5 if ( typeof define ===
"function" && define.amd ) {
7 define( [
'JSRootCore'], factory );
9 if (typeof JSROOT ==
'undefined')
10 throw new Error(
"This extension requires JSRootCore.js",
"JSRootMath.js");
12 if (typeof JSROOT.Math ==
"object")
13 throw new Error(
"This JSROOT Math already loaded",
"JSRootMath.js");
22 JSROOT.Math.lgam =
function( x ) {
23 var p, q, u, w, z, i, sgngam = 1;
24 var kMAXLGM = 2.556348e305;
25 var LS2PI = 0.91893853320467274178;
28 8.11614167470508450300E-4,
29 -5.95061904284301438324E-4,
30 7.93650340457716943945E-4,
31 -2.77777777730099687205E-3,
32 8.33333333333331927722E-2
36 -1.37825152569120859100E3,
37 -3.88016315134637840924E4,
38 -3.31612992738871184744E5,
39 -1.16237097492762307383E6,
40 -1.72173700820839662146E6,
41 -8.53555664245765465627E5
46 -3.51815701436523470549E2,
47 -1.70642106651881159223E4,
48 -2.20528590553854454839E5,
49 -1.13933444367982507207E6,
50 -2.53252307177582951285E6,
51 -2.01889141433532773231E6
54 if (x >= Number.POSITIVE_INFINITY)
55 return(Number.POSITIVE_INFINITY);
62 return (Number.POSITIVE_INFINITY);
73 z = q * Math.sin( Math.PI * z );
75 return (Number.POSITIVE_INFINITY);
76 z = Math.log(Math.PI) - Math.log( z ) - w;
90 return (Number.POSITIVE_INFINITY);
102 return( Math.log(z) );
105 p = x * this.Polynomialeval(x, B, 5 ) / this.Polynomial1eval( x, C, 6);
106 return( Math.log(z) + p );
109 return( sgngam * Number.POSITIVE_INFINITY );
111 q = ( x - 0.5 ) * Math.log(x) - x + LS2PI;
117 q += ((7.9365079365079365079365e-4 * p
118 - 2.7777777777777777777778e-3) *p
119 + 0.0833333333333333333333) / x;
121 q += this.Polynomialeval( p, A, 4 ) / x;
129 JSROOT.Math.Polynomialeval =
function(x, a, N) {
130 if (N==0)
return a[0];
133 for (var i=1; i <= N; ++i)
143 JSROOT.Math.Polynomial1eval =
function(x, a, N) {
144 if (N==0)
return a[0];
147 for (var i=1; i < N; ++i)
153 JSROOT.Math.ndtri =
function( y0 ) {
155 return( Number.NEGATIVE_INFINITY );
157 return( Number.POSITIVE_INFINITY );
160 -5.99633501014107895267E1,
161 9.80010754185999661536E1,
162 -5.66762857469070293439E1,
163 1.39312609387279679503E1,
164 -1.23916583867381258016E0
168 1.95448858338141759834E0,
169 4.67627912898881538453E0,
170 8.63602421390890590575E1,
171 -2.25462687854119370527E2,
172 2.00260212380060660359E2,
173 -8.20372256168333339912E1,
174 1.59056225126211695515E1,
175 -1.18331621121330003142E0
179 4.05544892305962419923E0,
180 3.15251094599893866154E1,
181 5.71628192246421288162E1,
182 4.40805073893200834700E1,
183 1.46849561928858024014E1,
184 2.18663306850790267539E0,
185 -1.40256079171354495875E-1,
186 -3.50424626827848203418E-2,
187 -8.57456785154685413611E-4
191 1.57799883256466749731E1,
192 4.53907635128879210584E1,
193 4.13172038254672030440E1,
194 1.50425385692907503408E1,
195 2.50464946208309415979E0,
196 -1.42182922854787788574E-1,
197 -3.80806407691578277194E-2,
198 -9.33259480895457427372E-4
202 3.23774891776946035970E0,
203 6.91522889068984211695E0,
204 3.93881025292474443415E0,
205 1.33303460815807542389E0,
206 2.01485389549179081538E-1,
207 1.23716634817820021358E-2,
208 3.01581553508235416007E-4,
209 2.65806974686737550832E-6,
