Photoshop, gradient map to transparent?

Question

I have the following image that I'd like to apply a gradient map to:

I would like the below gradient applied (note that the gradient maps to transparent). The problem is that rather than the gradient being applied, the whole image turns dark purple:

I'd like it to look like this (below) but rather than mapping to white, I'd like the white to essentially be replaced with transparent (if that's understandable):

From reading old forum posts on other websites, I'm getting that the gradient map tool might not support this functionality. Though if there is some way to achieve this on a transparent background via some other means, could someone provide a walkthrough? (I'm no PS expert)

Answer 1

Here's how I would achieve that effect:
1) Create a BW Effects layer, and select the mode that gives the most pleasing effect.
2) Edit>Copy Merged, then paste that into a new alpha channel
3) Invert the alpha channel
4) Delete or disable the bw effects layer
5) Select the active pixels (Control key (PC) or the Command key (Mac) while you single click on the alpha channel in the channels panel)
6) Create a new solid color layer using the purple you used above

The active selection of the alpha channel will automatically be applied as a transparency mask. That SHOULD do it. Good luck.