# flairby CERN

Advanced graphical user interface for particle simulation programs
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## F5.2.2} Functions

``` Square root, exponential, logarithms

Function        Description
~~~~~~~~        ~~~~~~~~~~~
sqrt(x)         Square root function
exp(x)          Exponential function
log(x)          Natural logarithm (base e)
log10(x)        Common logarithm (base 10)

Trigonometric functions
Function       Description
~~~~~~~~       ~~~~~~~~~~~
sin(x)         Trigonometric functions
cos(x)
tan(x)
asin(x)        Inverse trigonometric functions.
acos(x)
atan(x)
atan2(y, x)    Evaluates to atan(y/x),

Hyperbolic functions
Function       Description
~~~~~~~~       ~~~~~~~~~~~
sinh(x)        Hyperbolic functions
cosh(x)
tanh(x)
asinh(x)       Inverse Hyperbolic functions
acosh(x)
atanh(x)

Bessel functions
Function       Description
~~~~~~~~       ~~~~~~~~~~~
besj0(x)       Bessel function of the first kind of order 0
besy0(x)       ... second kind of order 0
besj1(x)       ... first kind of order 1
besy1(x)       ... second kind of order 1

Error integral and related functions
Function       Description
~~~~~~~~       ~~~~~~~~~~~
erf(x)         Error function
erfc(x)        Complementary error function
erfc(x) = 1 - erf(x)
inverf(x)      Inverse error function
invnorm(x)     Inverse normal distribution function
norm(x)        Normal (Gaussian) distribution function
norm(x) = 0.5*(1+erf(x/sqrt(2)))

Gamma function and related functions
Function       Description
~~~~~~~~       ~~~~~~~~~~~
gamma(x)       Gamma function
ibeta(p, q, x) Incomplete beta function
igamma(a, x)   Incomplete gamma function
lgamma(x)      Natural logarithm of gamma function:
lgamma(x) = log( gamma(x) )

Miscellaneous mathematical functions
Function       Description
~~~~~~~~       ~~~~~~~~~~~
abs(x)         Absolute value for real or complex x.
ceil(x)        Smallest integer not less than x
floor(x)       Largest integer not greater than x
int(x)         Integer part of x, truncated to zero.
lambertw(x)    Lambert-W Function
(the inverse of f(w) = w exp(w)).
rand(x)        Random number generator
sgn(x)         Sign function (-1 if x<0; 0 if x=0; 1 if x>0).

Functions for complex arguments
Function       Description
~~~~~~~~       ~~~~~~~~~~~
abs(x)         Absolute value of x: sqrt( real(x)**2 + imag(x)**2 )
arg(x)         Phase angle of x: atan(imag(x)/real(x))
imag(x)        Imaginary part of x
real(x)        Real part of x

String functions
Function             Description
~~~~~~~~             ~~~~~~~~~~~
exists("x")          Returns 1 if a variable with that name is defined,
0 otherwise.
strlen("s")          String length
substr("s",i,j)      Substring equivalent to str[i:j]
strstrt("str","key") Returns position of key in str

words( "str" )       Number of words in str
word("str",n )       Return nth word of str
sprintf("format",...)
C formatting of a string
gprintf( "format", ... )
gnuplot formatting of a string
system("cmd")        Returns the output of the shell command.

Column manipulation functions
Function             Description
~~~~~~~~             ~~~~~~~~~~~
column(x)            Returns the current value of that column
stringcolumn(x)      Returns the current value of that column as
string
valid(x)             Returns 1 is the current value of that
column is valid.

Time column handling functions
Function             Description
~~~~~~~~             ~~~~~~~~~~~
timecolumn(x)        Parses the column with the format in
set timefmt
tm_sec(x)            Return the seconds part of the time
tm_min(x)            Minutes part
tm_hour(x)           Hours
tm_mday(x)           Month day
tm_mon(x)            Month
tm_year(x)           Year
tm_wday(x)           Week day
tm_yday(x)           Year day

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