afdb0e20-1bf2-444b-b290-40cacb08fe2f 26 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Compatible vectoriing functionalities

data 12345632 mat :

algo style function: elements wise data over function data algo Vectorise i 1 data rows range j 1 data cols range Fnct i j el data i j el algo eval : for for Fnct 21 line :

13531 mat 78913 mat * 78921242735404533 mat

x algo x sin :

data algo Vectorise 0.8415 0.9093 0.1411 0.7568 - 0.9589 - 0.2794 - 32 mat

data i j el algo eval

x algo x 3 nthroot :

data algo Vectorise 1 1.2599 1.4422 1.5874 1.71 1.8171 32 mat

algo style matrices: elements wise between matrices u v VectMatrix i 1 u rows range j 1 u cols range M i j el u i j el v i j el algo eval : for for M 21 line :

u 12345632 mat :

v 0.5 3.5 1.5 4.5 2.5 5.5 32 mat :

u v algo u v * :

u v VectMatrix 0.5 7 4.5 18 12.5 3332 mat

u v algo u sqrt v * :

u v VectMatrix 0.5 4.9497 2.5981 9 5.5902 13.4722 32 mat

u v algo u 1 -^v * :

u v VectMatrix 0.5 1.75 0.5 1.125 0.5 0.9167 32 mat

u v algo u v * :

u 123422 mat 123422 mat 123422 mat 123422 mat 22 mat :

v 123422 mat 123422 mat 123422 mat 123422 mat 22 mat :

u v VectMatrix 710152222 mat 710152222 mat 710152222 mat 710152222 mat 22 mat

u 123422 mat 123422 mat 123422 mat 123422 mat 22 mat :

v 111122 mat 123422 mat 222222 mat 123422 mat 22 mat :

u v VectMatrix 337722 mat 710152222 mat 66141422 mat 710152222 mat 22 mat

An example of logic algorithm

Create the logic algo a b c algo logic i 1 a rows range L i el a i el b i el c i el algo : for L 21 line :

A 0000111181 mat :

B 0011001181 mat :

C 0101010181 mat :

A B C algo A B & (B C & (B C | (& | (:

A B C algo logic transpose 0001001118 mat

A B C algo B A C | (& (:

A B C algo logic transpose 0001001118 mat

algo style function: elements wise data over function [Fractal] data algo VectComplex ii 1 data rows range j 1 data cols range Fnct ii j el data ii j el algo eval : for for Fnct 21 line :

w 0 0.5 0.5 i * 050 0.5 1 0.5 0.5 i * + 0.5 50.5 0.5 i * 0.5 0.5 i * + i 0.5 i * 50 0.5 i * + 151 mat :

z algo z 5^:

S w 11211 submatrix algo VectComplex :

S 0 0.031 0.031 i * 0312500000 0.031 1 0.125 - 0.125 i * - 0.031 328440640.656 0.031 i * 0.125 - 0.125 i * - 121 mat

A 2381 - 4423 mat :

B 123422 mat :

2D rotation rule A transpose B * 1 - 01522203232 mat

B A transpose * #

A 12345678912345678963 mat :

B 98765432133 mat :

3D rotation rule A B * 302418846954138114903024188469541381149063 mat

B A * #

A 12345623 mat :

B 12345632 mat :

C A transpose :

Neither form is  a convention
wrt multiplication of vectors
Smath = Mathcad rule, i.e:
row/col pairwise multiplication A transpose B * #

C 14253632 mat

C B * #

Here, Smath respects the rule of
vector multiplication Convention C B * mat2sys sys2mat :

Convention transpose 1425362841061231261591841682012245201025153062412301836136 mat

algo style matrices: elements wise between matrices u v algo VectMatrix i 1 u rows range j 1 u cols range M i j el u i j el v i j el algo eval : for for M 21 line :

u 12345632 mat :

v 0.5 3.5 1.5 4.5 2.5 5.5 32 mat :

u v algo u v * :

u v algo VectMatrix 0.5 7 4.5 18 12.5 3332 mat

u 2381 - 4423 mat transpose :

v 714 - 2 - 1132 mat :

u v algo VectMatrix 141 - 12 - 8 - 8432 mat

u v algo u v sqrt * :

u v algo VectMatrix 5.291503 1 - 12 11.313708 8432 mat

algo style matrices: elements wise between matrices
 ... => assume the complex form u v algo VectMatrix i 1 u rows range j 1 u cols range M i j el u i j el v i j el algo : for for M 21 line :

u v algo u v sqrt * :

Data # :

u v algo VectMatrix 5.291503 1 - 6 i * 5.656854 i * 8432 mat

data data Clear :

Data 234522 mat :

x algo x 2 -^:

algo style function: elements wise data over function data algo Vectorise data data : i 1 data rows range j 1 data cols range Fnct i j el data i j el algo eval : for for Fnct 31 line :

V Data algo Vectorise :

V 322431024312522 mat

1 V sum sqrt / 0.015