Update Invoice with Invoice Line Item Amounts

trigger InvoiceLineItemTrigger on Invoice_Line_Item__c (after insert, after update, after delete, after undelete) {
    // Get the parent Invoice Ids.
    Set<Id> invoiceIds = new Set<Id>();
    for (Invoice_Line_Item__c lineItem : Trigger.new) {
        // Add the Invoice Id from each Line Item to the list
        invoiceIds.add(lineItem.Invoice__c);
    }

    // Map to relate parent Invoice Id to the Amount roll-up value from all child Invoice Line Item records
    // The first time we see the Invoice, we will make the map entry
    // Next time we will add the Amount to the existing value
    Map<Id, Decimal> invoiceToAmountMap = new Map<Id, Decimal>();

    for (Invoice_Line_Item__c lineItem : [SELECT Id, Invoice__c, Amount__c
                                            FROM Invoice_Line_Item__c
                                            WHERE Invoice__c IN :invoiceIds]) {

        Decimal newInvoiceAmount = lineItem.Amount__c;
        // If the map already has a value for this Invoice, add that to this amount
        if (existingInvoiceAmount.containsKey(lineItem.Invoice__c)) {
            Decimal existingMapValue = invoiceToAmountMap.get(lineItem.Invoice__c);
            newInvoiceAmount = newInvoiceAmount + existingInvoiceAmount;
        }
        // Now put the new amount into the map
        invoiceToAmountMap.put(lineItem.Invoice__c, newInvoiceAmount);
    }

    // List to put the Invoice records that need their Amount__c roll-up updated
    List<Invoice__c> invoicesToUpdate = new List<Invoice__c>();

    // Now we will make the Invoice records to update
    for (Id invoiceId : invoiceToAmountMap.keySet()) {
        Decimal invoiceAmount = invoiceToAmountMap.get(invoiceId);
        Invoice__c tempInvoice = new Invoice__c(
            Id = invoiceId,
            Amount__c = invoiceAmount
        );
        invoicesToUpdate.add(tempInvoice);
    }

    // update the invoices
    update invoicesToUpdate;
}