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Functions

Arguments to math functions in gnuplot can be integer, real, or complex unless otherwise noted. Functions that accept or return angles (e.g. sin(x)) treat angle values as radians, but this may be changed to degrees using the command set angles.

Math library and built-in functions
Function Arguments Returns
abs(x) int or real |x|, absolute value of x; same type
abs(x) complex length of x, √( Re(x)2 + Im(x)2 )
acos(x) any cos-1 x (inverse cosine)
acosh(x) any cosh-1 x (inverse hyperbolic cosine)
airy(x) real Airy function Ai(x) for real x
arg(x) complex the phase of x
asin(x) any sin-1 x (inverse sin)
asinh(x) any sinh-1 x (inverse hyperbolic sin)
atan(x) any tan-1 x (inverse tangent)
atan2(y,x) int or real tan-1(y/x) (inverse tangent)
atanh(x) any tanh-1 x (inverse hyperbolic tangent)
besj0(x) real J0 Bessel function of x in radians
besj1(x) real J1 Bessel function of x in radians
besjn(n,x) int,real Jn Bessel function of x in radians
besy0(x) real Y0 Bessel function of x in radians
besy1(x) real Y1 Bessel function of x in radians
besyn(n,x) int,real Yn Bessel function of x in radians
besi0(x) real Modified Bessel function of order 0, x in radians
besi1(x) real Modified Bessel function of order 1, x in radians
besin(n,x) int,realModified Bessel function of order n, x in radians
cbrt(x) real cube root of x, domain and range both real
ceil(x) any x⌉, smallest integer not less than x (real part)
conj(x) complex complex conjugate of x
cos(x) radians cos x, cosine of x
cosh(x) any cosh x, hyperbolic cosine of x in radians
EllipticK(k) real k in (-1:1) K(k) complete elliptic integral of the first kind
EllipticE(k) real k in [-1:1] E(k) complete elliptic integral of the second kind
EllipticPi(n,k) real n<1, real k in (-1:1) Π(n,k) complete elliptic integral of the third kind
erf(x) any erf(Re(x)), error function of real(x)
erfc(x) any erfc(Re(x)), 1.0 - error function of real(x)
exp(x) any ex, exponential function of x
expint(n,x) any En(x), exponential integral function of x
floor(x) any x⌋, largest integer not greater than x (real part)
gamma(x) any Γ(Re(x)), gamma function of real(x)
ibeta(p,q,x) any ibeta(Re(p,q,x)), ibeta function of real(p,q,x)
inverf(x) any inverse error function real(x)
igamma(a,z) complex igamma(a>0,z), igamma function of complex a>0,z
imag(x) complex Im(x), imaginary part of x as a real number
int(x) real integer part of x, truncated toward zero
invibeta(a,b,p) 0<p<1 inverse incomplete beta function
invigamma(a,p) 0<p<1 inverse incomplete gamma function
invnorm(x) any inverse normal distribution function real(x)
LambertW(z,k) complex, int kth branch of complex Lambert W function
lambertw(x) real principal branch (k=0) of Lambert W function
lgamma(x) real lgamma(Re(x)), lgamma function of real(x)
lnGamma(x) complex lnGamma(x) valid over entire complex plane
log(x) any ln x, natural logarithm (base e) of x
log10(x) any log10 x, logarithm (base 10) of x
norm(x) any norm(x), normal distribution function of real(x)
rand(x) int pseudo random number in the interval (0:1)
real(x) any Re(x), real part of x
sgn(x) any 1 if x > 0, -1 if x < 0, 0 if x = 0. ℑ(x) ignored
Sign(x) complex 0 if x = 0, otherwise x/|x|
sin(x) any sin x, sine of x
sinh(x) any sinh x, hyperbolic sine of x in radians
sqrt(x) any x, square root of x
SynchrotronF(x) real Synchtrotron function F
tan(x) any tan x, tangent of x
tanh(x) any tanh x, hyperbolic tangent of x in radians
uigamma(a,x) real uigamma(a,x), upper incomplete gamma function a>0,x
voigt(x,y) real convolution of Gaussian and Lorentzian
zeta(s) any Riemann zeta function

 

Special functions from libcerf (only if available)
Function Arguments Returns
cerf(z) complex complex error function
cdawson(z) complex complex Dawson's integral
faddeeva(z) complex rescaled complex error function w(z) = exp(-z²) × erfc(-iz)
erfi(x) real imaginary error function erfi(x) = -i × erf(ix)
FresnelC(x) real cosine (real) component of Fresnel integral
FresnelS(x) real sine (imaginary) component of Fresnel integral
VP(x,sigma,gamma) real Voigt profile
VP_fwhm(sigma,gamma) real Voigt profile full width at half max

 

String functions
Function Arguments Returns
gprintf("format",x,...) any string result from applying gnuplot's format parser
sprintf("format",x,...) multiple string result from C-language sprintf
strlen("string") string number of characters in string
strstrt("string","key") strings int index of first character of substring "key"
substr("string",beg,end) multiple string "string"[beg:end]
split("string","separator") string array containing individual fields of original string
join(array,"separator") array,string concatenates array elements into a string
strftime("timeformat",t) any string result from applying gnuplot's time parser
strptime("timeformat",s) string seconds since year 1970 as given in string s
system("command") string string containing output stream of shell command
trim(" string ") string string without leading or trailing whitespace
word("string",n) string, int returns the nth word in "string"
words("string") string returns the number of words in "string"

 

time functions
Function Arguments Returns
time(x) any the current system time
timecolumn(N,format) int, string formatted time data from column N of input data
tm_hour(t) time in sec the hour
tm_mday(t) time in sec the day of the month
tm_min(t) time in sec the minute
tm_mon(t) time in sec the month
tm_sec(t) time in sec the second
tm_wday(t) time in sec the day of the week
tm_week(t) time in sec ISO 8601 week of year
tm_yday(t) time in sec the day of the year
tm_year(t) time in sec the year
weekdate_iso(year,week,day) int time eqv to ISO 8601 standard week date
weekdate_cdc(year,week,day) int time eqv to CDC epidemiological week date

 

other gnuplot functions
Function Arguments Returns
column(x) int or string contents of column x during data input.
columnhead(x) int string containing first entry of column x in datafile.
exists("X") string returns 1 if a variable named X is defined, 0 otherwise.
hsv2rgb(h,s,v) h,s,v in [0:1] converts HSV color to 24bit RGB color.
index(A,x) array, any returns i such that A[i] equals x
palette(z) real 24bit RGB palette color mapped to z
rgbcolor("name") string 32bit ARGB color from name
stringcolumn(x) int content column x as a string.
valid(x) int test validity of column x during datafile input
value("name") string returns the current value of the named variable.
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