Animate slide on slider with external event

Animate slide on slider with external event

So far I have this:
    $("#slider").slider({
        orientation: "vertical",
        range: "min",
        animate: true,
        min: 1,
        max: 7,
        value: 4,
        change: function(event, ui) {
            $("#amount").val(ui.value);
        }
    });
    $('.slider-icon').click(function(e) {
        var upDown = ($(this).attr('id') == 'up' ? 1:-1);
        $("#slider").slider('value', $("#slider").slider('value')+upDown);
    });
How can I make it so that when they click on the up (or down) icon, it
animates the slide like it does when you click the bar, instead of
jumping to the notch?
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