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acosh

hyperbolic cosine inverse

Syntax

t = acosh(x)

Arguments

x, t

each is a real or complex vector or matrix. t has the sizes of x.

Description

acosh(x) returns t such that cosh(t)==x and real(t)>=0. -t are always other possible answers.

For real input numbers -1 < x < 1, real(t)==0 and imag(t) belongs to ]0, %pi[.

For complex numbers x, imag(t) belongs to [-pi, pi] and any t + k*%pi*%i with integer k are other possible answers.

Sample

Examples

x = [ -2 -1.001 -1 -0.999 -0.5  0
       2  1.001  1  0.999  0.5  0]'
t = acosh(x)
cosh(t) - x
cosh(-t) - x

// With complex numbers:
acosh([-0.01*%i  0.01*%i
       -0.1*%i   0.1*%i
       -%i       %i
       -10*%i    10*%i
       -1 - %i,  1 + %i
       -2 - 2*%i, 2 + 2*%i
       ])

See also


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