asech

Inverse hyperbolic secant in radians

Usage

asech(A)

• A should be an array, which can be complex or real.
• It returns an array containing the inverse hyperbolic secant (in radians) of each element of A.
• For real elements of A not lying in the interval $[0,1]$, it returns complex numbers. See example below.
• The output has the same size as A.

Example

Input

• asech(A) gives a complex number when abs(A) is negative or exceeds 1.

x = linspace(-2,2,20)
[x; asech(x)]

Output

x = 
Columns 1 to 9:
-2.0000  -1.7895  -1.5789  -1.3684  -1.1579  -0.9474  -0.7368  -0.5263  -0.3158
Columns 10 to 18:
-0.1053   0.1053   0.3158   0.5263   0.7368   0.9474   1.1579   1.3684   1.5789
Columns 19 to 20:
 1.7895   2.0000

ans = 
Columns 1 to 4:
-2.0000 + 0.0000i  -1.7895 + 0.0000i  -1.5789 + 0.0000i  -1.3684 + 0.0000i
 0.0000 - 2.0944i   0.0000 - 2.1638i   0.0000 - 2.2566i   0.0000 - 2.3902i
Columns 5 to 8:
-1.1579 + 0.0000i  -0.9474 + 0.0000i  -0.7368 + 0.0000i  -0.5263 + 0.0000i
 0.0000 - 2.6132i   0.3318 - 3.1416i   0.8218 - 3.1416i   1.2572 - 3.1416i
Columns 9 to 12:
-0.3158 + 0.0000i  -0.1053 + 0.0000i   0.1053 + 0.0000i   0.3158 + 0.0000i
 1.8199 - 3.1416i   2.9417 - 3.1416i   2.9417 + 0.0000i   1.8199 + 0.0000i
Columns 13 to 16:
 0.5263 + 0.0000i   0.7368 + 0.0000i   0.9474 + 0.0000i   1.1579 + 0.0000i
 1.2572 + 0.0000i   0.8218 + 0.0000i   0.3318 + 0.0000i   0.0000 - 0.5284i
Columns 17 to 20:
 1.3684 + 0.0000i   1.5789 + 0.0000i   1.7895 + 0.0000i   2.0000 + 0.0000i
 0.0000 - 0.7513i   0.0000 - 0.8849i   0.0000 - 0.9778i   0.0000 - 1.0472i