Advanced graphical user interface for particle simulation programs
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F3.6} Function evaluation

 Flair has the ability to evaluate functions in the place of
 numerical values in the CARD's what. Functions can be defined
 by entering the expression starting with the equal sign '='

 The same function evaluation can be used on the built-in calculator
 frame (under Tools). The expression is evaluated with the press of
 [Return] key.
 [Shift-Return] to add an extra line. To show that this is a
 continuation line insert a space character in front.

 e.g.  Dx: =1.5*mm*fwhm
       cosx: =sind(ang)
       with ang defined as "#define ang 10" with a previous card

 Set in the BEAM card the beam size to 1.5mm in FWHM
 The functions are kept in the input file as special decorator
 comments preceding the card with the format

 The input file will be saved as:
 BEAM           -20.0 -0.082425     -1.7 .353223007                 1.0PROTON
The special functions what(), body() and card() allow the user to refer to whats from the current card, another body card or any other card in the input file e.g * create a symmetric box around 0. All [XYZ]max are the * positive of the [XYZ]min RPP box Xmin:-10 Xmax:=-what(1) Ymin:-20 Ymax:=-what(3) Zmin:-30 Zmax:=-what(5) * create a plane using the what(6) of body 'box' plus 2mm XYP PlaneZ Z:=body(box,6)+2*mm * or using the card() function XYP PlaneZ Z:=card(RPP,box,6)+2*mm NOTES: 1. During loading of the input file in such a decorator is found then corresponding what will be replaced by the function expression. 2. During saving of the input file the card will be written with the decorator comment preceding it and the correct numerical evaluation of the function. 3. WARNING. If you manually change the numerical value in the input file with an editor, then next time you open through flair it will replace the value with the function evaluation. 4. What's where the sign is controlling the type of the value have to be manually inserted by the user and not by flair with the drop down box. For example in BEAM what(1) if positive means momentum, negative is energy. By entering a function in what(1) the drop down box in flair controlling the sign will be ignored. 5. Function can return also a string value e.g. a material name for dynamic material substitution #define MAT CARBON and later in the code ASSIGNMAT =MAT MYREGION 6. Due to limitation in processing speed of python, all #define are evaluated once. Therefore multiple #define will be overridden with the last value. This functionality is due to change in the future if a way is found. Global Variables and Functions Name Value Description ----- ------- ------------------- Constants ~~~~~~~~~ a 1/137.035989561 Fine constant pi 3.1415926535897931 e 2.7182818284590451 Euler's number c 299792458e2 Speed of light cm/s Na 6.0221367e23 Avogadro number re 2.8179409183694872d-13 Electron radius qe 1.60217646E-19 Electron charge fwhm 2*sqrt(2*log(2)) Full width at half maximum = 2.3548200450309493 Particle mass ~~~~~~~~~~~~~ amu 0.93149432 Atomic mass unit amuC12 0.93123890 Carbon12 unified atomic mass unit amugr 1.6605402E-24 Amu in g Mp 0.93827231 Proton mass in GeV Mn 0.93956563 Neutron mass in GeV Me 0.510998910e-3 Electron mass in GeV Metric distance ~~~~~~~~~~~~~~~ nm 0.1E-6 nano meter um 0.1E-3 micro meter mm 0.1 millimeter cm 1 centimeter dm 10 decimeter m 100 meter km 100E3 kilometer Imperial distance ~~~~~~~~~~~~~~~~~ inch 2.54 imperial inch feet 30.48 or ft imperial feet mile 160934.4 or mi imperial mile Time ~~~~ ns 1.0e-9 nano-second us 1.0e-6 micro-second ms 0.001 milli-second s 1 second min 60 minute hour 3600 hour day 86400 day week 7*86400 week month 365.25/12*86400 month as 1/12th of a year year 365.25*86400 year Energy ~~~~~~ eV 1e-9 electron volt keV 1e-6 kilo electron volt MeV 1e-3 Mega electron volt GeV 1.0 Giga electron volt TeV 1e3 Tera electron volt