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Use CIE to calculate LMS->RGB and DKL->RGB conversion matrices?

Our lab does not have access to a supported spectroradiometer, but we do have access to a datacolor spyder that will allow us to get luminance readings for gamma correction and we can also measure the CIE coordinates of our r,g&b guns. Is there a way to use the CIE coordinates to compute the LMS->RGB and DKL->RGB conversion matrices? The spyder gives us both xyY and XYZ coordinates.

Thanks,
–Jeff

There isn’t a definitive way to transform without knowing the full spectrum of your monitor. There are some approximations though: