv-bin-v.
[10 40 90]
[{1 2 3}{2 3 4}] [{1 3 4}{4 5 6}] [or]vv-bin-v.
[{1 2 3 4} {2 3 4 5 6}]
[{1 2 3}{2 3 4}] [{1 3 4}{4 5 6}] [and]vv-bin-v.
[{1 3} {4}]
[true false false true] [true true false false] [and]vv-bin-v.
[true false false false]
(* inner or scalar product *)
[1 2 3] [1 2 3] [*][+]vv-2bin-s.
14
[1.1 2.2 3.3] [3.3 4.4 5.5] [*][+]vv-2bin-s.
31.46
[{1 2 3}{4 5 6}] [{2 3}{2 6}] [and][or]vv-2bin-s.
{2 3 6}
[{1 2 3}{4 5 6}] [{2 3}{2 6}] [or][and]vv-2bin-s.
{2}
[{1 2 3}{4 5 6}] [{2 3}{2 6}] [and][and]vv-2bin-s.
{}
[{1 2 3}{4 5 6}] [{2 3}{2 6}] [or][or]vv-2bin-s.
{1 2 3 4 5 6}
[true false true] [false true true] [and][or]vv-2bin-s.
true
(* vectors to matrices *)
[1 2 3 4] v-1row-m.
[[1 2 3 4]]
[1 2 3 4] v-1col-m.
[[1] [2] [3] [4]]
[1 2 3 4] v-zdiag-m.
[[1 0 0 0] [0 2 0 0] [0 0 3 0] [0 0 0 4]]
[1 2 3 4] 0 v-e-diag-m.
[[1 0 0 0] [0 2 0 0] [0 0 3 0] [0 0 0 4]]
["Peter" "Paul" "Mary"] "" v-e-diag-m.
[["Peter" "" ""] ["" "Paul" ""] ["" "" "Mary"]]
[{1 2} {3 4 5} {6}] {} v-e-diag-m.
[[{1 2} {} {}] [{} {3 4 5} {}] [{} {} {6}]]
4 1 n-e-vector v-zdiag-m.
[[1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1]]
4 1 n-e-vector 0 v-e-diag-m.
[[1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1]]
4 'i n-e-vector 'o v-e-diag-m.
[['i 'o 'o 'o] ['o 'i 'o 'o] ['o 'o 'i 'o] ['o 'o 'o 'i]]
[1 2 3] [10 20] [+]vv-bin-m.
[[11 21] [12 22] [13 23]]
[1.1 2.2] [3.3 4.4 5.5 6.6] [+]vv-bin-m.
[[4.4 5.5 6.6 7.7] [5.5 6.6 7.7 8.8]]
[1.1 2.2] [4.4 5.5 6.6 7.7] [*]vv-bin-m.
[[4.84 6.05 7.26 8.47] [9.68 12.1 14.52 16.94]]
[{1 2 3}{4 5}] [{1}{2 3}{3 4}] [or]vv-bin-m.
[[{1 2 3} {1 2 3} {1 2 3 4}] [{1 4 5} {2 3 4 5} {3 4 5}]]
[{1 2 3}{4 5}] [{1}{2 3}{3 4}] [and]vv-bin-m.
[[{1} {2 3} {3}] [{} {} {4}]]
[1 2 3 4] [[id] [dup *] [dup dup * *]] [dupd i]vv-bin-m.
[[1 1 1] [2 4 8] [3 9 27] [4 16 64]]
(* sindeg cosdeg tandeg are defined in numlib.joy *)
[0.0 30.0 45.0] [ [sindeg] [cosdeg] [tandeg] ] [dupd i]vv-bin-m.
[[0 1 0] [0.5 0.866025 0.57735] [0.707107 0.707107 1]]
[peter paul] [[smith] [jones]] [cons]vv-bin-m.
[[[peter smith] [peter jones]] [[paul smith] [paul jones]]]
[peter paul] [[smith] [jones]] [cons]vv-bin-m size.
2
(* compare: *)
[peter paul] [ smith jones ] cartproduct.
[[paul jones] [paul smith] [peter jones] [peter smith]]
[peter paul] [ smith jones ] cartproduct size.
4
(* MATRICES *)
[[1 2] [3 4]] [[5 6] [7 8]] mm-vercat-m.
[[1 2] [3 4] [5 6] [7 8]]
[[1 2] [3 4]] [[5 6] [7 8]] mm-horcat-m.
[[1 2 5 6] [3 4 7 8]]
[[1 2 3] [4 5 6] [7 8 9] [10 11 12]] m-transpose-m.
[[1 4 7 10] [2 5 8 11] [3 6 9 12]]
(* matrices and scalars *)
[[1 2] [3 4] [5 6]] 10 [+]ms-cbin-m.
[[11 12] [13 14] [15 16]]
[[1 2] [3 4] [5 6]] 10 [-]ms-bin-m. (* not commutative *)
[[-9 -8] [-7 -6] [-5 -4]]
[[1 2] [3 4] [5 6]] 10 [*]ms-cbin-m.
[[10 20] [30 40] [50 60]]
[[1 2] [3 4] [5 6]] 0 [*]ms-cbin-m.
[[0 0] [0 0] [0 0]]
[[1 2] [3 4] [5 6]] 7 [popd]ms-bin-m.
[[7 7] [7 7] [7 7]]
[[1 2] [3 4] [5 6]] [succ] [i]ms-bin-m.
[[2 3] [4 5] [6 7]]
[[{1 2} {3 4}] [{5 6} {7 8}] ] {1 3 5 7} [and]ms-bin-m.
[[{1} {3}] [{5} {7}]]
5 [[1 2 3] [4 5 6] [7 8 9]] [-]sm-bin-m.
[[4 3 2] [1 0 -1] [-2 -3 -4]]
[[1 2 3] [4 5 6] [7 8 9]] 5 [-]ms-bin-m.
[[-4 -3 -2] [-1 0 1] [2 3 4]]
0 [[1 2 3] [4 5 6] [7 8 9]] [pop]sm-bin-m.
[[0 0 0] [0 0 0] [0 0 0]]
(* two matrices *)
[[1 2 3] [4 5 6]] [[10 20 30] [40 50 60]] mm-add-m.
[[11 22 33] [44 55 66]]
[[1 2 3] [4 5 6]] [[10 20 30] [40 50 60]] [+]mm-bin-m.
[[11 22 33] [44 55 66]]
[[1 2 3] [4 5 6]] [[10 20 30] [40 50 60]] [*]mm-bin-m.
[[10 40 90] [160 250 360]]
[[true true ] [false false]]
[[true false] [true false]] [or]mm-bin-m.
[[true true] [true false]]
[[true true ] [false false]]
[[true false] [true false]] [and]mm-bin-m.
[[true false] [false false]]
[[true true ] [false false]]
[[true false] [true false]] [xor]mm-bin-m.
[[false true] [true false]]
DEFINE (* 2 by 2 identity matrix *)
id2 == 2 1 n-e-vector 0 v-e-diag-m.
id2.
[[1 0] [0 1]]
id2 m-transpose-m.
[[1 0] [0 1]]
id2 [[1 2 3] [4 5 6]] mm-mul-m.
[[1 2 3] [4 5 6]]
[[1 2] [3 4] [5 6]] id2 mm-mul-m.
[[1 2] [3 4] [5 6]]
[[1 2] [3 4] [5 6]] id2 [*][+]mm-2bin-m.
[[1 2] [3 4] [5 6]]
[[1.1 2.2] [3.3 4.4] [5.5 6.6]] dup m-print
[[1.1 2.2] [3.3 4.4]] dup m-print
mm-mul-m m-print.
[ [1.1 2.2]
[3.3 4.4]
[5.5 6.6] ]
[ [1.1 2.2]
[3.3 4.4] ]
[ [8.47 12.1]
[18.15 26.62]
[27.83 41.14] ]
[[{1 2} {3 4}] [{4 5} {6 7}]] dup m-print
[[{1 3 5} {6}] [{2} {3 4 5}]] dup m-print
[and][or]mm-2bin-m m-print.
[ [{1 2} {3 4}]
[{4 5} {6 7}] ]
[ [{1 3 5} {6}]
[{2} {3 4 5}] ]
[ [{1} {3 4}]
[{5} {}] ]
(* END of test file mtrtst.joy *)