Octave Programming Tutorial/General mathematical functions
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General Mathematical Functions[edit | edit source]
Constants[edit | edit source]
eis the base of the natural logarithm.
ewithout arguments returns the scalar e.
e(N)returns a square matrix of e of size
e(N, M, ...)where the arguments are dimensions of some matrix of e.
CLASSis an optional argument that specifies the return type,
epsis the machine precision and returns the relative spacing between any floating point number and the next representable number. This value is system dependent.
epsreturns the value of
eps(X)returns the spacing between X and the next value.
epswith more than one argument is treated like
ewith the matrix value being
- All of the constant functions listed are defined exactly like
piis the ratio of the circumference to the diameter of any circle.
Iis the imaginary unit defined so
I^2 = -1.
Infis used for values that overflow the standard IEEE floating point range or the result of division by zero.
NaNis used for various results that are not well defined or undefined. Note that
NaNnever equals other
NaNvalues. Use the function
isnanto check for
realmaxis the largest floating point value representable.
realminis the smallest floating point value representable.
Arithmetic Functions[edit | edit source]
ceil(X)return the highest integer not greater than
Xor lowest integer not less than
fix(X)return the integer closest to
Xtowards 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).
Ordinary Trigonometry[edit | edit source]
tan(X)— the elemental functions that we all know and love. They take their arguments in radians.
asin(X)are the inverses of
sinand are able to compute arguments not contained in the range [-1,1].
atan2(Y, X)are the 2 available inverses of tan.
atanis a simple inverse whereas
atan2takes 2 arguments and returns an angle in the appropriate quadrant. More information on
atan2can be found here.
- Note that one can add the character d to any of the functions except
atan2and 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, loge NOT log 10
Hyperbolic Trigonometry[edit | edit source]
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.