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This page presents only helper functions that are generic enough. They were used in one or more contributions on RC and will be used again and again.<br>
;Note:
* Good helper function usually encapsulates typical set of actions for current tasks, supplies often used default values, interacting with other helper functions, etc.
* Many samples of using presented functions can be found here on RC.
* Many of these functions are already here on RC. But some of them are upgraded. So, this is the place to get latest versions.
<br><br>
=R Helper Functions=
One of the R's great powers is its unlimited number of great and good packages, virtually thousands of them. For any applications big or small you can find a package.<br>
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* The file names used are without extension (which will be added as ".png", ".dmp" and ".dat" when needed).
* Requesting dump file is useful if the generating/plotting time is big. Having a dump file makes it easy and fast to repeat plotting with different colors, titles, etc.
* If number of generated dots is very big then plotting from a dump file could be very slow too. Actually, plotv2() shows almost "pure" plotting time.<br><br>
{{Works with|R|3.3.1 and above}}
<lang r>
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The problem with these libraries is that they are forcing you to learn, actually, "new" language. In addition, there is no guarantee,
that they would be stable and maintained well.<br>
The good alternative is always to use just 2-3 small helper functions if it is possible for your task.<br>
The same I would suggest JavaScript users about "declarative JavaScript".
It reminds me OOP (Object Oriented Programming) hype! But OOP is dead already, and
now declarative JavaScript is hyped??
Don't let you be tricked again. Remember: you would need to learn and use "monster" libraries!?
What "declarative JavaScript" is promising (and actually partially giving you by presented new functions, tags, etc.)?<br>
This is a fantastically sounding: "You are telling any JavaScript what to do, but not programming actually".
Think! It is the same as good HFJS is doing! For example, using randhclr() and pmat01() is the same
as "telling a JavaScript": "Use the random hex color and plot a matrix you have". It's just 1 statement:<br>
pmat01(mat,randhclr()).
In other words, look at these new libraries as a probable set of good helper functions for your projects.<br>
So, all these new libraries are good for the certain type of projects. Especially, if a company, which
have created this particular library and using it for inner projects, - is a solid company and will support this library.
The good such sample is Facebook's JavaScript library React.js, which is having/supporting a lot of unique functions
and tags.<br> Think again: do you need all of them?
<lang javascript>
// HFJS#3old: v.1.1.Plot
function pmat01(mat, color) {
// DCLs
var cvs = document.getElementById('cvsId');
var ctx = cvs.getContext("2d");
var w = cvs.width; var h = cvs.height;
var m = mat[0].length; var n = mat.length;
// Cleaning canvas and setting plotting color
ctx.fillStyle="white"; ctx.fillRect(0,0,w,h);
ctx.fillStyle=color;
// MAIN LOOP
for(var i=0; i<m; i++) {
for(var j=0; j<n; j++) {
if(mat[i][j]==1) { ctx.fillRect(i,j,1,1)};
}//fend j
}//fend i
}//func end
// VOE.js v. 2.0 Generic JavaScript Plotting Helper Functions
// aev 10/01/17
// HFJS#1 Like in PARI/GP: return random number 0..max-1. 6/17/16
function randgp(max) {return Math.floor(Math.random()*max)}
// HFJS#2 Return random hex color as #RRGGBB. 3/10/17
function randhclr() {
return "#"+
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("00"+randgp(256).toString(16)).slice(-2)
}
// HFJS#3: v.2.0 Plot any matrix mat (filled with 0 & not 0 items). 7/23/16
// Set error p in the page: <p id="epId"></p>.
// (Note: this is optional, see below);
// fgc/bgc - FG/BG colors; sc - scale (0..max); rt - rotate 90 degree
// if true (once).
function pmat01(mat, fgc, bgc, sc, rt) {
// Setting basic vars for canvas and matrix
var cvs = document.getElementById('cvsId');
var ctx = cvs.getContext("2d");
ctx.save();
var w = cvs.width, h = cvs.height;
var m = mat[0].length, n = mat.length, k=0;
console.log("MAT rxc", n, "x", m); // n - rows. m - cols
if(n<21&&m<21) {matl2cons("MAT2PLOT",mat)}
// Setting BG and plotting FG colors
ctx.fillStyle=bgc; ctx.fillRect(0,0,w,h);
ctx.fillStyle=fgc;
if(sc!=1) {ctx.scale(sc,sc)};
// Plotting "dots" (!=0 values in matrix) & counting them.
