def ICM(input_dim, num_outputs, kernel, W_rank=1,W=None,kappa=None,name='ICM'):
    """
    Builds a kernel for an Intrinsic Coregionalization Model

    :input_dim: Input dimensionality (does not include dimension of indices)
    :num_outputs: Number of outputs
    :param kernel: kernel that will be multiplied by the coregionalize kernel (matrix B).
    :type kernel: a GPy kernel
    :param W_rank: number tuples of the corregionalization parameters 'W'
    :type W_rank: integer
    """
    if kernel.input_dim != input_dim:
        kernel.input_dim = input_dim
        warnings.warn("kernel's input dimension overwritten to fit input_dim parameter.")

    K = kernel.prod(GPy.kern.Coregionalize(1, num_outputs, active_dims=[input_dim], rank=W_rank,W=W,kappa=kappa,name='B'),name=name)
    return K