210 6.23974539184983293730E-9
214 6.02427039364742014255E0,
215 3.67983563856160859403E0,
216 1.37702099489081330271E0,
217 2.16236993594496635890E-1,
218 1.34204006088543189037E-2,
219 3.28014464682127739104E-4,
220 2.89247864745380683936E-6,
221 6.79019408009981274425E-9
224 var s2pi = 2.50662827463100050242e0;
227 var x, z, y2, x0, x1;
229 if ( y > (1.0 - 0.13533528323661269189) ) {
233 if ( y > 0.13533528323661269189 ) {
236 x = y + y * (y2 * this.Polynomialeval( y2, P0, 4)/ this.Polynomial1eval( y2, Q0, 8 ));
240 x = Math.sqrt( -2.0 * Math.log(y) );
241 x0 = x - Math.log(x)/x;
244 x1 = z * this.Polynomialeval( z, P1, 8 )/ this.Polynomial1eval( z, Q1, 8 );
246 x1 = z * this.Polynomialeval( z, P2, 8 )/ this.Polynomial1eval( z, Q2, 8 );
253 JSROOT.Math.igam =
function(a,x) {
254 var kMACHEP = 1.11022302462515654042363166809e-16;
255 var kMAXLOG = 709.782712893383973096206318587;
260 if (a <= 0)
return 1.0;
262 if (x <= 0)
return 0.0;
264 if( (x > 1.0) && (x > a ) )
265 return( 1.0 - this.igamc(a,x) );
268 ax = a * Math.log(x) - x - this.lgam(a);
285 while( c/ans > kMACHEP );
287 return( ans * ax/a );
290 JSROOT.Math.igamc =
function(a,x) {
291 var kMACHEP = 1.11022302462515654042363166809e-16;
292 var kMAXLOG = 709.782712893383973096206318587;
294 var kBig = 4.503599627370496e15;
295 var kBiginv = 2.22044604925031308085e-16;
297 var ans, ax, c, yc, r, t, y, z;
298 var pk, pkm1, pkm2, qk, qkm1, qkm2;
302 if (a <= 0)
return 0.0;
304 if (x <= 0)
return 1.0;
306 if( (x < 1.0) || (x < a) )
307 return ( 1.0 - JSROOT.Math.igam(a,x) );
309 ax = a * Math.log(x) - x - JSROOT.Math.lgam(a);
331 pk = pkm1 * z - pkm2 * yc;
332 qk = qkm1 * z - qkm2 * yc;
336 t = Math.abs( (ans - r)/r );
345 if( Math.abs(pk) > kBig )
353 while( t > kMACHEP );
359 JSROOT.Math.igami =
function(a, y0) {
360 var x0, x1, x, yl, yh, y, d, lgm, dithresh;
362 var kMACHEP = 1.11022302462515654042363166809e-16;
366 alert(
"igami : Wrong domain for parameter a (must be > 0)");
370 return Number.POSITIVE_INFINITY;
376 var kMAXNUM = Number.MAX_VALUE;
381 dithresh = 5.0 * kMACHEP;
385 y = ( 1.0 - d - this.ndtri(y0) * Math.sqrt(d) );
390 for( i=0; i<10; ++i ) {
391 if ( x > x0 || x < x1 )
394 if ( y < yl || y > yh )
405 d = (a - 1.0) * Math.log(x) - x - lgm;
411 if ( Math.abs(d/x) < kMACHEP )
417 if ( x0 == kMAXNUM ) {
420 while ( x0 == kMAXNUM ) {
422 y = this.igamc( a, x );
434 for( i=0; i<400; ++i ) {
435 x = x1 + d * (x0 - x1);
436 y = this.igamc( a, x );
437 lgm = (x0 - x1)/(x1 + x0);
438 if ( Math.abs(lgm) < dithresh )
441 if ( Math.abs(lgm) < dithresh )
455 d = (y0 - yl)/(yh - yl);
468 d = (y0 - yl)/(yh - yl);
475 JSROOT.Math.gamma_quantile_c =
function(z, alpha, theta) {
476 return theta * this.igami( alpha, z);
479 JSROOT.Math.gamma_quantile =
function(z, alpha, theta) {
480 return theta * this.igami( alpha, 1.- z);
483 JSROOT.Math.log10 =
function(n) {
484 return Math.log(n) / Math.log(10);
487 JSROOT.Math.landau_pdf =
function(x, xi, x0) {
490 if (xi <= 0)
return 0;
492 var u, ue, us, denlan;
493 var p1 =
new Array(0.4259894875,-0.1249762550, 0.03984243700, -0.006298287635, 0.001511162253);
494 var q1 =