// n - rows. m - cols
for(var i=0; i<n; i++) {
for(var j=0; j<m; j++) {
if(mat[i][j]!=0) { k++;
if(rt&&n==m) {ctx.fillRect(i,j,1,1)} else {ctx.fillRect(j,i,1,1)}
};
}//fend j
}//fend i
// Outputting matrix "signature": matrix sizes & number of dots.
var ms="Matrix("+n+"x"+m+") "+k+" dots";
// Set error p
//var ep=document.getElementById("epId").innerHTML;
//document.getElementById("epId").innerHTML=ep+"<br>"+ms;
console.log("Matrix 'signature':", ms); //matrix "signature"
ctx.restore();
}//func end
// HFJS#4: Helper mini-functions for testing. 7/21/16
// Log title and matrix mat to console
function matl2cons(title,mat) {console.log(title); console.log(mat.join`\n`)}
// Print title to document
function pttl2doc(title) {document.write('<b>'+title+'</b><br />')}
// Print title and matrix mat to document
function matp2doc(title,mat) {
document.write('<b>'+title+'</b>:<br />');
for (var i = 0; i < mat.length; i++) {
document.write(' '+mat[i].join(' ')+'<br />') }}
// Fractal matrix ASCII "pretty" printing to document.
// mat should be filled with 0 and not 0 integer;
// chr is a char substituting latter.
function matpp2doc(title,mat,chr) {
var i,j,re='',e; var m=mat.length; var n=mat[0].length;
document.write(' <b>'+title+'</b>:<pre>');
for(var i=0; i<m; i++) {
for(var j=0; j<n; j++) {
e=' '; if(mat[i][j]!=0) {e=chr}; re+=e;
}//fend j
document.write(' '+re+'<br />'); re='';
}//fend i
document.write('</pre>');
}
// HFJS#5: Return the Kronecker product of the a and b matrices. 8/19/16
// Note: both a and b must be matrices, i.e., 2D rectangular arrays.
function mkp2(a,b) {
var m=a.length, n=a[0].length, p=b.length, q=b[0].length;
var rtn=m*p, ctn=n*q; var r=new Array(rtn);
// Building final matrix filled with zeros.
for (var i=0; i<rtn; i++) {r[i]=new Array(ctn)
for (var j=0;j<ctn;j++) {r[i][j]=0} }
// Calculating final KP matrix.
for (var i=0; i<m; i++) {
for (var j=0; j<n; j++) {
for (var k=0; k<p; k++) {
for (var l=0; l<q; l++) {
r[p*i+k][q*j+l]=a[i][j]*b[k][l];
}}}}//all4forend
return(r);
}
// HFJS#6: Kronecker power of a matrix. Where: m - initial matrix, n - power
function matkronpow(m,n) {
if(n<2) {return(m)}; var fm=m;
for(var i=1; i<n; i++) {fm=mkp2(fm,m)};
return(fm);
}
// HFJS#7: Create and plot Kronecker product based fractal from matrix m
// (filled with 0 & not 0 integers); ord - order. 8/19/16
function cpmat(m, ord, fgc, bgc, sc, rt) {
var kpr=matkronpow(m,ord);
pmat01(kpr, fgc, bgc, sc, rt);
}
// HFJS#8: Return the Kronecker product based fractal matrix width. 4/2/17
function fmw(m,ord) {var w0=m.length, w=Math.pow(w0, ord); return(w) }
//
//VOE.js END
</lang>
=PARI/GP Helper Functions=
PARI/GP built-in plotting functions are good only for instant draft math function curves plotting.
Not to mention bad color support and scaling.<br>
In addition, there are no built-in string manipulation functions, except of concatenation.<br>
So, presented here helper functions help to fix some of these shortcomings. At the same time, they simplify
some often used common actions.
==Plotting Helper Functions==
Functions presented here are directly or inderectly related to plotting.
