Octave Programming Tutorial/General mathematical functions

General Mathematical Functions

Constants

• e is the base of the natural logarithm.

e without arguments returns the scalar e.

e(N) returns a square matrix of e of size N.

e(N, M, ...) where the arguments are dimensions of some matrix of e.

e(..., CLASS) where CLASS is an optional argument that specifies the return type, double or single.

• 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(1.0).

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 eps(1.0).

• All of the constant functions listed are defined exactly like e

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 NaN.

realmax is the largest floating point value representable.

realmin is the smallest positive floating point value representable.

Arithmetic Functions

• floor(X) and ceil(X) return the highest integer not greater than X or lowest integer not less than X, respectively.
• round(X) and fix(X) return the integer closest to X or truncate X towards zero, respectively.
• rem(X,Y) and 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 X and Y.
• abs(X) return absolute of x.
• sign(X) return sign of the x (-1, 0 or +1).

Ordinary Trigonometry

• cos(X), sin(x) and tan(X) — the elemental functions that we all know and love. They take their arguments in radians.
• acos(X), asin(X) are the inverses of cos and sin and are able to compute arguments not contained in the range [-1,1].
• atan(X) and 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 function of x
• log(x) , natural logarithmic of x, log_e NOT log ₁₀

Hyperbolic Trigonometry

• cosh(X), sinh(X) and 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.
• acosh(X), asinh(X) and atanh(X) are the inverses of cosh, sinh and tanh.
• Unlike their circular uncles they cannot be made to take their arguments in degrees.