qgis - How to extract elevation values at line start and end points from a DEM?

I am new to the whole gis-experience and need your help working with QGIS.

I have:

• DEM raster with heights (3d)



• line-shapefile which contains the rivers (2d)

I need: heights for "start" and "end" in lines (to get them 3d) then compare that heights with "flow direction" of the lines

qgis-help doesn't really help me out. Tried searching google, nothing useful found. I am pretty sure that it may be a really simple "standard-tool" that can do what I want. However I haven't found it yet.

Edit:

well, i am looking for a solution, not important wich way. dont have any experience with python.

i was working on that problem and think i am almost ready, but there seems to be a problem:

i extracted the nodes of the lines, they got the heights from the dem-grid. i even managed to add the values of the points back to the lines, but when i check the values, the "minimal height" (or maximal) dont always have the suitable x- and y-coordinates of the point.

example: there is a line (columns: name, id, start_x, start_y, end_x, end_y). i imported the point-values (x, y, z coordinates) into the line. got 6 new columns in the table: min_x, min_y, min_z, max_x, max_y, max_z

now the min and max coordinates are mixed up and dont compare to those from the points.

my thoughts now are:

• i delete the min_x, min_y, max_x, max_y


• rename "max_z" and "min_z" to "up" and "down"


• somehow i need to get the up_x, up_y and down_x, down_y from the points. maybe there is a way to do that in the field calculator like: (for up_x in table "lines") value = "x" FROM "points" WHERE "up.lines" = "z.points"

dont know if that can work in qgis or how the code should look like. maybe there is a way to manage this in python, but as i said, i dont have a clue about python.