<lang parigp>
\\ 2 old plotting helper functions 3/2/16
\\ HFGP#1 insm(): Check if x,y are inside matrix mat (+/- p deep).
insm(mat,x,y,p=0)={my(xz=#mat[1,],yz=#mat[,1]);
return(x+p>0 && x+p<=xz && y+p>0 && y+p<=yz && x-p>0 && x-p<=xz && y-p>0 && y-p<=yz)}
\\ HFGP#2 plotmat(): Simple plotting using a square matrix mat (filled with 0/1).
plotmat(mat)={
my(xz=#mat[1,],yz=#mat[,1],vx=List(),vy=vx,x,y);
for(i=1,yz, for(j=1,xz, if(mat[i,j]==0, next, listput(vx,i); listput(vy,j))));
print(" *** matrix(",xz,"x",yz,") ",#vy, " DOTS");
plothraw(Vec(vx),Vec(vy));
}
\\ 2 new plotting helper functions 11/27/16
\\ HFGP#3 wrtmat(): Writing file fn containing X,Y coordinates from matrix mat.
\\ Created primarily for using file in Gnuplot, also for re-plotting.
wrtmat(mat, fn)={
my(xz=#mat[1,],yz=#mat[,1],ws,d=0);
for(i=1,yz, for(j=1,xz, if(mat[i,j]==0, next, d++; ws=Str(i," ",j); write(fn,ws))));
print(" *** matrix(",xz,"x",yz,") ",d, " DOTS put in ",fn);
}
\\ HFGP#4 plotff(): Plotting from a file written by the wrtmat().
\\ Saving possibly huge generation time if re-plotting needed.
plotff(fn)={
my(F,nf,vx=List(),vy=vx,Vr);
F=readstr(fn); nf=#F;
print(" *** Plotting from: ", fn, " - ", nf, " DOTS");
for(i=1,nf, Vr=stok(F[i],","); listput(vx,eval(Vr[1])); listput(vy,eval(Vr[2])));
plothraw(Vec(vx),Vec(vy));
}
\\ HFGP#5 iPlotmat() Improved simple plotting using matrix mat (color and scaling added).
\\ Matrix should be filled with 0/1. 7/6/16, upgraded 4/8/17
\\ Writing a dump file fn according to the flag - dflg (0-no/1-yes).
\\ A dump file added mostly for the gnuplot plotting.
iPlotmat(mat,clr,fn="dfn.dat",dflg=0)={
my(xz=#mat[1,],yz=#mat[,1],vx=List(),vy=vx,xmin,xmax,ymin,ymax,c=0.625);
\\ Dumping if requested (dflg=1).
if (dflg==1,wrtmat(mat, fn));
for(i=1,yz, for(j=1,xz, if(mat[i,j]==0, next, listput(vx,i); listput(vy,j))));
xmin=listmin(vx); xmax=listmax(vx); ymin=listmin(vy); ymax=listmax(vy);
plotinit(0); plotcolor(0,clr);
plotscale(0, xmin,xmax,ymin,ymax);
plotpoints(0, Vec(vx)*c,Vec(vy));
plotdraw([0,xmin,ymin]);
if (dflg==0, print(" *** matrix: ",xz,"x",yz,", ",#vy," DOTS"));
}
\\ HFGP#6 iPlotV2(): Improved plotting from a file written by the wrtmat(). (color added)
\\ Saving possibly huge generation time if re-plotting needed. 7/6/16
iPlotV2(fn, clr)={
my(F,nf,vx=List(),vy=vx,Vr,xmin,xmax,ymin,ymax,c=0.625);
F=readstr(fn); nf=#F;
print(" *** Plotting from: ", fn, " - ", nf, " DOTS");
for(i=1,nf, Vr=stok(F[i]," "); listput(vx,eval(Vr[1])); listput(vy,eval(Vr[2])));
xmin=listmin(vx); xmax=listmax(vx); ymin=listmin(vy); ymax=listmax(vy);
plotinit(0); plotcolor(0,clr);
plotscale(0, xmin,xmax,ymin,ymax);
plotpoints(0, Vec(vx)*c,Vec(vy));
plotdraw([0,xmin,ymin]);
}
\\ HFGP#7 Plot the line from x1,y1 to x2,y2. 4/11/16
plotline(x1,y1,x2,y2,w=0)={plotmove(w, x1,y1);plotrline(w,x2-x1,y2-y1);}
\\ HFGP#8 Convert value expressed in degrees to radians. 5/7/16 (next 3 - same date)
rad2(degs)={return(degs*Pi/180.0)}
\\ HFGP#9 Convert value expressed in radians to degrees.
