Determining input color space primaries from spectrum data

If I person an output device, for which I person a known spectrum information for each of it's primaries, I should beryllium capable to cipher nan CIEXYZ of its primaries utilizing using nan integral equations together pinch nan CIE colour matching functions. I tin past cipher its respective CIExyY values, which for output instrumentality are ever wrong nan bound if nan xyY spectral locus - nan chromaticity diagram.

My mobility relates to calculating xyY of primaries of input device.

Suppose I person a known spectrum information for nan primaries of immoderate input instrumentality - beryllium it a integer scanner aliases a integer camera aliases immoderate different input device. It's colour filters are not perfect, this intends that moreover a axenic spectrum colour is represented arsenic non-zero values successful its ain RGB colour space. That intends that (if I'm correct) that nan full chromaticity sketch should dishonesty wrong of nan instrumentality RGB colour space, and it's primaries dishonesty extracurricular of nan sketch and beryllium represented by imaginary colors.

How do I cipher those imaginary primaries for nan input instrumentality fixed known spectrum for its primaries? If I'm not mistaken, I cannot simply usage nan integral formula, because that seems to beryllium only for output devices and nan resulting primaries would dishonesty successful nan locus.