Octave Programming Tutorial/General mathematical functions
General Mathematical Functions
e is the base of the natural logarithm.
e without arguments returns the scalar
e(N) returns a square matrix of
e of size
e(N, M, ...) where the arguments are dimensions of some matrix of
e(..., CLASS) where
CLASS is an optional argument that specifies the return type,
eps is the machine precision and returns the relative spacing between any floating point number and the next representable number. This value is system dependent.
eps returns the value of
eps(X) returns the spacing between X and the next value.
eps with more than one argument is treated like
e with the matrix value being
All of the constant functions listed are defined exactly like
pi is the ratio of the circumference to the diameter of any circle.
I is the imaginary unit defined so
I^2 = -1.
Inf is used for values that overflow the standard IEEE floating point range or the result of division by zero.
NaN is used for various results that are not well defined or undefined. Note that
NaN never equals other
NaN values. Use the function
isnan to check for
realmax is the largest floating point value representable.
realmin is the smallest floating point value representable.
ceil(X) return the highest integer not greater than
X or lowest integer not less than
fix(X) return the integer closest to
X or truncate
X towards zero, respectively.
mod(X,Y) returns x - y * fix( x ./ y ) or x - y * floor( x ./ y ), they are the same except when dealing with negative arguments.
hypot(X, Y) returns the length of the hypotenuse of a right-angle triangle with the adjacent and opposite of size
abs(X) return absolute of x.
sign(X) return sign of the x (-1, 0 or +1).
tan(X) — the elemental functions that we all know and love. They take their arguments in radians.
asin(X) are the inverses of
sin and are able to compute arguments not contained in the range [-1,1].
atan2(Y, X) are the 2 available inverses of tan.
atan is a simple inverse whereas
atan2 takes 2 arguments and returns an angle in the appropriate quadrant. More information on
atan2 can be found
here. Note that one can add the character
d to any of the functions except
atan2 and they will work in degrees rather than radians. For example:
asind(0.3) = asin(0.3*180/pi)
exp(x) , exponential funtion of x
log(x) , natural logarithmic of x, log
e NOT log 10
tanh(X) are analog to their more prosaic counterparts but deal with the unit hyperbola instead of the unit circle. They also take their arguments in radians.
atanh(X) are the inverses of
Unlike their circular uncles they cannot be made to take their arguments in degrees.