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86 lines
2.0 KiB
Plaintext
86 lines
2.0 KiB
Plaintext
8 months ago
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program define ghquadm
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* stolen from gllamm6 who stole it from rfprobit (Bill Sribney)
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version 4.0
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parse "`*'", parse(" ")
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local n = `1'
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if `n' + 2 > _N {
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di in red /*
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*/ "`n' + 2 observations needed to compute quadrature points"
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exit 2001
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}
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tempname x w xx ww a b
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local i 1
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local m = int((`n' + 1)/2)
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matrix x = J(1,`m',0)
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matrix w = x
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while `i' <= `m' {
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if `i' == 1 {
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scalar `xx' = sqrt(2*`n'+1)-1.85575*(2*`n'+1)^(-1/6)
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}
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else if `i' == 2 { scalar `xx' = `xx'-1.14*`n'^0.426/`xx' }
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else if `i' == 3 { scalar `xx' = 1.86*`xx'-0.86*x[1,1] }
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else if `i' == 4 { scalar `xx' = 1.91*`xx'-0.91*x[1,2] }
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else {
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local im2 = `i' -2
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scalar `xx' = 2*`xx'-x[1,`im2']
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}
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hermite `n' `xx' `ww'
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matrix x[1,`i'] = `xx'
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matrix w[1,`i'] = `ww'
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local i = `i' + 1
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}
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if mod(`n', 2) == 1 { matrix x[1,`m'] = 0}
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/* start in tails */
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matrix `b' = (1,1)
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matrix w = w#`b'
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matrix w = w[1,1..`n']
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matrix `b' = (1,-1)
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matrix x = x#`b'
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matrix x = x[1,1..`n']
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/* other alternative (left to right) */
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/*
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above: matrix x = J(1,`n',0)
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while ( `i'<=`n'){
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matrix x[1, `i'] = -x[1, `n'+1-`i']
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matrix w[1, `i'] = w[1, `n'+1-`i']
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local i = `i' + 1
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}
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*/
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matrix `2' = x
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matrix `3' = w
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end
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program define hermite /* integer n, scalar x, scalar w */
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* stolen from gllamm6 who stole it from rfprobit (Bill Sribney)
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version 4.0
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local n "`1'"
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local x "`2'"
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local w "`3'"
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local last = `n' + 2
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tempname i p
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matrix `p' = J(1,`last',0)
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scalar `i' = 1
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while `i' <= 10 {
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matrix `p'[1,1]=0
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matrix `p'[1,2] = _pi^(-0.25)
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local k = 3
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while `k'<=`last'{
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matrix `p'[1,`k'] = `x'*sqrt(2/(`k'-2))*`p'[1,`k'-1] /*
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*/ - sqrt((`k'-3)/(`k'-2))*`p'[1,`k'-2]
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local k = `k' + 1
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}
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scalar `w' = sqrt(2*`n')*`p'[1,`last'-1]
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scalar `x' = `x' - `p'[1,`last']/`w'
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if abs(`p'[1,`last']/`w') < 3e-14 {
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scalar `w' = 2/(`w'*`w')
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exit
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}
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scalar `i' = `i' + 1
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}
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di in red "hermite did not converge"
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exit 499
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end
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