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Weak lensing (WL) clustering is studied using 2D (angular) coordinates, whileredshift space distortions (RSD) and baryon acoustic oscillations (BAO) use 3Dcoordinates, which requires a model dependent conversion of angles andredshifts into comoving distances. This is the first paper of a series, whichexplore modelling multi-tracer galaxy clustering (of WL, BAO and RSD), usingonly angular (2D) cross-correlations in thin redshift bins. This involvesevaluating many thousands cross-correlations, each a multidimensional integral,which is computationally demanding. We present a new algorithm that performsthese calculations as matrix operations.  Nearby narrow redshift bins are intrinsically correlated, which can be usedto recover the full (radial) 3D information. We show that the Limberapproximation does not work well for this task. In the exact calculation, boththe clustering amplitude and the RSD effect increase when decreasing theredshift bin width. For narrow bins, the cross-correlations has a larger BAOpeak than the auto-correlation because smaller scales are filtered out by theradial redshift separation. Moreover, the BAO peak shows a second (ghost) peak,shifted to smaller angles. We explore how WL, RSD and BAO contribute to thecross-correlations as a function of the redshift bin width and present a firstexploration of non-linear effects and signal-to-noise ratio on thesequantities. This illustrates that the new approach to clustering analysisprovides new insights and is potentially viable in practice.

Combining spectroscopic and photometric surveys using angular cross-correlations I: Algorithm and modelling