deg2(rads)={return(rads*180.0/Pi)} \\value in rads×180.0 /p
\\ HFGP#10 Convert Polar coordinates r,a to Cartesian.
cartes2(r,a,rndf=0)={my(v,x,y); x=r*cos(a); y=r*sin(a);
if(rndf==0, return([x,y]), return(round([x,y])))}
\\ HFGP#11 Convert Cartesian coordinates x,y to polar.
polar2(x,y)={my(v,r,a); r=sqrt(x^2+y^2); a=atan(y/x); return([r,a])}
</lang>
==String Functions==
The first 4 are already here on RC. A few others I will keep on hold (hoping to create tasks later).
<lang parigp>
\\ SF#1 ssubstr(): Returns the substring of the string str specified by the start
\\ position s and a length n. If n=0 then to the end of str. 3/5/16
ssubstr(str,s=1,n=0)={
my(vt=Vecsmall(str),ve,vr,vtn=#str,n1);
if(vtn==0,return(""));
if(s<1||s>vtn,return(str));
n1=vtn-s+1; if(n==0,n=n1); if(n>n1,n=n1);
ve=vector(n,z,z-1+s); vr=vecextract(vt,ve); return(Strchr(vr));
}
\\ SF#2 stok(): Tokenize a string str according to 1 character delimiter d.
\\ Return a list of tokens. 3/5/16
\\ Note: It is using ssubstr().
stok(str,d)={
my(d1c=ssubstr(d,1,1),str=Str(str,d1c),vt=Vecsmall(str),d1=sasc(d1c),
Lr=List(),sn=#str,v1,p1=1,vo=32);
if(sn==1, return(List(""))); if(vt[sn-1]==d1,sn--);
for(i=1,sn, v1=vt[i];
if(v1!=d1, vo=v1; next);
if(vo==d1||i==1, listput(Lr,""); p1=i+1; vo=v1; next);
if(i-p1>0, listput(Lr,ssubstr(str,p1,i-p1)); p1=i+1);
vo=v1;
);
return(Lr);
}
\\ SF#3 sreverse(): Return the reversed string str. 3/3/2016
sreverse(str)={return(Strchr(Vecrev(Vecsmall(str))))}
\\ SF#4 srepeat(): Repeat a string str the specified number of times ntimes
\\ and return composed string. 3/3/2016
srepeat(str,ntimes)={
my(srez=str,nt=ntimes-1);
if(ntimes<1||#str==0,return(""));
if(ntimes==1,return(str));
for(i=1,nt, srez=concat(srez,str));
return(srez);
}
\\ SF#5 <<coming soon>>
</lang>
=gnuplot Helper File-Functions=
File for the load command is the only possible imitation of the fine function in the '''gnuplot'''.<br><br>
'''plotff.gp''' - Plotting from any data-file with 2 columns (space delimited), and writing to png-file.<br>
Especially useful to plot colored fractals using points, also for re-plotting.
<br>
{{Works with|gnuplot|5.0 (patchlevel 3) and above}}
<lang gnuplot>
## plotff.gp 11/27/16 aev
## Plotting from any data-file with 2 columns (space delimited), and writing to png-file.
## Especially useful to plot colored fractals using points.
## Note: assign variables: clr, filename and ttl (before using load command).
reset
set terminal png font arial 12 size 640,640
ofn=filename.".png"
set output ofn
unset border; unset xtics; unset ytics; unset key;
set size square
dfn=filename.".dat"
set title ttl font "Arial:Bold,12"
plot dfn using 1:2 with points pt 7 ps 0.5 lc @clr
set output
</lang>
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