AngularJS我正在尝试计算嵌套ng重复中包含的许多输入(ng模型）的结果

我正在学习AngularJS，并试图为几种产品创建一个简单的库存控制程序。我已经在谷歌上搜索了几个小时，浏览了很多问题，但还没能让我的代码正常工作。

每个产品应计算的公式为：

• 最终库存=初始库存+生产-销售

这是代码：http://codepen.io/swordf1zh/pen/zfwcB

HTML

<div ng-app="inventory">
    <form role="form" class="row" ng-controller="ProdCtrl">
        <!-- Secciones -->
        <div class="col-md-3" ng-repeat="section in sections">
            <blockquote class="text-center">{{section.name}}</blockquote>
            <div ng-repeat="product in products">
                <div class="form-group">
                    <div class="input-group">
                      <span class="input-group-addon">{{product.name}}</span>
                      <input type="number" 
                             class="form-control text-center" 
                             placeholder="Cantidad" 
                             ng-model="total" 
                             ng-change="calculate(section.id, product.id, total)">
                    </div>
                </div>
            </div>
        </div>
        <div class="col-md-3">
            <blockquote class="text-center">Final Inventory</blockquote>
            <div ng-repeat="product in products">
                <div class="form-group">
                    <div class="input-group">
                      <span class="input-group-addon">{{product.name}}</span>
                      <p class="form-control text-center">{{product.total}}</p>
                    </div>
                </div>
            </div>
        </div>
    </form>
</div>

JS

var app = angular.module("inventory",[]);
app.controller("ProdCtrl", ['$scope',
    function($scope) {
        $scope.sections = [
            {id:1, name:'Initial Inventory'},
            {id:2, name:'Production'},
            {id:3, name:'Sales'},
        ];
        $scope.products = [
            {id:1, name:'Prod1', total:0},
            {id:2, name:'Prod2', total:0},
            {id:3, name:'Prod3', total:0},
            {id:4, name:'Prod4', total:0}
        ];
        $scope.calculate = function( sectionId, productId, cantidad ){
            if( sectionId != 3 ){
                $scope.products[productId-1].total += cantidad;
            } else {
                $scope.products[productId-1].total -= cantidad;
            }
        };
    }
]);