Gnuplot Introductory Tutorials 3__ Math software

constants, operators, and functions Digital

Gnuplot that numbers can be divided into integers, real numbers and complex numbers:

Integer: Gnuplot is the same as the C language, with 4 byte stored integers. It can represent an integer between 2147483647 and +2147483647.

Real number: A significant number of digits representing about 6 or 7 digits, or numbers that are not greater than 308.

Plural: the plural is represented by {<real>,<imag>}. The real part of the complex number of <real> is,<imag>, and the two parts are represented by real numbers. such as 3 + 2i is indicated by {3,2}.

The principle of gnuplot is to store numbers in integers if they are stored in integers, otherwise stored in real numbers and then stored in complex numbers. For example, in gnuplot execution

Print 1/3*3
print 1./3*3

The results of 0 and 1.0 were obtained respectively. This is because the former uses an integer calculation, and the latter takes the result of a real number calculation. Perform

Print 1234.567
print 12345 + 0.56789
Print 1.23e300 * 2e6
print 1.23e300 * 2e8

The results of 1234.57, 12345.6, 2.46e+304 and undefined value are obtained respectively. These examples are limited by the number of significant digits and the maximum number of digits that can be represented by real numbers. This is what we should pay attention to. operator

The gnuplot operator is essentially the same as the C language. All operations can be done in integers, real numbers, or complex numbers.

Table 1 unary Operators

Symbol	Example	Explanation
-	-A	unary minus
~	~a	One ' s complement
!	!a	Logical negation
!	A!	Factorial

Table 2 Binary Operators

Symbol	Example	Explanation
**	A**b	exponentiation
*	A*b	Multiplication
/	A/b	Division
%	A%b	Modulo
+	A+b	Addition
-	A-b	Subtraction
==	A==b	Equality
!=	A!=b	Inequality
&	A&b	Bitwise AND
^	A^b	Bitwise EXCLUSIVE OR
|	A|b	Bitwise inclusive OR
&&	A&&b	Logical AND
||	a| | B	Logical OR
?:	A?b:c	Ternary operation

function

The parameters of a function in gnuplot can be integers, real numbers, or complex numbers. Table 3 is the function provided by Gnuplot.

Table 3 Gnuplot functions

Function	Auguments	Returns
ABS (x)	Any	Absolute value of x, |x|; Same type
ABS (x)	Complex	Length of x, sqrt (real (x) ^2 + imag (x) ^2)
ACOs (x)	Any	1/cos (x) (inverse cosine) in radians
Acosh (x)	Any	cosh−1 x (inverse hyperbolic cosine) in radians
ARG (x)	Complex	The phase of X in radians
ASIN (x)	Any	1/sin (x) (inverse sin) in radians
Asinh (x)	Any	sinh−1 x (inverse hyperbolic sin) in radians
Atan (x)	Any	1/tan (x) (inverse tangent) in radians
ATAN2 (y,x)	int or real	Tan−1 (y/x) (Inverse tangent)
Atanh (x)	Any	tanh−1 x (inverse hyperbolic tangent) in radians
Besj0 (x)	int or real	J0 Bessel function of X
BESJ1 (x)	int or real	J1 Bessel function of X
Besy0 (x)	int or real	Y0 Bessel function of X
Besy1 (x)	int or real	Y1 Bessel function of X
Ceil (x)	Any	Smallest integer not less than x (real part)
COS (x)	Radians	Cos x, cosine of X
Cosh (x)	Radians	cosh x, hyperbolic cosine of X
ERF (x)	Any	ERF (Real (x)), error function of the real (x)
ERFC (x)	Any	ERFC (Real (x)), 1.0-error function of real (x)
EXP (x)	Any	exponential function of X
Floor (x)	Any	Largest integer not greater than X (real part)
Gamma (x)	Any	Gamma (Real (x)), gamma function of the real (x)
Ibeta (p,q,x)	Any	Ibeta (p,q,x), Ibeta function of real (P,Q,X)
Inverf (x)	Any	Inverse error function of real (x)
Igamma (a,x)	Any	Igamma (a,x), Igamma function of real (A,X)
Imag (x)	Complex	Imaginary part of X as a real number
Invnorm (x)	Any	Inverse Normal distribution function of real (x)
int (x)	Real	Integer part of x, truncated toward zero
LAMBERTW (x)	Real	Lambert W function
Lgamma (x)	Any	Lgamma (Real (x)), Lgamma function of real (x)
Log (x)	Any	ln (x), natural logarithm (base e) of X
LOG10 (x)	Any	Log (x), logarithm (base) of X
Norm (x)	Any	Normal distribution (Gaussian) function of real (x)
RAND (x)	Any	Normal distribution (Gaussian) function of real (x)
Real (x)	Any	Rand (Real (x)), pseudo random number generator
SGN (x)	Any	Real part of X
Sin (x)	Any	1 if x>0,-1 if x<0, 0 if x=0. IMAG (x) ignored
Sinh (x)	Radians	Sin (x), sine of X
sqrt (x)	Radians	Sinh (x), hyperbolic sine x
Tan (x)	Any	sqrt (x), square root of X
Tanh (x)	Complex	Tan (x), tangent of X
Column (x)	Int	Column x during datafile manipulation.
Defined (X)	Variable name	Returns 1 if a variable X is defined, 0 otherwise.
TM Hour (x)	Int	The hour
TM Mday (x)	Int	The day of the month
TM min (x)	Int	The minute
TM Mon (x)	Int	The Month
TM sec (x)	Int	The second
TM Wday (x)	Int	The day of the week
TM Yday (x)	Int	The day of the year
TM year (x)	Int	The year
Valid (x)	Int	Test validity of column (x) during datafile Manip.

Here are some examples:

Plot [0.5:20] Besj0 (x), besj1 (x), Besy0 (x), besy1 (x)
plot [0:5] Erf (x), ERFC (x), Inverf (x)

user-defined functions and constants

In Gnuplot, the user can customize the function. A function can have 1 to 5 arguments. The syntax for its definition function is as follows:

<function-name> (<dummy1> {,<dummy2> {, ...}}) = <expression>

The syntax for user-defined constants is as follows:

<variable-name> = <constant-expression>

Here are some examples:

# constant W is 2.
w = 2                       
# constant q is an integer less than but closest to Tan (PI/2-0.1).
q = Floor (tan (PI/2-0.1))  
# function f (x) is sin (w*x), where w is constant.
f (x) = sin (w*x)             
# function sinc (x) is sin (pi*x)/(pi*x).
sinc (x) = sin (pi*x)/(pi*x)  
# function Delta (t) is a pulse function.
Delta (t) = (t = = 0) 
# function ramp (t) when it is less than 0 is zero, when its greater than 0 is a straight line with a slope equal to 1.
Ramp (t) = (T > 0) t:0 
# function min (a,b) takes the smaller number of both.
min (a,b) = (A < b)? a:b
Comb (n,k) = n!/(k!* (n-k)!)
Len3d (x,y,z) = sqrt (x*x+y*y+z*z)
plot f (x) = sin (x*a), a = 0.2, f (x), a = 0.4, f (x)

The

gnuplot  defined constants have only  pi  (pi = 3.14159).