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# coth

t = coth(x)

x

t

### 説明

tの要素は xの要素の双曲線コタンジェント(余接)と なります.

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

### 例

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

### 参照

• cotg — コタンジェント(余接)

### 履歴

 Version Description 6.1.0 Extension to sparse matrices.