def cosm(ctx, A):
    """
        Gives the cosine of a square matrix `A`, defined in analogy
        with the matrix exponential.

        Examples::

            >>> from mpmath import *
            >>> mp.dps = 15; mp.pretty = True
            >>> X = eye(3)
            >>> cosm(X)
            [0.54030230586814               0.0               0.0]
            [             0.0  0.54030230586814               0.0]
            [             0.0               0.0  0.54030230586814]
            >>> X = hilbert(3)
            >>> cosm(X)
            [ 0.424403834569555  -0.316643413047167  -0.221474945949293]
            [-0.316643413047167   0.820646708837824  -0.127183694770039]
            [-0.221474945949293  -0.127183694770039   0.909236687217541]
            >>> X = matrix([[1+j,-2],[0,-j]])
            >>> cosm(X)
            [(0.833730025131149 - 0.988897705762865j)  (1.07485840848393 - 0.17192140544213j)]
            [                                     0.0               (1.54308063481524 + 0.0j)]
        """
    B = 0.5 * (ctx.expm(A * ctx.j) + ctx.expm(A * -ctx.j))
    if not sum(A.apply(ctx.im).apply(abs)):
        B = B.apply(ctx.re)
    return B
