~wbetz/fesslix/flx_testing

# Copying and distribution of this file, with or without modification,
# are permitted in any medium without royalty provided the copyright
# notice and this notice are preserved.  This file is offered as-is,
# without any warranty.

# basic arithmetic operations

default flxoutput::checktol = true;
default flxoutput::float::prec = 4;

calc 1000;
calc 0000.5000e-2;
calc 0000.5000;

calc 1e-5;
calc 1e5;
calc 0.5e5;
calc 0.5e-5;
calc ans;

calc !1; calc !0; calc !-5;
calc 16^0.5;
calc 2*4;
calc 16/0.5;
calc 1+2 { stream=cout; }; calc 1-2;
calc 2<=4; calc 2<=2; calc 2>2; calc 4<=2; calc 4>=2;
calc 2==2; calc 2!=2; calc 2==4; calc 2!=4;
calc 1&&1; calc 1&&0; calc 0&&0; calc 0&&1;
calc 1||1; calc 1||0; calc 0||0; calc 0||1;
calc 1?2:3; calc 0?2:3;

const c1 = 1+2+3;
calc c1;
const c2 = 2*c1+1;
calc c2;
var v2 = 2*c1+1;
var v3 = evalc(v2);
calc v2;
const c1 = 1;
calc c2;
calc v2;
calc v3;

calc pi;
calc e;
calc 180°-PI;
calc 77%;

# Some strange comment: äöqoüß?°dd
calc cos(pi);;;
calc sin(pi);
calc -sin(-pi/2);
calc evalr(sin(pi));
calc cos(evalc(pi));
calc evalc(sin(pi));
calc abs(-5.55);
calc arccos(0);
calc arcsin(0);
calc arccot(0.5);
calc arctan(0.5);
calc arctanh(0.5);
calc cdfn(0);
calc cdfn(0.5);
calc cosh(0);
calc cot(0.5);
calc exp(0.5);
calc factorial(6);
calc failLSF(0);
calc faillsf(0.01);
calc hvi(0);
calc hvi(0.01);
calc hvi(-0.01);
calc cdfn_inv(0.5);
calc cdfn_inv(0.4);
calc frac(pi);
calc round(pi);
calc round(pi,2);
calc round(3.5);
calc ln(1); calc ln(2);
calc log(1); calc log(2);
calc loga(2,2); calc loga(3,2);
calc pdfn(0); calc pdfn(5);
calc relidx(1e-3); calc relidx(1e-6);
calc sig(-42.3); calc sig(52.2);
calc sinh(0.5);
calc sqrt(9);
calc tan(0.5);
calc tanh(0.5);
calc 1+2+4^5;
calc binomialcoeff(5,3);
calc tgamma(1.5);
calc igamma(1.5,2);
#calc igammal(1.5,2);
calc sum(h99=1,h99<=5,h99+1,h99);
# beta-functions
  const alpha = 10;
  const beta = 1e9;
  const p = 0.99999;
  calc ibeta_inv(alpha,beta,p) {checkTOL=false;};;
  calc ibeta(alpha,beta,ans) {checkTOL=false;};;
  calc betafun(alpha,beta) {checkTOL=false;};;

calc optimize1D(x,[4,5],(x-2)*(x-3));
const x = 0;
calc root(x,[0,sqrt(2)],x-1,bisec);
calc root(x,[0,sqrt(2)],x-1,rgfsi);
calc root(x,[0,sqrt(2)],(x-1)^3,bisec);
calc root(x,[0,sqrt(2)],(x-1)^3,rgfsi);
calc root(x,[0,4*sqrt(2)],(x-1)^3-1,bisec,stream=cout);
calc root(x,[0,4*sqrt(2)],(x-1)^3-1,rgfsi,stream=cout);
calc x;

mtxconst_print tmpmtx!{ mtxconst_new tmpmtx = {49}; };
mtxconst_print tmpmtx!{ mtxconst_new tmpmtx = {1;2;3}; };   
mtxconst_print tmpmtx2!{ mtxconst_new tmpmtx2 = { 1, 2, 3; 4, 5, 6; 7, 8, 9 }; };
mtxconst_print tmpmtx2!{
  mtxconst_new tmpmtx3 = {1,2,3};
  mtxconst_mult tmpmtx2 = tmpmtx3*tmpmtx;
};
mtxconst_print tmpmtx!{ mtxconst_op tmpmtx += {tmpmtx}; };
mtxconst_new karl(4,1,2);
mtxconst_print karl;
echo "rows=" & { mtxrows(karl) } { newline=false; };
echo ", cols=" & { mtxcols(karl) };
mtxconst_print karlt!{
  mtxconst_new karlt({karl});
  mtxconst_transpose karlt;
};
echo "rows=" & { mtxrows(karlt) } & ", cols=" & { mtxcols(karlt) };
calc mtxsum(karlt);
calc vec_norm2(karlt);
mtxconst_free karlt;
mtxconst_new karl = {1;2;3;4;5};
mtxconst_op karl(i) = i^2;
mtxconst_print karl;
calc mtxprod(karl);
mtxconst_new karl = {1;2;3;4;5};
mtxconst_op karl += {karl};
mtxconst_op karl -= 1;
mtxconst_op karl /= 2;
mtxconst_print karl;
mtxconst_new karl = {33};
mtxconst_print karl;

