coth hyperbolic cotangent

## Syntax

    t = coth(x)

## Arguments

x

  vector or matrix of real or complex numbers (full or sparse-encoded).

t

  a full-encoded vector or matrix of real or complex numbers.

## Description

The elements of `t` are the hyperbolic cotangent of elements of `x`.

`coth(0)` not being 0, the result for any input sparse-encoded matrix is always full-encoded (as for `cos()`).

## Examples

    x = [1, 2*%i]
    t = exp(x);
    (t-ones(x)./t).\(t+ones(x)./t)
    coth(x)
    coth([-0 0])

    // With sparses:
    s = sparse([1 1; 3 1; 2 2; 2 3; 1 3],[0.02 0.7 0.15 0.4 3],[3 3])
    coth(s)   // no longer sparse

    --> (t-ones(x)./t).\(t+ones(x)./t)
     ans  =
       1.3130353   0.4576576i

    --> coth(x)
     ans  =
       1.3130353   0.4576576i

    --> coth([-0 0])
     ans  =
      -Inf   Inf

    --> // With sparses:
    --> s = sparse([1 1; 3 1; 2 2; 2 3; 1 3],[0.02 0.7 0.15 0.4 3],[3 3])
     s  =
    (  3,  3) sparse matrix
    (  1,  1)      0.02
    (  1,  3)      3.
    (  2,  2)      0.15
    (  2,  3)      0.4
    (  3,  1)      0.7

    --> coth(s)   // no longer sparse
     ans  =
       50.006666   Inf         1.0049698
       Inf         6.7165918   2.6319324
       1.6546216   Inf         Inf

## See also

- cotg

## History

6.1.0 Extension to sparse matrices.