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How do I make an html text input readonly but be able to update with a script?

I have these inputs that take the values of a from a in my table when I click on a row. I want to make it so that the user cannot change the input themselves but want to bring values into them when a user clicks a table row. I will be passing these inputs in as a form. I know that when the input is like this:
that it will not be updated. Is there any other way to do it with an input. Is there a different type of tag I can use that can be passed through a form?

Rather than a read-only <input>, I'd go with a combination of a display element and a hidden form element. Something like:
<div id="my-display">This is a value</div>
<input id="my-input" name="my-input" type="hidden" />
And in the code update both:
$('#my-display').text(yourValue);
$('#my-input').val(yourValue);
You can style the display to the user however you like and don't have to worry about whether or not it "de-activates" the form input.
If you really want it to be an inactive input, you can use the same approach:
<input class="my-input" type="text" disabled />
<input class="my-input" type="hidden" name="my-input" />
Which may even save you a line of code here, since both can now use .val():
$('.my-input').val(yourValue);

Try disabled keyword as here
<div id="my-display">This is a value</div>
<input id="my-input" name="my-input" type="text" disabled/>
You can change the value by javascript as below:
document.querySelector('#my-input').value = 'the value you want to enter by javascript';

jQuery: Make a text input box selected

You know how when you open a new tab, you can start typing without having to select the search bar? I've got a text input box in HTML, and I'd like to be able to open my webpage and have that text input box immediately typeable, for lack of a better term. Say my input box looks like this:
<input type="text" class="myInput" value="add an item"></input>
I'm using HTML, CSS and JavaScript/jQuery right now. What code can I add to make sure the text input box is immediately typeable?

Use autofocus:
<input type="text" class="myInput" value="add an item" autofocus/>
From the input documentation on MDN:
This Boolean attribute lets you specify that a form control should have input focus when the page loads, unless the user overrides it (e.g. by typing in a different control). Only one form element in a document can have the autofocus attribute, which is a Boolean. It cannot be applied if the type attribute is set to hidden (that is, you cannot automatically set focus to a hidden control). Note that the focusing of the control may occur before the firing of the DOMContentLoaded event.

<input type="text" class="myInput" value="add an item" autofocus>
https://www.w3schools.com/TAgs/att_input_autofocus.asp

in html use autofocus, in jquery use $('.myInput').focus()

How to repeat the tabindex from 1 after it has gone to the last element with a tabindex?

So, for example, here's a script:
<!-- Random content above this comment -->
<input type="text" tabindex="1" />
<input type="text" tabindex="2" />
<input type="text" tabindex="3" />
<input type="text" tabindex="4" />
<input type="text" tabindex="5" />
<input type="text" tabindex="6" />
<!-- Nothing underneath this comment -->
So, when the user presses tab and goes through the six textboxes, reaches the last one and then presses tab, it would go to the content above the first comment, right? Well, how do I make it start from tabindex="1" again?

Unfortunately, you can't do that without javascript. You can listen to a TAB (and make sure it's not SHIFT+TAB) key press on your last element and manually set the focus to your first element inside the handler. However, binding this logic to keyboard events (i.e. specific input method) is not universal and may not work when using:
A mobile browser
Some other entertainment device (smart tv, gaming console, etc. - they typically use a D-Pad for jumping between focusable elements)
An accessibility service
I suggest a more universal approach which is agnostic of how the focus is changed.
The idea is that you surround your form elements (where you want to create a "tabindex loop") with special "focus guard" elements that are focusable too (they have a tabindex assigned). Here is your modified HTML:
<p>Some sample content here...</p>
<p>Like, another <input type="text" value="input" /> element or a <button>button</button>...</p>
<!-- Random content above this comment -->
<!-- Special "focus guard" elements around your
if you manually set tabindex for your form elements, you should set tabindex for the focus guards as well -->
<div class="focusguard" id="focusguard-1" tabindex="1"></div>
<input id="firstInput" type="text" tabindex="2" class="autofocus" />
<input type="text" tabindex="3" />
<input type="text" tabindex="4" />
<input type="text" tabindex="5" />
<input type="text" tabindex="6" />
<input id="lastInput" type="text" tabindex="7" />
<!-- focus guard in the end of the form -->
<div class="focusguard" id="focusguard-2" tabindex="8"></div>
<!-- Nothing underneath this comment -->
Now you just listen to focus events on those guard elements and manually change focus to the appropriate field (jQuery used for the sake of simplicity):
$('#focusguard-2').on('focus', function() {
// "last" focus guard got focus: set focus to the first field
$('#firstInput').focus();
});
$('#focusguard-1').on('focus', function() {
// "first" focus guard got focus: set focus to the last field
$('#lastInput').focus();
});
As you see, I also made sure that we snap back to the last input when the focus moves backwards from the first input (e.g. SHIFT+TAB on the first input). Live example
Note that the focus guards are assigned a tabindex value too to make sure they are focused immediately before/after your input fields. If you don't manually set tabindex to your inputs, then both focus guards can just have tabindex="0" assigned.
Of course you can make this all work in a dynamic environment as well, when your form is generated dynamically. Just figure out your focusable elements (less trivial task) and surround them with the same focus guards.
Hope that helps, let me know if you have any issues.
UPDATE
As nbro pointed out, the above implementation has the unwanted effect of selecting the last element if one hits TAB after the page loads (as this would focus the first focusable element which is #focusguard-1, and that would trigger focusing the last input. To mitigate that, you can specify which element you want initially focused and focus it with another little piece of JavaScript:
$(function() { // can replace the onload function with any other even like showing of a dialog
$('.autofocus').focus();
})
With this, just set the autofocus class on whatever element you want, and it'll be focused on page load (or any other event you listen to).

