rotational matrix in R -

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i want achieve algorithm in r. cannot start code because having proble figuring out problem clearly. problem related rotational matrix, actully pretty challenging.

the problem follow:

  1. the historical data of monthly flows x transformed y transformation matrix r where, y = rx (3) procedure obtaining transformation matrix described in detail in appendix of tarboton et al. (1998), here summarize description. transformation matrix developed standard basis (basis vectors aligned coordinate axes) orthonormal not have basis vector perpendicular conditioning plane defined (3). 1 of standard basis vectors replaced vector perpendicular conditioning plane. operationally amounts starting identity matrix , replacing last column . basis set in no longer orthonormal. gram schmidt orthonormalization procedure applied remaining 1 standard basis vectors obtain orthonormal basis includes vector perpendicular conditioning plane. last column of matrix y, , , r matrix has property rt = r^(-1). first components of vector can denoted last component , i.e., . hence, simulation involves re-sampling conditional pdf ( )

the numerical example of frame work presented s example in figure


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