new Array(1.0 ,-0.3388260629, 0.09594393323, -0.01608042283, 0.003778942063);
495 var p2 =
new Array(0.1788541609, 0.1173957403, 0.01488850518, -0.001394989411, 0.0001283617211);
496 var q2 =
new Array(1.0 , 0.7428795082, 0.3153932961, 0.06694219548, 0.008790609714);
497 var p3 =
new Array(0.1788544503, 0.09359161662,0.006325387654, 0.00006611667319,-0.000002031049101);
498 var q3 =
new Array(1.0 , 0.6097809921, 0.2560616665, 0.04746722384, 0.006957301675);
499 var p4 =
new Array(0.9874054407, 118.6723273, 849.2794360, -743.7792444, 427.0262186);
500 var q4 =
new Array(1.0 , 106.8615961, 337.6496214, 2016.712389, 1597.063511);
501 var p5 =
new Array(1.003675074, 167.5702434, 4789.711289, 21217.86767, -22324.94910);
502 var q5 =
new Array(1.0 , 156.9424537, 3745.310488, 9834.698876, 66924.28357);
503 var p6 =
new Array(1.000827619, 664.9143136, 62972.92665, 475554.6998, -5743609.109);
504 var q6 =
new Array(1.0 , 651.4101098, 56974.73333, 165917.4725, -2815759.939);
505 var a1 =
new Array(0.04166666667,-0.01996527778, 0.02709538966);
506 var a2 =
new Array(-1.845568670,-4.284640743);
510 if (u < 1e-10)
return 0.0;
513 denlan = 0.3989422803*(ue/us)*(1+(a1[0]+(a1[1]+a1[2]*u)*u)*u);
516 denlan = Math.exp(-u)*Math.sqrt(u)*
517 (p1[0]+(p1[1]+(p1[2]+(p1[3]+p1[4]*v)*v)*v)*v)/
518 (q1[0]+(q1[1]+(q1[2]+(q1[3]+q1[4]*v)*v)*v)*v);
520 denlan = (p2[0]+(p2[1]+(p2[2]+(p2[3]+p2[4]*v)*v)*v)*v)/
521 (q2[0]+(q2[1]+(q2[2]+(q2[3]+q2[4]*v)*v)*v)*v);
523 denlan = (p3[0]+(p3[1]+(p3[2]+(p3[3]+p3[4]*v)*v)*v)*v)/
524 (q3[0]+(q3[1]+(q3[2]+(q3[3]+q3[4]*v)*v)*v)*v);
527 denlan = u*u*(p4[0]+(p4[1]+(p4[2]+(p4[3]+p4[4]*u)*u)*u)*u)/
528 (q4[0]+(q4[1]+(q4[2]+(q4[3]+q4[4]*u)*u)*u)*u);
531 denlan = u*u*(p5[0]+(p5[1]+(p5[2]+(p5[3]+p5[4]*u)*u)*u)*u)/
532 (q5[0]+(q5[1]+(q5[2]+(q5[3]+q5[4]*u)*u)*u)*u);
535 denlan = u*u*(p6[0]+(p6[1]+(p6[2]+(p6[3]+p6[4]*u)*u)*u)*u)/
536 (q6[0]+(q6[1]+(q6[2]+(q6[3]+q6[4]*u)*u)*u)*u);
538 u = 1/(v-v*Math.log(v)/(v+1));
539 denlan = u*u*(1+(a2[0]+a2[1]*u)*u);
544 JSROOT.Math.Landau =
function(x, mpv, sigma, norm) {
545 if (sigma <= 0)
return 0;
546 var den = JSROOT.Math.landau_pdf((x - mpv) / sigma, 1, 0);
547 if (!norm)
return den;
551 JSROOT.Math.inc_gamma_c =
function(a,x) {
552 return JSROOT.Math.igamc(a,x);
555 JSROOT.Math.chisquared_cdf_c =
function(x,r,x0) {
556 return JSROOT.Math.inc_gamma_c ( 0.5 * r , 0.5* (x-x0) );
559 JSROOT.Math.Prob =
function(chi2, ndf) {
560 if (ndf <= 0)
return 0;
563 if (chi2 < 0)
return 0;
567 return JSROOT.Math.chisquared_cdf_c(chi2,ndf,0);
570 JSROOT.Math.gaus =
function(f, x, i) {
571 return f[
'fParams'][i+0] * Math.exp(-0.5 * Math.pow((x-f[
'fParams'][i+1]) / f[
'fParams'][i+2], 2));
574 JSROOT.Math.gausn =
function(f, x, i) {
575 return JSROOT.Math.gaus(f, x, i)/(Math.sqrt(2 * Math.PI) * f[
'fParams'][i+2]);
578 JSROOT.Math.expo =
function(f, x, i) {
579 return Math.exp(f[
'fParams'][i+0] + f[
'fParams'][i+1] * x);
582 JSROOT.Math.landau =
function(f, x, i) {
583 return JSROOT.Math.Landau(x, f[
'fParams'][i+1],f[
'fParams'][i+2],
false);
586 JSROOT.Math.landaun =
function(f, x, i) {
587 return JSROOT.Math.Landau(x, f[
'fParams'][i+1],f[
'fParams'][i+2],
true);