PeV 1e6 Peta electron volt J eV/qe Joule Gy eV/qe/kg Gray Metric ~~~~~~ yotta 1e24 zetta 1e21 exa 1e18 peta 1e15 tera 1e12 giga 1e9 mega 1e6 kilo 1e3 hecto 1e2 deca 1e1 deci 1e-1 centi 1e-2 milli 1e-3 micro 1e-6 nano 1e-9 pico 1e-12 femto 1e-15 atto 1e-18 zepto 1e-21 yocto 1e-24 Special variables ----------------- frame Frame number as set in the timeframe Mass of particles ----------------- To get the mass of particles as defined in FLUKA use the name particle name prefixed with the letter m Suffic +/- is replaced with p/n Intermediate - are removed e.g. PROTON mass = mPROTON 4-HELIUM mass = m4HELIUM MUON- mass = mMUONn MUON+ mass = mMUONp Physics functions ----------------- p2T(p,m) convert momentum in kinetic energy T2p(T,m) convert kinetic energy to momentum dT2dp(T,dT,m) convert kinetic energy spread into momentum spread T2g(T,m) convert kinetic energy to relativistic gamma g2b(g) gamma to beta X0(Z,A) radiation length in [g/cm2] lhad(A) ~hadronic interaction length (g/cm2) (1-100GeV) Card reference functions ------------------------ body(n,w) return the w'th what of body named 'n' body(BLKBODY,4) - return what(4) of BLKBODY card(t,n,w) return the w'th what of card tag 't' with name 'n' if n is string or ordered 'n' if n is integer card(BEAM,0,1) - return BEAM energy of first BEAM card card(USRBIN,enedep,1) - return what(1) of USRBIN with name=enedep spline(n,t) return the interpolation point/vector of spline names 'n' for time t. It can be used for movies, setting the camera position from the frame number, or dose calculations for the intervention planning tool =spline('camera.pos', frame).x what(n) return the n'th what of current card Mathematical Functions -------------------------- acos(x) radian based trig functions asin(x) atan(x) cos(x) sin(x) tan(x) acosd(x) degrees based trig functions asind(x) atand(x) cosd(x) sind(x) tand(x) atan2(y,x) return arctan(y/x) omega(x) return solid angle for x-radians polar angle omegad(x) return solid angle for x-degrees polar angle radians(x) convert degrees to radians degrees(x) convert radians to degrees acosh(x) Hyperbolic functions asinh(x) atanh(x) cosh(x) sinh(x) tanh(x) exp(x) Exponential e**x log(x) Natural logarithm of x log1p(x) log(1+x) log10(x) Logarithm based 10 of x sqrt(x) pow(x,y) x**y factorial(n) n! abs(x) absolute value of x ceil(x) ceiling, smallest integral variable >= x copysign(x,y) return x with sign of y float(x) return x as float, 0 on failure floor(x) largest integral variable <= x fmod(x,y) module x % y hypot(x,y) hypotenuse sqrt(x**2+y**2) int(x) return integer part of x, 0 on failure (e.g. with string) len(x) return length of string, number of items in a vector trunc(x) return the nearest integral towards 0 Vector operations ~~~~~~~~~~~~~~~~~ Vectors can be defined as Vector(x,y,x) or with curly brackets {x, y, z} Coordinates can be accessed as .x .y .z or [0], [1], [2] vector.x or vector[0] Operators: + - addition/subtraction of two vectors a+/-b * scale with a number 2.0*a * dot dot product a*b or ^ cross cross product a^b or a.cross(b) length() length of vector a.length() norm() normalize vector x(), y(), z() return x, y or z component orthogonal() return a vector orthogonal to current direction() return string describing direction X/Y/Z phi() return azimuthal angle of vector theta() return polar angle of vector perp() return perpendicular component of vector Arrays, tuples and lists ~~~~~~~~~~~~~~~~~~~~~~~~ [1,2,...] [] define lists or arrays which are mutable (1,2,...) () defines tuples which are immutable LIST[index] [index] returns the index item of list TUPLE[index] [index] returns the index item of list Tuples can be used for multiple runs with different materials assignments e.g. #define MATS ('LEAD', 'GOLD', 'SILICON', 'COPPER') #define I 0 ASSIGNMAT =MATS[I] REGION and I can be used as a Loop variable from the Runs Frame to loop from 0..2
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