Here my solution where you no need any other elements. As you can see elements will be looping inside <form> elements.
$('form').each(function(){
var list = $(this).find('*[tabindex]').sort(function(a,b){ return a.tabIndex < b.tabIndex ? -1 : 1; }),
first = list.first();
list.last().on('keydown', function(e){
if( e.keyCode === 9 ) {
first.focus();
return false;
}
});
});

Here is my solution, considering the first input has the "autofocus" attribute set:
Add this after your form element (with HTML5 it can be any tag):
<div tabindex="6" onFocus="document.querySelector('[autofocus]').focus()"></div>

Yes, after tabbing through the inputs it will jump on suitable elements that do not have a tab order specified. But also, after tabbing all "tabbable" elements, the focus will jump "outside" your page content, onto the browser's UI elements (tabs, menus, bookmarks, etc)
I think the easiest way is to handle the keyup event on the last input and intercept TAB usage (and SHIFT+TAB for that matter)

I wd suggest you to increase your tabindex ie. >100
and also give the tabIndex to your "content" container div
please note that your content container must have tabindex less than input boxes for ex.99 .
when you press tab on last input box manually set focus on your content div using javascript (you can use keypress handlers for tab key)
document.getElementById("content").focus();
you must giv tabindex to your "content" to set focus to it.
now if you press tab focus will automatically shift to first input box.
hope this will help.
Thank you

cyclic tab order with jquery

Is there a nice way to set a desktop-like tab order in a form with jquery? the form has four text inputs and two buttons; after the last button loses focus, I want the first text input to get focus and start tab order from the beginning (to 2nd tb, to 3rd tb...). I did this:
$('body').delegate('#second_button', 'blur', function() {
$('#first_input_text').focus();
});
but it only works in Opera. Chrome IE9, And Firefox do set focus on first text input but when user press tab again it goes to address bar instead of the second text input. I could set above binding to all elements in cycle but is there a more elegant solution?

You need to add a tabindex attribute to each form element - example :
<FORM action="..." method="post">
<P>
<INPUT tabindex="1" type="text" name="field1">
<INPUT tabindex="2" type="text" name="field2">
<INPUT tabindex="3" type="submit" name="submit">
</P>
</FORM>
Documentation here

How to skip fields using javascript?

I have a form like this:
<form name="mine">
<input type=text name=one>
<input type=text name=two>
<input type=text name=three>
</form>
When user types a value in 'one', I sometimes want to skip the field 'two', depending on what he typed. For example, if user types '123' and uses Tab to move to next field, I want to skip it and go to field three.
I tried to use OnBlur and OnEnter, without success.
Try 1:
<form name="mine">
<input type=text name=one onBlur="if (document.mine.one.value='123') document.three.focus();>
<input type=text name=two>
<input type=text name=three>
</form>
Try 2:
<form name="mine">
<input type=text name=one>
<input type=text name=two onEnter="if (document.mine.one.value='123') document.three.focus();>
<input type=text name=three>
</form>
but none of these works. Looks like the browser doesn't allow you to mess with focus while the focus is changing.
BTW, all this tried with Firefox on Linux.

Try to attach tabindex attribute to your elements and then programmaticaly (in javaScript change it):
<INPUT tabindex="3" type="submit" name="mySubmit">

You could use the onfocus event on field two, which will be called when it receives focus. At that point, field 1's value should be updated and you can perform your check then.

If you used the method you describe, and they worked, the focus would also change when the user clicks on the field, instead of tabbing to it. I can guarantee you that this would result in a frustrated user. (Why exactly it doesn't work is beyond me.)
Instead, as said before, change the tabindex of the appropriate fields as soon as the content of field one changes.

<form name="mine">
<input type="text" name="one" onkeypress="if (mine.one.value == '123') mine.three.focus();" />
<input type="text" name="two">
<input type="text" name="three">
</form>

Try onkeypress instead of onblur. Also, on the onfocus of field two is where you should be sending to three. I'm assuming you don't want them typing in two if one is 123 so you can just check that on two's onfocus and send on to three.