lbm_timecovars = function( vars, ti) {
# where time exists and there are seasonal components,
# additional variables are created/needed here: cos.w, sin.w, etc..
# for harmonic analysis: to add an offset to a trig function (b) must add cos to a sin function
# y ~ a + c*sin(x+b)
# y ~ a + c*sin(b)*cos(x) + c*cos(b)*sin(x)
# .. as C*sin(x+b) = C*( cos(b) * sin(x) + sin(b) * cos(x) )
# y ~ b0 + b1*x1 + b2*x2
# where:
# a = b0
# c^2 = b1^2 + b2^2 = c^2*(sin^2(b) + cos^2(b))
# c = sqrt(b1^2 + b2^2)
# b1/b2 = tan(b)
# b = arctan(b1/b2)
# more than 3 harmonics would not be advisable .. but you would add them here..
out = data.frame( ti=ti )
if ("yr" %in% vars) out$yr = trunc( ti )
if ("dyear" %in% vars) out$dyear = ti - out$yr # fractional year
if ("cos.w" %in% vars) out$cos.w = cos( ti )
if ("sin.w" %in% vars) out$sin.w = sin( ti )
if ("cos.w2" %in% vars) out$cos.w2 = cos( 2*ti )
if ("sin.w2" %in% vars) out$sin.w2 = sin( 2*ti )
if ("cos.w3" %in% vars) out$cos.w3 = cos( 3*ti )
if ("sin.w3" %in% vars) out$sin.w3 = sin( 3*ti )
out$ti = NULL
return(out)
}
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