mtxconst_print tmpmtx!{ mtxconst_new tmpmtx = seq(i=0,i<9.5,i+1); };
mtxconst_print tmpmtx!{ mtxconst_op tmpmtx ^= 2; };
mtxconst_print olaf!{
  mtxconst_new olaf = {1,5,8,99};
  mtxconst_op olaf(i)= sin(i);
};
calc mtxcoeff(olaf,0,1);
calc max({karl}, {olaf});
calc min({karl}, {olaf});
calc min(x, c1,c2,{karl},{olaf},v2,v3);
calc max(x, c1,c2,{karl},{olaf},v2,v3);
mtxconst_2octave Olaf;

fun f1(4) = $1+$2+$3+$4;
calc f1(1,2,3,4);

const x=1;
calc x;
sfor (i;10) {
  calc (integ(x=[0,pi],sin(x),gp=i)-2)/2;
};
calc x;

const x=0;
  const start=0;
  const end=20;
  var funI = 5*x^16+x^15-x^8+9*x-3;
const a = integ(x=[start,end],funI,gp=40);
calc a;
sfor (i;10) {
  funplot i, (integ(x=[start,end],funI,gp=i)-a)/a;
};
sfor (i;10;true) {
  funplot i, deg2gauss(i), i*pi {checkTOL=false;};
};

funplot 1e52;

mtxconst_new cv(5,1,0);
sfor (p;5) {
 sfor (M;5) {
  const np = 0;
  sfor (k;p;true) {
   const np = np + binomialcoeff(M+k-1,k);
  };
  mtxcoeff cv(M-1,0) = np;
 };
 funplot p,{cv} {checkTOL=false;};
};

mtxconst_print tmpmtx!{
  mtxconst_new tmpmtx = {1;2;3};
  mtxconst_new tmpmtx2 = {3;2;1};
  mtxconst_op tmpmtx *= {tmpmtx2};
};

catch_error {
  calc error(1);
};

echo {0.0123}$udef:"%4.2f";
echo {0.0123}$udef:"%4.2e";
echo {0.0123}$udef:"\t\\Some number %4.2e to be printed.";


# Plotting Legendre Polynomials
# =============================
filestream lp ( "output/test_1_lp.txt") ;
filter (j;tmpmtx!{ mtxconst_new tmpmtx = seq(j=-1,j<=1,j+0.1); } ) {
  funplot j, {tmpmtx2!{
    mtxconst_new tmpmtx2 = seq(i=1,i<=8,i+1);
    mtxconst_op tmpmtx2(i) = hlegendrepoly(i,j);
  }} {stream=lp;checkTOL=true;};
};

# Plotting Gegenbauer Polynomials
# =============================
filestream hgp ( "output/test_1_hgp.txt") ;
mtxconst_new tmpmtx2 = seq(i=1,i<=8,i+1);
filter (j;tmpmtx ) {
  funplot j, {tmpmtx3!{
    mtxconst_new tmpmtx3({tmpmtx2});
    mtxconst_op tmpmtx3(i) = hgegenbauerpoly(i,j);
  }} {stream=hgp;checkTOL=false;};
};

# Print the hierarchic Lengendre polynomials
# ==========================================
sfor(i;10) {
  print_hlegendrepoly(i){verbose=false;};
};


echo "integer=" & { PI*1000 }$int;



const c1 = rgammal(1.5,2);
const c2 = rgammal_inv(1.5,c1);
funplot c1, c2;

const c1 = cdf(4,gumbel,mu=5,sd=2);
const c2 = cdf_inv(c1,gumbel,mu=5,sd=2);
funplot c1, c2;

const c1 = cdf(4,gamma,mu=5,sd=2);
const c2 = cdf_inv(c1,gamma,mu=5,sd=2);
funplot c1, c2;

funplot p-0.99999,alpha,beta;
calc objexec(:c1,{const c2=2; const c1=c1+c2; const p=0; const alpha=0; const beta=0;}::{c2,p,alpha});
funplot p,alpha,beta, c1,c2;

# maximize entropy of a distirbution given constraints
const x =0;
const alpha = 2;
const pt = 0.1;
fun bf(1) = $1*(1-pt)/pt;
fun entr(1) = entropy(beta,alpha=$1,beta=bf($1));
funplot entr(1), entr(1.01), entr(1.1);
alp = Optimize1d(x,[0.001,10],-entr(x));
bet = bf(alp);
funplot pt, alp, bet, entr(alp);

calc rnd_y2x(0.4,beta,alpha=4,beta=9);



strconst alfons = "No comment";
echo $strconst(alfons);
strconst alfons = " not a single word!!!";
echo $strconst(alfons);
strconst alfons = "Alfons will say" & $strconst(alfons);
echo $strconst(alfons);
echo $substr($strconst(alfons),p:0,c:!);
echo $substr($strconst(alfons),c:w,s:" not");
echo $substr($strconst(alfons),c:w,l:4);
strconst numstr = "alf-5.334bernd";
funplot numberfromstring(numstr);
echo $strconst(numstr);

echo "-- start of loop";
for_each stri in ("alf,;bernd,;gustaf,;claus";",;") {
  echo $strconst(stri);
};
echo "-- end of loop";